Intelligent Systems at the Service of Mankind

Intelligent Systems at the Service of Mankind

Intelligent Systems at the Service of Mankind Volume I November 2003

Edited by Wilfried Elmenreich, J. A. Tenreiro Machado, and Imre J. Rudas

The views and opinions expressed in all the papers of this book are the author’s personal ones. The copyright of the individual papers belongs to the authors. Copies cannot be reproduced for commercial profit. c 2004, Copyright protected.

Printed in Germany.

Table of Contents

Preface

v

1

Intelligent Control

1

A Modified Renormalization Algorithm Based Adaptive Control Guaranteeing Complete Stability for a Wide Class of Physical Systems J´ozsef Tar, Imre J. Rudas, Jan´os F. Bit´o, and Krzysztof R. Kozłowski . . .

3

Minimal linearization via HOSVD in LMI based control P´eter Baranyi, Yeung Yam, Domonkos Tikk, and P´al Michelberger . . . .

15

Automatic Language Control of Electrical Drives. Background and Applications J. F. Martins, A. J. Pires, R. Vilela Mendes, and J. A. Dente . . . . . . . .

29

Application of Fractional Calculus in Mechatronics J. A. Tenreiro Machado, Ramiro S. Barbosa, Fernando Duarte, and Nuno Ferreira . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

Module Library for Rapid Prototyping and Hardware Implementation of Vector Control Systems J´ozsef V´as´arhelyi, M´aria Imecs, J´anos J. Incze, and Csaba Szab´o . . . . .

53

Robotics

65

A Robust Certainty Grid Algorithm for Robotic Vision Wilfried Elmenreich and Raimund Kirner . . . . . . . . . . . . . . . . .

67

Force-feedback Tests for Medical Robots Iulian Iordachita, Alexandru Patriciu, Dumitru Mazilu, Gheorghe Catrina, and Dan Stoianovici . . . . . . . . . . . . . . . . . . . . . . . . . .

79

Gait Analysis of Natural and Artificial Walking Systems Manuel F. Silva, J. A. Tenreiro Machado, and Ant´onio M. Lopes . . . . .

87

2

i

Marker-Based Mobile Robot Positioning in Respect of Displacement of the Markers Istv´an Nagy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

A Real-Time Optimization for 2R Manipulators E. J. Solteiro Pires, J. A. Tenreiro Machado, and P. B. de Moura Oliveira . 109 Forward Kinematics of a Stewart Platform Mechanism Domagoj Jakobovi´c and Leo Budin . . . . . . . . . . . . . . . . . . . . . 121 3

Intelligent Manufacturing Systems

133

Communication Issues in Multi-Agent-Based Plant Automation Scheduling Yoseba K. Penya and Thilo Sauter . . . . . . . . . . . . . . . . . . . . . 135 Advanced Factory Automation System for Deburring and Dressing of Automotive Engine Parts Ulrich Berger and Raffaello Lepratti . . . . . . . . . . . . . . . . . . . . 145 Petri Net-Based Optimization of Production Systems Szilvia Gyapay, Andr´as Pataricza, J´ozsef Sziray, and Ferenc Friedler . . . 157 Production Part Approval Process in Quality Management System Marianna Lendvay and Attila L. Bencsik . . . . . . . . . . . . . . . . . . 169 Application of Product Model in Internet Based Robot Control L´aszl´o Horv´ath and Imre J. Rudas . . . . . . . . . . . . . . . . . . . . . 179 4

Data Mining and Learning Systems

187

Representing Directed and Weighted Graphs and Their Properties in a Relational Spatial Database Model ´ Agnes B. Nov´ak and Zsolt Tuza . . . . . . . . . . . . . . . . . . . . . . . 189 An Integrated Intelligent System for Data Mining and Decision Making Filip Ujevic and Nikola Bogunovic . . . . . . . . . . . . . . . . . . . . . 199 Business Rules Modeling by Means of F-logic, UML and Ontologies (problems and possible solutions) ˇ Mirko Cubrilo and Mirko Malekovi´c . . . . . . . . . . . . . . . . . . . . 211 Document Clustering Using Concept Set Representation L´aszl´o Kov´acs and P´eter Baranyi . . . . . . . . . . . . . . . . . . . . . . 225 Text Mining for Documents Annotation and Ontology Support Jan Paralic and Peter Bednar . . . . . . . . . . . . . . . . . . . . . . . . 237

ii

Fuzzy Relational Thesauri in Information Retrieval: Automatic Knowledge Base Expansion by Means of Classified Textual Data Domonkos Tikk, Jae Dong Yang, P´eter Baranyi, and Anik´o Szak´al . . . . 249 How to Combine Various Factors to Select Appropriate Knowledge Elicitation Technique? Sandra Lovrenˇci´c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Personal Agents in Distance Learning Systems Marko Rosic, Slavomir Stankov, and Vlado Glavinic . . . . . . . . . . . 271 Forgetfulness in Multi-Agent Systems ˇ Mirko Malekovi´c and Mirko Cubrilo . . . . . . . . . . . . . . . . . . . . 283 5

Algorithms and Methods

297

Multi-Head Rules in Equivalent Transformation Takahiko Ishikawa, Kiyoshi Akama, Hiroshi Mabuchi, and Yuichi Yamamoto299 Genetic Scheduling Algorithm for High-Level Synthesis ´ am Mann, and Andr´as Orb´an . . . . . . . . . . . 311 P´eter Arat´o, Zolt´an Ad´ Parameterization Through Null Space — A New Redundancy Resolution Method for Differential Kinematic Problems in Comparison to Other Methods Zsolt Kem´eny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Achieving Dependability in Time-Triggered Networks by Sensor Fusion Wilfried Elmenreich and Philipp Peti . . . . . . . . . . . . . . . . . . . . 335 Implementation of VLSI Routing Algorithms ´ am Mann, Csaba Megyeri, and Bence Golda, B´alint Laczay, Zolt´an Ad´ Andr´as Recski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 6

System Modeling

361

Intelligent Engineering Modeling by Active Models L´aszl´o Horv´ath and Imre J. Rudas . . . . . . . . . . . . . . . . . . . . . 363 Optimizing Algorithms for System Level Synthesis P´eter Arat´o, Tibor Kand´ar, and Bence Cs´ak . . . . . . . . . . . . . . . . 373 A Verification and Validation Model for Software Systems J´ozsef Sziray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Modelling Communication Requirements and Network Services in Distributed Systems with UML Antun Brumnic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

iii

Analysis of Systems with Backlash and Impacts through the Describing Function Ramiro S. Barbosa and J. A. Tenreiro Machado . . . . . . . . . . . . . . 411 Mathematical Model of the Half Bridge Resonant Converter Zolt´an Puklus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 UML Statechart-Based Verification and Testing of Embedded Systems Bal´azs Beny´o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

iv

Preface The “information revolution” of our time permeates the entire lifestyle of our generation. While emerging visions of the “Information Society” with its financial, legal, business and privacy aspects became increasingly prominent during the past few years, the “traditional scene” of information technology, that is industrial automation preserved its significance as the field of ceaseless development, too. Since the old-fashioned concept of “Hard Automation” applicable only to industrial processes of fixed, repetitive nature and manufacturing large batches of the same product [1] were thrust to the background by keen market competition, the key element of this development remained the improvement of “Machine Intelligence”. Despite of the fact that L. A. Zadeh already introduced the concept of “Machine Intelligence Quotient” in 1996 to measure machine intelligence [2], this term remained more or less a mysterious meaning best explicable on the basis of practical needs. The weak point of hard automation is that the system configuration and the operations are fixed and cannot be changed without incurring considerable costs and downtime. Mainly it can be used in applications that call for fast and accurate operation in large batch production. Whenever a variety of products have to be manufactured in small batches and consequently the work-cells of a production line should be quickly reconfigured to accommodate a change in product, hard automation becomes inefficient and fails due to economic reasons. In these cases a new, more flexible way of automation, the so-called “Soft Automation” is expedient and suitable. The most important “ingredient” of soft automation is its adaptive ability of efficiently coping with changing, unexpected or previously unknown conditions, and working with a high degree of uncertainty and imprecision since in practice increasing precision can be very costly. This adaptation must be realized without or with limited human interference: this is one essential component of machine intelligence. Another important factor is that engineering practice often has to deal with complex systems of multiple variable and multiple parameter models almost always with strong non-linear coupling. The conventional analytical techniques-based approaches for describing and predicting the behavior of such systems in many cases are doomed to failure from the outset, even in the phase of the construction of a more or less appropriate mathematical model. These approaches normally are too categorical in the sense that in the name of “modeling accuracy” they try to describe all the structural details of the real physical system to be modeled. This significantly can increase the intricacy of the model and may result in a huge computational burden without achieving considerable improvement

v

of precision. The best paradigm exemplifying this situation may be the classic perturbation theory: the less significant the achievable correction, the more work has to be invested to obtain it. A further important component of machine intelligence is a kind of “structural uniformity” giving room and possibility to model arbitrary particular details a priori not specified and unknown. This idea is similar to the ready-to-wear industry, which introduced products, which can be slightly modified later on in contrast to tailor-made creations aiming at maximum accuracy from the beginning. These subsequent corrections can be carried out by machines automatically. This “learning ability” is a key element of machine intelligence. To realize the above philosophy in a mathematically correct and perfect way L.A. Zadeh separated Hard Computing from Soft Computing quite a long time ago. This revelation immediately resulted in distinguishing between two essential complementary branches of machine intelligence: the Hard Computing based Artificial Intelligence and the Soft Computing based Computational Intelligence. In the last decades it became generally known that Soft Computing employing fuzzy logic, artificial neural networks, and probabilistic reasoning is a fruitful orientation towards designing intelligent systems. Moreover, it became generally accepted that soft computing rather than hard computing, should be viewed as the foundation of real machine intelligence [3] via exploiting the tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness, low solution cost and better rapport with reality. Further research in the past decade rather confirmed the view that the typical components of the present soft computing as fuzzy logic, neurocomputing, evolutionary computation and probabilistic reasoning are of complementary nature and that the best results can be applied by their combined application. In our days the two complementary branches of Machine Intelligence, that is Artificial Intelligence and Computational Intelligence serve as the basis of Intelligent Engineering Systems. The huge number of scientific results published in Journal and conference proceedings worldwide substantiates this statement. The present book contains several articles taking different viewpoints in the field of intelligent systems. The first chapter comprises five papers on intelligent control. The second chapter gives an insight on intelligent robotics. Following five papers on the subject of intelligent manufacturing systems are presented. The fourth chapter deal with the subjects of data mining and learning systems. Chapter five presents algorithms and methods in the scope of an intelligent system. Chapter six containing seven papers on system modeling concludes the book.

Imre J. Rudas

J. A. Tenreiro Machado

vi

Wilfried Elmenreich

Bibliography [1] C. W. De Silva. Automation intelligence. Engineering Application of Artificial Intelligence, 7(5):471–477, 1994. [2] L. A. Zadeh. Fuzzy logic, neural networks and soft computing. Communications of the ACM, 37:77–84, 1994. [3] L. A. Zadeh. Berkeley initiative in soft computing. IEEE Industrial Electronics Society Newsletter, 41(3):8–10, 1994.

vii

viii

Chapter 1 Intelligent Control

A Modified Renormalization Algorithm Based Adaptive Control Guaranteeing Complete Stability for a Wide Class of Physical Systems József K. Tar1, Imre J. Rudas1, János F. Bitó1, and Krzysztof R. Kozáowski2 1

Institute of Mathematical and Computational Sciences, Budapest Polytechnic, John von Neumann Faculty of Informatics, Budapest, Hungary {tar, rudas, bito}@nik.bmf.hu 2

Chair of Control, Robotics, and Computer Science, PoznaĔ University of Technology, PoznaĔ, Poland [email protected]

Abstract — A new branch of Computational Cybernetics based on principles akin to that of the traditional Soft Computing (SC) is outlined. Via restricting its applicability to a relatively limited class of non-linear, coupled MIMO systems’ control considerable computational advantages as a priori known, uniform, lucid, and reduced model- and structure size can be achieved. Furthermore, the often intricate and stochastic parameter tuning is replaced by simple and short explicit algebraic procedure especially fit to real time applications. It is proven in this paper that under quite common conditions the "Complete Stability" of the operation of the so obtained controllers can be guaranteed. It also is shown that the approach is quite versatile. Simulation examples are presented for the control of a 3 DOF SCARA arm suffering from various nonlinearities. It is concluded that the method is promising and probably imposes acceptable convergence requirements in problem classes considerably wider than the control of electromechanical devices.

1 Introduction The basic components of Soft Computing were almost completely developed by the sixties. In our days it roughly is a kind of integration of neural networks and fuzzy systems enhanced with high parallelism of operation, and supported by several deterministic, stochastic or combined parameter-tuning methods (learning). Its main advantage is that it evades the development of intricate analytical system models. Instead of that typical problem classes has been identified for the solution of which typical uniform architectures has been crystallized (e.g. multilayer perceptron, Kohonennetwork, Hopfield-network, Cellular Neural Networks, CNN Universal Machine, etc.). Fuzzy systems also use membership functions of typical (e.g. trapezoidal, triangular or step-like, etc.) shapes, and the fuzzy relations can also be utilized in a standardized way by using different, even parametric classes of fuzzy operators. The "first phase" of applying traditional SC is the identification of the problem class and finding 3

TAR, RUDAS, BITÓ, KOZàOWSKI the appropriate structured for dealing with it, normally is easy. The next phase, i.e. determining the necessary size of the structure and fitting its parameters via machine learning is far less easy. For neural networks certain solutions starts from a quite big initial network and apply dynamic pruning for getting rid of the "dead" nodes [1]. An alternative method starts with small network, and the number of nodes is increased step by step (e.g. [2-3]). Due to the possible existence of "local optima", for a pure "backpropagation training" inadequacy of a given number of neurons cannot be concluded simply. To evade this difficulty "learning methods", also including stochastic elements, were seriously improved in the last decade (e.g. [4-7]). In spite of this development it can be stated that for strongly coupled non-linear MIMO systems traditional SC still has several drawbacks. The number of the necessary fuzzy rules strongly increases with the degree of freedom and the intricacy of the problem. The same is true for the necessary neurons in a neural network approach. External dynamic interaction on which normally no satisfactory information is available influences the system's behavior in dynamic manner. Both the big size of the necessary structures, the huge number of parameters to be tuned, as well as the "goal" varying in time still mean serious problem. It seems to be reasonable to risk the supposition that "generality" and "uniformity" of the "traditional SC structures" excludes the application of plausible simplifications which may be characteristic to a whole set of typical tasks. This makes the idea rise that several "simplified" branches of SC could be developed for narrower problem classes if more specific features could be identified and taken into account in the uniform structures. The first steps in this direction were made in the field of Classical Mechanical Systems (CMSs) [8], while further refinements were published in [9], on the basis of principles detailed e.g. in [12]. This approach used the internal symmetry of CMSs, the Symplectic Group (SG) of Symplectic Geometry in the tangent space of the physical states of the system. The "result" of the "situation-dependent system identification" was a symplectic matrix mirroring the effects of the inaccuracy of the rough dynamic model initially used as well as the external dynamic interactions not modeled by the controller. By considering the problem from a purely mathematical point of view, independently of CMSs, it became clear that all the essential steps used in the control can be realized by other mathematical means than symplectic matrices. The SG can be replaced by other Lie groups defined in a similar manner by the use of some "basic quadratic expression" [10]. In this approach the Lie group used in the control does not describe any internal physical symmetry of the system to be controlled. Regarding the convergence of the method satisfactory conditions were presented for SISO systems and preliminary indications were drawn that proper extension of the proof can be expected for MIMO systems, too [10]. Also, in [11] by introduction of the "Partially Stretched Orthogonal Transformations" a computationally exceptionally efficient transformation was introduced which is not comprised in the set of the originally proposed Lie groups defined by simple quadratic expressions. In this paper satisfactory condition is given for the Complete Stability of the control for MIMO systems. Simulation examples are presented for the control of 3 DOF SCARA arm structure by the use of the "Generalized Lorentz Group" (GLG) and the "Minimum Operation Symplectic Transformations" also defined in [10].

4

A MODIFIED RENORMALIZATION ALGORITHM …

2 The Control Problem in General From purely mathematical point of view the control problem can be formulated as follows: there is given some imperfect model of the system on the basis of which some excitation is calculated for a desired reaction of the system used as the input of the controller id as e=M(id). The system has its inverse dynamics described by the unknown function resulting in a realized ir instead of the desired one, id: ir=\(M(id))= f(id). (In Classical Mechanics these values are the desired and the realized joint accelerations, while the external free forces and the joint velocities serve as the parameters of this temporarily valid and changing function.) Normally any information on the behavior of the system can be obtained only via observing the actual value of the function f(). In general it can considerably vary in time. Furthermore, no any possibility exists to "directly manipulate" the nature of this function with the exception of the direct manipulation of its actual input from id to certain id* „deformed“ value. The controller’s aim is to achieve and maintain the id=f(id*) state. [Only the nature of the model function M(id) can directly be determined.] The Modified Renormalization Algorithm consists in seeking a series of linear transformations as: i 0 ; S1f i 0 i 0 ; i1 S1i 0 ; ... ; S n f i n 1 i 0 ; i n 1 S n 1i n ; S n n o I (1) of

It is evident that (1) does not unambiguously determine the possible appropriate quadratic matrices. This ambiguity can be utilized via choosing "simple" linear transformations possibly having the properties as fast and computationally efficient invertibility and the ability of being as close to the identity transformation as possible. So let G be a nonsingular quadratic, otherwise arbitrary constant matrix. Let the set ^v (i ) ` a linearly independent complete set of vectors corresponding to the dimensions of G. Let this set called "special according to G" if it satisfies the restrictions v ( i )T Gv ( j )

G ij .

(2)

The elements of this set form the columns of a special matrix V, and that this matrix trivially satisfies the equation

V T GV

G Ÿ V 1

G 1 V T G

(3)

that is the calculation of the inverse of such matrices in general is very easy and computationally cost-efficient, they form a group and may have the determinant r1. The unimodular sub-group trivially is a Lie group with the generators satisfying the restrictions GH  H T G

0

(4)

ª 0 Iº 2 « I 0» , and g 1,...,1,c , ¬ ¼ result in the Orthogonal, the Symplectic, and the Generalized Lorentz Group, respectively ("c" is the velocity of light here chosen to be 1). The appropriate special sets are the orthonormal, the symplectic, and the Lorentzian sets. In these examples G is either symmetric (I, g) or skew-symmetric (‚), consequently H can be constructed of skewsymmetric or symmetric J matrices, respectively, as H=G-1J. It is easy to prove that the columns of the following matrix form a generalized Lorentzian set: The special cases in which G corresponds to I, ‚

5

TAR, RUDAS, BITÓ, KOZàOWSKI º » f 2 / c 2  1»¼

ªe( f ) f 2 / c 2  1 e( 2 ) ... e( DOF ) « f / c2 0 ... 0 «¬

f

(5)

In this solution the physically interpreted vector f is accomplished with a fictitious (DOF+1)th component, and it is placed into the last column of a generalized Lorentzian. [The e(2), …, e(DOF) set can be obtained by rigidly so rotating a whole set of orthonormal basis vectors, e.g. the columns of the unit matrix, that this operation alters only the 2D subspace spanned by f and e(1).] In strict analogy with (3) the proper Lorentzian transforming the observed acceleration into the desired one can be calculated as L

T

º 1 ª... fD »g « 2 D2 f / c  1¼ ¬...

ª... « ¬...

º fR » g 2 R2 f / c  1¼

(6)

To avoid numerical problems arising in connection with zero vectors it is advantageous to add a physically not interpreted ("dummy"), non-zero, constant component to f, so for a 3DOF system we use Lorentzians of 5 rows and 5 columns. As it was done in [10], the Minimum Operation Symplectic transformations have bigger size but can be constructed by similar rotations and stretches. They have the structure as follows: ~ ~ (1) ª f (1) u ( 2 ) e (3) ...  f ( 2)  u 0 ...º S « ( 2) (7) » ~ (1) (1) ( 2 ) ~ u 0 ... f u e ( 3) ...¼ ¬f with u

1 ª (1) f ( 2)T f (1) ( 2) º «f  ( 2)T ( 2 ) f » f (1)T f (1) ¬ f f ¼ (1)T ( 2 ) ª ( 2) f f º 1 f  (1)T (1) f (1) » ( 2 )T ( 2 ) « f f ¬ f f ¼

(1)

u ( 2) ~ (1) f ~ (1) u

(1)

f ~ , f ( 2) ( 2 )T ( 2 ) f f f f u (1) ~ ( 2) ,u u (1)T u (1)  u ( 2)T u ( 2 ) (1)T

(1)

(8)

( 2)

f f f  f ( 2 )T f ( 2 ) u ( 2) u (1)T u (1)  u ( 2 )T u ( 2) (1)T

(1)

In (8) f(1) has the dimension of DOF+1 (also containing a "dummy" one) and f(2) can be obtained from f(1) via a permutation of its components. An alternative possibility also considered in the simulation in this paper is the use of El Hini’s abstract rotations [11]. J

I  s  1

bb T , T bT b

WJ

(9)

In this operation vector b simply is rotated into the direction of vector a by the orthogonal matrix W, and it also is rescaled by introducing the scalar factor s:=_a_/_b_. W makes a rotation concerning only the two-dimensional sub-space stretched by a and b. It is evident that if v is orthogonal to b, then Jv=v. If c=Eb, then Jc=sEb, that is this transformation applies stretch/shrink only in the desired direction, and leaves the orthogonal sub-space of the pair a and b unchanged. Following this direction-selective shrink/stretch, rotation comes as a gentle operation. 6

A MODIFIED RENORMALIZATION ALGORITHM …

3 Proof of Complete Stability In the realm of Cellular Neural Networks the concept of Complete Stability is often used as a criterion. It means that for a constant input excitation the network asymptotically converges to a constant response. If the variation of the input is far slower that the network’s dynamics, with a good accuracy, the net provides with a continuous response corresponding to some mapping of the time-varying input. The same idea is applied when we seek for series pertaining to a constant desired response. The f i n o i 0 requirement can be expressed in more or less restricted forms. For instance, assume, that there exists 0I  [ H @>I  [ G @xˆ # x d  [

wf G  H xˆ wx

(13)

For the convergence we need decreasing error, that is f Sx  x d d K f x  x d which means that

[

wf wf G  H xˆ d K [ w f Gxˆ or Hx d  Hxˆ d K Hx d wx wx wx

(14)

For a finite generator H Hxˆ and Hx d must be approximately of the same norm and same direction that is the angle between them is acute because it was supposed that xˆ # x d , and because the matrix multiplication is a continuous operation. Due to the 7

TAR, RUDAS, BITÓ, KOZàOWSKI

positive definite nature of f ': angle between Hxd and 

wf multiplication with it also can result in an acute wx

wf Hxˆ (13) has the following geometric interpretation: wx

Hx d

š Hx

š -f'Hx š Hx d -f'Hx

The allowed set of the vectors of reduced norm Figure 1: Geometric interpretation of the convergence criteria On the basis of Figure 1 it is evident that under quite general conditions the algorithm can converge to the desired solution. For instance, in the Euler-Lagrange equations of a Classical Mechanical System the inertia matrix can be roughly approximated by a small scalar inertia plus a big additive „vector“ term. The positive definite nature of the inverse of the actual inertia matrix of the system can guarantee convergence for this problem class. To keep the desired value in the vicinity of the actual one, which also is a necessary criterion of convergence, instead of the joint accelerations its "interpolated" version is taken into account, that is a "regulated correction" is applied as: [

xd  f



1  max x

d

, f



,O

1  H 1  H 2  1  H 1

[ 1[

, xˆ d



f  O xˆ d  f



(15)

For large relative difference the „regulating factor“ OoH2 (a small value moderating the norm of the transformation matrices to be applied), while for small difference it approaches (1+H1), with a mall positive H1 meaning a kind of slight extrapolation of the tendency.

4 Simulation Results The motion of the same 3DOF SCARA arm structure was considered along the same nominal trajectory with the same velocity with the same adaptive law applying Lorentzian and symplectic matrices. In Figure 2 the phase trajectories and the joint coordinate errors are compared with each other. Apart from the "transient part" the very much similar behavior belonging to the two choices is apparent. The same can be stated for the behavior of the regulating factor and the joint generalized forces described in Figure 3.

8

A MODIFIED RENORMALIZATION ALGORITHM … Phase Space

Phase Space

13.90

13.92 11.70

10.21

9.49 7.27

6.52

5.05

2.83

2.84 0.62

-0.86

-1.59 -3.81

-4.55

-6.03

-8.24 -2.75

-1.95 qp1 qp2 qp3

-1.15

-0.34

0.46

1.27

-8.24 -2.76

2.07

-1.95 qp1 qp2 qp3

-1.15

-0.34

0.46

1.27

2.07

Joint Coordinate Errors -- T ime

Joint Coordinate Errors -- T ime 0.07

0.08

0.05

0.06

0.03

0.04

0.01

0.02

-0.01

0

-0.03

-0.02

-0.05

-0.04

-0.07

-0.06 -0.08

-0.09 0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

Figure 2: The Phase Space and the joint coordinate errors for the control versus time using the Generalized Lorentz (left side) and the Minimum Operation Symplectic Transformations (right side) [q1, q2 in rad (solid and dashed), q3im m (dotted), time measured in ms units]

The nominal velocity along the same geometric path was doubled for further comparison. In Figure 4 the phase space and tracking error for the fast non-adaptive motion is described. In Figure 5 the phase space and the joint coordinate errors for the control using the Generalized Lorentz and the Minimum Operation Symplectic Transformations are compared to each other. The significance of the non-linearities drastically increased in the forthcoming figures in which the viscous, Coulomb and adhesive friction forces were introduced in the robot joints and in the external disturbance forces not modeled by the controller. Furthermore, the mechanical degree of freedom of the problem has been doubled by introducing deformable joints also not modeled by the controller. In this case the manipulation of a part (moving it along an elevating arc, then inserting it into a part along a vertical straight line) was considered. In the case of the adaptive control El Hini’s partially stretched rotations were applied. In Fig. 6 the adaptive and the non-adaptive controls’ simulated results are compared to each other. The drastic change in the sign of the acceleration of the desired trajectory, and the that of the friction forces depending on the relative velocity’s sign of the parts in contact completely destroy the non-adaptive control. The presence of the unmodeled deformable joints also has contribution in the fluctuation of the control. However, introduction of adaptivity considerably improves the situation. Further details of the adaptive control are given in Figure 7. It can well be seen that the trajectory tracking error of the end-point as well as the deformation of the deformable components is treated properly. The regulation factors suffers very significant variation, therefore it takes significant part in the control. The rotation angle of the El Hini Transformation usually is very small in comparison to the full rotation 2S. (The shrinking factor is almost identical 9

TAR, RUDAS, BITÓ, KOZàOWSKI Joint Generalised Forces - T ime

Joint Generalised Forces - T ime 15e3

17e3

11e3

13e3 9e3

7e3

5e3

3e3

1e3 -1e3

-3e3 -5e3

-7e3

-9e3

-11e3

-13e3

-15e3 -19e3

-17e3 0

200

400

600

800

1000

0

1200

200

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1000

1200

Regulating Factor

R e g u la t i n g F a c t o r

1 .2

1.2

1 .0

1.0

0 .8

0.8

0 .6

0.6

0 .4

0.4

0 .2

0.2 0

0

0

200

400

600

800

1000

0

1200

200

400

600

800

Figure 3: The joint generalized forces [Q1, Q2 in Nm (solid and dashed), Q3 in N (dotted)] and the regulating factor (nondimensional) versus time [ms] for the Lorentzian and the symplectic matrices based identification to 1 therefore it is not plotted.) This is in harmony with the requirement to be met for the complete stability (e.g. the need for near identity transformations). The variation of the external disturbance force to be defied y the controller also is very significant.

5 Conclusions In this paper a novel branch of computational cybernetics was outlined. It is based on the idea of the partial and situation-dependent system-identification, the modified renormalization transformation, application of simple Lie groups as sources of uniform structures and easily invertible solutions, some linear interpolation-like regulating technique and the application of "dummy" components to avoid numerical singularities. It was theoretically proven that the combination of these simple and fastoperating components can result in a completely stable controller for a wide class of Phase Space

Joint Coordinate Errors -- T ime

27.80

0.3 22.88

0.2

17.96 13.04

0.1 8.12

0

3.20 -1.72

-0.1 -6.64

-0.2

-11.56 -16.48 -2.75

-1.95 qp1 qp2 qp3

-1.15

-0.34

0.46

1.27

2.07

-0.3 0

200

400

600

800

1000

1200

Figure 4: The phase space and the joint coordinate error for the fast non-adaptive motion [the same notation and units as in Figure 2] 10

A MODIFIED RENORMALIZATION ALGORITHM … Phase Space

Phase Space

27.8

28.0

20.4

20.6

13.0

13.2

5.7

5.8

-1.7

-1.7

-9.1

-9.1

-16.5 -2.75

-1.95 qp1 qp2 qp3

-1.15

-0.34

0.46

1.27

2.07

-16.5 -2.77

-1.96 qp1 qp2 qp3

-1.16

-0.35

0.46

1.27

2.07

Joint Coordinate Errors -- T ime

Joint Coordinate Errors -- T ime

0.12

0.3

0.08 0.2

0.04 0.1

0 -0.04

0

-0.08 -0.1

-0.12 -0.16

-0.2 0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

Figure 5: The Phase Space and the joint coordinate errors for the control using the Generalized Lorentz and the Minimum Operation Symplectic Transformations for a fast nominal motion [the same notation and units as in Figure 2]

problems as e.g. in the control of mechanical devices. Computer simulation was used to verify and exemplify the operation of the method for a 3 DOF SCARA paradigm controlled by the use of the Generalized Lorentz Group and the Minimum Operation Symplectic Transformations and El Hini’s partially stretched rotations. Research aiming at further potential fields of applications seems to be expedient.

Acknowledgments The support by the FANUC's "Financial Assistance to Research and Development Activities in the Field of Advanced Automation Technology Fund", by the Hungarian National Research Fund OTKA T 34651, and that of the Hungarian-Polish Bilateral Scientific and Technology Co-operation Fund TéT PL-2/01 is gratefully acknowledged.

References [1] [2] [3] [4] [5]

R. Reed. Pruning Algorithms - A survey. IEEE Transactions on Neural Networks, (4):740–747, 1993. S. Fahlmann and C. Lebiere. The cascade-correlation learning architecture. Advances in Neural Information Processing Systems, (2):524–532, 1990. T. Nabhan and A. Zomaya. Toward generating neural network structures for function approximation. Neural Networks, (7):89, 1994. G. Magoulas, N. Vrahatis and G. Androulakis. Effective backpropagation training with variable stepsize. Neural Networks, (10):69–82, 1997. C. Chen and W. Chang. A Feedforward neural network with function shape autotuning. Neural Networks, (9):627–641, 1996.

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TAR, RUDAS, BITÓ, KOZàOWSKI

Figure 6: The Phase Space and the deformation of the internal degrees of freedom (motor and robot shaft data [q1, q2 [rad] (solid and dashed), q3 [m]) vs. time for the non-adaptive (left side) and the El Hini Transformations based adaptive (right side) control, time measured in ms units [6]

W. Kinnenbrock. Accelerating the standard backpropagation method using a genetic approach. Neurocomputing, (6):583–588, 1994. [7] A. Kanarachos and K. Geramanis. Semi-stochastic complex neural networks. In Proceedings of the IFAC-CAEA '98 Control Applications and Ergonomics in Agriculture, pages 47–52, 1998. [8] J.K. Tar, I.J. Rudas and J.F. Bitó. Group theoretical approach in using canonical transformations and symplectic geometry in the control of approximately modelled mechanical systems Interacting with unmodelled environment. Robotica, (15):163–179, 1997. [9] J.K. Tar, I.J. Rudas, J.F. Bitó and O.M. Kaynak. A new utilization of the Hamiltonian formalism in the adaptive control of mechanical systems under external perturbation. Intelligent Automation and Soft Computing, 5(4):303–312, 1999. [10] J.K. Tar, M. Rontó. Adaptive Control Based on the Application of Simplified Uniform Structures and Learning Procedures. Zbornik Radova, 24(2):174–194, 2000. [11] Yahya El Hini. Comparison of the application of the symplectic and the partially stretched orthogonal transformations in a new branch of adaptive control for mechanical devices. In Proceedings of the 10th International Conference on Advanced Robotics, pages 701–706, Budapest, Hungary, August 22-25, 2001. [12] V.I. Arnold. Mathematical Methods of Classical Mechanics. (in Hungarian) MĦszaki Könyvkiadó, Budapest, Hungary, 1985.

12

A MODIFIED RENORMALIZATION ALGORITHM …

Figure 7: The trajectory tracking error of the end-point [m], the regulating factor [nondimensional], the angle of abstract El Hini rotation [rad], and the 3rd component of the external disturbance force [N] vs. time [ms]

About the Authors József K. Tar received his Master’s degree in Physics in 1981 from the Loránd Eötvös University, and PhD degree in 1989 in Budapest, Hungary. His research focuses on the adaptive control of very inaccurately modelled coupled non-linear systems. Imre J. Rudas, IEEE Fellow Grade Member, received a Master’s degree in Mathematics in 1977 from the Loránd Eötvös University, and PhD degree in 1987 from the Technical University in Budapest, Hungary. His research interests include non-conventional fuzzy operators of tuneable parameters, adaptive control, and robotics. János F. Bitó, IEEE Senior Member, graduated as physicist in 1958 from the József Attila University, Szeged, Hungary. He obtained a DSc degree in 1971. His research activity, among others, covered plasma physics, soft computing and robotics. Krzysztof R. Kozáowski, IEEE Senior Member, received the M.S. degree in electrical, and PhD degree in control engineering from PoznaĔ University of Technology in 1973, and 1979, respectively. He also obtained the M.S. degree in mathematics form A. Mickiewicz University in PoznaĔ in 1972. His current research interests include robot dynamics and control, hybrid control of robots, path planning for cooperating mobile robots, and various aspects of sensory feedback in robotics.

13

14

Minimal linearization via HOSVD in LMI based control ∗ P´eter Baranyi1,2 , Yeung Yam3 , Domonkos Tikk1,2 and P´al Michelberger4 1 Dept.

of Telecommunications & Telematics Budapest University of Technology and Economics, Budapest, Hungary [email protected], [email protected] 2 Intelligent

3 Dept.

Integrated Systems Japanese–Hungarian Laboratory Budapest, Hungary Automation and Computer Aided Engineering The Chinese University of Hong Kong Shatin, N.T., Hong Kong [email protected] 4 Research

Group for Mechanics Hungarian Academy of Sciences Budapest, Hungary

Abstract — In this paper we propose a HOSVD (Higher Order Singular Value Decomposition) based approach to LMI based control design and stability analysis techniques. The proposed method deals with the analytic differential equations of dynamic models and automatically finds their TS model representation. As a further advantage, it optimizes the complexity of the resulting TS model with respect to approximation accuracy.

1

Introduction

Having the recently proposed powerful algorithms (and associated theory) for convex optimization, we can now solve very rapidly many convex optimization problems for which no traditional “analytic” or “closed form” solution are known (or likely to exist). This fact has far-reaching implications for engineers: it changes our fundamental notion of what’s being a solution to a problem. There are “analytical solutions” to a few very special cases in the wide variety of problems in systems and control theory, but in general ∗

This paper is supported by FKFP 180/2001, OTKA F030056, T034233, T34212 and D034614. P´eter Baranyi is supported by Z. Magyary scholarship.

15

BARANYI, YAM, TIKK, MICHELBERGER

non-linear problems cannot be solved. Applying the recent numeric convex optimization techniques, a control engineering problem that reduces to solving even a large number of convex algebraic Riccati inequalities should also be regarded as “solved”, even though there is no analytic solution. A number of problems that arise in Systems and Control such as optimal matrix scaling, digital filter realization, interpolation problems that arise in system identification, robustness analysis and state feedback synthesis via Lyapunov functions, can be reduced to a handful of standard convex and quasi-convex problems that involve Linear Matrix Inequalities (LMI). Extremely efficient interior point algorithms have recently been developed for and tested on these standard problems. With regard to the above the use of TS modelling (Takagi - Sugenlo modelling) [1] is motivated by the fact that it can easily be cast or recast as convex optimization which involves LMIs. The controller design and the Lyapunov stability analysis of a non-linear system can, hence, be reduced to solving an LMI problem in many cases. Based on this idea Tanaka et al. and Wang et al. have introduced various powerful controller design methods and relaxed stability theorems [2, 3, 4, 5]. TS model is a kind of convex combination or superposition of linearized models. The convex combination is defined by antecedent membership functions (say basis functions). Actually, TS model is a kind of standard Tensor Product (TP) based approximation, where the approximation points become linear models. Since the TS model has the universal approximation property, we may conclude that any kinds of differential equation systems can be given in TS model form, whereupon the execution of numerical techniques, such as LMI, leads to a controller design and stability analysis. Despite this advantageous idea discussed above the use of TS models is practically limited. The reason of this is that though the TS model has the universal approximation property in theory [6, 7, 8, 9], it suffers from the problem of exponential complexity with regard to approximation accuracy, e.g., K´oczy and Hirota [10]. It means that the number of linearized models in the convex combination grows exponentially as the approximation error tends to zero. Particularly, in the general case of TS model, the number of linearized models grows to infinity while zero approximation error is achieved. Moreover, for TS model it is shown, that if the number of linearized models is bounded, the resulting set of function is nowhere dense in the space of approximated functions [11, 12]. In conclusion, the exponential complexity explosion of TS models, cannot be eliminated, so the universal approximation property of these modelling approaches cannot be exploited straightforwardly for practical purposes. The mutually contradicting results naturally pose the question as to what extent the model approximation is deemed accurate enough for the available complexity. From the practical point of view, though, it is enough to achieve an “acceptably” good approximation, where the given problem determines the factor of acceptability in terms of ε. The task is, hence, to find a possible trade-off between the specified accuracy and the complexity. Motivated by the above conflicts the main objective of this paper is twofold. The first is to propose a HOSVD based method capable of implementing various kinds of differential equation systems of a dynamic models in TS model form with specific basis functions whereupon the LMI based controller design techniques and stability analysis can be executed. The second is to find a tradeoff between the TS modelling accuracy, hence system performance, and the controller complexity which is bounded by the available real time computation power at hand.

16

MINIMAL LINEARIZATION VIA HOSVD IN LMI BASED CONTROL

The previous works [13, 14, 15, 16, 17, 18, 19, 20] of this paper gives detailed introduction to the concepts utilized in this paper especially to the aspects of HOSVD in fuzzy rule base complexity reduction.

2

TS model and its restricted approximation property in practice

Dynamical system models of plants operating around particular operating conditions are often obtained as multi-model representations of the form sx(t) = Ai x(t) + Bi u(t) y(t) = Ci x(t) + Di u(t);

(1)

where sx(t) = x(t) ˙ for a continuous-time system or sx(t) = x(t + 1) for a discrete-time system. The multi-model (1) can be alternatively specified by the sequence of system matrices   Ai Bi . (2) Si = Ci Di Such a model belongs to the more general class of so- called polytopic models sx(t) = A(p)x(t) + B(p)u(t)

(3)

y(t) = C(p)x(t) + D(p)u(t); where p is time varying and may include some elements of x(t). The  system matrix varies within a fixed polytope of matrices S(t) ∈ {S1 , S2 , . . . , SN } = { N i=1 αi Si : αi ≥ N 0, i=1 αi = 1}. The systems S1 , S2 , . . . , SN are called vertex systems. If the convex combination of the vertex system matrices are defined by basis functions w(p) given over p then we obtain the explicit form of TS- fuzzy model: S(p) =

N 

wi (p)Si

i=1

 with {∀p : N i=1 wi (p) = 1, ∀i, p : wi (p) ≥ 0}. When the basis functions are decomposed for dimensions we deal with a higher order structure as: S(p) =

I1  I2  i1 =1 i2 =1

···

IN  N 

wn,in (pn )Si1 ,i2 ,...,iN

(4)

iN =1 n=1

where values In pn are the elements of p. As a matter of fact, the basis is normalized: {∀n, pn : in =1 wn,in (pn ) = 1, ∀i, n, pn : wn,i (pn ) ≥ 0}. Equation (4) is equivalent with the explicit form of MISO TS (Takagi-Sugeno ) fuzzy model defined by fuzzy rules: IF antecedent set w1,i1 AND antecedent set w2,i2 . . . AND antecedent set wN,iN THEN Si1 ,i2 ,...,iN The explicit form of TS model (4) can be reformulated in terms of tensor product as:  N  wn (pn ) , (5) S(p) = S n=1

17

(N +1)

BARANYI, YAM, TIKK, MICHELBERGER

(for definition and notation of tensor product see Appendix) where the row vector wn (pn ) ∈ RIn contains the antecedent membership functions (or say basis functions) wn,in (pn ), the N + 2 -dimensional coefficient tensor S ∈ RI1 ×I2 ×···×IN ×O×L is constructed from the matrices Si1 ,i2 ,...,iN ∈ RO×L . The first N dimensions of S are assigned to the dimensions of the parameter space P . The next two are assigned to the output and input vectors, respectively. Let us briefly study the TS model as an approximator of dynamic models. Without the loss of generality let us consider a two dimensional problem as a demonstration. Suppose that the following dynamic model is given: x¨(t) = f (x(t), ˙ x(t), u(t)) This equation can be approximated over a compact domain by a convex combination of linearized models: J I  

x¨(t) =

w1,i (x(t))w ˙ ˙ x(t), u(t)) 2,j (x(t))fi,j (x(t),

(6)

i=1 j=1

˙ x(t), u(t)) = (ai,j x(t) ˙ + bi,j x(t) + ci,j u(t)). fi,j (x(t), In state space form x˙ =

I  J 

w1,i (x1 )w2,j (x2 )Ai,j x(t) + Bi,j u(t)

(7)

i=1 j=1

which takes the form x˙ = A ×1 w1 (x1 ) ×2 w2 (x2 ) ×3 xT (t)+ +B ×1 w1 (x1 ) ×2 w2 (x2 ) ×3 uT (t) =

 x˙ = S ×1 w1 (x1 ) ×2 w2 (x2 ) ×3 xT (t) uT (t) . Zero approximation error is achieved, in general case, if I and J goes to infinity. They, however, becomes constant I, J = C1 , C2 < ∞ if a specified approximation error ε is acceptable. If ε is numerically zero then the right side and the left side of Eq. (7) is considered to be numerically equivalent, which implies for a large variety of engineering applications that any function can be computed in the form of Eq. (7) by computer in finite time. As a conclusion two important theorems should be addressed in this Section. These theorems are cited from [11]. First, if the number of basis functions wn,i (xn ) in each input dimension, and hence, the number of models is bounded by I, J, and I · J, respectively, then the set of TS approximators in the form (7) is not capable of approximating with arbitrary accuracy a particular continuous function, this is also true for multi variable case (5). Further, exploiting the above statement, [11] shows that the set of TS approximators with bounded number of basis functions is nowhere dense in the space of continuous functions with respect to the Lp norm p ∈ [1, ∞]. Second, the number of linearized models grows exponentially when the approximation error tends to zero. Because of this contradiction finding a tradeoff between the approximation accuracy and complexity is highly desired [15].

18

MINIMAL LINEARIZATION VIA HOSVD IN LMI BASED CONTROL

3

From differential equations to TS model form

This Section proposes a method capable of extracting the TS model from a given differential equation. The complexity of the resulting TS model is determined by the given approximation error. In order to facilitate further reading, first the TS approximation of a function f (x) ∈ RN is introduced via HOSVD then the approximation of differential equations are discussed. Let an N dimensional hyper rectangular grid be defined by values an = [an,1 , an,2 , . . . , an,In ],

n = 1, . . . , N.

We require the grid to be uniformly distributed on the sampled space: Definition 3.1 Let RN ⊃ Ω = [a1 , b1 ] × · · · × [aN , bN ], further let {λn }∞ k=1 be a sequence of finite subsets of Ω with #λk = k. If #(λk ∩ ω) |ω| 0 ∃k0 ∀ω ∈ Ω ∀k ≥ k0 : − (8) #λk |Ω| then the set λk are uniformly distributed on the domain Ω. Here #(λk ∩ ω) denotes the cardinality of the finite set (λk ∩ ω), and |ω| is the Lebesque measure of ω.

Remark 3.1 In our denotation, k, the number of sample points equals N n=1 In . Then let the given function f (x) ∈ RN be sampled over the grid points as: bi1 ,i2 ,...,iN = f (z),

(9)

where z = [a1,i1 , a2,i2 , . . . , aN,iN ] and ∀n : in ∈ [1, In ]. Let the HOSVD then be executed in exact mode on tensor B (see appendix) created from N r elements bi1 ,i2 ,...,iN which leads to B = B n=1 Un . Therefore the TS approximation is: f(x) = B r

N 

wnr (xn ),

(10)

n=1 r

where row vector wnr (xn ) ∈ RIn contains the extracted basis. The points of the extracted basis functions are included in matrices U: r (an,in ) = uin ,j , wn,j

(11)

r In order to obtain a simple bi-linear approximation, let the extracted functions wn,j (xn ) be constructed by linear pieces between the characteristic points (an,in , uin ,j ). The number of extracted basis functions on the nth input dimension equals the n-mode rank of tensor B. In this light we can conclude that a minimal basis is obtained. Consequently, the number of basis functions equals the number of columns in the singular matrix Un , and the values of the basis functions over the grid lines equal the elements of the columns in the singular matrix, respectively. Thus, the more dense grid we define, the more precise basis functions we obtain, and the size of tensor B r increases minimally.

19

BARANYI, YAM, TIKK, MICHELBERGER

If the rank of tensor B sampled from f (x) tends to a constant while we increase λk , the density of the hyper rectangular grid, to infinity, then we can state that the “rank” of the given function f (x) is finite: ∀n : rankn (f (x)) = lim rankn (B) = cn . λk :k→∞

(12)

This implies that the given function can exactly be transformed to tensor product based form. If the rank of B goes to infinity then the tensor product representation, which has finite number of terms, obviously becomes an approximation. If the number of larger singular values, which are not considered to be numerically zero, tends to constant and only the number of small values may increase with the density of the grid, then we obtain a quantity, which can be considered the numerical rank of the given function f (x). In the case of TS model the basis functions wn,i (xn ) must hold a specific property required by the fuzzy concept, e.g., the membership functions should be bounded by [0, 1]. Let this property be called: Property 3.1 (Non-Negativeness: NN) Antecedent function w(x), x ∈ X, has the nonnegativeness property if ∀x : w(x) ∈ [0, 1]. (13) An other important property is: Property 3.2 (Sum-Normalization: SN) Basis functions wi (x),i = 1, . . . , I, x ∈ X, have the sum-normalization property if they fulfill: ∀x :

I 

wi (x) = 1.

(14)

i=1

This Property 3.2 is also called Ruspini -partition in the related fuzzy literature. This additional property required, for instance, in Tanaka’s LMI based stability theorems [1-5]: The basis functions defined by the column vectors of Un resulted by HOSVD may not be interpretable as fuzzy membership values, because the bound of the elements in Un is [−1, 1]. Another crucial point is that the resulting basis functions do not guarantee the Ruspini -partition, namely, property SN. This fact would destroy the effectiveness of the whole concept if the resulting tensor product form is for further studies in, for instance, Tanaka’s stability analysis, where the antecedent functions assumed to have property SN and NN. Condition SN is essential in the theory of polytopic models as well. Since the column vectors of matrices Un define the basis or membership functions let the above two properties be formulated for matrices:  Definition 3.2 (SN and NN matrix) A given matrix U is called sum-normalized if (U) =  1 (where operator (A) sums up the column vectors of A as: (A) = A1). A given matrix U is called non-negativeness if all of its elements are bounded by [0, 1]. The next part of this Section is intended to recall additional transformations from [20] to the above HOSVD method pertaining to NN and SN conditions. Let this goal be specified by the following theorem:

20

MINIMAL LINEARIZATION VIA HOSVD IN LMI BASED CONTROL

Theorem 3.1 (SN and NN basis matrices) Assume that executing HOSVD on tensor B ∈ N

RI1 ,I2 ,...,IN , results in B = S ⊗ [ Un Udn ], where the size of matrix Un is (In × Inr ). n=1

Discarding of singular values and their corresponding singular vectors stored in Udn ∈ N r  = B r ⊗ Un . Matrix Un can RIn ×(In −In ) , where “d” denotes “discarded”, yields B always be transformed to SN and NN matrix Un subject to

n=1

r N

N

B r ⊗ Un = B ⊗ Un n=1

(15)

n=1

r

Notation Un denotes here that Un is SN and NN normalized, further, B means that B r is modified subject to equ. (15). Transformation techniques to yield the normalized system in (15) are introduced and detailed via various examples in [13, 14, 15, 16, 19, 20]. The last part of this Section is to show in Method 3.1 how to extract a minimized basis to TS modelling from given differential equations. The difference from the above introduced TS function extraction is that approximation points becomes matrices. Method 3.1 Assume that the differential equation system of a dynamic model is given in the form of   x˙ = f (x(t), u(t), p). (16) y Vector p ∈ RN varies in the parameter space P in which the given system is nonlinear (vector p may contain some elements of x as well). The goal of this method is to find tensor product based approximation   x˙ = f (x(t), u(t), p) ∼ (17) = y r ∼ = (S

N 



wrn (pn )) ×N +2 xT (t) uT (t) ,

n=1

wrn (pn )

where the size of vector is minimized and it is SN and NN. Step 1: Let (16) be sampled  a high density rectangular grid defined

or linearized over by grid points pi1 ,i2 ,...,iN = pi1 pi,2 . . . piN :   x˙ (18) = f (x(t), u(t), pi1 ,i2 ,...,iN ) = y 

= Si1 ,i2 ,...,iN ×2 xT (t) uT (t) . Step 2. Let HOSVD, extended with SN and NN transformation, be executed on tensor S in such a way that the SVD is performed only on dimensions n ∈ [1, N ]. Dimensions N + 1 and N + 2 are not reduced. Therefore one obtains:   x˙ = f (x(t), u(t), p) ∼ (19) = y

21

BARANYI, YAM, TIKK, MICHELBERGER

 ∼ =

S

r

N 

wrn (pn )

 ×N +2 xT (t) uT (t) .

n=1

Basis functions wn,i (pn ) are determined as above. Along in the same line as in the previous discussion, the density λ of the grid points is increased until an acceptable εa is achieved.

4

Demonstrative example

This example is a controller design to a simple mass-spring-damper mechanical system. First of all, it is shown that the differential equations of the model have analytically been derived to a TS fuzzy model [3], in order to execute PDC controller design. Then it is assumed in the example that the analytical derivation between the TS fuzzy model and the differential equations is unknown and hard to solve. Therefore, Method 3.1 is utilized to find a complexity minimized TS fuzzy model. The example shows that the proposed transformation finds a minimal form of the TS fuzzy model which existence is proven by the analytic design. The example shows that the transformed model is capable of recovering the same structure as revealed in the analytically derived model. Finally, the controller is determined from the minimized model, which results in a complexity minimized controller.

u

m x d

k

Figure 1: Mass-spring-damper system Consider the non-linear mass-spring-damper mechanical system as depicted on Figure 1 and its dynamical equation, m · x¨(t) + g(x(t), x(t)) ˙ + k(x(t)) = φ(x(t)) ˙ · u(t)

(20)

where m is the mass and u(t) stands for the force. The function k(x(t)) is the nonlinear or uncertain stiffness coefficient of the spring, g(x(t), x(t)) ˙ is the non-linear or uncertain term damping coefficient of the damper, and φ(x(t)) ˙ is the non-linear input term. Assume that g(x(t), x(t)) ˙ = d(c1 x(t) + c2 x˙ 3 (t)), k(x(t)) = c3 x(t) + c4 x3 (t), and 3 ˙ ∈ [−b, b] and φ(x(t)) ˙ = 1 + c5 x˙ (t). Furthermore, assume that x(t) ∈ [−a, a], x(t) a, b > 0. The above parameters are set as: m = 1, d = 1, c1 = 0.01, c2 = 0.1, c3 = 0.01, c4 = 0.67, c5 = 0, a = 1.5, and b = 1.5. Equation (20) then becomes: x¨(t) = −0.1x˙ 3 (t) − 0.02x(t) − 0.67x3 (t) + u(t).

22

(21)

MINIMAL LINEARIZATION VIA HOSVD IN LMI BASED CONTROL

The non-linear terms are −0.1x˙ 3 (t) and −0.67x3 (t). The non-linear state-space model is:   1 ˙ u(t). (22) x(t) = A(x1 (t), x2 (t))x(t) + 0 We refer to the results of an analytic derivation presented in the paper written by [3], which says that Eq. (22) can exactly be represented by a TP model as: ˙ x(t) =

2  2 

2

a a w1,i (x1 (t))w2,j (x2 (t))Aai,j x(t)+Bu(t) = Aa ⊗ wna (xn (t))x(t)+Bu(t). n=1

i=1 j=1

(23) Superscript “a” denotes that this result is obtained via analytic derivations. The basis functions wna (xn (t)) are depicted on Figure 2. 1

1

w 1,a 1

r 1, 1

w

0.5

w 2,a 1 w2,r 1

r 1, 2

w

0.5

w2,r 2 w 2,a 2

w 1,a 2 0

1.5

+1.5

0

x

1.5

+1.5

x

Figure 2: Antecedent functions of the original approximation via analytical derivation and the antecedents extracted by the TS fuzzy model transformation In the followings we assume that the analytic derivation from the model (22) to a TS fuzzy model (23) is unknown, like in usual practical cases. The proposed TS fuzzy model transformation goes about generating the complexity minimized TS fuzzy model, and we expect that it finds four linear models like in the case of the analytic design. According to the proposed method, let us sample the state-space model (22) over the dense (400 × 400) approximation grid points defined by x1,i = −1.5 + (i − 1)3/399 and x2,j = −1.5 + (j − 1)3/399:   −0.1x21,i −0.02 − 0.67x22,j s , i, j = 1, . . . , 400. Ai,j = 1 0 Let us execute HOSVD, extended with SN and NN transformations, on tensor As ∈ R400×400×2×2 constructed from Asi,j . Let us keep all the nonzero singular values. We find that the rank of tensor As is two on the first two dimensions. Note that if we increase the density of sampling grid to infinity the limes of the rank of the sampled tensor remains 2 on the first two dimensions. Actually, the proof of this statement is the analytic derivation itself, see Eq. (23). The numerically obtained antecedent functions wr (x(t)) are depicted on Figure 2. The antecedent fuzzy sets are in Ruspini -partition. This means that PDC controlled design techniques can immediately be executed on the resulted TS fuzzy model

23

BARANYI, YAM, TIKK, MICHELBERGER

form. One of the advantages of the minimization is that the PDC design (or any further LMI analysis) can be restricted to the four fuzzy rules in the present case. The PDC results in a controller that has four fuzzy rules. Therefore, the controller takes the form of:  2 2    2 r r r w1,i (x1 (t))w2,j (x2 (t))Fi,j x(t) = − F ⊗ wn (xn (t)) x(t). u(t) = − n=1

i=1 j=1

Let the feedback gains in F be simply defined by the simple pole-replacement technique  in thepresent case. Let the closed-loop eigenvalues of the four linear systems be −2 −2 . Fi,j = pole(Ai,j , B, −2, −2). Finally let the stability of the controlled nonlinear system be analyzed. Let us apply the stability criteria introduced by [3] (see, criteria C14 in the paper):

Figure 3: Control result. x˙ and x are depicted by dash and solid line respectively. The control signal is depicted by dash dot line.

N

Theorem 4.1 (Quadratical stability) Dynamic system (20) where u(t) = −F ⊗ wrn (pn (t)) n=1

is quadratically stable if and only if Reλi (H) = 0, where H is an indicator matrix whose elements are defined in the paper of [3]. In the present example the eigenvalues of H are −2.0, −2.0, 2.0 and 2.0. Therefore the designed controller quadratically stabilizes the nonlinear system. Figure 3 shows the effect of the controller.

24

MINIMAL LINEARIZATION VIA HOSVD IN LMI BASED CONTROL

5 Conclusions The main novelty of this paper is to propose a method capable of automatically transforming, according to a given approximation accuracy, any differential equation systems of dynamic models to TS model form, which can easily be formed as convex optimization and whereupon LMI based control design can, hence, be performed. This paper also points out an important fact as the motivation of the present approach, that the widely adopted linearization by TS forms can not arbitrarily well describe a given model, it needs to consider the tradeoff between complexity and approximation accuracy. Our future work is to replace the product in TS with the Rudas’s [21, 22] type generalized operator which may offer a continuous tuning between smooth and robust feature of the controlled system.

Appendix Definition 5.1 (n-mode matrix of tensor A) Assume an N th order tensor A ∈ RI1 ×I2 ×...×IN . The n-mode matrix A(n) ∈ RIn ×J , J = k Ik contains all the vectors in the nth dimension of tensor A, where k = 1, . . . , N and k = n. The ordering of the vectors is arbitrary in A(n) . This ordering shall, however, be consistently used later on. (A(n) )j is called an jth n-mode vector. Note that any matrix of which the columns are given by n-mode vectors (A(n) )j can readily be restored to become tensor A. The restoration can be executed even in case when some rows of A(n) are discarded since the value of In has no role in the ordering of (A(n) )j [23, 24]. Definition 5.2 (n-mode sub-tensor of tensor A) Assume an N th order tensor A ∈ RI1 ×I2 ×···×IN . The n-mode sub-tensor Ain =α contains elements ai1 ,i2 ,...,in−1 ,α,in+1 ,...,iN . Definition 5.3 (n-mode tensor partition) Assume an N th order tensor A ∈ RI1 ×I2 ×···×IN . The n-mode A are Bl ∈ RI1 ×I2 ×···×In−1 ×Jl ×In+1 ×...IN and denoted   partitions of tensor as A  = B1 B2 · · · BL n , where L is the number of partitions (l = 1, . . . , L) and Jl . In = l

Definition 5.4 (Scalar product) The scalar product A, B of two tensors A, B ∈ RI1 ×I2 ×···×IN  def   is defined as A, B = · · · bi1 i2 ...iN ai1 i2 ...iN . i1

i2

iN

Definition 5.5 (Orthogonality) Tensors of which the scalar product equals 0 are mutually orthogonal. def

Definition 5.6 (Frobenius norm) The Frobenius norm of a tensor A is given by A =



A, A.

Definition 5.7 (n-mode matrix-tensor product) The n-mode product of tensor A ∈ RI1 ×I2 ×···×IN and a matrix U ∈ RJ×In , as denoted by A ×n U, is an (I1 × I2 × · · · × In−1 × J × In+1 × · · · × IN )-tensor of which the entries are given by A ×n U = B, where B(n) = U · A(n) . N

Let A ×1 U1 ×2 U2 × · · · ×N UN be denoted as A ⊗ Un for brevity. n=1

25

BARANYI, YAM, TIKK, MICHELBERGER

Theorem 5.1 (Matrix singular value decomposition (SVD)) Every real valued (I1 × I2 )T matrix F can  be written as the product of F = U · S · V = S ×1 U ×2 V, in which 1. U = u1 u2 · · · uI1 is a unitary (I1 × I1 )-matrix, 2. V = v1 v2 · · · vI2 is a unitary (I2 × I2 )-matrix, 3. S is an (I1 × I2 )-matrix with the properties of (i) pseudo-diagonality: S = diag(σ1 , σ2 , . . . , σmin(I1 ,I2 ) ) (ii) ordering: σ1 ≥ σ2 ≥ · · · ≥ σmin(I1 ,I2 ) ≥ 0. The σi are the singular values of F, and the vectors Ui and Vi are, respectively, an ith left and an ith right singular vector. There are major differences between matrices and higher-order tensors when rank properties are concerned. These differences can directly affect the way an SVD generalization look like. As the matter of fact, there is no unique way to generalize the rank concept. In this paper we restrict the description to n-mode rank only. Definition 5.8 (n-mode rank of tensor A) The n-mode rank of A, denoted by Rn = rankn (A), is the dimension of the vector space spanned by the n-mode matrices as rankn (A) = rank(A(n) ). Theorem 5.2 (Higher Order SVD (HOSVD)) Every tensor A ∈ RI1 ×I2 ×···×IN can be written as the product N  Un (24) A=S n=1

in which   1. Un = u1,n u2,n . . . uIN ,n is a unitary (IN ×IN )-matrix called n-mode singular matrix. 2. tensor S ∈ RI1 ×I2 ×...×IN whose sub-tensors Sin =α have the properties of (i) all-orthogonality: two sub-tensors Sin =α and Sin =β are orthogonal for all possible values of n, α and β : Sin =α , Sin =β  = 0 when α = β, (ii) ordering: Sin =1  ≥ Sin =2  ≥ · · · ≥ Sin =In  ≥ 0 for all possible values of n. (n) The Frobenius norm Sin =i , symbolized by σi , are n-mode singular values of A and the vector ui,n is an ith singular vector. S is termed core tensor. The computation of the HOSVD in exact mode is done by executing SVD on each dimension of A. Namely, Un in Eq. (24) is determined by executing SVD (Theorem 5.1) on the n-mode matrix A(n) of tensor A as:    Dn 0



d d T V V , (25) A(n) = Un Un n n 0 Ddn where diagonal matrix Dn contains the retained, and Ddn contains the discarded n-mode (n) singular values σi . Matrix Ddn has only zero elements and Dn contains the non-zero singular values as diagonal elements, so the number of diagonal elements in Dn is rankn (A). Therefore: A(n) = Un Dn VnT .

26

MINIMAL LINEARIZATION VIA HOSVD IN LMI BASED CONTROL

Then the product of Dn VnT yields S(n) , which, after restoring S(n) into tensor Sn , leads to: A = Sn ×n Un Determination of Un+1 is done in the same way. Again, let SVD be executed on n + 1mode matrix (Sn )(n+1) of tensor Sn obtained in the above step. This results in: T , (Sn )(n+1) = Un+1 Dn+1 Vn+1

where diagonal matrix Dn+1 contains the retained n + 1-mode singular values. Then T into tensor Sn+1 we have: restoring the product of S(n+1) = Dn+1 Vn+1 A = Sn+1 ×n Un ×n+1 Un+1 . Repeating the above step on each dimension leads to Eq. (24). More detailed discussion of HOSVD and detailed algorithm is given in papers [16, 19, 20].

References [1] T. Takagi and M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. on SMC, 15:116–132, 1985. [2] K. Tanaka and M. Sugeno. Stability analysis and design of fuzzy control systems. Fuzzy Sets and Systems, 45(2):135–156, 1992. [3] K. Tanaka, T. Ikeda, and H. O. Wang. Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H∞ control theory, and Linear Matrix Inequalities. IEEE Trans. Fuzzy Systems, 4(1), 1996. [4] K. Tanaka, T. Ikeda, and H. O. Wang. Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based design. IEEE Trans. Fuzzy Systems, 31(2):250–265, 1998. [5] H. O. Wang, K. Tanaka, and M. F. P. Griffin. An approach to fuzzy control of non-linear systems: Stability and design issues. IEEE Trans. Fuzzy Systems, 4(1):14–23, 1996. [6] K. Hornik, M. Stinchcombe, and H. White. Multilayer feedforward networks are universal approximators. Neural Networks, 2:359–366, 1989. [7] G. Cybenko. Approximation by superposition of sigmoidal functions. Mathematics of Control, Signals and Systems, 2:303–314, 1989. [8] E. K. Blum and L. K. Li. Approximation theory and feedforward networks. Neural Networks, 4(4):511–515, 1991. [9] V. K˚urkov´a. Kolmogorov’s theorem and multilayer neural networks. Neural Networks, 5:501–506, 1992. [10] L. T. K´oczy and K. Hirota. Size reduction by interpolation in fuzzy rule bases. IEEE Trans. on SMC, 27:14–25, 1997. [11] D. Tikk. On nowhere denseness of certain fuzzy controllers containing prerestricted number of rules. Tatra Mountains Math. Publ., 16:369–377, 1999. [12] D. Tikk, P. Baranyi, and R. J. Patton. Polytopic and TS models are nowhere dense in the approximation model space. In IEEE Int. Conf. System Man and Cybernetics (SMC’02), pages 150–153, Hammamet, Tunisia, 2002. [13] P. Baranyi, A. R. V´arkonyi-K´oczy, Y. Yam, R. J. Patton, P. Michelberger, and M. Sugiyama. SVDbased reduction of TS model approximation. To appear in IEEE Trans. Electronics. [14] P. Baranyi, Y. Yam, A. R. V´arkonyi-K´oczy, and R. J. Patton. SVD based reduction to MISO TS models. IEEE Transaction on Industrial Electronics, 50(2):232–242, 2003.

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[15] P. Baranyi, Y. Yam, D. Tikk, and R. J. Patton. Trade-off between approximation accuracy and complexity: TS controller design via HOSVD based complexity minimization. In J. Casillas, O. Cord´on, F. Herrera, and L. Magdalena, editors, Interpretability Issues in Fuzzy Modeling, number 128 in Studies in Fuzziness and Soft Computing, pages 249–277. Springer-Verlag, Heidelberg, 2003. [16] P. Baranyi and Y. Yam. Complexity reduction of a generalised rational form. In D. Ruan and E.E. Kerre, editors, Fuzzy If-Then Rules in Computational Intelligence: Theory and Applications, number SECS 553 in The Kluwer international series in engineering and computer science, pages 135–160. Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000. [17] P. Baranyi, Y. Yam, C.T. Yang, P. Varlaki, and P. Michelberger. Inference algorithm independent SVD fuzzy rule base complexity reduction. International Journal of Advanced Computational Intelligence, 5(1):22–30, 2001. [18] P. Baranyi, Y. Yam, P. Varlaki, and P. Michelberger. Singular value decomposition of linguistically defined relations. International Journal of Fuzzy Systems, 2(2):108–116, 2000. [19] Y. Yam. Fuzzy approximation via grid point sampling and singular value decomposition. IEEE Trans. SMC, 27:933–951, 1997. [20] Y. Yam, P. Baranyi, and C. T. Yang. Reduction of fuzzy rule base via singular value decomposition. IEEE Trans. Fuzzy Systems, 7(2):120–132, 1999. [21] I. J. Rudas and O. Kaynak. New types of generalized operations. Computational intelligence: Soft computing and fuzzy-neuro integrationwith applications. Springer NATO ASI Series. Series F: Computer and Systems, Sciences, 192:128–156, 1998. [22] I. J. Rudas and O. Kaynak. Entropy-based operations on fuzzy sets. IEEE Transactions on Fuzzy Systems, 6:33–40, 1998. [23] L. D. Lathauwer, B. D. Moor, and J. Vandewalle. A multi linear singular value decomposition. SIAM Journal on Matrix Analysis and Applications, 21(4):1253–1278, 2000. [24] L. D. Lathauwer, B. D. Moor, and J. Vandewalle. An introduction to independent component analysis. Jour. Chemometrics, 14:123–149, 2001.

About the Authors P´eter Baranyi received degrees M.Sc. in electrical engineering (1994), M.Sc. in Education of Engineering Sciences (1995) and Ph.D. (1999) from the Technical University of Budapest. He received the International Dennis Gabor Award in (2000). His research focuses on fuzzy and neural network techniques. Yeung Yam (M’92) received the B.S. degree from the Chinese University of Hong Kong and the M.S. degree from the University of Akron, OH, both in physics, in 1975 and 1977, respectively, and the M.S. and Sc.D. degrees in aeronautics and astronautics from the Massachusetts Institute of Technology, Cambridge, in 1979 and 1983, respectively. His research interests include analysis, design, and identification of control systems. Domonkos Tikk received his B.Sc. and M.Sc. degree in computer science both from E¨otv¨os L´or´and Science University in Hungary in the years 1993 and 1995, respectively. He received his doctoral degree in engineering in 2000 from Budapest University of Technology and Economics in Hungary. His research interests include data mining, text mining, automatical categorization methods, fuzzy systems, and soft computing techniques. P´al Michelberger He received M.Sc. in Mechanical and Military Engineering (1952) at Technical University of Budapest, Candidate of Technical Sciences (Ph.D., 1960), D.Sc. (1970). His research interest include analysis, design, and identification of control systems for vehicle designs.

28

Automatic Language Control of Electrical Drives. Background and Applications J. F. Martins1,2, A. J. Pires1,2, R. Vilela Mendes2, and J. A. Dente2 1

LabSEI – Laboratório de Sistemas Eléctricos Industriais Escola Superior de Tecnologia de Setúbal, Instituto Politécnico de Setúbal, Portugal [email protected] 2

Laboratório de Mecatrónica, Instituto Superior Técnico, Lisboa, Portugal

Abstract — A new formal language concept for automatic control of electrical drives is presented. The proliferation of these systems promises improved efficiency and reliability, reduced maintenance and operative costs, and a more environment friendly operation. However, they exhibit considerable complexities related with their behaviour such as large uncertainties at structural and parameter levels, multidimensionality, and strong mutual interactions. The integration of these systems with information processing techniques allows a better adaptative modelling of their behaviour. The electrical drive system is assumed as a linguistic source producing a certain language. A developed grammatical inference algorithm is used in order to extract the productions that govern a grammar representing that language. The formalism of the developed formal language based control algorithm is presented and experimental results are discussed.

1 Introduction High performance motion control applications, using induction motor drives, are of critical importance. Although several advance motion controllers can perform such task, often the controller design requires complicated theoretical and numerical procedures under the desired control specifications. The application of soft computing techniques within electrical drives intelligent controllers design has presented promising features. A wide variety of high-quality strategies, using Artificial Neural Networks, Fuzzy Logic or Genetic Algorithms, have been reported in the literature [1] [2] [3]. Typical features of electrical drive systems include a considerable degree of dynamical complexity. They are highly non-linear coupled systems, with large uncertainties at the structural and parameter levels. They are multidimensional and contain highly unknown nonlinearities. When fast performance is required for evolving non-linear systems, classical methods yield a limited representation of the real system. It becomes necessary to complement, and even correct, this classical modelling with other information processing techniques that allows a better modelling 29

MARTINS, PIRES, VILELA MENDES, DENTE other information processing techniques that allows a better modelling of their behaviour. A new formal language approach in modelling electrical drive systems was already proposed [4], where the drive is assumed as a linguistic source producing a certain language. A grammatical inference algorithm extracts the productions of the drive’s language grammar. An advantage over other information processing techniques relies on the fact that, in the formal language approach, the structure of the productions is not established in advance. Different types of productions are established according to the incoming words from the linguist source. This method provides good recognition results and a reasonable quantitative accuracy, for the identification of unknown dynamics [5]. Fault detection in control systems, based on the distance between the words generated by the faulty system and the grammar that represents the non-faulty system, is another application of this technique [6].

2 Formal Language Concepts The formal language procedure considers a linguistic source that generates the words within the produced language. In this way any dynamical system is assumed as a linguistic source capable of generating a certain language, characterised by a grammar that can generate all the words in that particular language. This grammar, denoted by G, defines the structural features of the words produced by the linguistic source and, in this way, models the source itself [7]. G is a 4-tuple (1), where the terminal alphabet ¦T is constituted by symbols that make up the resulting words, the non terminal alphabet ¦N is constituted by symbols that are used to generate the patterns, the start symbol S is a special non-terminal symbol that is used to begin the generation of words, and the set of productions P is a set of rules (in the form DoE, where D and E are strings) that determines the generation of words [8]. G = (P, ¦N, ¦T, S)

(1)

Both alphabets – terminal and non terminal – must be established from the codification of the variables obtained from the dynamical system. Within our established formal language formalism the codification of the output variable – y – produces the terminal alphabet and the codification of the input variable – u – produces the non-terminal alphabet (2). y

Codificati   o y j  ¦T on

u

Codificati  o Ui  ¦ N on

(2)

The learning algorithm must establish the relations between both alphabets (input and output information) in order to produce terminal words that denote the output variable evolution. In this way p-type productions are considered assuming the general form (3). Sequence y1...yp, of length p, is constituted by terminal symbols, U is any non-terminal symbol, yp+1 is a terminal symbol, and G is a special non-terminal symbol that can be replaced by any non-terminal symbol. A p-type production has p terminal symbols in the left part of the production, denoting the previous dynamic evolution of the output variable. y1  y p U o y1  y p y p 1G

30

(3)

AUTOMATIC LANGUAGE CONTROL OF ELECTRICAL DRIVES Given this general form production (3), since the left part of any production contains at least one non-terminal symbol, this grammar can be classified as context sensitive in the Chomsky hierarchy [9]. To establish the grammar productions a grammatical inference based algorithm was developed [5]. Out of a set of sample words, resulting from the codification of the dynamic evolution of the system input/output variables, the basic learning algorithm has a simple paradigm in order to establish the set of productions:  A 0-type production is considered for every symbol of the terminal alphabet that occurs in the sample.  A (n+1)-type production is considered if the established n-type production already exists. One must note that the structure of the formal language productions is not established in advance. According to the word samples involved, one can obtain different types of productions (0-type, 1-type, ...) in the resulting grammar. This feature allows the modelling of different behaviours detected in a dynamical system.

3 Formal Language Control and Experimental Results As an example consider the non-linear dynamical system (4), where x denotes the state variable, u the command and y the output. Note that the input command can only be –1, 0 or +1. ­ ° x k 1 x k  x k 1  2u k ® °y ¯ k xk

­ x  ^1,2,3,4` with ® k ¯u k  ^ 1,0,1`

The three manifolds presented in Figure 1 define the working domain of the above dynamical system. The grammar that represents this dynamical system presents a P set with one 0-type production, two 1-type productions and twenty-four 2-type productions. A four symbol terminal alphabet and a three symbol non-terminal alphabet where considered, as presented in Table 1. yk l ¦T 1la 2lb 3lc 4ld

uk l ¦ N -1 l A 0lB +1 l C

Table 1: Alphabets considered for the dynamical system (4)

31

(4)

4

4

3

3

x[k+1]

x[k+1]

MARTINS, PIRES, VILELA MENDES, DENTE

2

2 1 4

1 4 4

3 x[k]

4

3

3

2

2 1

1

3

2

2 1

x[k]

x[k-1]

1

(a)

x[k-1]

(b)

x[k+1]

4 3 2 1 4 4

3

3

2

2 1

x[k]

1

x[k-1]

(c) Figure 1: Working Domain of the Dynamical System (4) with: (a) uk=–1; (b) uk=0; (c) uk=+1 Once the grammar, representing the dynamical system, is obtained (thus defining the structure of the words produced by the linguistic source), it can be considered as a model of this source. In this way the set of productions can be used to predict the evolution of the dynamical system, establishing the sequence of commands (non-terminal alphabet) necessary to take the system from one state to another. This sequence of non-terminal symbols should be established according some performance objective. Consider that a terminal word, denoting the sequence of values that the system should follow, is given. Knowing the initial state, for each symbol in the terminal word one should choose the appropriate non-terminal symbol that takes the system to the nearest state to the objective. Whenever the desired value is not reached, due to some perturbation, the objective terminal word is rewritten in order to fulfil the initial objective. As a control example consider that the objective terminal word (5) should be reached by the dynamical system (4).

w obj

^c b c b a a b c c c a c c`

The dynamical evolution of the system’s output, considering a initial terminal symbol ‘d’, is presented in Figure 2, where the objective word is depicted with a solid line (rectangular marker) and the actual word reached with a dashed line (circular marker).

32

(5)

AUTOMATIC LANGUAGE CONTROL OF ELECTRICAL DRIVES

Terminal Symbols

d

c

b

a

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time

Figure 2: Controlled Evolution of the Dynamical System (4) One should note that in order to go from an objective terminal word symbol to another the system could go through other terminal symbols. According to the internal dynamics (4) and the available non-terminal alphabet it is not possible to reach the terminal symbol ‘c’ from the symbol ‘a’. That is, doesn’t exist any production [[aUo[[acG, where [ denotes any terminal symbol and U any non-terminal symbol. It is necessary to successively apply the productions baAobaaG, aaCoaabG and abCoabcG, when the purpose is to reach the terminal symbol ‘c’ from the symbol ‘a’. Due to this physical limitation the obtained terminal word necessary differs from the objective terminal word. As presented in Figure 2, the objective terminal word (5) is not obtained but the terminal word (6), where the reached objective terminal symbols are underscored. Every symbol in the objective terminal word is reached, however the actual terminal word has some additional symbols. The reached terminal word doesn’t belong to the grammar, but is, considering the physical limitation of the dynamical system, the best approximation. Taken into account the limited input command (only three symbols are considered), the grammar establishes the best non-terminal word (input command) so that the objective terminal symbols (output variable values) are reached in the shortest period of time. w reached

^d b a a b c a a b c a a b a a b c c b a a b c c`

The considered electrical drive system is composed by a simple volts/Hz speed command and an induction motor drive with a variable mechanical load. With low slip performing operation, a normal condition for this type of electrical drive, the volts/Hz speed regulator is able to impose the desired speed through the stator currents frequency. Some difficulties arise at low speed operating conditions, where the resistive voltage drop becomes mandatory, or due to an increase of the rotor time constant, resulting from a rotor resistance increase. This last condition, which corresponds to a parameter change, is particular severe since it increases the value of the slip. The highly oscillatory nature of the system prevents a full conventional approach closed-loop compensation, when fast dynamical responses are required. 33

(6)

MARTINS, PIRES, VILELA MENDES, DENTE

Neglecting the volts/Hz regulator power inverter dynamics, the behaviour of the electrical drive can be described by a set of functional relationships (7), where Z denote the drive speed and f the induction motor stator frequency. These functional relationships are dependent of the electrical drive set of parameters, denoted by P, and of the external torque, denoted by T. g P ,T Z kk  p , f k

Z k 1

(7)

The proposed formal language controller, being a model of the drive, will produce the appropriate stator frequency in order to obtain the desired speed. Figure 3 presents the considered drive system with the correspondent grammatical modelling, where the input variable is codified into the non-terminal alphabet and the output variable into the terminal alphabet of the considered grammar.

Stator Frequency

V/Hz

V/Hz Regulator

Induction Machine

Torque

Input

Speed

Mechanical Load

ELECTRICAL DRIVE

Non-Terminal Alphabet

Grammar

Output Terminal Alphabet

Figure 3: Induction Motor Electrical Drive. In order to overcome open-loop inverse modelling instabilities problems the linguistic controller was combined with a conventional feedback controller (Figure 4), assuring global stability [10], as an indirect compensation control loop. The conventional controller (implemented as a PI controller) is used to assure a significative covering of the electrical drive’s working domain during the learning period, where the obtained grammar infers a relation between the input and the output of the electrical drive. Linguistic Controller

+ Speed Reference

_

Conventional Controller

Stator Frequency

+ +

Electrical Drive

Load Torque

Figure 4: Linguistic Controller Control Loop

34

AUTOMATIC LANGUAGE CONTROL OF ELECTRICAL DRIVES It is very difficult to obtain an adequate training data set from an open-loop training scheme. Due to nonlinearities of the drive, if the system is excited with a random signal it remains within a restricted part of the working domain. This data set collection does not describe the system dynamics on its all-operating region. The coarse closed-loop PI conventional controller scheme, used in the learning process, serves as a guide for the drive’s output signal to travel through the operating region. After this modelling phase is finished the output of the conventional controller vanishes to zero. To obtain a representative training data set, a sinusoidal reference signal, with a combination of amplitudes and frequencies, is supplied as input variable, to obtain output variable values in the operating region of the system. In this way, the amplitude and frequency values can be set within the limits of the drive’s response, thus avoiding the filtering problem, and allowing the collected data to be a good training set of the system’s operating domain. Figures 5 and 6 show the experimental dynamical performance, when a sinusoidal reference is considered, for both controllers when working alone. The drive’s speed reference is denoted as a continuous black line and the actual speed is denoted as a continuous grey line. The conventional controller results (with the linguistic controller switched off) are presented in Figure 5 and the linguistic controller results in Figure 6, where a better dynamical behaviour of the linguistic controller can be observed. The good accomplishment within the learning phase allows a good language modelling, and thus a good control feature, through the performing region of the drive. It is important to note that for the speed response presented in Figure 6 the PI conventional controller it is not intentionally switched off but its output remains naturally extremely close to zero. The input of the electrical drive is assured exclusively by the signal provided by the linguistic controller. One of the major advantages regarding the use of grammatical inference linguistic controllers is its ability to adapt themselves to new operating situations. Whenever a change of parameters occurs the inferred functional relationship (7) are no longer exact, since they are parameter dependent. In this case it is important to correct the grammar productions (3) that denote the mentioned functional relationship, in order to model this new situation keeping the grammar up to date. 100

Speed [pu]

80

60

40

20

0 0

2

4

6

8

10

12

14

16

18

Time [seg]

Figure 5: Conventional Controller Speed Response.

35

20

22

MARTINS, PIRES, VILELA MENDES, DENTE 100

Speed [pu]

80

60

40

20

0 0

2

4

6

8

10

12

14

16

18

20

22

Time [seg]

Figure 6: Linguistic Controller Speed Response. For a particular set of parameters P1 the electrical drive establishes the functional relationship (8), inferred by a grammar with a set of productions of the type (3).

Z k 1

g1 Z kk  p , f k

(8)

For a different set of parameters P2 the functional relationship (8) is no longer valid, and a new one (9) must be inferred by the linguistic algorithm.

Z k 1

g 2 Z kk  p , f k

(9)

Since this new set of parameters doesn’t correspond to new operating conditions, in the sense of new areas of the working domain of the drive, the idea is to adapt the existent productions instead of creating new ones. This procedure doesn’t increase the complexity of the grammar keeping it as a good model of the considered source. For the same operating point the correspondent production is corrected adjusting the non-terminal symbol (10), which corresponds to an adjustment of the linguistic controller command action. Ut  1 Ut  'U

(10)

Figure 7 shows an automatic adaptation of the linguistic controller to the previous described new situation (changes within the electrical drive’s parameters), considering the updating scheme presented in Figure 4. After a change in the induction machine rotor time constant (still unknown for the inferred grammar) the following of the speed reference is ensured by the conventional controller action. However, immediately the correction of the considered production is started. With this new situation incorporated the new production is again sufficient to establish the control of the drive, vanishing the conventional controller command action towards zero.

36

AUTOMATIC LANGUAGE CONTROL OF ELECTRICAL DRIVES

4 Conclusions and Remarks This paper proposes a new formal language approach in modelling and controlling electrical drive systems. An advantage over other information processing techniques relies on the fact that, in the proposed formal language approach, the structure of the productions is not established in advance. Different types of productions are established according to the incoming words from the linguist source. This method provides good recognition results and a reasonable quantitative accuracy, for the identification of unknown dynamics. The acquired linguistic modelling provides the implementation of a linguistic based control topology. The control topology consists in an indirect compensation control loop. It combines the linguistic controller, as a direct compensator, and a conventional controller that allows the covering of the working domain in the learning phase. The experimental results obtained with this topology showed the abilities that this control technique provide. The linguistic controller adapts itself to changes in the system dynamics, acquiring therefore some autonomy in its functioning. The integration of these linguistic techniques within the electrical drive control loop allows a better adaptative modelling of their behaviour, and thus a better control performance. Furthermore, this integration allows the use of these techniques for other features such as anomaly detection [6]. 100

Speed [pu]

80

60

40

20

0 0

4

8

12

16

20

24

28

Time [seg]

(a)

37

32

36

40

44

48

52

MARTINS, PIRES, VILELA MENDES, DENTE 100

Linguistic Controller Command

Command Action [pu]

80

60

Conventional Controller Command

40

20

0 0

4

8

12

16

20

24

28

32

36

40

44

48

52

Time [seg]

(b) Figure 7: Automatic adaptation of the linguistic controller to new drive’s parameters. (a) Output Response. (b) Command Actions

References [1] P. Vas; Artificial-Intelligence-Based Electrical Machines and Drives, Oxford Science Publications, 1999. [2] S. Mondal, J. O. P. Pinto and B. K. Bose; “A Neural Network Based Space Vector PWM Controller for a Three-Level Voltage-Fed Inverter Induction Motor Drive”, in IEEE IAS Annu. Meet. Conf. Rec., Chicago, USA, 2001. >3@ K. Itoh, M. Iwasaki and N. Matsui; “Autonomous Motion Controller Design Using Genetic Algorithms”, in IEEE IAS Annu. Meet. Conf. Rec., Chicago, USA, 2001. [4] J.F. Martins, A.J. Pires, R. Vilela Mendes, J.A. Dente; “Modelling Electromechanical Drive Systems: A Formal Language Approach”, in 1st ICAF Conference on Mechatronic Systems, Darmstad, Germany, 2000. [5] J. F. Martins, J. A. Dente, A. J. Pires, R. Vilela Mendes; “Language Identification of Controlled Systems: Modelling, Control and Anomaly Detection”; IEEE Trans. on Systems, Man and Cybernetics (Part C), vol. 31, no. 2, pp. 234-242, May 2001. >6@ J. F. Martins, P. J. Costa Branco, A. J. Pires, J. A. Dente; "Fault Detection using ImmuneBased Systems and Formal Language Algorithms"; in Proc. of the 39th IEEE Conf. on Decision and Control, Sidney, Australia, December 2000. [7] K.S. Fu and T. L. Booth; “Grammatical inference: Introduction and Survey – Part I”, in IEEE Trans. on SMC, vol 5, no. 1, pp 409-423, January 1975. [8] A. Saloma; Computation and Automata, Cambridge University Press, 1985. >9@ N. Chomsky; Aspects of the theory of syntax, MIT Press, Cambridge, Massachusetts, 1965. [10] H. Gomi and M. Kawato; “Neural Network Control for a Closed-Loop System Using Feedback-Error-Learning”, Neural Networks, vol. 6, pp 933-946, 1993.

38

AUTOMATIC LANGUAGE CONTROL OF ELECTRICAL DRIVES

About the Authors J. F. Martins graduated in electrical engineering at Instituto Superior Técnico (IST), Technical University of Lisbon, in 1990. He received his M.Sc. and Ph.D. degrees in electrical engineering at the same institute, respectively in 1996 and 2003. His research areas are in control of electrical drives, advanced learning control techniques for electromechanical systems, grammatical inference learning algorithms and non-linear systems. A. J. Pires graduated in Electrical Engineering at Instituto Superior Técnico (IST), Technical University of Lisbon, in 1985. He received his M.Sc. in 1988 and his Ph.D. in 1994 in electrical engineering at the same institute. His research areas are in electrical machines, power electronics, intelligent control systems for electrical drives and non-linear systems. R. Vilela Mendes graduated in electrical engineering at Instituto Superior Técnico (IST), Technical University of Lisbon, in 1960, and received the Ph.D. degree in physics from the University of Texas, Austin, in 1970. His main interests are currently nonlinear dynamics of multiagent systems and quantum information. J. A. Dente graduated in electrical engineering and received the Ph.D. degree in electrical engineering from the Instituto Superior Técnico (IST), Technical University of Lisbon, in 1975 and 1986, respectively. His primary areas of interest are in electrical machines, motion control, and he is presently engaged in research on advanced learning control techniques for electromechanical systems.

39

40

Application of Fractional Calculus in Mechatronics J. A. T. Machado1, Ramiro Barbosa1, Fernando Duarte2, and Nuno Ferreira3 1

Institute of Engineering, Polytechnic Institute of Porto, Porto, Portugal {jtm,rbarbosa}@dee.isep.ipp.pt 2

School of Technology, Polytechnic Institute of Viseu, Viseu, Portugal {fduarte}@mat.estv.ipv.pt 3

Institute of Engineering, Polytechnic Institute of Coimbra, Coimbra, Portugal {nunomig}@isec.pt

Abstract — Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of mechanical systems.

1 Introduction The generalization of the concept of derivative Dαf(x) to non-integer values of α goes back to the beginning of the theory of differential calculus. In fact, Leibniz, in his correspondence with Bernoulli, L’Hôpital and Wallis (1695), had several notes about the calculation of D1/2f(x). Nevertheless, the development of the theory of Fractional Calculus (FC) is due to the contributions of many other mathematicians such as Euler, Liouville, Riemann and Letnikov [1−3]. In the fields of physics and chemistry [1], FC is presently associated with the modeling of electro-chemical reactions, irreversibility and electromagnetism. The adoption of the FC in control algorithms has been recently studied using the frequency and discrete-time domains [4−5]. Nevertheless, this research is still giving its first steps and further investigation is required. Bearing these ideas in mind, this paper is organized as follows. Section 2 outlines the fundamental aspects of the theory of FC. Section 3 introduces the main algorithms to approximate fractional-order derivatives. Section 4 presents several case studies on the implementation of FC based models in the analysis and control of mechanical systems. Finally, section 5 draws the main conclusions.

41

MACHADO,BARBOSA,DUARTE,FERREIRA

2 Main Mathematical Aspects of the Theory of Fractional Calculus Since the foundation of the differential calculus the generalization of the concept of derivative and integral to a non-integer order α has been the subject of several approaches. Due to this reason there are various definitions of fractional-order integrals (Table 1) which are proved to be equivalent [1−3]. Based on the proposed definitions it is possible to calculate the fractional-order integrals/derivatives of several functions. For example, according with [3] we have the formulae of Table 2. Nevertheless, the problem of devising and implementing fractionalorder algorithms is not trivial and will be the matter of the next sections.

(I ϕ)(x ) = Γ(1α) ³ α a+

Riemann-Liouville

(

)

α Grünwald-Letnikov I a + ϕ (x ) =

x

a

ϕ(t )

(x − t )1−α

d t, a < x , α ∈ C

ª [( x −a ) h ] Γ(α + j ) º 1 ϕ( x − jh )» lim «h α Γ(α) h → +0 « Γ( j + 1) » j =0 ¬ ¼

¦

{ }

L I 0α+ ϕ = L{ϕ} s α , Re(α ) > 0

Laplace

Table 1: Some definitions of fractional-order integrals

ϕ( x ) , x ∈ R

( x − a )β−1 e λx ­ sin(λx ) ® ¯cos(λx ) e

(γx ) ® ¯cos(γx )

λx ­ sin

(I ϕ)(x ) , x ∈ R , α ∈ C α +

Γ(β ) (x − a )α+β−1 , Re(β) > 0 Γ(α + β )

λ− α e λx , Re(λ ) > 0 ­ sin(λx − α π 2 ) λ− α ® , λ > 0,Re(α ) > 1 ¯cos(λx − α π 2 ) e λx

(λ2 + γ 2 )α 2

­ sin(γx − αφ) φ = arctan (γ λ ) , ® ¯cos(γx − αφ) γ > 0,Re(λ ) > 1

Table 2: Fractional-order integrals of several functions

3 Approximations to Fractional-Order Derivatives In this section we analyze two methods for implementing fractional-order derivatives, namely the frequency-based and the discrete-time approaches, and its implication in control algorithms. In order to analyze a frequency-based approach to Dα, with α ∈ R such that 0 < α < 1, let us consider the recursive circuit represented on Figure 1a: n

I=

¦ I i , Ri +1 = i =0

C Ri , Ci +1 = i , ε, η > 1 ε η

42

(1)

APLICATION OF FRACTIONAL CALCULUS IN MECHATRONICS

where η and ε are scale factors, I is the current due to an applied voltage V and Ri and Ci are the resistance and capacitance elements of the ith branch of the circuit. The admittance Y (jω) is given by: I ( jω) Y ( jω) = = V ( jω)

n

jωCε i

¦ jωCR + (ηε)i

(2)

i =0

Figure 1b shows the asymptotic Bode diagrams of amplitude and phase of Y(jω). The pole and zero frequencies ( ωi and ω′i ) obey the recursive relationships: ω′i +1 ωi +1 ω ω′ = = εη , i = ε , i +1 = η ω′i ωi ω′i ωi

(3)

From the Bode diagram of amplitude or of phase, the average slope m′ can be calculated as: log ε m′ = (4) log ε + log η Consequently, the circuit of Figure 1a represents an approach to Dα, 0 < α < 1, with m′ = α, based on a recursive pole/zero placement in the frequency domain. As mentioned in section 2, the Laplace definition for a derivative of order α ∈ C is a ‘direct’ generalization of the classical integer-order scheme with the multiplication of the signal transform by the s operator. Therefore, in what concerns automatic control theory this means that frequency-based analysis methods have a straightforward adaptation to their fractional-order counterparts. Nevertheless, the implementation based on the Laplace definition (adopting the frequency domain) requires an infinite number of poles and zeros obeying a recursive relationship [4]. In a real approximation the finite number of poles and zeros yields a ripple in the frequency response and a limited bandwidth. 20 log10 |Y(jω)|

log η

I +

I0

In

I1

log ε

Δdb

20m’ db/dec 20 db/dec

V

R

R/ε

R/εn

C

C/η

C/ηn

−

ω1 =

1 RC

ω2 =

ω1′ =

a)

η RC

log ω

εη RC ω ′2 =

εη2 RC

b)

Figure 1: a) Electrical circuit with a recursive association of resistances and capacitances; b) Bode diagram of amplitude of Y(jω) Based on the Grünwald-Letnikov definition of a derivative of fractional order α of the signal x(t), Dαx(t), leads to the expression:

43

MACHADO,BARBOSA,DUARTE,FERREIRA D

α

ª 1

x (t ) = lim « h→0

∞

Γ(α + 1)

º

(− 1)k x (t − kh )» α ¦ Γ(k + 1)Γ(α − k + 1) «h » ¬

(5)

¼

k =0

where Γ is the gamma function and h is the time increment. This formulation [5] inspired a discrete-time calculation algorithm, based on the approximation of the time increment h through the sampling period T, yielding the equation in the z domain:

{

}

1 Z D α x (t ) ≈ α X (z ) T

∞

(− 1)k Γ(α + 1) z −k ¦ k! Γ(α − k + 1) k =0

§ 1 − z −1 · ¸ =¨ ¨ T ¸ ¹ ©

α

(6)

An implementation of (6) corresponds to a r-term truncated series given by:

{

}

1 Z D α x (t ) ≈ α X (z ) T

(− 1)k Γ(α + 1) z −k ¦ k! Γ(α − k + 1) k =0 r

(7)

Clearly, in order to have good approximations, we must have a large r and a small T. An important aspect of fractional-order controllers can be illustrated through the elemental control system represented in Figure 2, with open-loop transfer function G(s) = Ks−α (1 < α < 2) in the forward path. The open-loop Bode diagrams (Figure 3) of amplitude and phase have a slope of −20α dB/dec and a constant phase of −απ/2 rad, respectively. Therefore, the closed-loop system has a constant phase margin of π(1 − α/2) rad, that is independent of the system gain K. Likewise, this important property is also revealed through the root-locus depicted in Figure 4.

R(s)

+

G (s ) = −

K

C(s)

sα

Figure 2: Block diagram for an elemental feedback control system of fractional order Į 20 log10 |G(jω)|

arg{G(jω)} −20α dB/dec

log ω

−

π 2

−α

π 2

−π

log ω

Figure 3: Open-loop Bode diagrams for a system of fractional order 1 < Į < 2

44

APLICATION OF FRACTIONAL CALCULUS IN MECHATRONICS +∞ ← K

Im(s)

s-plane

π−π/α

Re(s)

π−π/α

K=0

+∞ ← K

Figure 4: Root-locus for a feedback control system of fractional order 1 < Į < 2

4 Control of Mechanical Systems In this section we study the adoption of fractional-order algorithms in the dynamics and control of mechanical systems. 4.1 Describing Function of Systems with Backlash The standard approach to the backlash study is based on the adoption of a geometric model that neglects the dynamic phenomena involved during the impact process. Due to this reason often real results differ significantly from those predicted by that model. In this section, we use the describing function (DF) method to analyse systems with backlash and impact phenomena [6], usually called dynamic backlash. The proposed mechanical model consists on two masses (M1 and M2) with backlash and impacts as shown in Figure 5. A collision between the masses M1 and M2 occurs when x1 = x2 or x2 = h + x1. In this case, we can compute the velocities of masses M1 and M2 after the impact ( x1′ and x 2′ ) by relating them to the previous values ( x1 and x 2 ) through Newton’s rule:

(x´′1 − x´′2 ) = −ε (x1 − x 2 ),

0 ≤ ε ≤1

(8)

where ε is the coefficient of restitution. In the case of a fully plastic (inelastic) collision ε = 0, while in the ideal elastic case ε = 1. x1 , x1

x 2 , x 2

f(t)

M2 M1 Side A

h

Side B

Figure 5: System with two masses subjected to dynamic backlash

45

MACHADO,BARBOSA,DUARTE,FERREIRA By application of the principle of conservation of momentum M 1 x1′ + M 2 x 2′ = M 1 x1 + M 2 x 2 and of (8), we can find the sought velocities of both masses after an impact: x (M − εM 2 ) + x 2 (1 + ε)M 2 x1 (1 + ε)M 1 + x 2 (M 2 − εM 1 ) , x 2′ = (9) x1′ = 1 1 M1 + M 2 M1 + M 2 We can calculate numerically the Nyquist diagram of −1/N(F,ω) for an input force f(t) = F cos(ωt) applied to mass M2 and an output position x1(t) of mass M1. Figure 6 shows the Nyquist plots for F = 50 N and ε = {0.1,…,0.9} and for F = {10, 20, 30, 40, 50} N and ε = 0.5, respectively, considering M1 = M2 = 1 Kg and h = 10−1 m. The charts reveal the occurrence of a jumping phenomenon, which is a characteristic of nonlinear systems. This phenomenon is more visible around ε ≈ 0.5, while for the limiting cases (ε → 0 and ε → 1) the singularity disappears. Moreover, Figure 6b shows also that for a fixed value of ε the charts are proportional to the input amplitude F. The validity of the model is restricted to an input force f(t) with frequency higher than a lower-limit ωC ≈ [(2F/M2h)2(1−ε)5]1/4 and lower than an upper-limit ωL = 2(F/M2h)1/2, corresponding to an amplitude of x1(t) within the clearance h/2. In the middle-range occurs a jumping phenomena at frequency ωJ ~ (F/M2h)1/2. Figure 7 shows the log-log plots of Re{−1/N} and Im{−1/N} versus ω with F = 50 N and ε = {0.1, 0.3, 0.5, 0.7, 0.9}, for the cases of the static and dynamic backlash. The classical static backlash model corresponds to the DF of a linear system of a single mass M1+M2 followed by the geometric backlash having as input and as output the position variables. Comparing the results for the static and the dynamic backlash models we conclude that: − The charts of Re{−1/N} are similar for low frequencies (where they reveal a slope of +40 dB/dec) but differ significantly for high frequencies. − The charts of Im{−1/N} are different in all range of frequencies. Moreover, for low frequencies, the dynamic backlash has a fractional slope inferior to +80 dB/dec of the static model. 3000

1200 ε =0.1

2500

F=50

ε =0.5

1000 ε =0.2

F=40

ω=40

2000

800

ω=35

1500

Im (-1/N)

Im (-1/N)

ε =0.3 ε =0.4

ω = 25

ε =0.7

500 ω=20

F=10

200

ε =0.8

ω =20

ε =0.9

ω=15

0

ω =30

F=20 400

ε =0.6 ω=25

ω = 15

ε→1

500

1000

1500

ω = 35

600

ε =0.5

ω=30

1000

0 -500

F=30

ω = 40

0 0

2000

500

1000

1500

R e(-1/N)

Re(-1/N)

a)

b)

Figure 6: Nyquist plot of −1/N(F,ω) for a system with dynamic backlash, for: a) F = 50 N and ε = {0.1, …, 0.9}; b) F = {10, 20, 30, 40, 50} N and ε = 0.5

46

APLICATION OF FRACTIONAL CALCULUS IN MECHATRONICS 10

4

10

4

Static

Static 10

ε =0.7, 0.9 ε =0.5 ε =0.3

3

10

10

10

ε =0.1

1

10

10

Dynam ic 10

10

ε =0.9

Dynam ic

1

0

-1

0

10

10

ε =0.1 ε =0.3 ε =0.5 ε =0.7

2

2

Im (-1/N)

Re(-1/N)

10

3

-1

10

10 0

1

10 ω (rad/s)

10

2

-2

-3

10

0

10

1

10

2

ω (rad/s )

Figure 7: Plots of Re{−1/N(F,ω) } and Im{−1/N(F,ω) } for a system with dynamic backlash versus the exciting frequency ω, for F = 50 N and ε = {0.1, 0.3, 0.5, 0.7, 0.9} A careful analysis must be taken because it was not demonstrated that a DF fractional slope would imply a fractional-order model. In fact, in this study we adopt integer-order models for the system description but the fractional-order slope is due to continuous/discrete dynamic variation that results due to the mass collisions [6]. 4.2 Trajectory Control of Redundant Manipulators A redundant manipulator possess more degrees-of-freedom (dof) than those required to establish an arbitrary position and orientation of the gripper. We consider a manipulator with n dof whose joint variables are denoted by q = [q1,q2,...,qn]T and a class of operational tasks described by m variables x = [x1,x2,...,xm]T, m < n. The relation between the joint vector q and the manipulation vector x corresponds to the direct kinematics: x = f (q ) (10)

Differentiating (10) with respect to time yields: x = J (q )q

(11)

Hence, from (11) it is possible to calculate a q(t) path in terms of a prescribed trajectory x(t). A solution is:

q = J # (q )x

(12)

where J# is one of the generalized inverses of the J. The joint positions can be computed through the time integration of the velocities (12) according with the block diagram depicted in Figure 8. Δx

xref

+

Δq J#(q)

−

++

x

q Delay

Direct Kinematics

Figure 8: Diagram of the closed-loop inverse kinematics algorithm J#

47

MACHADO,BARBOSA,DUARTE,FERREIRA An important aspect is that repetitive trajectories in the operational space do not lead to periodic trajectories in the joint space. This is an obstacle for the solution of many tasks because the resultant robot configurations have similarities with those of a chaotic system. We consider a 3R planar manipulator and during the experiments it is adopted Δt = 10−3 s and l1 = l2 = l3 = 1 m. Figure 9 depicts the 3R-robot phase-plane joint trajectories, when repeating a circular motion with frequency ω0 = 3 rad/s, center at r = [x2+y2]½ =1 m and radius ρ = 0.1 m. Besides the position and velocity drifts, leading to different trajectory loops, we have points that are ‘avoided’. Such points correspond to arm configurations where several links are aligned. In order to capture information about the system during all the dynamic evolution we devised an experiment that addresses the frequency response for two alternative exciting signals: a doublet-like and a white noise distributed throughout the 500-cycle trajectories. Figure 10 depicts the resulting amplitude Bode diagrams of the type:

Q1 ( s ) (s α + z) =K α X ref ( s ) ( s + p)

(13)

where K is the gain, z and p are the zero and pole, respectively, and α is the zero/pole fractional-order. For the doublet excitation it results α ≈ 1.0 in contrast with the case of white noise excitation where we get a fractional value α ≈ 1.3. This is due to the memory-time property of fractional-order dynamics because they capture the dynamic phenomena involved during all the time-history of the experiment, in contrast with integer-order derivative that just capture a “local” dynamics [7]. 4 3

dq 1/dt

2 1 0

-1 -2 -3

-3

-2

-1

0 q1

1

2

3

Figure 9: Phase plane trajectory for the 3R- robot joint 1 at r = 1 m, ρ = 0.1 m, ω0 = 3 rad/s

48

APLICATION OF FRACTIONAL CALCULUS IN MECHATRONICS 100

20

90 15

70 ρ=0.1

60 1 ref dB

10 ρ=0.5

|q /x |

|q 1/xref| dB

ρ=0.3

80

ρ=0.3

5

50 ρ=0.5

40 30 20

ρ=0.1

0

10 0

-5 -3 10

10

-2

10

-1

10 ω (rad/s)

0

10

1

10

-10 -3 10

2

10

-2

10

-1

10 ω (rad/s)

0

10

1

10

2

a) b) Figure 10: Frequency response of the 3R robot ω0 = 3 rad/s, r = 2 m, ρ ∈ {0.10, 0.30, 0.50} m for: a) A doublet-like; b) A white noise perturbation during 500-cycle trajectories

4.3 Position/Force Control of Manipulators This section studies the position/force robot control, involving contact between the gripper and the environment, using fractional-order controllers in the hybrid algorithm proposed by Raibert and Craig [8]. The dynamical equation of an n dof robot interacting with the environment is given by:  + C(q, q ) + G(q) − J T (q)F IJ = H(q)q

(14)

where τ and q are the n × 1 vectors of joint torques and positions, H(q) is the n × n inertia matrix, C(q, q ) and G(q) are the n × 1 vectors of centrifugal/Coriolis and gravitational terms and F is the m × 1 vector of the force that the environment exerts in the gripper. In this study we adopt the 2R robot (Fig. 11a) and we consider the schematic structure of the position/force hybrid control algorithm depicted in Fig. 11b. Yc

y

Kinematics

yc xc q2

qes

−

Yd

l2

+

S

Jc−1

I−S

JcT

Position controller

J2g

J1g

l1

J2m

q1

θ x

J1m

Fd

τff

+

τes

+

I−S

Jc

T

τP +

Robot and environment

τF Fc Force controller

−

a)

+

q

b)

Figure 11: a) 2R robot and constraint surface; b) Position/force hybrid controller

49

MACHADO,BARBOSA,DUARTE,FERREIRA The numerical values adopted for the 2R robot are m1 = 0.5 kg, m2 = 6.25 kg, r1 = 1.0 m, r2 = 0.8 m, J1m = J2m = 1.0 kgm2 and J1g = J2g = 4.0 kgm2. In this paper we consider the yC (xC) Cartesian coordinates to be position (force) controlled. The constraint plane is determined by the angle θ (Figure 11a) and the contact displacement xc of the robot gripper with the constraint surface is modelled through a linear system with a mass M, a damping B and a stiffness K with dynamics: Fc = Mxc + Bx c + Kxc (15) For comparison purposes we adopt fractional-order (FO) and PID algorithms for the position/force controllers. In our case, for implementing FO algorithms of the type C(s) = K sα, we adopt a 4th-order discrete-time Padé approximation (ai, bi, ci, di ∈ R, n = 4): C P (z ) ≈ K P C F (z ) ≈ K F

a 0 z n + a1 z n −1 + .. + a n

(16a)

b0 z n + b1 z n −1 + ... + bn c0 z n + c1 z n −1 + .. + cn

(16b)

d 0 z n + d1 z n −1 + ... + d n

where Kp/KF are the position/force loop gains. We analyze the system performance both for ideal transmissions and robots with backlash at the joints according with model (9). Moreover, we compare the response of FO and the PD: CP(s) = Kp + Kd s and PI: CF(s) = Kp + Ki s−1 controllers, in the position and force loops [9]. Both algorithms were tuned by trial and error having in mind getting a similar performance in the two cases. The resulting parameters were FO: {KP,αP}≡{105, 1/2}, {KF ,αF}≡{103,−1/5} and PD/PI: {Kp,Kd}≡{104,103}, {Kp,Ki}≡{103,102} for the position and force loops, respectively. Moreover, it is adopted the operating point {x,y}≡{1,1}, a constraint surface with parameters {θ,M,B,K}≡{π/2,103,1.0,102} and a controller sampling frequency fc = 1 kHz. In order to study the system dynamics we apply, separately, rectangular pulses, at the position and force references, that is, we perturb the references with {δycd,δFcd} = {10−1,0} and {δycd,δFcd} = {0,10−1}. The time responses (Figures 12 and 13) reveal that, although tuned for similar performances in the first case, the FO is superior to the PD/PI in the cases with dynamical phenomena at the robot joints [9].

5 Conclusions This paper presented the fundamental aspects of the FC calculus, the main approximation methods for the fractional-order derivatives calculation and the implication of the FC concepts on the extension of the classical automatic control theory. Bearing these ideas in mind, several motion control systems were described and their dynamics was analyzed in the perspective of fractional calculus. It was shown that fractional-order models capture phenomena and properties that classical integer-order simply neglect. In this line of thought, this article is a step towards the development of motion control systems based on the theory of FC.

50

APLICATION OF FRACTIONAL CALCULUS IN MECHATRONICS −4

15 dyc PID FO

dFc PID FO

10 dy(m)

dy(m)

0.1

x 10

0.05

5 0

0

0

0.2

0.4

−5 0

0.6

0.2

Time (s)

0.4

0.6

Time (s) 0.15 dyc PID FO

0.1

0.1 dFx(N)

dFx(N)

0.05

dFc PID FO

0 −0.05

0.05

−0.1

0

−0.15 −0.2 0

0.2

0.4

0.6

−0.05 0

0.2

Time (s)

0.4

0.6

Time (s)

Figure 12: Time response for the 2R ideal robot with FO and PD/PI controllers −3

12

−4

x 10

10 dFc PID FO

10

6

6 4

4 2

2

0

0 −2 0

dFc PID FO

8 dy(m)

dy(m)

8

x 10

0.2

0.4

−2 0

0.6

0.2

Time (s)

0.4

0.6

Time (s)

0.015 dyc PID FO

dyc PID FO

0.1

0.005

dFx(N)

dFx(N)

0.01

0

0.05

−0.005 −0.01 −0.015 0

0 0.2

0.4

0.6

Time (s)

0

0.2

0.4

0.6

Time (s)

Figure 13: Time response for the 2R robot with backlash for FO and PD/PI controllers

51

MACHADO,BARBOSA,DUARTE,FERREIRA

References [1]

K. B. Oldham and J. Spanier. The Fractional Calculus. Academic Press, New York, 1974.

[2]

K. S. Miller and B. Ross. An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley and Sons, New York, 1993.

[3]

S. G. Samko, A. A. Kilbas and O. I. Marichev. Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, Amsterdam, 1993.

[4]

A. Oustaloup. La Dérivation Non Entière: Théorie, Synthèse et Applications. Editions Hermes, Paris, 1995.

[5]

J. A. Tenreiro Machado. Analysis and Design of Fractional-Order Digital Control Systems. SAMS Journal Systems Analysis, Modelling, Simulation, 27:107−122, 1997.

[6]

Ramiro S. Barbosa and J. A. Tenreiro Machado. Describing Function Analysis of Systems with Impacts and Backlash. Nonlinear Dynamics, 29(1−4): 235−250, July 2002.

[7]

Fernando B. Duarte and J. A. Tenreiro Machado. Chaotic Phenomena and Fractional-Order Dynamics in the Trajectory Control of Redundant Manipulators. Nonlinear Dynamics, 29(1−4): 315−342, July 2002.

[8]

M. Raibert and J. Craig. Hybrid Position/Force Control of Manipulators. ASME Journal of Dynamic Systems, Measurement, and Control, 102(2): 126−133, 1981.

[9]

J. A. Tenreiro Machado, Ramiro S. Barbosa, and N. M. Fonseca Ferreira. Fractional-Order Position/Force Control of Mechanical Manipulators. In Proceedings of the CIFA’2002 Conférence Int. Francophone d'Automatique, pages 641−646, Nantes, France, July 2002.

About the Authors J. A. T. Machado was born in 1957. He graduated and received the Ph.D. degree in electrical and computer engineering from the Faculty of Engineering of the University of Porto, Portugal, in 1980 and 1989, respectively. Presently he is Coordinator Professor at the Institute of Engineering of the Polytechnic Institute of Porto, Dept. of Electrical Engineering. His main research interests are robotics, modeling, control, genetic algorithms, fractional-order systems and intelligent transportation systems. Ramiro Barbosa was born in 1971. He graduated in Electrical Engineering - Industrial Control from Institute of Engineering of Polytechnic Institute of Porto, Portugal, in 1994 and received the Master’s degree in Electrical and Computer Engineering from the Faculty of Engineering of the University of Porto, Portugal, in 2000. Presently he teaches at the Institute of Engineering of the Polytechnic Institute of Porto, Dept. of Electrical Engineering. His research interests include modelling, control, fractional-order systems, and nonlinear systems. Fernando Duarte was born in 1950. He graduated in Mathematics from University of Aveiro, Portugal, in 1982 and received the Ph.D. degree in Electrical and Computer Engineering from the Faculty of Engineering of the University of Porto, Portugal, in 2003. Presently he is Professor at the School of Technology, Polytechnic Institute of Viseu, Dept. of Mathematics. His main research interests are robotics, modeling, control, fractional-order systems. Nuno Ferreira graduated with the B.A. degree in the Institute of Engineering of the Polytechnic Institute of Coimbra, in 1994, the degree in Electrotechnical Engineering at the University of Porto, in 1996 and the Master’s degree in Electrotechnical and Computer Engineering in 1999. Presently he is Professor at the Institute of Engineering, Polytechnic Institute of Coimbra, Dept. of Electrotechnical Engineering. His main research interests are robotics and nonlinear systems.

52

Module Library for Rapid Prototyping and Hardware Implementation of Vector Control Systems József Vásárhelyi 1, Mária Imecs2, János J. Incze2 and Csaba Szabó2 1

Department of Automation, University of Miskolc, Miskolc, Hungary [email protected] 2

Department of Electrical Drives and Robots, Technical University of Cluj, Cluj-Napoca, Hungary {imecs, Ioan.Incze, Csaba.Szabo}@edr.utcluj.ro

Abstract — The paper focuses on the implementation of the most common blocks for the field-oriented AC drives. With the created Module Library the rapid prototyping and fast implementation of their vector control systems becomes possible. The control system structures are implemented in configurable logic cells using FPGA design environment. The performances of some proposed control structures were compared with the simulation results based on Simulink models.

1 Introduction Most motor control applications are concerned with vector control for AC drives. Vector control systems for induction motors give the best dynamic behaviour. Analysing these systems some modularity can be observed, which help fast implementation of motor control applications in reconfigurable structures [2], [8]. Reconfigurable hardware was used in the last years for vector control system implementations. We speak about dynamic reconfiguration of a control system for AC drives, if the real-time application (software) changes the computing platform structure (hardware). In vector control systems, the reconfigurability was introduced by Imecs et all. in [1]. In this concept, each configuration is considered as a state of a logic state machine. When a reconfiguration condition occurs, the system will start the reconfiguration process in which it will switch the current configuration to the next corresponding one. This type of configuration procedure is the context switching and was developed by Sanders in [4]. While context switching is a reconfiguration technology for Field Programmable Gate Arrays (FPGA), the logic state machine with different control system structures in each state is a reconfiguration method for the control systems presented in Figure 1.

53

VÁSÁRHELYI, IMECS, INCZE, SZABÓ P o w e r-on I n it

STA TE1

STA TE2

C o n fig u r a tio n 1

C o n fig u r a tio n 2

STA TEn C o n fig u r a tio n „n”

Figure 1: State machine with different vector control structures for each state. In order to make possible the reconfiguration, there is a need for a profound analysis of the required control structures. Kelemen and Imecs in [3] have presented most of the basic control structures for AC drives. A part of the analysis is presented in the next section.

2 Analysis of Vector Control Scheme The dynamic behaviour of the AC machines is improved by vector control procedures based on the field-orientation principle. The necessity of reconfiguration is based on the observation that the performance of the drive is depending on the vector control structure correlated with the type of the supply power frequency converter [7], [8]. The analysis of the control schemes was performed based on the following criteria: -

Given two vector control structures where common modules exist: • Which are the common modules in the same position and with the same function? • Which are the common modules with different functionality? • Which are the particular modules of each reconfigurable structure? - When a reconfiguration condition occurs, is it possible the variable-value transfer for the modules on the same position or no parameter transfer allowed? - It is possible the variable-value transfer of the PI controllers of the different schemes? - It is possible to give a general mathematical form of all the modules? - As a result of the analysis, the Module Library should be universal for rapid prototyping of any vector control system and from the prototype the implementation should directly result. Let us analyse such a reconfigurable vector control structure with two configurable states. This vector control structure presents the generalities of the most common con-

54

MODULE LIBRARY FOR RAPID PROTOTYPING trol schemes and in the meantime contains some particular modules. The reconfigurable state machine presented in Figure 1 for the vector control structure presented in Figure 2 is working in State 1 as a tandem converter [5], [6] and [7]. The tandem converter is working with two inverters; they are: a Current Source Inverter (CSI), which is controlled in current, and the other a Voltage Source Inverter (VSI) controlled in voltage. AC line Ref iDC

ʌ Flux Controller

ΨrRef

+

Ref isd λr

Controller

ωrRef

Ref isq

Ref isq λr

-

Speed-1 Controller

-

+ -

isd isq

Ref isd λr Ref isq λr 2

+

CSI Current

usdȜr

CooT

Ref vsd

[D(-Ȝr)]

1 usqȜr VsC vRef sq Current Controllers

cosȜr

Mechanical Angular Speed

VA1

fs Synchronisation İ CSI

Ȍr

VA2

Diode Rectifier

Ld Cd

PAM-CSI

1

Ref xsd

Ref vsd

Ref xsq

Ref vsq

VsRef

PWM logic γsRef SVM

VA3

vsd vsq

[vs]

PhT [A]

isd isq

[D(Ȝr)]

Zp

Ȧr

εRef s

CooT isdȜr isqȜr

Identified Field

2

sinȜr

Ȧ

Thyristor Rectifier

DC-link current controller

Ref isd

Ref isq λr

Į

iDC

isRef

- Speed-2

+

+

2 3

ȥrd

ȥmd

ȥsd

ȥrq

ȥrCo ȥmq

ȥmCo ȥ sq

1

PWMVSI VsId

[vs] 2

PhT [A]

1

[is]

Phase Transformation

2

3xC

ȥsC

Stator-flux Rotor-flux Air-gap-flux Stator-flux Computation Compensation Compensation Computation

Induction motor

Figure 2: Reconfigurable vector control structure with two configuration states. The most part of the energy is converted by the CSI, controlled by Pulse Amplitude Modulation (PAM), operating with reduced number of commutation - in comparison with the VSI, controlled by Pulse-Width Modulation (PWM), which supplies only the reactive power required to improve the quality of the motor currents in order to compensate them into sine wave form. For the case of the logic state machine in State 2, only the CSI is working. Its currents are synchronized with respect to the control variables of the stator-current vector. The transition from State 1 to State 2 is made when the VSI fails and the control structure need to be reconfigured in order to be able to control the AC drive with the Current Source Inverter. State 3 (represented in Figure 1) could be another configuration of the vector control system when the CSI fails and only the VSI is able to control the motor (at reduced load conditions). A possible representation of the transition from one state to other, in fact, may be a demultiplexer and a multiplexer, but one should note that, these components might be carried out in reality, while they are intended to be abstract entities, which did not need any implementation at all [2].

55

VÁSÁRHELYI, IMECS, INCZE, SZABÓ One may observe in the module analysis, that the flux computation modules are common in both control schemes and so they will be one of the most used modules in the Module Library. As the three flux-computation modules can be computed in a single phasor equation, they will represent a single module, with the following equations: Ψrd = (1 + σ r ) (usd − Rsisd )dt − [(1 + σ r )Lσs + Lσr ]isd ;

³

³(

)

Ψrq = (1 + σ r ) usq − Rsisq dt − [(1 + σ r )Lσs + Lσr ]isq .

(1.a) (1.b)

In this way in the Module Library for the flux computation we will have one module, but if it is needed, can be created easily all the component modules for the partial flux computations (Ψsd,q, Ψmd,q, Ψrd,q) separating the stator-field computation (ΨsC) and the flux compensation modules (ΨmCo, ΨrCo). In addition, the library can handle both flux-oriented control schemes, such as rotor-flux-oriented and stator-fluxoriented one for any supplying mode of the induction motor. One of the most common modules (often-used one) is the Vector Analyser (VA), and as is illustrated in Figure 2, it is used to compute the module and position of different space-phasor variables. Its equations are given in the general form, as follows: g = g d2 + g q2 ; sin λ =

gq g

; cos λ =

gd g

.

(2.)

Other two modules, which are very common in all control structures, are the direct and reverse Coordinate Transformation blocks (CooT[D(Ȝ)], CooT[D(-Ȝ)]) described by the general equation: g sdλr = g sd cos λ r ± g sq sin λ r ;

(3.a) g sqλr = g sq cos λ r # g sd sin λ r ; (3.b) One should mention also other usual modules such as the direct and reverse Phase Transformation modules (PhT[A] and PhT[A]-1 - for currents and voltages). These modules have also general character. For all the above-mentioned modules, when reconfiguration occurs, there is no need for variable-value transfer because these modules make all computation operations using only the actual sampled values. The modules where one have to consider the variable-value transfer is for example the so called control strategy blocks, represented in this case by the PI controllers of speed, flux and currents. The actual variable value depends on the previous value of the PI controller output, for this reason the reconfiguration process should store these variable values in order to avoid oscillation at the PI controller outputs (i.e. initialising the new PI starting conditions). These modules are called together “control strategy block”, as they can be realised in many ways (i.e. using adaptive- or robust procedures, fuzzy logic, etc.). The variable-value transfer of the PI controllers in the case when (as in Figure 2) the output variables of the controllers are different in each state (in one case this is the current reference i sdRef,qλr and in the other case it is the voltage one v sdRef,qλr ), the parameter

56

MODULE LIBRARY FOR RAPID PROTOTYPING transfer cannot be solved. This justifies why the reconfiguration method applied here is context switching. From the analysis results, that a Module Library can be created for fast modelling. The modularity presents importance if the implementation target is based on reconfigurable hardware, such as Field Programmable Gate Arrays (FPGAs) or Configurable System on a Chip (CSoC) [8].

3 Module Library Characteristics The creation of a Module Library was motivated by the fact that the simulation of the reconfiguration process it is not possible or it is difficult while no tools exist for this kind of simulation. On the other hand recently it has become possible to implement digital signal processing algorithms on FPGAs directly from Matlab Simulink® environment. This above mentioned possibility gave the idea to implement the described Module Library, which is completely parametrical and any change on the structure of the vector control system can be applied very fast and easy in the implementation hardware. The elements of the library are the most common modules of a vector control system (as were described in the previous paragraph), and each of them presents a standalone unit in the library. Consequently, a vector control system can be synthesised in FPGA structures due to the independent character of the modules. Most of vector control system implementations use 16 bit two’s complement fixedpoint data format. Here this format was also adopted for the input variables of each module. Inside the module for constant representation it was adopted the same data format, but the binary point has variable position, depending on the motor variables. For an implementation targeted the major advantage of using the Module Library is: the computation speed increases. It results from the parallel algorithm computation of both components (d, q) and the parallel computation of each module. This would be a significant advantage compared to the DSP sequential implementations.

4 Simulation and Rapid Prototyping with Module Library With the created Module Library, theoretically any vector control system can be tested, simulated and implemented. Using the Module Library a vector control system based on reconfigurable hardware can be implemented in short time. The rated data of the motor used for simulation are: 5.5kW, 50Hz, 220Vrms, 14Arms, sleep 4% and 4 pole-pairs. The simulation was performed for the presented vector control system structures, as follows: -

First: It was simulated configuration of State 1 – CSI+VSI, i.e. the tandemfed induction motor and then State 2 – the CSI-fed one. Second: It was performed the reconfiguration process; the motor started in State 1 and after 0.5s its system was reconfigured to State 2.

57

VÁSÁRHELYI, IMECS, INCZE, SZABÓ The results of the library computing elements were compared with simulation results produced by the modelled system realized in Simulink environment. One can conclude that some variables are working better with the Module Library (for example the PI implementation), but in some cases, the quantisation error was not satisfactory against our expectancies.

VSI-C Current A]

200 150 100 50

60 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

40

1

Stator currend [A]

CSI Current [A]

Stator Current [A]

The following diagrams show the simulation results for the running motor and reconfiguration in the above mentioned conditions. Figure 3 shows the stator-current waveform resulting as the sum of the output currents of the CSI and of the VSI. Also the figure shows that after reconfiguration the stator current results as the sum of CSI output currents and the capacitor ones. Figure 4 to Figure 6 represents several spacephasors of the CSI and VSI output currents. Figure 7 and Figure 8 represents the computed rotor-flux and stator-flux space-phasors. While the resultant stator flux and computed rotor flux is represented in Figure 10. Figure 9 shows the resultant statorterminal-voltage space-phasor. The reconfiguration of the control structure (i.e when the VSI fails and the CSI will work alone) it is observable in all the figures. The reconfiguration effects are observable also in the motor parameters (speed and torque) as shown in Figure 11and Figure 12.

50 0 -50 -100

0

-20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

-40 50

-50

1

-100

0.8

0

0.6 0.4

-150

0

0.1

0.2

0.3

0.4

0.5 time [s]

0.6

0.7

0.8

0.9

1

-50

Stator current q [A]

Figure 3: Current waveforms before and after reconfiguration.

60

0.2 0

time[s]

Figure 4: Stator-current space-phasor (simulated results).

VSI or Capacitor currentd [A]

100

40 Stator currend [A]

20

20 0

-20 -40 50

50

0

-50 50 1 0.8

0

0.8

-50

0.6

-50

0.4 Stator currentq [A]

1

0

0.6

0.4

0.2 0

VSI or Capacitor currentq[A]

time[s]

Figure 5: Current-Source Inverter output current space-phasor.

58

-100

0.2 0

time[s]

Figure 6: VSI or capacitor output-current space phasor.

1.5 Resulting stator-flux [Wb]

Computed rotor-flux [Wb]

1

1

d

d

0.5

0

-0.5

-1 1

0.5 0 -0.5 -1 1

0.5

1

0.5

0.8

0

1

0.6

Computed rotor-flux [W b]

-1

0.6 0.4

-0.5

0.2 0

time[s]

q

0.8

0

0.4

-0.5

Resulting stator-flux q [Wb]

Figure 7: Rotor-flux space-phasor.

0.2

-1

0

time[s]

Figure 8: Stator-flux space-phasor. Resultant Rotor-flux[Wb]

1

Computed Rotor-flux[Wb]

Stator terminal-voltage[V]

500

0

0.5

0

1 0.8

0

0.6 0.4

-200

0.2 -400

Stator terminal-voltageq [V]

0

Resultant Stator-flux[Wb]

200

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5 time[s]

0.6

0.7

0.8

0.9

1

1 0.5 0

Figure 10: Computed rotor- and stator-flux.

100

100

50

80

0

60 -50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Speed [rad/s]

Electric angular speed[rad/s]

0.2

1.5

time[s]

Figure 9: Stator-terminal-voltage spacephasor.

0.1

0.5

0 -500 400

0

1

1

Electromagnetique torque[Nm]

150

40

20

100 50

0 0

-50

0

0.1

0.2

0.3

0.4

0.5 time[s]

0.6

0.7

0.8

0.9

-20 -20

1

Figure 11: Electric angular speed and electromagnetic torque.

0

20

40

60 80 Torque [Nm]

100

120

140

Figure 12: Speed-torque dynamic mechanical diagram.

The method used for reconfiguration was the context switching method previously named ping-pong [1]. In this case, there is no need for parameter transfer at all, as both vector control systems are working in parallel and all the modules are working also in parallel. This allows us to exploit all the parallelism of the vector control algorithm and the implementation possibilities in FPGA.

59

VÁSÁRHELYI, IMECS, INCZE, SZABÓ

5 Implementation Possibilities For comparison the performance of the implemented modules with the simulation results obtained from the Simulink models, there one has to take into account the following aspects: the evolution of the module computation compared to the model, the quantisation error produced by the module, the time delay introduced by the module, the hardware resources occupied by the implemented module.

25

Saturated PI speed computed, implemented, and quatisation error at PI output 40 saturated and computed PI speed output

Simulated Output current of flux controller [A]

25

Quantisation error Computed of the computed Output current of output current flux controller[A]

In the followings, we will analyse some modules considering the above-mentioned criteria. For a simplified analysis of the modules, the simulation for the vector control scheme in Figure 2 was performed without reconfiguration and for the tandem converter structure, which corresponds for selection 1 of the multiplexer inputs. Figure 13 and Figure 14, represents the d-component evolution of the flux controller and reverse coordinate transformation CooT[D(-λ)], respectively. 20 15 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

15 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5 time [s]

0.6

0.7

0.8

0.9

1

20 0 -20 -40

1

0.2 quantizastion error of PI speed

20

0.1

0

0

40

20

10

0 -20 -40

1 saturated and implemented PI speed output

10

20

0

0.1

0.2

0.3

0.4

0.5 time[s]

0.6

0.7

0.8

0.9

10 0 -10

1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

-2

10

0 -4 0.1 x 10

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

5 0

-5

Simulated Output Voltageq

0.1

0

0.1

0.2

0.3

0.4

0.5 time[s]

0.6

0.7

0.8

0.9

1

of the CooT[D(-l)]

0

Computed Output Voltageq

-2

of the CooT[D(-l)]

0

Quantisation error of the computed output voltage

2

Simulated Output Voltaged

of the CooT[D(-l)]

2

Quantisation error Computed Output Volatged of the computed otuput voltage of the CooT[D(-l)] [V]

Figure 13: Outputs of the modelled and implemented flux and speed PI controller and the resultant quantisation error. 2

0

-2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 -3 0.1 x 10

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.2

0.3

0.4

0.5 time[s]

0.6

0.7

0.8

0.9

1

2

0

-2 1

0

-1

0.1

Figure 14: Voltage reference d-q component at the output of module reverse coordinate transformation CooT[D(-λ)]. The output q component of the block CooT[D(-λ)] is presented in Figure 15. As results from the diagrams in Figure 13 and Figure 15, there is no significant difference between the simulated motor variables and the computed ones obtained at the output of the corresponding library module. The quantisation error of the computed variables are minimal excepting the module CooT[D(-λ)], where the quantisation error of the reference voltage Usd is between –5 and +5. Even under these circumstances, the results are promising. The

60

MODULE LIBRARY FOR RAPID PROTOTYPING time delay and the hardware resource consumed by the analysed modules are presented in Table 1 and Table 2. Release 4.1.03i - Map E.33 Xilinx Mapping Report File for Design Design Information ----------------------------------------------------------------------------------------Target Device: x2v40 Target Speed: -6 Mapped Date: Tue Mar 26 15:16:39 2002 Design Summary ----------------------------------------------------------------------------------------Number of Slices: 24 out of 256 9% Number of Slices containing unrelated logic: 0 out of 24 0% Total Number 4 input LUTs: 24 out of 512 4% Number used as Shift registers: 24 Number of GCLKs: 1 out of 16 6% Total equivalent gate count for design: 5731 The Average Connection Delay for this design is: 1.283 ns The Maximum Pin Delay is: 4.126 ns The Average Connection Delay on the 10 Worst Nets is: 1.614 ns Listing Pin Delays by value: (ns) d < 1.00 < d < 2.00 < d < 3.00 < d < 4.00 < d < 5.00 d >= 5.00 178 68 22 9 1 0 Table 1: Hardware Resources Consumed and Time Delay Introduced by the Module Flux Controller. Time-space-phasor diagram of the PI reference Vsd,q

400

350

Output Voltage Vsd [V]

300

Reference Vsd [V]

250 200 150

200 0

-200

100 50

-400

0 -50

-600 1000

-100 -400

1

500

0.8

1

-200 0

0.4

0.6 0.4

200

Output Voltage Vsq [V]

0.2 Reference Vsq [V]

0.6

0

0.8

400

-500

0.2 0

time[s]

0 time [s]

Figure 15: Time-space-phasor diagram of the reference PI-Vsd,q modules.

61

Figure 16: Reference stator-terminalvoltage space-phasor computed in CooT[D(-λ)].

VÁSÁRHELYI, IMECS, INCZE, SZABÓ

Release 4.1.03i - Map E.33 Xilinx Mapping Report File for Design Design Information ----------------------------------------------------------------------------------------Number of Slices: 25 out of 3072 20% Number of Slices containing unrelated logic: 0 out of 625 0% Total Number 4 input LUTs: 1.222 out of 6144 19% Number used as LUTs: 1208 Number used as a route-thru: 14 Total equivalent gate count for design: 15579 The Delay Summary Report The Score for this design is: 5342 The Average Connection Delay for this design is: 1.969 ns The Maximum Pin Delay is: 10.256 ns The Average Connection Delay on the 10 Worst Nets is: 7.306 ns Listing Pin Delays by value: (ns) d

@

2.2 The canonical formulation of the forward kinematics The idea behind this approach [1] is to use the elements of the rotation matrix, rather than the angle values, to represent orientation: ªnx ox a x º & & & « B R >n o a @ «n y o y a y »» . (7) «¬ n z o z a z »¼

The elements of the rotation matrix are interdependent in the following fashion: & & 2 2 2 n ˜ n nx  n y  nz 1 , (8) & & 2 2 2 o ˜ o ox  o y  oz 1 , (9) & & n ˜ o nx ox  n y o y  nz oz 0 , (10) & & & a nuo . (11) Without loss of generality we can position the origins of the local coordinate systems of the base and mobile platform at the strut joints with index one, as shown in Figure 1, which gives us the following parameter values: b1x b1 y p1x p1 y b2 y p 2 y 0 . (12)

123

JAKOBOVIû, BUDIN Zp

p4

p5 Yp

p3 p2

p6

Xp p1

Zb b5

b6

b

Yb b3 b1

Xb

b2

Figure 1: Positioning of coordinate systems for base and mobile platform After extensive simplifications, the forward kinematics can be expressed as a system of 9 equations with 9 unknowns: 2 2 2 nx  n y  nz 1, (13) 2

2

ox  o y  oz 2

2

tx  ty  tz

2

2

(15) (16)

A1t x  A2 n x  A ,

(17)

B1t x  B2 n x  B3 o x  B4 t y  B5 n y  B6 o y  B ,

(18)

C 41t x  C 42 n x  C 43 o x  C 44 t y  C 45 n y  C 46 o y

C4 ,

(19)

C 51t x  C 52 n x  C 53 o x  C 54 t y  C 55 n y  C 56 o y

C5 ,

(20)

C 61t x  C 62 n x  C 63 o x  C 64 t y  C 65 n y  C 66 o y

C6 ,

(21)

where the constants are A1 b2 x p 2 x , A2

B5

2

0,

nxt x  n yt y  nzt z

B1

(14)

l1 ,

nx ox  n y o y  nz oz oxt x  o y t y  oz t z

1,

b3 x p 2 x  b2 x p 3 x , B2 p 2 x p3 y b3 y p 3 x p3 y

, B6

b2 x , A

b3 x  b2 x p3 x p3 y

K 2 p2 x . , B3

b3 y , B

Ci 3

B3 piy  bix piy , C i 4

B4 piy  biy ,

Ci 5

B5 piy  biy pix , C i 6

B6 piy  biy piy ,

A2 pix  B2 piy  bix pix , (24)

K p  K 2 p3 x K2 pix  3 2 x piy . p2 x p 2 x p3 y 2

Ki

b3 y p3 y ,

(23)

A1 pix  B1 piy  bix , C i 2

Ki 

b3 x , B4

K 3 p 2 x  K 2 p3 x . p 2 x p3 y

C i1

Ci

(22)

2

2

2

2

2

(l i  bix  biy  p ix  p iy  l1 ) 2

124

.

(25)

FORWARD KINEMATICS OF A STEWART PLATFORM MECHANISM The optimization function F2 and the related variables vector X2 are then defined as

n

F2

2 x

2

 2

2

2

2



2

2

2

2

 n y  n z  1  o x  o y  o z  1  t x  t y  t z  l1



2 2

 n x o x  n y o y  n z o z  n x t x  n y t y  n z t z  A1t x  A2 n x  A 2

2

2

· § oxt x  o y t y  oz t z 2 ¸ § C 41t x  C 42 n x  C 43 o x  C 44 t y · ¨ ¸  ¨  B1t x  B2 n x  B3 o x ¸  ¨¨ ¸    C n C o C ¸ © ¨ 45 y 46 y 4 ¹  B t  B n  B o  B 4 y 5 y 6 y ¹ © 2

(26)

2

§ C 51t x  C 52 n x  C 53 o x  C 54 t y · § C 61t x  C 62 n x  C 63 o x  C 64 t y · ¸ , ¸ ¨ ¨ ¸ ¨ C n  C o  C ¸ ¨ C n  C o  C 55 y 56 y 5 65 y 66 y 6 ¹ ¹ © © & T X 2 n x n y n z o x o y oz t x t y t z .

>

@

2.3 Reduced canonical formulation The equations (19)-(21) are of linear form which can be used to reduce the number of variables without introducing additional complexity in the system. Three of the six variables tx, nx, ox, ty, ny and oy can be replaced with linear combinations of the other three, which leaves us with only six unknowns. For instance, if we choose to eliminate the following variables t x D11 n x  D12 o x  D13 o y  D1 ,

ty

D 21 n x  D 22 o x  D 23 o y  D 2 ,

ny

D31 n x  D32 o x  D33 o y  D3 ,

(27)

we can define another target function as

n

F3

2 x

2

 2

2

2

2

 2

2

2

2

2

 n y  n z  1  o x  o y  o z  1  t x  t y  t z  l1



2 2

 n x o x  n y o y  n z o z  n x t x  n y t y  n z t z  A1 t x  A2 n x  A 2

2

 o x t x  o y t y  o z t z  B1 t x  B2 n x  B3 o x  B4 t y  B5 n y  B6 o y  B & T X 3 nx nz o x o y oz t z .

2

>

(28)

@

It is possible to further reduce the number of unknowns to as low as three, but with inevitable increase in equation complexity [1]. That way the fourth optimization function can be defined as F4

>n o x



@

 n y ox  nx  n y  ox  o y  1 2

x

2

2

2

2

2

ªn x t y  n y t x 2   A1t x  A2 n x  A 2  « «¬2 A1t x  A2 n x  A n x t x  n y t y  t x 2  t y 2  l1 2 1  n x 2  n y 2







º ª2E1 n x  E 2 o x  E 3 o y  E o x t x  o y t y » « 2 2  «  o x t y  o y t x  E1 n x  E 2 o x  E 3 o y  E » » « 2 2 2 2 2 »¼ «¬ t x  t y  l1 1  o x  o y & T X 4 nx ox o y ,









>

@

where the constant elements are

125

2

º » »¼

2



(29)

JAKOBOVIû, BUDIN E1

B 2  B1 D11  B 4 D 21  B5 D31 ,

E2

B3  B1 D12  B 4 D 22  B5 D32 ,

E3

B6  B1 D13  B 4 D 23  B5 D33 ,

E

(30)

B  B1 D1  B 4 D 2  B5 D3 .

2.4 Vector defined rotation The arbitrary orientation can be described with a single rotation about a universal rota& tion vector [3]. If the rotation vector, whose length equals one, is denoted with k and the rotation angle with T , then we can use the components of their product & & (31) r T ˜k to represent a potential solution to the forward kinematics problem [2]: & T X 5 t x t y t z rx ry rz . (32)

>

@

The conversion from roll-pitch-yaw angles to rotation vector and vice versa can be found in [3]. The optimization function F5 is defined in the same way as the function & F1, only the elements of the rotation matrix have to be calculated from vector r prior to function evaluation.

3 The optimization algorithms The forward kinematics problem is presented as five optimization functions for which the optimization algorithm has to find the minimum, the value of the functions being the error of the estimated solution. Several optimization methods have been applied to each of the functions in order to find an effective combination which would allow for real-time application. The algorithms applied in this work are Powell's method, Hooke-Jeeves', steepest descent search, Newton-Raphson's (NR) method, NR method with constant Jacobian and Fletcher-Powell algorithm. Each of the algorithms is found to be more suitable for some types of functions than for others, which can be perceived from experimental results later in this paper. 3.1 Estimating the initial solution by variable elimination The most reduced canonical formulation (function F4) of forward kinematics problem contains only three independent variables. The choice of those variables can be altered in the reduction process, so it is possible to have different variable triplets in threedimensional reduced form. However, a single solution in three-dimensional space represents not one, but a whole family of hexapod configurations, because a single configuration is fully described only in six-dimensional space. The form of the set of hexapod configurations included in a single solution is determined by the variables not present in the remaining three. For example, if the reduced form solution is represented with variables nx, ox and oy, then none of the variables which define the mobile position, i.e. variables tx, ty and tz, are not present in the solution. Hence, every hexapod configuration with mobile platform orientation matching the three values of nx, ox and oy, but with any arbitrary position, will be represented with the same solution in three-dimensional space. The exact position values are restored through constants' values once the transformation to six-dimensional space is undertaken. This property is used to effectively estimate the initial forward kinematics solution, presuming an orientation of the mobile platform from the previous last known position.

126

FORWARD KINEMATICS OF A STEWART PLATFORM MECHANISM

4 Experimental results Solving of forward kinematics was simulated in static and dynamic conditions. The static experiments included all the combinations of five optimization functions and six optimization algorithms applied to 20 test configurations. The goal was to find the combination which would yield the best results considering the convergence, speed and accuracy. The most promising combinations were then tested in dynamic conditions, where the algorithm had to track a preset trajectory of the mobile platform with as small error and as large sampling frequency as possible. Those combinations include Hooke-Jeeves' algorithm with function F1 and Fletcher-Powell method with functions F2 and F3, but the most successful optimization method was NewtonRaphson's algorithm applied to function F3. That combination has achieved the best results in dynamical testing as well. In dynamic simulation, the starting hexapod configuration is known and serves as an initial solution. During the sampling period T the algorithm has to find the new solution, which will become the initial solution in the next cycle. Several hexapod movements were defined as time dependant functions of the position and orientation of mobile platform. One of those trajectories, hereafter denoted as A, is defined with § S· § S· xt 2 ˜ sin ¨ t ¸, y t 2.2 ˜ cos¨ t ¸, z t 7  1.5 ˜ sin 2t , © 2¹ © 2¹ (33) §t· D t 25 ˜ sin 1.8t , E t 20 ˜ sin ¨ ¸  5 ˜ cos4t , J t 15 ˜ arctan2t  4 , © 2¹ 0dt d 4. The results of the dynamic simulation are presented in the form of a graph where errors in the three rotation angles and three position coordinates of the mobile are pictured. The sampling period T was set to 1 ms, which equals to a 1000 Hz sampling frequency. The errors shown represent the absolute difference between the calculated and the actual hexapod configuration. Due to the large number of cycles, the error is defined as the biggest absolute error value in the last 100 ms, so the graphs in each point show the worst case in the last 100 ms of simulation. The errors are presented separately for angles, in degrees, and position coordinates. The errors for movement A and Newton-Raphson algorithm with function F3 are shown in Figure 2 and Figure 3.

Absolute error

1. u 1012 5. u 1013 1. u 1013 5. u 1014 1. u 1014 5. u 1015 1. u 1015

0

10

20 Cycle index

30

Figure 2: Absolute angle error (D = ,E= ,J= NR algorithm with F3, movement A

127

40

),

JAKOBOVIû, BUDIN

Absolute error

5. u 1014 2. u 1014 1. u 1014 5. u 1015

0

10

20 Cycle index

Figure 3: Absolute coordinate error (x = ,y= with F3, movement A

30

,z=

40

), NR algorithm

The achieved level of accuracy is very high as the absolute error is not higher than 10-12 both for angles and coordinates. Another trajectory is derived from the described one by enlarging some of the amplitudes in (33), which is denoted as movement B (the altered values are in boldface): § S· § S· xt 2 ˜ sin ¨ t ¸, y t 2.2 ˜ cos¨ t ¸, z t 8  3 ˜ sin 2t , © 2¹ © 2¹ (34) §t· D t 55 ˜ sin 1.8t , E t 30 ˜ sin ¨ ¸  5 ˜ cos4t , J t 15 ˜ arctan2t  4 , © 2¹ 0dt d 4. The movement B errors are shown in Figure 4 and Figure 5. While still low, the error for movement B has two distinctive peaks at certain points in simulated motion. What is the cause of those peaks? Mathematical analysis has shown ([4], [5], [6]) that there may exist up to 40 distinctive solutions for forward kinematics problem for Stewart platform with planar base and mobile platform. Those 40 solutions are divided in two groups of 20 between which the only difference is the sign of the z coordinate. In another words, only one half of those mathematical solutions have a physical meaning, i.e. those with positive z axis value. But the existence of multiple solutions for the same set of strut lengths may prove as a problem for the solving method.

Absolute error

1. u 109 1. u 1010 1. u 1011 1. u 1012 1. u 1013 1. u 1014 0

10

20 Cycle index

30

Figure 4: Absolute angle error (D = ,E= ,J= NR algorithm with F3, movement B

128

40

),

FORWARD KINEMATICS OF A STEWART PLATFORM MECHANISM

Absolute error

1. u 1010 1. u 1011 1. u 1012 1. u 1013 1. u 1014 1. u 1015 0

10

20 Cycle index

Figure 5: Absolute coordinate error (x = ,y= with F3, movement B

30

,z=

40

), NR algorithm

Let us suppose that in one hexapod configuration there exists no other forward kinematics solution for actual set of strut lengths, but that in some other configuration there exist several of them. If hexapod in its movement passes through those two configurations, then at a certain point in between there has to be a division point where the number of solutions increases. In those division points the solving algorithm may, unfortunately, begin to follow any of the possible paths, because any of them represents a valid forward kinematics solution! That is exactly the problem that occurs in movement B: the algorithm may or may not follow the correct trajectory. If the latter is the case, than the absolute error looks like in Figure 6 and Figure 7.

Absolute error

1 0.001 1. u 106 1. u 109 1. u 1012 0

10

20 Cycle index

30

Figure 6: Absolute angle error (D = ,E= ,J= NR algorithm with F3, movement B - division

40

),

1 Absolute error

0.001 1. u 106 1. u 109 1. u 1012 0

10

20 Cycle index

30

Figure 7: Absolute coordinate error (x = ,y= ,z= with F3, movement B – division

40

), NR algorithm

The algorithm will randomly follow either the correct trajectory or the equivalent one. It is important to note that in both cases the optimization function remains very low (app. 10-30 to 10-20) during the whole process because both trajectories depict a 129

JAKOBOVIû, BUDIN valid solution to the forward kinematics problem. The problem is, only one of them represents the actual hexapod configuration in each point of time. The error between junction points in Figure 6 and Figure 7 actually shows the distance between the two equivalent trajectories. 4.1 The adaptation method Without any additional information about the hexapod configuration, such as may be obtained from extra transitional displacement sensors, there is unfortunately no way to determine which of the existent solutions to the forward kinematics problem for the same set of strut lengths describes the actual hexapod configuration. Nevertheless, with some assumptions we may devise a strategy that should keep the solving method on the right track. If the change of the direction of movement is relatively small during a single period, which is in this case only 1 ms, then we can try to predict the position of the mobile platform in the next cycle. We can use the solutions from the past cycles to construct a straight line and estimate the initial solution in the next iteration. Let the solution in & & & the current iteration be P0 and the solutions from the last two cycles P1 and P2 . Then we can calculate the new initial solution using one of the following methods: & & & X 0 2 ˜ P0  P1 , (35) & & & X 0 1.5 ˜ P0  0.5 ˜ P2 , (36) & & & T1 0.5 ˜ P0  P1 , ½ & & & °° T2 0.5 ˜ P1  P2 , ¾ . (37) & & &° X 0 2.5 ˜ T1  1.5 ˜ T2 ¿°

 



The above methods were tested in conjunction with NR algorithm and function F3 for all the simulated trajectories. The results are very good: the solving method was now able to track the correct solution during the whole simulation process for all three estimation methods. The number of conducted experiments was several hundred times and every time the algorithm's error margin was below 10-11 both for angles and coordinates. However, the described algorithm adaptation will only be successful if the assumption of a small direction change during a few iterations is valid. To test the algorithms behaviour, simulated movement B was accelerated by factor 2, 4 and 8, while maintaining the same cycle duration of 1 ms. Only by reaching the 8-fold acceleration, when the total movement time equals a very unrealistic half a second, did the algorithm produce significant errors, while still holding to the correct solution. In this case only some differences can be perceived between the three proposed estimation methods. If we set an error margin of 10-3 for angles (in degrees!) and 10-5 for coordinates, then the percentage of breaking those margins for the three adaptation methods will be approximately equal to those shown in Table 1. Adaptation method Error breaching percentage

As (35) 6%

As (36) 11 %

Table 1: The percentage of breaching error margins

130

As (37) 3.6 %

FORWARD KINEMATICS OF A STEWART PLATFORM MECHANISM There is no way of telling, without extensive mathematical analysis for every planned mobile platform movement, whether hexapod will pass any division points or hyperplains. That is why the sampling period must be kept as low as possible, to assure relatively small direction changes during a few cycles.

5 Conclusion Combining several representations of the forward kinematics problem with optimization techniques, an efficient method for solving the problem was found. For the purposes of real-time simulation, several mobile platform trajectories were mathematically predefined. The task of a forward kinematics solving method was then to track the position and orientation of the mobile platform, knowing the starting position. The solving method was able to determine the exact position and orientation of the mobile platform within insignificant error margins (less than 10 to the power of –12 of the minimum hexapod dimension) and with 1000 Hz sampling frequency. The problem of equivalent trajectories was noted: because of the existence of multiple solutions to forward kinematics, there may exist more than one path that mobile platform can follow while having exactly the same strut lengths in every point of the way. The solving algorithm may, under some circumstances, skip to an equivalent trajectory at certain division points. It has to be said that every such path represents an equal correct solution of the forward kinematics, but only one of them represents the true mobile platform trajectory. An empirical algorithm was devised which can increase the probability of finding the right solution, and it proved itself successful in every test case. Unfortunately, it cannot be proven that it will do so in every imaginable movement of the mobile platform. The solving method will always find the right solution if the change in the position or moving direction of the mobile platform is relatively small during a few sampling periods. If that condition is fulfilled, the described method can be used in realtime forward kinematics solving.

References [1] B. Dasgupta and T.S. Mruthyunjaya. A Canonical Formulation of the Direct Position Kinematics Problem for a General 6-6 Stewart Platform. Mech. Mach. Theory, 29(6):819827, 1994. [2] J. -P. Merlet. Direct Kinematics of Parallel Manipulators. IEEE Transactions on Robotics and Automation, 9(6):842-845, 1993. [3] R. P. Paul. Robot Manipulators. The MIT Press, Cambridge, 1981. [4] M. Raghavan. The Stewart Platform of General Geometry has 40 Configurations. Journal of Mechanical Design, 115:277-282, June 1993. [5] M Husty. An Algorithm for Solving the Direct Kinematic Of Stewart-Gough-Type Platforms. ftp://ftp.mcrcim.mcgill.edu/pub/techrep/1994/CIM-94-01.pdf, 1994. [6] F. Wen and C. Liang. Displacement Analysis of the 6-6 Stewart Platform Mechanisms. Mechanism and Machine Theory, 29(4):547-557, 1994.

About the Authors Domagoj Jakoboviü received B. Sc. degree (1996) and M. Sc. degree (2001) in electrical engineering from Faculty of Electrical Engineering and Computing, University of Zagreb. His

131

JAKOBOVIû, BUDIN interests include optimization, genetic algorithms, algorithm design and validation, knowledge representation and parallel kinematic structures. He is a student member of IEEE. Leo Budin received the BE, MS and doctoral degrees, all in electrical engineering, from the University of Zagreb, Croatia. His current research interests include distributed systems, realtime systems, soft computing and problem solving environment in engineering. He is a mem-

ber of IEEE and ACM.

132

Chapter 3 Intelligent Manufacturing Systems

Communication Issues in Multi-Agent-Based Plant Automation Scheduling Yoseba K. Penya, Thilo Sauter Institute of Computer Technology, Vienna University of Technology, Vienna, Austria {yoseba, sauter}@ict.tuwien.ac.at

Abstract — The current state of the art in production planning is still dominated by largely centralized solutions. More distributed approaches require a substantial increase in communication, and network load becomes an important factor. This paper presents a distributed plant automation approach based on mobile software agents and investigates the network load generated by the agents in terms of communication and migration. Particular emphasis is given to the impact of the planning horizon and prioritization, which leads to extensive rescheduling processes. It appears that scheduling approaches that plan several steps in advance need substantially more communication overhead, but can be made less susceptible to snowball effects associated with rescheduling.

1 Introduction As far as the production planning is concerned, the current state of the art in plant automation is still dominated by centralized solutions. Nevertheless, distributed approaches are the focus of much research work. The most obvious benefit of distributing functions of, e.g., the MES (manufacturing execution system) or the control level is a tremendous increase in flexibility, the ultimate goal being an autonomous self-organization of the entire production process. Another advantage less often addressed is scalability. Distributed approaches no longer need powerful central computers to execute the planning tasks, or at least they alleviate the performance requirements. This is beneficial especially in large plants. On the other hand, the reduction of local computing power in distributed systems comes at the price of an increased demand for communication. When the elements of such a system increase their flexibility, autonomy and intelligence, they need to exchange more information in order to successfully synchronize and coordinate themselves. The network constitutes a shared resource within the plant automation system. This is particularly important for distributed solutions (such as the one addressed by the EU-funded Project PABADIS, Plant Automation Based on Distributed Systems [1,2]) that make use of mobile software agents to enhance the control of the individual manufacturing process. In spite of their benefits, the necessary migration for every step of the production process increases the network traffic. Consequently, it is worthwhile to investigate the impact that a distributed approach has on the network load and where the limits of scalability are.

A shorter early version of this paper appeared in the Proceedings of the 6th IEEE International Conference on Intelligent Engineering Systems (INES), pages 339-343, Opatija, Croatia, May 2002.

135

PENYA, SAUTER The remainder of the paper is organized as follows: in the section 2 we introduce the main features of the multi-agent system used in PABADIS, section 3 describes the scheduling approach, section 4 explains the model used in the simulation, section 5 presents and discusses the results, and section 6 draws conclusions and outlines future work.

2 Plant Automation as an Information System The classical representation of Plant Automation is that of a three-layered pyramid, where the machinery is on the lowest (control) level and two layers of more complex plant-wide control, and planning functions are above it. This approach starts from the assumption that every production cell has a minimum degree of intelligence to provide some information that will be used by the upper layer for scheduling, dispatching, and other management tasks. In other words, the plant is conceived as a network of information points. Traditionally, the information stream flows to a central place, where it is processed by an ERP (enterprise resource planning) system that controls the plant as a whole, issues production orders and records the results. Unlike this approach of concentrating all the responsibility, intelligence, and production management in one point, latest trends tend to distribute these three tasks at least partly between several units that have smaller processing power but communicate and cooperate to enhance the overall plant automation functionalities. In PABADIS, a plant is composed of abstract entities called Cooperative Manufacturing Units (CMU) that comprise both an intelligence module and a production module, which can involve one or more machines. All the CMUs are connected to a common network, so they can cooperate in the manufacturing process. There are three types of CMUs (in [2], they are called BIIOs, Basic Intelligent Independent Objects, which is essentially the same):  Logical CMUs for computational services such as complex scheduling algorithms, database search etc.,  Manufacturing CMUs for the physical processing of the products,  SCADA CMUs providing an interface to the SCADA system that controls the plant. Basically, PABADIS can be seen as an enhancement of a MES, with a clear focus on a product-oriented view (this is why the approach is mainly targeted at single-piece production), rather than the more process-oriented approach of classical MES. According to [3], functions covered by the MES are the following:  Resource allocation, scheduling, and dispatching: This most complicated function of the MES manages the resources of the plans and performs ERP order execution. On the one hand, the goal of this function is to optimize the usage of resources, such as machines, tools, labor skills, or materials. On the other hand, the product creation must be optimized as well. In PABADIS this functionality is distributed in the community of software agents which act individually with respect to their own tasks, such as product creation or machine optimization.  Document control, data collection, product tracking and genealogy, process management and performance analysis: This function provides information to the ERP system regarding the current situation of the production and product processing.

136

COMMUNICATION ISSUES IN MULTI-AGENT-BASED…  Maintenance management, which tracks and directs the activities to maintain the equipment and tools, in order to ensure their availability for manufacturing and to ensure scheduling for periodic or preventive maintenance.

3 Scheduling of a Multi-Agent-Based Plant As mentioned before, the CMUs in PABADIS are composed of a manufacturing module and an intelligence module. The latter is in fact a stationary agent called Residential Agent (RA) that represents the CMU in the network. It provides the network with an interface to the physical resources and functionalities the CMU offers. The interface is used by the Product Agents (PA), which are mobile software agents that guide the product through its manufacturing process. In the same way that the Residential Agents know everything about the CMU they represent, the Product Agents possess all the necessary data to optimize the development of the product they are in charge of. Therefore, when a PA arrives at a CMU, it exactly knows which parameters must be indicated to the RA, in order to get its work-piece processed. Product Agents are created in an entity called Agency, which is the interface of the PABADIS agent community to an ERP system. It processes the demand and transforms it into XML documents – one per work order. The Agency parses the documents and creates a product agent that will be responsible for the creation of the corresponding workpiece. The Agency also collects the reports of the product agents. Finally, there is another key element within PABADIS: the Look-up Service (LUS) [4]. It acts as white pages mechanism for the product agents, so they know where to migrate when they need a specific functionality. Every CMU notifies the LUS of its joining the network, and provides it with data about the functionalities it offers. The LUS periodically renews its data, so that when a PA requests some information, it is up to date. Figure 1 illustrates the main components of the PABADIS system.

PABADIS XML PA Doc.

XML PA Doc.

XML-Parser

XML-Parser

CMU

RA

CMU

RA

XML PA Doc. ...

XML-Parser CMU

RA

Agency

ERP

Figure 1: Components of the PABADIS System

3.1 Scheduling Much has been said, written, and discussed about constrained scheduling and the benefits of using software agents in planning processes in general [5, 6, 7] or for specific use cases that implement different solutions to tackle the problem [8, 9]. In PABADIS, the schedul-

137

PENYA, SAUTER ing is distributed (physically and operatively); the problem is divided into small bits, since it is carried out in local operations at CMU level between Product Agents and Residential Agents. On the one hand, PAs represent the resource consumers, on the other hand, RAs represent the resource owners. Consequently, they have to negotiate with each other to reach an agreement. Specifically, the scheduling is performed in two ways [10]:  Horizontal fashion: The RAs collect the incoming requests for processing and generate a schedule of tasks from different PAs that need to be processed on the respective CMU.  Vertical fashion: The PAs generate a list with all possible CMUs where their tasks could be carried out. The combination of both tables forms a matrix representing the whole schedule.

3.2 Depth of Scheduling and priorities The scheduling process is in its simplest form a kind of first-come first-serve model, which is easy to solve. Nevertheless, this simple schema does not fit the requirements imposed by current Plant Automation systems. There must be a mechanism to prioritize the manufacturing of special products to account for urgent demands. Therefore, PABADIS supports priority-based scheduling. When a PA requests a time slot that has been already reserved by a lower-priority PA, the RA arbitrates the conflict by assigning the time slot to the high-priority PA. Since the lower-priority PA must reallocate its resources, the RA notifies it of the new situation to let the PA start a rescheduling process. If the PA still has a higher priority than other PAs, this may lead to a rescheduling cascade effect [11] propagating through the whole agent community. The solution that PABADIS promotes to reduce this effect is the introduction of a “depth of scheduling” parameter. This variable gives the number of tasks a Product Agent plans before starting the manufacturing process. Depending on the value of this parameter, the scheduling can be classified in three categories:  Advance scheduling: The PA allocates the resources for all tasks in the work order. Thus, the PA analyses the whole work order and chooses the best possible way of execution. The depth of scheduling parameter is equal to the number of tasks the work order comprises.  Step-by-step scheduling: In this case a PA allocates a resource for the next task only when the current one is completed. In fact, real scheduling is not necessary for the RA, which makes the optimization of resource usage almost impossible. The depth of scheduling parameter is equal to 1.  Hybrid approach: In this case a PA analyses a work order several steps in advance (the number specified by depth of scheduling parameter) and allocates resources for this certain number of tasks, but not for the whole work order. 3.3 Life Cycle of a Product Agent Figure 2 illustrates the program flow of a Product Agent. After parsing the XML document with the work order, it contacts the Look-up Service to find out about which CMUs provide the functionalities needed for the execution of the work order. The LUS returns a list of matching CMUs and also adds a rough estimate for the time required by each CMU to finish the task. This information is then used by the PA to outline a graph where all the possible paths for the accomplishment of the work order are represented and can be or-

138

COMMUNICATION ISSUES IN MULTI-AGENT-BASED… dered with respect to their overall processing time. Of course, other criteria for the decision might be used as well: workload of the CMU, cost, status of the stocks, etc. Subsequently, the PA selects the best path and starts allocating a “depth of scheduling” number of tasks on the CMUs that compose such path. This process includes the negotiation with the RAs about which time slot is available and which PA with lower priority can be forced to give way. Afterwards, the PA starts the migration and physical manufacturing of its associated work-piece. In case that the depth of scheduling was less than the total amount of tasks needed, it starts a new allocation procedure and so on, until the work piece is finished. parse XML work order ask LUS for needed CMU list depth of scheduling tasks allocation Yes Allocation error

Error? No Move to next CMU

Yes

Error?

Migration error

No Perform Task

All tasks finished?

No

Yes Move to Agency and report

Figure 2: Program flow of a Product Agent

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PENYA, SAUTER

4 Model of the System The objective of the simulation is to evaluate the influence that the behavior of the agents has on the network load. For this purpose, a model representing a worst-case PABADIS environment with the following characteristics is investigated:  The goal is to measure the migrations of the agents and the interchanged messages, as well as the time when they are performed or sent.  All the parameters (number of agents, number of tasks that compose a work order, etc.) remain fixed, whereas the depth of scheduling and number of product agents with higher priority are the variables to be tuned and observed.  Only one kind of product is manufactured, hence the work orders of all Product Agents are identical. Moreover, all Residential Agents represent similar CMUs, therefore each work order is composed of a fixed number of identical tasks.  Migration time is supposed to be negligible. Hence, there is no need to include time slots for migrations in the scheduling. Furthermore, the migration is performed before the task but in the same time slot.  Although all CMUs are alike, the PAs cannot reserve two time slots with the same RA. They must perform a task and then move to a different machine.  Each PA starts its life cycle at the Agency and it must return there upon completion of the work order to report about the operation that was carried out. Thus, there is always an extra movement (not necessary for the manufacturing of the product) that must be done by the Product Agent. The simulation itself is not based on a real agent platform (like the Grasshopper platform used in the PABADIS project) and several machines, but for the sake of simplicity on a multi-threaded Java program running on a single PC. The flow of the program is as follows: a daemon thread starts four Residential Agent threads and afterwards ten Product Agent threads consecutively and with a small pause in between to have enough time to finish the allocation of resources. The agents allocate their required resources from the first time step on, so the first time interval is devoted to initial operations. Furthermore, all the high priority PAs are launched when the ordinary PAs have finished their respective allocation procedures. Since by that time the previous PAs have already reserved time slots in the CMUs, the highest possible number of rescheduling processes will happen (one per task and high priority PA). Identifier Depth of Scheduling A0 1 (step by step) A2 1 (step by step) A4 1 (step by step) B0 5 (50% of tasks) B2 5 (50% of tasks) B4 5 (50% of tasks) C0 10 (full advance) C2 10 (full advance) C4 10 (full advance)

high priority PAs 0 2 4 0 2 4 0 2 4

Table 1: Experiments performed in the simulation

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COMMUNICATION ISSUES IN MULTI-AGENT-BASED… Table 1 shows the set-up details of the individual experiments. The work order length is set to ten tasks that require each one time step for execution. The daemon thread acts also as the clock of the system, so every time it ticks, all the PAs and RAs are notified. After simulation starts, the Product Agents contact the LUS and then begin to allocating a number of tasks defined by the “depth of scheduling” parameter. According to the program flow shown in Figure 2, they wait afterwards until they are able to move and perform an operation on a CMU. Moreover, if the task was the last to do, they quit and return to the Agency. If the task is the last allocated but they needed to allocate more (thus, the depth of scheduling is less than the total number of tasks), they restart the allocation process. To account for the network traffic, the daemon thread registers all messages sent and migrations performed upon notification of the entity that did it. Effectively, only the numbers are counted. The final value of the network traffic is then estimated. Taking into account that the maximum length of an Ethernet packet is 1500 bytes, a segmentation of the agent is indispensable. Furthermore, the header information for Ethernet (11 bytes), IP (20 bytes), and TCP (20 bytes) must also be included. The agent size assumed here is 3,000 bytes for the code and 1,200 bytes for the data of the work order. This makes three packets and in total 4123 bytes that need to be moved, each time the agent migrates from one CMU to another. The messages exchanged between the agents are very short, they are assumed to have just 10 bytes each, which is enough to convey information about CMU status, time slot availability, or schedule details. However, the header overhead is significant, and so a total of 61 bytes must be sent over the network. Concerning the rescheduling processes that can be initiated be Product Agents with a higher priority, an additional restriction was imposed on the timing. It is essential to avoid rescheduling when the affected agent is migrating or is about to migrate. Therefore, the time slot that is going to be reassigned must be at least one time step after the request from the high priority agent is received.

5 Results Table 2 shows the main results of the experiments. At first sight, it can be seen that migrations are not affected by the variation in the change of scheduling or the number of PAs with higher priority. They are always 11 per PA, this is, one for each task and one more for the return to the Agency (the high priority agents are not counted to ensure comparability). Figure 3 shows the average of the experiments (A for A0, A2 and A4; B for B0, B2 and B4, etc.). It illustrates the behaviors of the system over time. The number of rescheduling processes depends only on the number of high-priority PAs and the number of tasks to be performed. Thus, with 8 high-priority PAs and 10 tasks, 80 rescheduling processes happen. There is no snowball effect because there are only two different priorities, and the affected PAs are not able to cause more rescheduling processes (the other PAs have at least the same priority).

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PENYA, SAUTER Identifier A0 A2 A4 B0 B2 B4 C0 C2 C4

Finishing Time Messages Migrations Bytes transmitted 26 1840 110 615270 28 1834 110 614904 27 1982 110 623932 27 4772 110 794122 28 3699 110 728699 28 2544 110 658214 30 6981 110 928871 30 5567 110 842617 30 4414 110 772284 Table 2: Results of the measurements

Another interesting effect regarding rescheduling is that if the PAs do some advance scheduling, a higher number of high priority agents results in a decrease of total messages needed in the experiment. The reason is the scheduling strategy of the agents. The PA aims to allocate all the tasks consecutively. If there is a gap in its schedule, this means that other PAs reserved the slots in between. Thus, when rescheduling, the PA assumes that earlier time slots are already reserved and therefore does not try to allocate them, which saves messages. For instance, if a PA has allocated the following resources: t = 10, t = 11, t = 13, and it receives a notification of rescheduling at t = 10, the PA will start rescheduling from t = 13 on. It supposes that if it previously did not succeed in allocating resources for t = 12, it will not succeed in the future. This effect is especially relevant with advanced planning, since the saving is bigger than in step-by-step or hybrid scheduling (see Table 2). Figure 3 shows the network load for each scheduling modality. Advance scheduling (type C) requires most of the network traffic at the beginning, where the PAs send all the messages. Afterwards, they migrate to the CMUs without any further exchange of information. The hybrid approach (type B) presents a diagram with pronounced peaks, corresponding to the moments where the allocation is performed. Data Transmitted (bytes)

100000 80000 A

60000

B

40000

C

20000 0 0

5

10

15

20

25

30

Time elapsed (seconds) Figure 3: Average behavior regarding the depth of scheduling

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COMMUNICATION ISSUES IN MULTI-AGENT-BASED… Since the depth of scheduling is 5 and the PAs start allocating from t = 1, the time slots with higher network traffic are 6, 11, and then 16, 21, etc, but obviously the peaks are smaller since there are fewer agents. Finally, the type A experiments (step-by-step scheduling) do not show significant peaks (only when in the same time slot some PAs return to the Agency and others migrate to perform a task) and distribute the network load uniformly. Figure 4 shows the average of the results with the number of high priority PAs as parameter. It confirms what was exposed by Figure 3: experiments with a lower number of high priority PAs need to interchange a higher amount of data, due to the previously explained improvement in the allocation procedure. Data transmitted (bytes)

150000

0 high-p Pas

100000

2 high-p Pas 50000

4 high-p Pas

0 0

5

10 15 20 Time elapsed (seconds)

25

30

Figure 4: Average behavior regarding number of high priority Product Agents

6 Conclusion and future work The model presented in this paper illustrates the impact on the network load that different scheduling modalities for a plant automation system based on mobile software agents have. The simulation demonstrated that snowball effects due to rescheduling processes and extra migrations may be avoided by using only two different priority levels, and by ensuring that an agent to that is going to be rescheduled is not about to arrive at the target CMU. Evidently, the simulation model used was rather coarse. In the course of the project, however, it will be refined to account for, e.g., non-uniform task execution times per CMU, which will open new possibilities for optimization. The simulations seems to suggest that full-in-advance scheduling creates an extremely high network load at the beginning of the process and is therefore inferior to a step-bystep scheduling or an approach with a low depth of scheduling where the load is more balanced. From the viewpoint of network load, this is certainly true. However, the simulation cannot judge the benefits of a larger scheduling depth such as better optimization results that might outweigh the temporarily higher network traffic. Still, future investigations have to explore the impact the number of agents has on the load. Particularly during the negotiation phase, it is anticipated that the load will dramatically increase with the number of agents. The available network bandwidth may therefore easily put an upper limit to the practically achievable scheduling depth. Of course, it has to be noted that it is highly unlikely that all PAs start at the same time. In practice, they can be released with short delays in between. The only critical situation will be then a rescheduling process affecting a large number of agents.

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References [1]

PABADIS, IST-1999-60016, www.pabadis.org

[2]

T. Sauter and P. Palensky. Network Technology for Distributed Plant Automation. In Proceedings of the 5th IEEE International Conference on Intelligent Engineering Systems, pages 407-412, Helsinki, Finland, September 2001.

[3]

MES Association, www.mesa.org

[4]

Y. K. Penya, S. Detter, T. Sauter. Plug-and-Participate Functionality for Agent-Enabled Flexible Automation. In Proceedings of the 6th IEEE International Conference on Intelligent Engineering Systems, page 136, Assiut, Egypt, March 2002.

[5]

C. Le Pape. Classification of scheduling problems and selection of corresponding constraint-based techniques. In Proceedings of the 1993 IEE Colloquium on Advanced Software Technologies for Scheduling, pages 1/1-1/3, 1993

[6]

P. Prosser. The future of scheduling-DAI?. In Proceedings of the 1993 IEE Colloquium on Advanced Software Technologies for Scheduling, pages 8/1-8/2, 1993

[7]

T. Grant. Overview And Conclusions. In Proceedings of the 1996 IEE Colloquium on Intelligent Planning and Scheduling Solutions, pages 7/1-7/4, London, U.K., 1996

[8]

B. Drabble. Modern planning and scheduling technologies. In Proceedings of the 1996 IEE Colloquium on Intelligent Planning and Scheduling Solutions, pages 3/1-3/6, London, U.K., 1996

[9]

J. Reaidy, P. Massotte, L. Yingjiu and D. Diep. Product and process reconfiguration based on intelligent agents. In Proceedings of the 2001 IEEE International Conference on Systems, Man, and Cybernetics, pages 3397-3402, Tucson-Arizona, U.S.A., October 2001

[10] A. Bratoukhine, Y.K. Penya and T. Sauter. Intelligent Software Agents in Plant Automation. In Proceedings of the 3rd International NAISO Symposium on Engineering of Intelligent Systems, page 77, Malaga, Spain, September 2002 [11] M. Fletcher and S. M. Deen. Task rescheduling in multi-agent manufacturing. In Proceedings of the 10th International Workshop on Database and Expert Systems Applications, pages 689-694, Florence, Italy, September 1999

About the Authors Yoseba K. Penya received his Master’s degree in computer science in 2000 from the Deusto University in the Basque Country. Since July 2000 he is research assistant at the Vienna University of Technology and his area of expertise include multi-agent systems, scheduling in plant automation and e-commerce techniques applied to energy management. Thilo Sauter received his Dipl.-Ing. and doctorate degrees in electrical engineering from the Vienna University of Technology in 1992 and 1999, respectively. From 1992 to 1996 he was a research assistant at the Institute of General Electrical Engineering, working in the area of programmable logic and analog ASIC design. Since 1996, he has been with the Institute of Computer Technology, where he is head of the center of excellence for fieldbus systems and leading the factory communications group. He is member of the Austrian technical committee ÖVE MR65SC concerned with fieldbus standardization. His current research interests are integrated sensor systems and communication networks in automation, with a focus on interconnection issues of fieldbus systems and IP-based networks.

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Advanced Factory Automation System for Deburring and Dressing of Automotive Engine Parts Ulrich Berger, Raffaello Lepratti Chair of Automation Technology, Brandenburg Technical University, Cottbus, Germany {berger.u,lepratti}@aut.tu-cottbus.de

Abstract — Today the automotive sector is dominated by high variety of types and increasing product diversification. Thus, OEM manufacturers reintegrate key technologies back in the enterprise, due to competitive reason and to stabilize leadership in innovation. As an example, state-of-the-art fuel and diesel engine cylinder heads achieve higher complexity and filigrane structure, therefore careful treatment of specimen as well as net-shape machining processes with high quality output are a major requirement in this sector. An advanced factory automation system, based on an industrial robot (6-axis joint coordinate), has been developed in order to obtain the described results. A graphical interactive programming system enables the shop-floor personal simple and user friendly corrections at deburring results for individual workpiece types. A possibility was given to the system user, with which deburring errors can be easily removed through short operator interaction. Thereby, each authorized robot cell operator can contribute to guaranty process quality without special technical training.

1 Introduction Cylinder heads of Diesel engines are usually made of aluminium alloys in a mold casting process. After the casting, solidification and down cooling phases the cylinder head shows air inclusions, micro cracks and pipes on its surfaces. Adjoin to the investment casting process, risers, gates and burr formations appear. Additionally more or less strongly minted burr forms in dependency of the wear state of the forming tool and at all components boundary by tolerance between the tool components (steel mould sections and sand core). As result: The form of the cylinder heads changes consistently up to some millimetres during the production time. In order to obtain functional and aesthetical quality grades, a deburring and dressing operation must apply. According to economical and safety requirements, this operation is mostly performed by industrial robot systems.

2 Project Goals Because of the described problems simple intervention possibilities have to be conceived and developed in accordance with the system user qualifications. Correction values are to be given at a central standard terminal for all workpiece outlines, which must be processed. If the central terminal is a standard PC, the input of correction value has to take place by

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BERGER, LEPRATTI means of an appropriate software tool in a simple and self-describing way, for example by a visually interactive control surface. Thereby each authorized robot cell operator could insert correction values in extreme easily manner for removing all kinds of form deviations on all cylinder head types and, consequently, arrange a global adjustment of the production system. Furthermore a constantly high deburring and dressing quality could be guaranteed during the entire production period without additional investments or downtimes for robots reprogramming. Main goal of the planned project is therefore a quality and productivity increase of cylinder heads and, by lowering of reprogramming costs, to obtain a still more economical production.

3 State-of-the-Art 3.1 Robots in the automation For automation purposes industrial robots are used for difficult and monotonous working tasks under hazardous working conditions. The today’s main application fields are spot and arc welding, manipulation of tools and workpieces, coating, spray painting, commissioning, palletising and, with relevant increasing importance, also manufacturing in the automotive industrial sector. According to the system providers and robot end users very large progresses have also been achieved in the last years regarding geometric accuracy, trajectories exactness, task reproducibility, flexibility and individual task adaptation, so that a clear upgrade to earlier versions is now recognizable. Moreover the robot installation costs have been significantly dropped, due to theirs diffused employment. For this reasons, the use of industrial robots is getting more and more interesting also for other areas of applications. Two of these areas are deburring and dressing tasks. 3.2 Deburring with industrial robots The worker in a foundry is normally confronted with physical loads due to noise, dust, vibrations as well as psychological one by constantly repetitive activities. This requires a complete automation of deburring and dressing processes. Apart from quality and safety reasons, there are further arguments for automating such processes: An industrial robot omits no outline and guarantees a complete proceeding of all workpiece surfaces. On the contrary humans can forget a processing of section outlines by extensive tasks, particularly with outside distractions. In today’s production systems the robot takes up the workpiece with the grip arm and drives it for deburring along the tools. Its motion path is given by number and order of the Teach-In programmed space points and is normally the same by every flow cycle. In case of too large workpiece form deviations it is necessary to reprogramming a part of the stored space points. This procedure is very time as well as cost intensive and obstructs therefore significantly the production running. In order to avoid this incommodity and to obtain constantly good deburring and dressing results, it is necessarily to investigate fast reactions to all modifications and differences of individual workpieces. This is already possible by different methods [1]. 1) A flexibly stored robot tool is driven along the workpiece outlines and the distance tool-workpiece is estimated by a path measuring system. If the deflection oversteps a defined limit value this process is repeated until the given value does not be exceeded any more. The advantage of this procedure are optimal deburring results and an ensured process

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ADVANCED FACTORY AUTOMATION SYSTEM …OF AUTOMOTIVE ENGINE PARTS security, also in the series production. The higher operating time due to repeated measurements of individual outlines has though an unwanted effect. 2) An other possibility consists in the use of alternative program routines for individual outline areas. If a deviation occurs an alternative program routine with corresponding shifted point values is selected and carried out in the main robot program [2]. Process safety and unchanged cycle running time are advantageous characteristics of this method. An extra alternative program however is necessary for each different outline. Thus program complexity is considerable raised. 3) In a further procedure the workpiece is measured by means of lasers before the handling process. Together with the measurement the robot path is calculated. The obtained results regarding quality and process security are very good and an application in a series production quite possible. A prerequisite for an application of this technique is a really good contours accessibility. In case of deburring and dressing of cylinder heads an application of this or a similar procedure with optical measurement cannot be easily employed.

4 Design of the Project The planned programming system can be divided into three main tasks: The automatic modification of robot path process, the data communication between PC and robot control and the execution of the correction value input at standard PC. For each focus it is important to find optimal technically and economically methods in order to develop a high quality global concept. During the concept development it has to be taken into consideration that all three solutions must be compatible to each other. 4.1 Automatic Correction In this project section it has to be developed, how to react to deviations for all workpiece types of every form and at any time through an automatic modification of the robot path process. This correction in the programming system must take place without influencing production and treatment processes and must be integrated in the series production without additional equipment technology and complex extra programming effort. The only additional admissible component is a standard PC. Furthermore waiting periods in the program running have to be prevented and the clarity of the program structure should remain protected. The corrections should be done at a selected cylinder head surface in form of entire, side or corner surface shifting and should take place for every individual area in several steps in positive direction for stronger deburring and in negative direction for weaker deburring. The solution previews a modification of the robot programs using simple “variable sentences”. The variable changes are effected inserting correction values at PC and from there these values are transferred to the robot control. For each robot, each workpiece type and form the entered values must be stored in a separate variable sentence and available any time. Afterwards only the appropriate variable sentence is called by robot control during the milling proceeding and processed in the robot program. Each workpiece surface has to be divided into areas, so that a single different variable can be assigned to each individual area. The path of the robot is shifted within the amount of the respective variable [4].

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BERGER, LEPRATTI 4.1.1. Production of the shifting In order to produce a separate shifting of individual areas every workpiece surface has to divide ideally into nine parts (Figure 1). An accurate reproduction of the correction of the workpiece surfaces can be reached only if the area selection at PC is limited to: (i) one individual area (corresponding to the areas 1, 2, 3 and 4; called corner shifting), (ii) two neighbouring areas (corresponding to the areas 5, 6, 7 and 8; called side shifting) or (iii) all areas of the surface (corresponding to the area 9; called total shifting).

Figure 1. All nine workpiece surface areas, which can be shifted Corner shifting If the system user during the final inspection of a workpiece determines that the deburring result of a surface corner does not correspond to the required quality, he selects at PC the corresponding area from the nine areas, which are represented in Figure 1, and inputs the desired correction value. The user selects for example the area 1 and enters a correction value į. Referring to Figure1 the point p1 has to be shifted and the shifting must take place around the opposite diagonal point, that means in this case point p4. Figure 2 shows a detailed view of the surface movement in case of a p1 corner shifting. All surface points are shifted by the same angle (1) and the shifting result of point 1, 2 and 3 are shown in the equations (2), (3) and (4).

D

E

J

Figure 2: Detail view of corner shifting

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(1)

ADVANCED FACTORY AUTOMATION SYSTEM …OF AUTOMOTIVE ENGINE PARTS p1 p1'

e˜

p 2 p 2' p 3 p 3'

D ˜S

180 E ˜S b˜ 180 J ˜S a˜ 180

a 2  b2 ˜ b˜

D ˜S 180

D ˜S

(2),(3),(4)

180 D ˜S a˜ 180

On the assumption that a and b are perpendicular to each other, from the equations (2), (3) and (4) follows: p1 p1c

G

p 2 p 2c

G˜

p 3 p 3c

G˜

p 4 p 4c

0 A B

b 2

a  b2 a a 2  b2

G ˜B

(5),(6),(7),(8) G ˜A

a 2

a  b2 b

(9),(10)

a 2  b2

By shifting of point p1 the neighbouring points p2 and p3 are inevitably influenced and also shifted (6) (7). The coefficients A and B depend on cylinder head geometry and represent, how strongly the influence of the neighbouring points is. Referring to normally cylinder heads A and B amount between 20% and 50% and therefore the divergences from the desired deburring results can be neglected. Side shifting If now the program user ascertains that the deburring result at neighbouring areas (corners) does not correspond to the required quality, he can choose the appropriate corner pair (area 5, 6, 7 or 8 of Figure 1) at the PC display and input the necessary correction. The user selects for example the area 7 and then the areas 3 and 4 will be processed at the same time. The shifting occurs around the opposite axis p1p2. The shifting movement is represented in Figure 3 and the shifting results are shown in Table 1.

Figure 3: Side shifting

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BERGER, LEPRATTI Total shifting A correction of all areas represents a linear shifting of the entire surface. All four points p1, p2, p3, p4 are shifted by the same value and direction. 4.1.2 Conversion of correction values The next step concerns with the interpretation of the correction values and their conversion for obtaining the right cylinder head positioning by means of the robot. The robot coordinate system refers to the robot flange and its origin is situated in the Tool Centre Point (TCP). This and the distances between programmed points and rotation axis, necessary for the conversion of the correction value, are also shown in Figure 4. Pair of points

Shifting

Rotation

p1 p 2

G

p2 p4

G

p3 p4

G

p1 p3

G

180 b ˜S 180 G˜ a ˜S 180 G˜ b ˜S 180 G˜ a ˜S

G˜

Table. 1: Side shifting results

Corner shifting A correction shifting of a corner by the value į at p1 can be exactly positioned only if the following rotations take place at the robot: 1. Rotation around the z-axis in negative direction by the angle ȕ1. The resulting shifting are equations (11) and (12): x Positive shifting of p1 and p2 G 1c

E 1 ˜ a1

(11)

E1 ˜ a 2

(12)

x Negative shifting of p2 and p4 G 2c

2. Rotation around the y’-axis (already rotated y-axis through the 1st rotation) in negative direction by the angle ȕ2. Equation (13) and (14) represent the shifting of the four surface corners x Negative shifting of p1 and p2 G 1s

 E 2 ˜ b1

(13)

G 2s  E 2 ˜ b2

(14)

x Negative shifting of p2 and p4

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ADVANCED FACTORY AUTOMATION SYSTEM …OF AUTOMOTIVE ENGINE PARTS

Figure 4: Orientation of the workpiece coordinate system The entire shifting of p1 is therefore the total of two linear shifting. These go however in two quite different directions and their addition should be regarded vectorially. Since a correction value may usually not be larger than 1mm, the total can be approximated to a linear addition. For p1 follows: G p1 G1c  G1s

(15)

E1 ˜ a1  E 2 ˜ b1

The point p4 should remain in the same position. It is however influenced by both described rotations and is shifted unavoidable by the value įV. In order to reset the point p4 to the original position it is necessary to translate it backwards by įV. G p4

G 2c  G 2s

 E 1 ˜ a 2  E 2 ˜ b2

G V

(16)

For the other two points p2 and p3: G p2

G 2c  G 1s

 E1 ˜ a 2  E 2 ˜ b1

(17)

G p3

G 1c  G 2 s

E 1 ˜ a1  E 2 ˜ b2

(18)

For reducing as much as possible the influences on the shifting of points p2 and p3, their amount must be equally.  E1 ˜ a 2  E 2 ˜ b1

E1 ˜ a1  E 2 ˜ b2

Ÿ E1 ˜ a1  a 2 E 2 ˜ b2  b1

E1 E2

b2  b1 a1  a 2

K

B A

(19) (20)

The coefficient K has a relevant meaning. It represents the proportionality between the height and width of the area, which has to be processed, and considers thereby the geometrical distinctions between the different workpiece types. In order to obtain a desired correction result the two rotation angles may be not free selected but their relation must correspond to the coefficient K. From equation (15), (16) and (20) a first order equations system with three variables ( ȕ1, ȕ2 and įV ) results (22). It must be paid attention to the position of the point p1, which shifting due to rotation and translation must correspond exactly by į. That means the value įV must be subtracted from the total shifting į (21).

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BERGER, LEPRATTI GD

(21)

G  GV

­ ° G D E 1 ˜ a1  E 2 ˜ b1 ° ®G V  E 1 ˜ a 2  E 2 ˜ b2 ° E1 B K ° A E ¯ 2

(22)

The solution of the upper system leads to the following equations: ­ ° ° ° ® ° °G °¯ V

E1

G 2˜ A

E2

(23)

G

2˜B G § a 2 b2 · ˜¨  ¸ 2 © A B¹

These results could be applied partly to all four corner points p1, p2, p3 and p4. The only difference consists in the translation value įV, to which a different values has to be assigned depending on the selected area. The corresponding translation values are shown in Table 2.

GV

Selection

G § a2

b · ¨  2¸ 2© A B¹ G § a1 b2 · ¨  ¸ 2© A B¹ G § a 2 b1 · ¨  ¸ 2© A B¹ G § a1 b1 · ¨  ¸ 2© A B¹

p1 p2 p3 p4

Table. 2: Assignment values for įV Side shifting A side shifting of the neighbouring points p1 and p3 involves a rotation around the z-axis (Figure 4). The other two points on the opposite edge (p2 and p4) are inevitably shifted too. Also in this case a translation in the opposite direction is therefore necessary in order to compensate for the workpiece position and obtain the desired corrections. Equations (11) and (12) could be applied and the equations system (22) can be shortened for the regarded case as follows: ­G T ® ¯ GV

E 1 ˜ a1 Ÿ E1 ˜ a

G ­° E ® 1 A °¯G V G ˜ a 2

(24)

Both quantities, i.e. the translation value įV and the rotation angle ȕ1, possess different values depending on the selected area. The following table (Table 3) shows how to adapt the equation system for each case of selection.

Total shifting For a total surface shifting by the correction value į the equation system (22) has the following form:

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ADVANCED FACTORY AUTOMATION SYSTEM …OF AUTOMOTIVE ENGINE PARTS G

(25)

GT

An exactly reproduction of the entered correction values can only be obtained if the right axis orientation will be token into consideration. Neighbouring points

GV

E1

p1 p2

G˜

b2 B

G

p3 p4

G˜

b1 B

G

p1 p3

G˜

a2 A

G

p2 p4

G˜

a1 A

G

B

B A

A

Table. 3: Assignment values for įV and ȕ1 4.2 Communication PC/RC An important aspect in the development of this project is the test of possibilities for the data communication between computers and robotic control. Particularly the data transmition rate and its influence on the production process (process obstruction or even interruption) and on the robot program running are to be considered like most important selection criteria. Possible risks must be emphasized, measured and, if possible, minimized. Moreover, all data, which are necessary for the transfer of the correction value from PC to the robot control, should be stored before data sending for preventing a damage by overrun. A repeated storing on two independent protection media (e.g. two fixed disks) is suggested. For the integration of the data transport into the programming system is preferred the use of a factory LAN. Apart from the technical advantages and the simple handling, the data transfer over a Local Area Network is for the future a very developable technology, because further industrial robots and PCs can be connected to this network at any time. A possible connection form is represented in Fig 5. In order to avoid overrun, data misinterpretation and back-up in robotic control during the input of correction values at PC modules (files) with variable sentences may be transferred individually and only after proceeding the previous transferred corrections, it may receive new data. That can occur by using a flag (Boolean variable), which is set if the robot is busy and reset as soon as the operation phase is concluded. 4.3 Visualization of the Corrections The system user must have the possibility to execute all kinds of corrections into the system without competences in programming of robot. The input of the necessary values has to take place in a very simple and understandable manner. Therefore a program interface for the visualisation of workpieces with all individual outlines, which can be processed, has been developed. The system user executes the correction only by clicking on the corresponding outline area by means of PC mouse. The input is restricted to more or less-Button for removing material. Sequentially on the program interface background the necessary variables with the related values are calculated and transferred to the robot control [3].

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BERGER, LEPRATTI For the development of the visualisation interface all restrictions, which have been mentioned in the previous chapters has been considered. Apart from the general boundary condition requests a specific file format and file content form are requested for the correctly data transfer to the robot control (see paragraph 4-A). The visualization surface consists of “formularies”, which can be called by the user partially in any order. An example of formulary for the selection of the surface area and for input of necessary correction values is represented in Figure 6.

5

Summary and Outlook

Casting operations for cylinder heads from aluminum alloys cause different geometric deviations. These can endanger the further machining and handling of the workpiece. It is necessary to maintain these deviations during automation solution based on industrial robot systems. The described system is designed for fast and reliable interaction between the human operator and the industrial robot controller. The interaction is based on an interactive programming system with which it is possible to realise simple and user-friendly corrections within deburring and dressing operations.

Figure 5: Communication between PC and robot control The structure of the programming system allows many possibilities of extension and further development. It allows also on-line data exchange of the PC-based modules to the robot controller and enables a mass storage. Likewise, the program protection of the robot controller can be managed within the network. By using a factory LAN, every robot can recall data from the network (e.g. number of items, down-time etc.). Further development is still necessary for recognition of deburring errors. Here it could be possible, if an optical recognition and monitoring of the deviation with automatic correction value transfer can take over this function. This additional station (separated from the deburring process) could monitor statistically the results and transmit necessary corrections of the system.

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Figure 6: Formulary for the selection of surface and values input

6

Acknowledgments

The project paper was a project collaboration with the DaimlerChrysler AG in Stuttgart (Germany). For the Project tests ABB Robots have been employed. The authors would like to thank the fruitful cooperation.

References [1] R. Wagner, Robotersysteme zum kraft-geführten Entgraten grobtolerierter Leichtmetallwerkstücke mit Fräswerkzeugen, Stuttgart University, Springer-Verlag, Berlin Heidelberg 1998. [2] D. Huck, Informationsverarbeitung in der Robotik, Springer-Verlag, 1997. [3] U. Berger, R. Lepratti, Intelligent PC-based User Control Interface for On-line Correction of Robot Programs in Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision (ICRACV 2002), Singapore, December 2 - 5, 2002. [4] U. Berger, R. Lepratti, Intelligent Control System for the Automatic Correction of Deburring and Dressing Process with Industrial Robots, in Proceedings of 11th International Workshop on Robotics in Alpe-Adria-Danube, (Balatonfüred, Hungary), 2002, pp. 298-303.

About the Authors Ulrich Berger owns a Diploma degree of Mechanical Engineering from the University of Stuttgart and a Doctorate degree in Engineering Sciences (Dr.-Ing.) from the University of Bremen. His professional career embraces several responsible positions in the automotive sector and research institutions. Since 2001 he is full Professor at the University of Technology, Cottbus, Chair of Automation Engineering. His lecture topics cover innovative production automation technologies, control/automation theory and robot systems. Raffaello Lepratti studied at Politecnico di Milano in Italy and at the Brandenburg Technical University of Cottbus in Germany, where he obtains a Diploma degree of Electronic Engineering. Since 2001 he is scientific collaborator at the Brandenburg Technical University, Chair of Automation Technology. His research focuses on man-machine communication systems and new robot application systems in the automotive industry.

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Petri Net-Based Optimization of Production Systems Szilvia Gyapay , Andr´as Pataricza , J´ozsef Sziray , Ferenc. Friedler Department of Measurement and Information Systems, Budapest University of Technology and Economics, Budapest, Hungary gyapay,pataric @mit.bme.hu Department of Informatics, Sz´echenyi University, Gy˜or, Hungary [email protected] Department of Computer Science, University of Veszpr´em, Veszpr´em, Hungary [email protected]

Abstract — Petri nets are widely used as an underlying framework for formalizing UML-based system models. Based on their precise semantics and easy-to-understand graphical representation, they are appropriate to model production systems together with their quantitative properties. The production of desired materials can be modeled as a reachability problem of its Petri net model. However, traditional reachability analysis techniques can result in a state space explosion, while numerical methods for invariant computations give either sufficient or necessary conditions. The current paper presents efficient semi-decision and optimization methods for the reachability problem based on Process Network Synthesis algorithms: Solution Structure Generation (SSG) and Accelerated Branch and Bound (ABB) algorithms. We show that the ABB algorithm can be used to solve scheduling problems efficiently and can be extended for other Petri net analysis. Obviously, the combined methodology can be used for a variety of application fields like IT systems, workflow optimization, etc., including production processes as a special case.

1 Introduction Due to the increasing complexity of IT systems, the formal verification and validation of system models are required. Petri nets provide one of the most efficient tools to model parallel processes and high-level abstraction. Petri nets as specification formalism are widely used to model systems, especially concurrent and distributed systems: by means of places and tokens within the places nets can specify concurrency, sequential composition, mutual exclusion and non-determinism. Since system models could be very large the traditional Petri nets analysis techniques such as reachability analysis based on the state graph can result in state space explosion.

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Frequently, the objective of the reachability analysis is only the proof of the nonexistence of an unwanted situation, for instance, a dangerous combination of the states. In such cases semidecisions try to prove the soundness of the system in an indirect way by showing that an unwanted situation would not fulfill a necessary condition at the system level. Obviously, if this proof is successful then it is an evidence of the non-existence of the unwanted case but if the proof is unsuccessful further analysis is needed. The main advantage of the semidecision-based techniques is that the necessary conditions are frequently easy to analyze abstractions of the original system behavior. Recently, a number of semidecision algorithms using the results of linear algebra and integer programming have been developed [1] [2] [3]. On the one hand, these numerical methods are much more efficient (often with polynomial runtime) than traditional reachability methods. On the other hand, sacrificing the preciness of analysis they provide only either sufficient or necessary conditions for the reachability problem [4]. In the related topic production optimization, efficient algorithms were elaborated for Process Network Synthesis problems based on the reformulation of the problem to produce desired products from given raw materials by resource allocation. Recently, first results of the process graph based algorithms have been exploited and applied in several fields of computer science (e.g., to the syndrome-decoding problem of diagnostics of multiprocessor systems [5]). Based on the state equation, a necessary condition for the reachability of a particular state in the state space of the Petri net is provided by linear algebraic techniques: a chord connecting the start and the end points of the required trajectory is computed without any details about the real trajectory. Thus the non-reachability of a system state could be decided: – if the state equation has no solution (there is no chord) then the state is not reachable – otherwise the state could be reachable. Formalizing the reachability problem of Petri nets as a mixed integer linear programming problem together with an appropriate target function (e.g., time or cost function), we propose a semidecision method based on Process Network Synthesis (PNS) algorithms. After a short introduction to Petri nets (Section 2) and Process Network Synthesis (Section 3), the theoretical relationship between Petri nets and P-graphs is discussed in Section 4. In Section 4.2, differences between Petri nets and PNS are described while Section 5 provides a Petri net example to demonstrate the adaptation of the Accelerated Branch and Bound algorithm. Finally, further research directions are discussed, i.e., the adaptability of PNS algorithms to other Petri net analysis.

2 Petri Nets and the Reachability Problem Before the introduction to the reachability problem, we give a short overview about Place/Transition nets. 2.1 Place/Transition nets where and are disjoint sets of defines the edges from places is a weight function on edges. Places

A P/T net (see Fig. 1) is a 4-tuple places and transitions, respectively. to transitions and conversely, while

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p6

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Figure 1: An example P/T net

can contain tokens and transitions can consume from and also produce tokens to places according to the weight function. are denoted by The input and output places or transitions of an element are and , respectively. In other words, a P/T net is a directed bipartite graph, where the two disjoint node types are places and transitions, respectively, connected by directed and weighted arcs. A marking is a -dimensional vector over naturals composed of the numbers of tokens in the corresponding places. A given marking represents the state of the net which can be changed by firing transitions. A transition can fire (is enabled) if each of its input places contains at least as many tokens as is specified by the weight function, i.e., . The firing of a transition removes the determined amount of tokens from the input places, and tokens are produced for the output places. 2.2 Reachability problem A sequence of firings describes the changes in the state of the Petri net along a particular trajectory. The reachability problem is to decide whether from an initial marking a given marking as a starting point there exists a legal trajectory to a target marking, i.e., whether there exists a firing sequence from the initial marking to the final marking denoted by . The transition vector of a firing sequence is a -dimensional vector over naturals composed of the number of the occurrences of each transition in the sequence. In case of a huge system model, the decision of the existence of such a trajectory by the construction of the state graph can result in state space explosion. The methods avoiding the state space explosion provide the transition vector describing the chord between the initial marking and the final marking. Thus these methods produce only semidecision methods because they deliver either the answer ’no’ or ’I do not know’ instead of a surely fireable trajectory. This way semideci-

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raw materials

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Figure 2: An example P-graph representing a PNS problem

sions are effective in excluding unwanted solutions. The main difference between the firing sequence completely describing trajectory and the transition vector generated by the semidecision algorithm is that the latter one describes only the number of occurrences of the individual transitions and neglects their order. The fireability of the resulted transition vectors is satisfied only in case of some specific Petri net subclasses, e.g., state machines. In case of general Petri nets, the output of the semidecision algorithms requires an additional filtering of the transition vectors.

3 Process Network Synthesis In chemical engineering, PNS algorithms are used to determine an optimal resource allocation and scheduling for the production of desired products from given raw materials. 3.1 Problem definition A PNS problem is represented by a so-called Process graph (shortly P-graph), which is a directed bipartite graph consisting of material containers and operating units. Operating units consume their input materials and produce their output materials while the directed arcs between materials and operating units symbolize the flow of materials in the network. In addition, costs are assigned to raw materials and operating units and balance equations for material production. The objective of a PNS problem is to find a solution structure of a minimal cost, i.e., a sub P–graph, which represents how final products can be efficiently synthesized from raw materials. In the P–graph of Fig. 2, products A and B are to be synthesized from raw materials E and F by the four operating units. 3.2 PNS algorithms By means of PNS algorithms, sufficient and necessary conditions for feasible solution structures are determined defining the entirely solution space. These requirements are given by five axioms [6] discussed shortly in the following describing the specific combinatorial properties required to have in order to be a feasible solution structure.

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– if the state equation has no solution (there is no chord) then the state is not reachable – raw materials must not be produced – and all products have to be synthesized. The efficient algorithms for PNS problems [7] exploit these combinatorial properties. The solution space is reduced in polynomial time by the Maximal Structure Generation (MSG) algorithm removing the redundant operating units and materials surely not playing any role in a feasible solution. The Solution Structure Generation (SSG) algorithm generates all of the feasible shop recipes. Obviously, a combination of two shop recipes is a feasible solution as well. The subsequent Accelerated Branch and Bound algorithm (ABB) estimating the optimal solution can deal with combinations of complex shop recipes instead of individual operations thus drastically reducing the search space. This reduction can reach orders of magnitude even in the case of small scaled problems.

4 Unifying Concepts Obviously, the combination of the Petri net based paradigm of modeling complex systems with the efficiency of the PNS approach in resource allocation and scheduling optimization promises an important synergetic effect for a wide class of problems. Based on their semantic resemblance, a unified treatment can be defined for Petri nets and PNS problems. At first, the structural, then the semantic analogies are defined. 4.1 Joint features As it shown in the previous summary, the structural similarity between Petri nets and P–graphs is straightforward (Table 1). P–graph of a PNS problem material containers operating units raw materials final products cost of materials and products cost of operating units rate for operating units material quantities

Petri Nets places transitions corresponding places are marked at the initial marking corresponding places are marked at a final marking cost of places (time) e.g., firing time of transitions weight of incoming and outcoming edges of the corresponding transition number of tokens

Table 1: The assignment of PNS and Petri Nets elements In the Petri net terminology, the five axioms of the PNS problem define a partial reachability problem where the initial state corresponding to the marked states representing raw

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materials and the designated end state has to cover all and only the places corresponding to products. The restriction ‘partial reachability’ means that the final marking of all places except these specific output places does not care. Please note that in another interpretation if we use the notion of information and information processing steps instead of materials and physical operations the PNS problem can be applied for a large spectrum of partially observable IT systems. Our objective in merging Petri nets and PNS are the following ones. – On the one hand, if traditional Petri nets are enriched by numerical cost functions and their objective function to be optimized then we can use this methodology for searching the optimal solution of an arbitrary weighted reachability of the special structure described in Section 3.2. Please note, that for a wide class of Petri net related quantitative problems the solution complexity is a major limiting factor to build faithful models. For instance, stochastic Petri nets can be currently solved in state spaces roughly of the size of only while PNS can cope with essentially larger problems. – On the other hand, the extension of the traditional PNS approach by the feasible modeling power of Petri nets allows to model and solve highly complex production problems like those in logistics or in feasible manufacturing cells. The PNS algorithms can be used for Petri net reachability analysis in three steps. First, the non-existence of the maximal structure means that there exists no trajectory from the initial marking, i.e., the final marking is not reachable. Second, algorithm SSG provides every feasible solution structure as a set of their contained operating units, i.e., the results are represented as characteristic vectors of the contained transitions of the trajectories in Petri nets. Finally, algorithm ABB gives the optimal solution structure in form of a vector denoting the number of the use of the individual operating units, i.e., it provides the transition vector of a possible optimal trajectory of the corresponding Petri net. 4.2 Essential differences Thereupon its chemical use, PNS problems can contain some structures which are numerically untreatable in case of Petri nets. In the chemical production, a specific kind of materials is used: the catalyst. In Fig. 3, a P-graph and a Petri net of a catalyst are shown not carrying the same meaning. For instance, whenever the production of a compound requires a catalyst it can be produced and taken for the production where the cost of the catalyst container can be the cost of the catalyst production. Meanwhile, a token in the graphically identical Petri net can not be produced if it represents a state variable which is unmarked in the initial state. Obviously, cycles may frequentally contain siphons in Petri nets, i.e., such subnets, which remain unmarked if they do not contain a proper marking in the initial state. Therefore it is not assured that the optimal results determined by algorithm ABB are realizable, i.e., fireable from the initial marking. Due to the above facts, for an arbitrary Petri net the satisfaction of the five axioms is necessary but not sufficient to represent a feasible solution net for the (partial) reachability

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raw raw

catalyst catalyst

op.unit

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(a) Catalyst in Petri net

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(b) Catalyst in PNS

Figure 3: Catalyst in Petri net (left) and in PNS (right)

problem. For instance, a net containing a catalyst place that is not reachable from the initial marking can be contained by the result net computed by PNS algorithms. In the literature, some specific Petri net subclasses exist that always provide feasible solution nets in case of the satisfaction of the five axioms. Some of them are state machines and sound workflow nets [8]. In addition, a slight difference holds in the optimal solution computations. Algorithm ABB computes a solution represented by the contained operating units and it also defines the number of the produced materials that number can be even rational. On the contrary, transition vectors have to contain integers, i.e., the numbers of the firings. In the following, algorithm ABB is adapted to a scheduling problem represented by a Petri net.

5 An Example: Adaptation of ABB Algorithm Based on their similarity, algorithm ABB is adapted for an example Petri net. The model depicted in Fig. 4 shows the repair of computer types A and B. A mechanic can repair either one A or one B typed computer and even both of them AB at the same time. The task assignment and their repair take 1, 1, 2 and 2, 1, 3 time units, respectively. In the initial state (depicted in Fig. 4) there are three faulty A and three B typed computers, respectively. The objective is to find the optimal task allocation to the mechanics in order to repair the faulty computers (i.e., to reach the final state shown in Fig. 5). Thanks to a degree of freedom in the composition of the model we can introduce a constraint on the number of mechanics available to perform the repair job in a variety of forms. – In the traditional Petri net style of modeling we can represent the number of mechanics available by a proper initial marking of the net and the set of solutions can be estimated by changing this initial marking. Obviously, this approach suffers from the problem originating in the pure scalability of the model. This way, if the number of mechanics is changed then the reachability graph has to be repeatedly generated. (Its complexity can be slightly reduced only by identifying parts covered in the previous analysis. For instance, if we increase the number of the mechanics, all the

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Figure 4: An allocation problem: initial state

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Figure 5: An allocation problem: the state to reach

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solutions estimated in the previous case remain feasible but the entire reachability graph has to be traversed in order to identify the new branches.) – In the pure Petri net styled modeling we can associate a cost to hiring a new mechanic. In this case, this associated cost will held to keep the number of mechanics involved low but their number will be still influenced by the cost factors assigned to the other parts operating on the production flow. – Finally, we can include a numeric constraint to the number of mechanics. This will confine the solution space in the optimization phase, moreover, it can be used to make cuts in the reachability graph. If these cuts are locked then the generation of the reachability tree for an increased number of mechanics can be done in an incremental way by extending the tree starting from the point where the cuts were made.

6 PNS algorithms in Other Petri Net Analysis Tools Based on their resemblance, PNS algorithms are appropriate not only for reachability analysis but can be also extended for other Petri net analysis problems. T-invariant In Petri net analysis, T-invariants play an important role. A T-invariant is a set of transitions (a transition vector) such that their firing do not change the state of the net. The invariants are determined by the solution of a linear equation system. The lack of such a method for T-invariant computing is that it does not assure the fireability of the result transition vector while the use of algorithm ABB can provide a fireable transition vector if the net is appropriate. Another point where the unified approach promises interesting results is the case when the production process underlies temporal constraints, i.e., if some production process has to precede another one. In Petri net domain, such problems occur frequently during validation and verification where the objective is to check the validity of a temporal constraint typically given in the form of a temporal logic expression. The typical approach discussed below is to construct such a product B u¨ chi net [9] automaton, which has as a solution space firing sequences satisfying both the logical constraints from the original structure and the temporal one. ¨ Buchi net In more details, B¨uchi net is a product automaton of a Petri net of the modeled system (it is required to be a 1-safe Petri net, i.e., for every place and reachable marking holds) and the B¨uchi automaton of the negation of an LTL formula to be checked for the system. If the constructed net accepts no words then the formula holds for the system. Since the automaton is a net itself having an initial state and accepting states it can be extended with source and sink transitions. If there is no T–invariant then the automaton is empty. T–invariant computation has a traditional solution algorithm introduced by Martinez and Silva [2]. The algorithm generates the basis containing the minimal T–invariants, i.e., other T–invariant can be easily computing from the basis elements. Since algorithm SSG generates every feasible solution network it is a redundant method. Based on the original method, algorithm SSG can be improved to provide the minimal feasible basis.

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7 UML-based Model Generation One main technical disadvantage of both the PNS approach and Petri nets that they require the construction of large or even extremely large models. This model construction is a main bottleneck both in the efficiency of the analysis end in the quality of the model. In order to avoid the troubles induced by the manual creation of large scale models, we plan to automatically generate these models from UML models [10, 11]. Our current analysis indicates that the standard UML profile intended to describe schedulability can be used without modifications for our problem field as well [12].

8 Conclusion The discussed combination of the efficient PNS algorithms with the modeling power of Petri nets provides an efficient tool to improve the analysis of UML models. Based on their graphical and semantical similarity, PNS algorithms can be adapted to Petri net analysis and evaluation. The current paper examined their unified treatment: joint and different features and further application possibilities of PNS methods to Petri net analysis problems.

Acknowledgement This work was supported by projects FKFP 0193/1999 and OTKA T038027.

References [1] J. Desel. Petrinetze, Lineare Algebra und lineare Programmierung, volume 26 of Teubner-Texte zur Informatik. B. G. Teubner Stuttgart-Leipzig, 1998. [2] M. Silva, E. Teurel, and J. M. Colom. Linear algebraic and linear programming techniques for the analysis of Place/Transition net systems. In G. Rozenberg W. Reisig, editor, Lectures on Petri Nets I:Basic Models, volume 1791 of LNCS, pages 309–373. Springer, 1998. [3] S. Melzer and J. Esparza. Checking system properties via integer programming. In European Symposium on Programming, pages 250–264, 1996. [4] A. Pataricza. Semi-decisions in the validation of dependable systems. In Proc. IEEE DSN’01, The IEEE International Conference on Dependable Systems and Networks, pages 114–115, 30.June– 4.July 2001. [5] B. Polg´ar, Sz. Nov´aki, A. Pataricza, and F.Friedler. A process-graph based formulation of the syndrome decoding problem. In IEEE DDECS, pages 267–272, 2001. [6] F. Friedler, K. Tarjan, Y. W. Huang, and L.T. Fan. Graph-theoretic approach to process synthesis: Axioms and theorems. Chemical Engineering Science, 47(8):1973–1988, 1992. [7] F. Friedler, J. B. Vajda, and L.T. Fan. Algorithmic approach to the integration of total flowsheet synthesis and waste minimization. In M. M. El-Halwagi and D. P. Petrides, editors, Pollution Prevention via Process and Product Modifications, volume 90 of AIChE Symposium Series, pages 86–87, 1995. [8] Wil van der Aalst. Structural characterizations of sound workflow nets. In Computing Science Reports 96/23, Eindhoven University of Technology, Eindhoven, 1996. http://citeseer.nj. nec.com/vanderaalst96structural.html. [9] J. Esparza and S. Melzer. Model checking LTL using constraint programming. In Proceedings of Application and Theory of Petri Nets, 1997. [10] A. Pataricza, G. Csert´an, G. Rom´an, V. Kereszt´ely, and J. Sziray. UML-based control of industrial processes. In IEEE International Conference on Intelligent Engineering Systems, pages 49–52, 2000.

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[11] A. Pataricza, Gy. Csert´an, O. Dob´an, A. G´abor, and J. Sziray. Process modeling and optimization in UML. In IEEE International Conference on Intelligent Engineering Systems, 2001. [12] Real–Time UML Submission Consortium. Response to the OMG RFP for Schedulability, Performance, and Time, 1996. http://www.omg.org/cgi-bin/doc?ptc/2003-03-02.pdf.

About the Authors Szilvia Gyapay is a second year PhD student at the Department of Measurement and Information Systems, Budapest University of Technology and Economics. Her interests include operation research methods and Petri net reachability analysis. Andr´as Pataricza has a Diploma in Electrical Engineering from the Technical University of Budapest and Candidate of Technical Science from the Hungarian Academy of Sciences. His research interests include dependable systems and formal methods based verification and validation. J´ozsef Sziray has a Diploma in Electronic Engineering and PhD from the Technical University of Budapest. His research interests include test design for hardware and software systems, as well as verification and validation of software. Ferenc Friedler Ferenc Friedler, professor and head of Department of Computer Science, University of Veszpr´em. His research interests include process systems engineering and operations research.

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Production Part Approval Process in Quality Management System Marianna Lendvay1, Attila L. Bencsik2 1

Institute of Microelectronic and Technology Budapest Polytechnic Faculty of Kandó Kálmán Electrical Engineering H-1084 Budapest, TavaszmezĘ u. 15-17. [email protected] 2

Institute of Mechanical and System Engineering Budapest Polytechnic Faculty of Bánki Donát Mechanical Engineering H-1081 Budapest, Népszínház u. 8. [email protected]

Abstract – The paper presents the Production Part Approval Process in the quality management system. It’s a system to acquire the purchaser’s approval, concerning certain item, production, material or service. The adoption of a quality management system should be a strategic decision of an organisation. The design and implementation of an organisation’s quality management system is influenced by varying needs, particular objectives, the products provided, the processes employed and the size and structure of the organisation. The quality management system requirement specified in the QS 9000 Requirement’s are complementary to requirements for products. The QS 9000 promotes the adoption of a process approach when developing, implementing and improving the effectiveness of a quality management system, to enhance customers satisfaction by meeting customer requirements.

1 Introduction Speaking about manufacturing and service, the word quality is frequently used. To satisfy their customers, the companies are trying to provide products and services conforming to the international standards of quality management and requirement system. In this paper we review the QS 9000 requirement system which is based on the ISO 9000 standard family. We give the details of one key document of the QS 9000, the production part of approval process. Approval of the means of production is indispensable for effective production, therefore this document is essential for every company using the QS 9000.

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2 General Requirements Of Quality Management Systems To introduce the quality management system, the organisations should perform the following tasks:  definitions of the processes required for implementation of the quality management system and that how these will be applied in the organisation,  determination of the order and the interaction of these processes,  definition of the criteria and methods which are essential for successful operation and control of these processes,  procurement of resources and information sources needed for the processes and for their supervision,  supervision, measurement, and analysis of these processes, as well as  activities which are needed for the planned results and continuous development of the processes. The organisation should document its quality management system, therefore the documentation should contain a declaration of quality policy and of the quality aims, the handbook of quality management, the documented procedures required by the international standards, and the documents which the organisation needs for effective planning and control of its process. The top management should prove its commitments to the implementation and introduction of the quality control system as well as to the continuous development of the system by:  calling the attention to the importance of compliance to the customer and law requirement  defining the quality policy and quality aims  evaluating the management  providing the required resources The quality aims should define all related functions and levels of the organisation. They should be understandable and be in harmony with the quality policy. Resources needed for the quality aims should be defined and planned. Sphere of authorities and responsibilities as well as their functions with their functions should be defined and communicated. A quality management manual should be made including:  application field of the quality management system,  documented procedures formed in the system or their references  description of the interactions between the processes of the quality management system. To ensure continuous readiness, operability and efficiency for the system, the top management should examine the quality management system at planned time intervals. The examination should include:

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results of audits, customer indications, outcome of the process, product suitability, preventive and corrective activities, activities required by earlier examinations of the management, alterations which can influence the quality system

3 Elements of the QS 9000 Requirement System The QS 9000 is a system of quality requirements that aims customer needs in a more effective way than earlier. It keeps the requirements of the ISO 9000 standard series; at the same time it surpasses them. It has very definitive requirement to the internal system of sub-contractors of automotive industry. It demands a uniform internal organisation for all the sub-contractors and suppliers. In an independent outer audit system it suggests examination of the process of the quality management system. Based on the documentation system of the company and on the standard requirements, an authorised certification organisation controls the suitability of the process and the methods in the practice. In case of suitability, the organisation issues a certification and later it supervises the status of the system periodically. Because the quality improvement should be already ensured at the supplier systems, therefore the following groups are involved it:  Suppliers providing base material or auxiliary material for manufacturing.  Firms, as subcontractors, providing direct services to the manufacturer. The requirement system includes the following elements: 1. Top management responsibility 2. Quality management system 3. Contract review 4. Controlling technical planning 5. Processing documents and data 6. Procurement 7. Processing customer supplied product 8. Product identification and traceability 9. In-process control 10. Supervision and examination 11. Supervision of controlling, measuring and testing equipment 12. Inspection and test status 13. Processing non-conforming product 14. Corrective and preventive activity 15. Handling, storage, packaging, maintenance and delivery 16. Processing records of quality policy 17. Internal audits of quality policy 18. Training 19. Customer service

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LENDVAY, BENCSIK 20. Statistical methods 21. PPAP - Production Part Approval Process 22. APQP - Advanced Product Quality Planning 23. QSA - Quality System Assessment 24. MSA Measurement System Analysis

4 Production Part Approval Process /PPAP/ The PPAP defines the general requirements needed for the part approval. It includes the production materials and materials in bulk. Its aim is to get the supplier to understand well all the planning and manufacturing regulations and specific requirements of the customer, and by this, making the process able to produce product suitable to the requirement at the given intensity of production. The method should be applied for outer and inner supplier of production materials in bulk and for production and service parts. For materials in bulk it is only needed if the customer requires it. Suppliers of production and service parts should follow the PPAP, unless the customer gives up his right to this in written form. I the following cases, from the product approval organisation of the customer, the supplier should get a total approval: 1. At introducing a new part or product (e.g. new part, material, colour) 2. At repair of an error of part delivered earlier. 3. At changes to the production, to the product, in the design record, specification or materials. 4. In all other cases required by the customer. 4.1 The PPAP requirements: For part approval, the parts should be sampled from a characteristic production cycle. Unless the customer orders another schedule, this cycle should be on an interval between one and eight hours and should result at least 300 pieces specific products in succession. Related to the production cycle, the tooling, product measurements, methods, operating personnel and the environment, this cycle should equal to the production cycle. Each discrete process of the production and each product coming from separate position should be measured and controlled. In case of materials in bulk, no material quantity is specified and the sample should be delivered in steady state. The supplier should meet all specified requirement. In case of any result out of specification, the supplier can not deliver the part. The supplier should do his best to fulfil the planning specification. It this is not possible, he should meet the customer to get the proper repair processes. In accordance wit the PPAP, the inspections and the examinations should be made by an approved laboratory. The lab report should include the name of the lab doing the examination, the dates of the examinations and the used system of standards. The test report should not contain statement of general validity. In case of special agreement, the examination can be made in the customer's lab. The supplier should have the required records and items for each part or part family, which should be accessible to the customer during the PPAP. In case of alteration to the PPAP requirement, the supplier should get a previous approval.

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PRODUCTION PART APPROVAL PROCESS IN QUALITY MANAGEMENT SYSTEM 4.2 Needed documents: 1. Design records The supplier should have all the design records related to the products, its components and details. In case of electronic design record, hard copy of the design record is also needed. Only one design record is required to the products, parts or components. 2. Documents of changed manufacturing The supplier should have all approved documents of changed manufacturing approved and introduced to the manufacturing but not filed to the design record of changed manufacturing 3. Approval for manufacturing (if required) If the design record prescribes it, the supplier should have an customer's approval for manufacturing. 4. Design error, analysis of method and effect (DFMEA) – in the case of supplier responsibility for the design The supplier should have the DFMEA for the parts and materials. This analysis should conform to the requirements of QS 9000. 5. Process charts A process chart, made by the supplier, is required, in addition that it fulfils the demands of the customer, it describes clearly and properly the steps and succession of production processes. 6. Process error, method and effect analyses (PFMEA) The supplier should have a PFMEA fulfilling the requirement of the QS 9000. In case of processes producing similar parts of the same manufacture family, the same design or process design error, analysis of method and effect can be used. 7. Results of the dimension control The supplier should have made the dimension controls required in the control plan and should prove their suitability. The measurement should cover all processes of the production, the dates of the design records, the number of modifications and the documents of changed manufacturing. Moreover, as a pattern, an examined part should be provided. In addition, the number of modifications, the dates of drafting, the name of the supplier, the number of part should be fixed on all supplementary documents (e.g. on supplementary drawings). These should be enclosed to the quantitative results, in accordance to the quantitative results, in accordance with the table of preservation/filing requirement. The dimensions, characteristics given in the design record or in the control plan, together with the actual results, can be listed properly in the form of results of the dimension controls. 8. Results of the material examination and the compliance test I. Records of the material examination The supplier should have examined every base material listed in the design record or in the control plan with chemical, physical or metallurgical specifications. The examined quantity, the result of the examination, the modification number and the date of examination, from the list of approved subcontractors, the name and code of subcontractors supplying the material should be given.

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LENDVAY, BENCSIK II. Records of output examinations. These should be done on every base material on which requirement of output or function is defined by the design record or the control plan. The report should contain the modification number and the date of the design record for the examined part, the approved document of changed manufacturing, and the date of examination. 9. Examination of the initial processes I. General requirements The ability of initial process should be defined in such a way that it can be acceptable for all special characteristics defined by the supplier or the customer. To reveal the effects of the measurement errors to the measurement, an analysis of the measurement system should be made. The aim of the requirement is to define whether the process is capable to output a product proper for the customer requirement. The examination of the initial process aims the variables and not the characteristic data. The examinations of the initial process are of short time and they can not foreshadow the changes of the work force, equipment, measurement system. With customer's approval, requirement of initial data can be replaced by the results of long time taken from same or similar processes. II. Quality indicators The examination of the initial process should be summarised by ability or output indicators. The Cpk – is an indicator of the ability for stable operation. The assessment of sigma depends on the spreading in the sub-group (R/d2, S/c4). The Ppk is an output indicator, and in this case the sigma assessment is based on total spreading. Short time examinations are: aim of the initial examination is to understand the operation changes and not to form an indicator. If sufficient data volume is available to assemble an control card (at least 100 unique samples), then the Cpk should be computed for a stabile operation. For unstable processes, in accordance with the specification, use of Ppk with predictable pattern is suggested. If the data volume is not sufficient for the examination, the customer's part approval organisation should be informed. III. Acceptance criteria for the initial examinations For the processes seemingly stabile, the following criteria should be applied: Indicator value > 1,67

The process conforms to the customer requirements, using the control plan, the process can be started

1,33 d Indicator value d1,67

The process can be acceptable at present, but may require corrections. It is useful to survey the results of the examinations and, if required, to change the control plan.

Indicator value < 1,33

The process fails to perform the acceptance criteria and needs modifications.

IV. Unstable processes If the customer-supplier does not accept the process, the causes of difference, if it is possible, are to be eliminated before filing the PPAP. The supplier should inform the customer about the unstable process and file a plan of corrective action.

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PRODUCTION PART APPROVAL PROCESS IN QUALITY MANAGEMENT SYSTEM V. Operations with one-sided tolerance or with non-linear distribution For tolerances of this type, the possible acceptance criteria should be defined together with the customer. These criteria may be an indicator of other type or data processing method. It is worth attempting to find the causes of non-normal distribution and following the changes. VI. Strategy for the case of non-satisfied acceptance criteria For the cases of non-repairable process or no unperformable time limit of the PPAP filing date, the supplier should meet the customer for approval a corrective action and a modified control plan. The scattering should be lowering till the Ppk or the Cpk reaches or exceeds the value 1.33, or the customer gives his contribution. 10. Analysis of measurement system (MSA) examinations The analysis of measurement system examinations should have done at every new or modified measurement equipment. 11. Qualified laboratory documentation The supplier should prove that the employed laboratories conform with the QS 9000. 12. Control plan The supplier should have a control plan, in accordance with the QS 9000, containing every controls used for process control. 13. Part filing certificate (PSW) Without a customer's requirement, a distinct PSW should be filed for every part. The gained information from the required measurements and examinations should be given in these. If the parts come from more tools, the supplier has to evaluate of dimension in every category: The tools, templates should be identified in the series of PSW Form/Pattern/Production process or in a document enclosed to the PSW. The supplier should control the conformity to the requirements of every measurement and results of examination and whether all documents are available to the customer. If the customer requires that, and it is intelligible, the PSW can be filed electronically. Without a customer's requirement, the supplier should record the part weight, as it is written in the PSW in kg and with accuracy of four decades (ten thousandth part). The weight data is without the weight of transport protective material, auxiliary material and packaging. The product weight is defined by the average weight of ten products selected by chance. 14. Approval report of the outer appearance (AAR) If the design record needs appearance requirement, then filing of the approval report of the outer appearance is needed. This should give the required specification. To get the disposition, sample pieces should be filed to the organisations required by the customer. In general, the AAR can be drafted for parts having colour, granularity or surface quality. 15. Control list of requirement for material in bulk The control list of requirement for material in bulk should be approved together by the supplier and the customer. Without a specific request of the customer request (NR), all defined requirement should be fulfilled. The customer may define other requirements.

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LENDVAY, BENCSIK Process chart

P C

V P

V

K

K U

V

D

V

K

V

V

D

V

D: Decide; V: Execution; K: Collaborate; I: Information;

PC: PPAP-Co-ordinate; VP: Product management; KU: Customet

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I

I

D

PRODUCTION PART APPROVAL PROCESS IN QUALITY MANAGEMENT SYSTEM 16. Sample parts In accordance with the customer's needs and the file application, a sample product should be provided. 17. Master sample The supplier should store a master sample from the period of approval. This should be stored until a new master sample is approved by the customer, or the sample is used for design record or in the control plan. 18. Auxiliary instrument of control If required, at the time of PPAP filing, the supplier should provide the customer with an auxiliary instrument of control for the part specific assembling. It must be stated, that the auxiliary instrument conforms to the requirements of part dimensions. Every modification of auxiliary instrument of control should be recorded. These instruments should be treated as active parts, therefore maintenance of the full life span of the part should be provided. The auxiliary instrument of control can include the fixings, measurements, models, templates, which are specific to the product. 19. Customer specific requirements In connection with every customer specific requirements, records of suitability should be made.

5 Making PPAP for a Given Product The following process chart shows the application of PPAP method for a given product (cable strand). If the part approval report is approved by the customer, the product can be manufactured with the required quantity.

References [1] QS-9000 Quality System Requirements, - Third Edition, Chrysler Corporation, Ford Motor Company, General Motors Corporation, 1999. [2] Vincze, Pál: Production Part Approval Process for a Concrete Product, Diploma Work, BMF – KVK, Budapest, 2000. /Consultant: dr. Lendvay, Marianna/ [3] Quality Managament Systems. Requirements (ISO 9001 : 2001) [4] Kovács, Olivér: Production Part Approval Process for a Concrete Product, Diploma Work, BMF – KVK, Budapest, 2001. /Consultant: dr. Lendvay, Marianna/

About the Authors Marianna Lendvay received a Master’s degree in mechanical engineering and a doctorial degree in technical sciences both from Technical University of Budapest in the years 1977 and 1989, respectively. Her research interests include technical reliability, quality assurance, industrial design. Attila L. Bencsik received a Master’s degree in electrical engineering and a doctorial degree in technical sciences both from Technical University of Budapest in the years 1970 and 1990, respectively. His research fields are quality management systems, technical diagnostic for mechanical systems, robotics and mechatronics.

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Application of Product Model in Internet Based Robot Control László Horváth, Imre. J. Rudas John von Neumann Faculty of Informatics Budapest Polytechnic, Budapest, Hungary [email protected] [email protected]

Abstract – In this paper the authors provide a discussion on integration product modeling with robot control environments in order to enhance the utilization of geometric and other product and production equipment related model descriptions in robotics. Growing significance of robots in highly flexible manufacturing systems motivated research in the related methodology. Difficulties at reproduction of modeled product geometry at its applications resulted in growing importance of on line real time communication between a centralized product modeling and several model applications. The reported research concentrates on creation and application of model data information understandable by robot controls, on communication of model data with robot environments through the Internet, and finally on some related telerobotics issues. It covers one of the actual problem complexes in integration of engineering modeling with its shop floor level applications. Systems integration, data model, data communication and model processing have been investigated. Paper introduces the modeling environment considered taking into account the robot control aspect. Following this, key issues regarding robot tasks and their shape model based control are explained. Then an approach to interactive application of Internet based telerobotics for product model driven control of robots is outlined. Finally, possibilities for integration of remote robot control applications with product modeling environments are discussed.

1

Introduction

Concept of product model has been developed to establish models for description of all product-related aspects. Comprehensive, sophisticated, reference model based description of product information can serve any product related engineering activities including robotics. Advanced integrated product design and manufacturing rely upon this technology increasingly. Product modeling was developed into a sophisticated technology during last ten years. Application of robots and robot like equipment is growing in manufacturing and other product model related areas. Robotics is an inherently sophisticated technology.

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HORVÁTH, RUDAS Control and programming of robots have become sophisticated but waiting for their integration with product modeling is still on. The authors would like to produce some contribution to advancements in this area of importance. The utmost purpose of research in this field is integration of three hi-tech areas, namely engineering modeling, teleoperation of robots and Internet technology in a single globalized system. Human ideas about products during design and development of a product are frequently changed even if the distance between sites of product modeling and robot intensive manufacturing is large. Application of a product model that has been created on a remote modeling system can be relied on one of the following three concepts. The first concept is the troublesome model data exchange. It requires a modeling system on the model application side that is able to understand and reconstruct the model according the original model information and design intent. The second concept is application of agents. This is an advanced and appropriate concept but it is uncomfortable to apply at the present day continuous development of products where product design changes frequently. The third concept is teleoperation of the robot from the original modeling system in which the model has been created. This is the trend for future model applications therefore the authors would like to contribute to implementations of this concept. Researchers are working on several aspects of the reported work. Recently, intelligent autonomous robots are based a lot of advanced methods for programming and motion control [1], [2]. Knowledge based intelligent methods as adaptive neurofuzzy inference [3] can be applied to assist control processes. Multiple armed and cooperating robots need intelligent methods for motion coordination [4], [5]. Previous activities of the authors in this area are modeling of manufacturing process and human intent [6]. The reported research is also connected to an earlier research on robot control [7]. This paper is about model creation, handling and communication aspects of application of advanced product modeling in robotics. Distinguished attention is devoted to shape models of mechanical parts but other partial model components of the product model defined by STEP, ISO 10303 are of equal importance. Paper introduces the modeling environment considered taking into account the robot control aspect. Following this key issues regarding robot tasks and their shape model based controls are explained. Then an approach to interactive application of Internet based telerobotics for product model driven control of robots is outlined. Finally, possibilities for integration of remote robot control applications with product modeling environments are discussed.

2

Product model information for robot control

Models for description of parts, form features, sequences of part shape modifications, assembly relationships and manufacturing processes are the most important structural units of models of mechanical systems from the point of view of robotics. The related models and their associativities can be followed in Figure 1. Figure 1 outlines an up-to-date product model where associativities connect model entities and other associativities can be defined to connect this modeling environment with robot modeling environments.

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APPLICATION OF PRODUCT MODEL IN INTERNET BASED ROBOT CONTROL A part model involves curves and surfaces that carry useful geometric information for robot control. Topology describes place of these geometric entities in the modeled boundary structure of the part shape. Application oriented shape aspects are represented in this system as form features. An assembly model is created by topology driven relating geometric entities on the matched parts. Part model

Assembly model

Transformation

Structure

Geometry

Part model instances

Topology

Relationships

Form features

Fastening method

Attributes

Application oriented product model instance

Figure 1: Robotics related entities in typical product models Control of a robot is geometry centered and uses information described by part geometry. Topology can be used to know where a geometric entity is in the modeled boundary structure. Figure 2/a illustrates a part that is in the working envelope of a robot. Curve C1 that lies in surface S1 is to be followed by a robot trajectory. Following this Part V1 is placed in position on the base part by using of three relationships r1-r3. Avoiding obstruct V2 should be taken into account at the design of robot trajectory. These are two typical operations at applications of robots.

C1 S1

follow curve C1 on surface S1

V1 a)

b)

r3 r2

r1 V2

V2 V1

c)

pick V1 move V1, avoid obstruct V2 place V1 according to assembly relationships

d)

Figure 2: Part geometry for robot control

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HORVÁTH, RUDAS Non-uniform rational B-spline curve and surface descriptions are appropriate to any shape, from the straight line to free form curve, and from the flat surface to the free form surface. It is often allowed to simplify the curve geometry to linear. Application of this concept result polyhedral part shape description where large quantity of small flat surfaces is applied to approximate of the shape. Robot operations need input information for the task of robot, form features on the part to be gripped, shape of obstacles in the working envelope and geometric information for path control depending on actual task of the robot. At the same time pick and place robots need not geometric information for the purpose of path control, painting or welding robots need not information about gripping of the part. Part geometry changes during machining operations so that actual shape of the part should be communicated using machining process model information for material removals. This information is defined by form feature driven modeling of shape modifications of the part by machining and allowance values. Despite their dedicated modules for planning of robot control, present day industrial modeling systems do not offer appropriate tools for integration of part modeling and manufacturing process modeling with robot control systems on a level necessary for a fully integrated system.

3

Robot process model

Software and human sources of product model information are within product design organizations, separate or remote from robot environments. The alternative of on-site reproduction of these capabilities is generally not available at the robot station so that they should be got by remote activity. Application of telerobotics must be considered. Advancements in Internet and other related technologies give a new possibility for cooperation of product modeling and robot control. Perhaps the most important feature of these systems is that human performance can be utilized through network. The authors investigated the modeling background of remote activities in the field of control of engineering devices.

Model of the robot process

Robot process

Part models Assembly models

Task 1

Robot model

Operation 1

Models of objects in the environment of the model

Action 1 Reflex 1

Related product models

Active robot system

Model of the application process (e.g. machining. welding, painting).

Figure 3: Structure of the robot process model and its product model connections

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APPLICATION OF PRODUCT MODEL IN INTERNET BASED ROBOT CONTROL A multi-layered robot process model structure and its relationships with product model entities have been proposed by the authors (Figure 3). Tasks, operations, actions and reflexes are on the levels of this model. This follows the command structure described in [8]. A robot can manipulate different objects described together with the manipulation strategy within a task. Operation is related to a single object. Operation consists of independently executed actions. A reflex means direct transformation of current sensor data into motion.

4

Internet based solution for telerobotics

Future anticipated capacity of Internet makes it to be suitable as remote communications medium for robot teleoperation. Software at a host directs the motions of a robot connected to another host. A main drawback of this solution is that Internet produces non-deterministic communication time delay between hosts. Moreover, time delay varies with the amount of information to be transmitted. Considering Internet, there are two alternative solutions for product model based remote control. The host, from which remote operation is done, has direct access to all necessary model data. It can transmit model data for processing to a remote model application system or it processes the model information into machine independent form of robot control data. The authors prefer the second solution. Approach of the authors emphasizes geometric model driven nature of task, operation and action. A task is a sequence of object manipulations, for example, at assembly, part feeding or welding. Geometric model information is required for objects to be manipulated. This information can be used at recognition of type and shape of objects, programming grippers, calculation targets and trajectories, analysis of collision, etc. A tipical simple operation is pick and place of parts. This operation can involve actions involving positioning and orientation of parts, moving parts along paths and placing them in contact. Geometric model information is necessary for environmental objets such as parts to be welded and obstacles within the working envelope of the robot. Path to manipulate an object to a goal location can be predefined or real time generated by using of geometric model data. Mobile robots require geometric information about their environment. At the same time autonomous robots can process their own visual data about the environment around their path. Telerobotics is supposed to be coupled with autonomous robotics in the reported work. This means remote control of intelligent robots. According to the intelligence of the remotely operated system, operating mode of a telerobot can be [9] direct continuous control, shared continuous control, discrete command control, supervisory control and learning control. We share this idea at modeling of robot control. The main purpose of teleoperation is sending task-related information including product model data to intelligent remotely controlled robots. At the same time some results of human decisions are communicated too. Remote control uses information feedback from the robot control. Safe operation can be achieved following this approach. Application of product models is equally important at programming, teleoperation and teleinspection of robots. The robot control system considered by the authors can be followed on Figure 4. Because teleoperation is driven by geometry of parts both in the product and the robot station, the model complex has components on both sides.

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HORVÁTH, RUDAS One could think that the objective is a fully automated system. Consequently, remote inspection and monitoring using a vision system as used in manually controlled teleoperation are not necessary. This is a misunderstanding the real world robot control tasks. Human communication can not be omitted because human interactions are necessary. Inspections and 'dry run' tests, for example, are interactive activities. Manually controlled robot operations are necessary during manufacturing operations. In the every day practice a mix of human and model driven controls is applied. Effective user interface and visual navigation are inevitable in order to establish effective interactivity. The second way of the communication between the product modeling and the robot control computer is about characteristic shape information gained from processing of video from the robot workspace. This information can be used for calculation of actual and real position information. Recognition of 3D curved and other objects is of basic importance. At the same time robot movements can be viewed using controls as zoom, image quality, and size. This requires appropriate speed of data transfer. Consequently, control is done by using of product model data, while a feedback is established on the basis of information on characteristic elements extracted from pictures. Teleoperation of robots is considered to establish over the World Wide Web. Telerobotics server processes requests of the teleoperating client. Appropriate configuration and operation of a Web server are basic requirements. Web users must be able to control the robot remotely. Experiments on telerobotics to reveal some basic characteristics of the control and the related communications under given circumstances can be conducted by using of telerobotics interface to simulated robots.

Human command driven control information to the robot

Product geometry driven control information to the robot Processing of product model

Processing of camera geometry

Robot control unit Control information

Autonomous intelligent robot

Internet connection Simplified work space geometry

Geometric processing

Camera

Robot station

Product model

Remote control station

Figure 4: The process of teleoperation of a robot

5

Product model driven remote control of robots

Part modeling, manufacturing process modeling, production equipment modeling, data and human communication modeling and robot control modeling use common framework, data base, user interface and other resources for these activities in integrated modeling systems. Remote elements of a complex system for the above outlined and other related activities as telerobotics are integrated by the application of Internet technology including appropriate protocols as TCP/IP.

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APPLICATION OF PRODUCT MODEL IN INTERNET BASED ROBOT CONTROL Computer resources are distributed amongst product design sites, production planning sites, job shop level and outside robot control units. They may be installed in different buildings, in different cities, in different countries or even in different continents. Significance of teleoperation is growing because of the trend for enlarged distances between cooperating industrial organizations. Computing activities constituting an actual robot related complex task are distributed amongst these resources. The applied computer model can be considered as a special production model with a lot of associativity and constraint definitions. One of main benefits of the above outlined approach is processing model data in its original creating system. Reconstruction of the exchanged model by a modeling system other than the original modeling system, with lower modeling capabilities resulting deterioration of the computer descriptions is eliminated. This solution also eliminates problems associated with entity conversions of the conventional model data translation between different modeling systems. Another advantage of the method is that original human creator of the model can be present at its application. Finally, it is generally impossible to make available as highly flexible and enough sophisticated modeling system at normal robot applications as available at product development environments. The modeling environment handles all information and software tools for simulation including description and analysis of kinematics as well as advanced graphics.

6

Conclusions

Based on a discussion of the related problem complex, an approach and methodology have been outlined in this paper. The related research of the authors is motivated by advancements in technologies applied by Internet based telerobotics. These technologies have been developed to a level, where widespread industrial application is realty. The authors investigated some aspects of product model driven teleoperation of robots on the basis of their earlier researches in product and production modeling as well as robot control. The final objective is to establish a robot control that utilizes advancements in product modeling and information from product models existing in engineering design environments. The main contribution by the authors is about integration of different modeling processes. The authors offered a robot process model together with associative integration of robot control systems with product modeling systems. This paper outlined the problem complex and discussed some details of the related modeling. Intelligent autonomous robot system and mixed human and model driven control system with feedback are assumed. Wide range of potential applications of the method involve manufacturing such as machining, assembly, welding and painting, working in geometrically modeled hazardous environment as well as product development related robot experiments.

Acknowledgments The authors gratefully acknowledge the grant provided by the OTKA Fund for Research of the Hungarian Government. Project number is T 026090 and T 037304.

References [1] Jurgen Gulder, Vadim L. Utkin, Rudolf Bauer. A three Layered Hierarchical Path Control System for Mobile Robots, Algorithms and Experiments, Robotics and Autonomous Systems, No. 14, pp 133-147, 1995.

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HORVÁTH, RUDAS [2] S. S. Lyengar, A. Elfes. Autonomous Mobile Robots: Perception, Mapping and navigation, IEEE Computer Society Press, 1991 [3] M. Onder Efe, Okyay Kaynak, Bogdan M. Wilamowski. Creating a Sliding Mode in a Motion Control System by Adopting a Dynamic Defuzzification Strategy in an Adaptive Neuro Fuzzy Inference System, In Proceedings of the 2000 26th Annual Conference of the IEEE Industrial Electronics Society, Nagoya, Aichi, Japan, IEEE, Nagoya, Aichi, Japan, pp. 894-899, 2000. [4] Antal K. Bejczy, Tzyh-Jong Tarn. Redundancy in Robotics: Connected Robot arms as Redundant Systems, In Proceedings of INES'2000, 2000 IEEE International Conference on Intelligent Engineering Systems, Ljubljana, Slovenia, 2000, pp 3-10, 2000. [5] Yasuhisa Hasegawa, Toshio Fukuda. Motion Coordination of Behavior-based Controller for Brachiation Robot, In Proceedings of the 1999 IEEE International Conference on Systems, Man, and Cybernetic, Human Communication and Cybernetics, IEEE, Tokyo, VolumeVol. 6, 896-901, 1999. [6] L. Horváth, I. J. Rudas. Intelligent Computer Methods for Modeling of Manufacturing Processes and Human Intent, In Journal of Advanced Computational Intelligence, Vol. 20, No. 3. pp. 111-119, 1998 [7] J. K. Tar, K. Kozlowski, I. J. Rudas, L. Horváth. The Use of Truncated Joint Velocities and Simple Uniformized Procedures in an Adaptive Control of Mechanical Devices, In Proceedings of the First Workshop on Robot Motion and Control (ROMOCO’99), Kiekrz, Poland, pp. 129-134, 1999. [8] Jörg Vogel, Bernhard Brunner, Klaus Landzettel, Gerd Hirzinger. Operate a Robot over the Internet!, http://www.robotic.dlr.de/VRML/Rotex/index.html, 2000. [9] Ken Taylor, Barney Dalton. Issues in Internet Telerobotics, In Proceedings of the International Conference on Field and Service Robotics, Canberra, Australia, 1997.

About the Authors László Horváth received his Master’s degree in Engineering from the Technical University of Budapest. He received his Ph.D. degree in Applied Intelligent Computing from the Hungarian Academy of Science in 1993. His research focuses on Modeling of Design Intent, Development of Highly Integrated and Environment Adaptive Objects for Engineering Modeling and Robot Modeling for Product Model Based Application of Industrial Robots. He is active as the Vice Dean for research of John von Neumann Faculty of Informatics, Budapest Polytechnic and as a professor in intelligent engineering modeling. He is a Senior Member of IEEE. Imre J. Rudas received his Master’s Degree in Mathematics from the Eötvös Loránd University, Budapest while the Ph.D. in Robotics from the Hungarian Academy of Sciences in 1987. His present areas of research activity are: Robot Control, Soft Computing, Computed Aided Process Planning, Fuzzy Control and Fuzzy Sets. He is active as the Vice President of Budapest Polytechnic and as a professor and Head of Department of Mathematical and Computational Sciences. He is a Fellow of IEEE, Administrative Committee member of the industrial Electronics Society, member of the International Board of the Robotics & Automation Society.

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Chapter 4 Data Mining and Learning Systems

Representing Directed and Weighted Graphs and Their Properties in a Relational Spatial Database Model. Ágnes B. Novák1, Zsolt Tuza2 1

Department of Mathematics and Computer Sciences Budapest Polytechnic, Budapest, Hungary [email protected] 2

Computer and Automation Institute Hungarian Academy of Sciences, Budapest, Hungary [email protected]

Abstract — The spatial database model described here is a slightly modified version of the PLA database [3]. In this paper we extend the PLA model for the purpose of representing directed and weighted graphs. In this new model, named PLAX, first we give the constraints for a PLAX database, representing an Eulerian directed graph. Then we modify the algorithm for Eulerian circuits and path already worked out in [6], using the original PLA model. This new algortihm for PLAX is illustrated by a worked-out example.

1 Introduction In this paper we continue the systematic investigation we worked out in [7], [5], [6] and [8]. The PLA-Model was introduced by the US Bureau of the Census for representing topological properties of geographic data (maps) [1]. The redundancy, the necessary relations for describing the topology of a spatial object, and the reconstruction of the original object in the PLA model are investigated in [5]. In [7] we concentrated on checking the connectivity and 2-connectivity of the graph. Constraints for bipartite graph and Eulerian circuits were given in [6]. The results are reformulated in new algorithms in [8]. The conceptual model of the PLA-Database is the relational model. The structure of it is reviewed in the next section. Also there we introduce a possible extension for storing directed and weighted graphs. In Section 3. integrity constraints are given for the PLAX database representing an Eulerian graph. We give also the modified algorithm for checking Eulerian circuit and path. Finally, we summarize the results and mention some open questions in the Conclusion.

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B. NOVÁK, TUZA

2 The spatial database model PLA and its extension, PLAX In this section we briefly review the PLA-Model. One can find a detailed explanation concerning the background of this and other spatial models in [3], [5] and [7]. The aim of this model is the representation of the topology of a „typical” map - or, equivalently, a plane graph together with its regions (faces) - in terms of relational databases. In the original context of the PLA-Model, the geometric entities are referred as kcells (k=0,1,2), naming the dimension k of the entity in question. Instead of these we shall refer to them simply by their original, geometric names. In order to unify terminology we shall use the terms point, line (for undirected, arc for directed) and area for a vertex, edge and face. 2.1 The PLA-Database In this section we give the scheme of the database. Here we omit the set of conditions, which restricts the type of graphs to the 2-connected planar graphs. There is a detailed discussion in [7]. Here we recall the necessary parts of the description of the PLA-Model. In this paper we allow any type of graphs. However, the model corresponds to the first four conditions in the sense that each condition determines a relation, so the scheme of the relational database is DB(R1, R2, R3, R4) where the schemes of the relations R1, R2, R3, R4 are as follows: (i) R1(LINE, FROM, TO) indicating the name, the „starting” point, and the „end” point of the line. The objects stored in the database are undirected, but in order to obtain a unique representation of the areas there is a need for some orientation. In the sequel, to avoid ambiguity, we suppose that the points are labelled with natural numbers, and the starting point of each line is always the vertex labelled with the smaller number. (ii) R2(LINE, LEFT, RIGHT), where the attributes correspond to the name of the line, the name of the area on left side and the name of the area on the right side of the line. The right and left sides are determined in accordance with the previous relation, that is, if the line e goes from point i to point j (i.e., i<j is assumed) and its bordering areas are x and y, as in Figure 1. below, then x is on the left and y is on the right side of the line e. x i

j

y

Figure 1: The left (x) and right (y) sides of an edge (iii) R3(AREA, POINT, LINE, LABEL), where the first attribute is the name of the area whose neighborhood is represented in this relation. It is assumed that every area is surrounded by an alternating cycle of lines and areas. So the second attribute means the name of the point, the third one is the name of the line on the border of the area (satisfying the condition given next), and the last attribute is the serial number with respect to the area named in the first attribute. The labels are consistent with the orientation, that is, the

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REPRESENTING DIRECTED AND WEIGHTED GRAPHS... enumeration of points and lines in the cycle corresponds to the clockwise orientation, except for the infinite area Af . We propose to assume that, in case of the infinite area, the orientation is counterclockwise when viewed from the interior of the area - that is, clockwise with respect to the region surrounded by the boundary cycle. (This convention is necessary for recognising Af, it applies in the plane but not on the sphere.) In each row of the relation, the point and the line are incident and the line is the successor of the point in the corresponding orientation. (iv) R4(POINT, LINE, AREA, LABEL), where POINT means the name of the point whose neighborhood is stored in the relation, LINE is the name of the line, AREA is the name of the area in the neighborhood, and LABEL is a serial number. Similarly to the previous paragraph, the orientation is clockwise (but now for all points, without any exception), and of course the line is on the boundary of the area. Let us emphasize that, for describing spherical objects, the only difference is that the “infinite area” is not distinguished, i.e., the boundary of each area is listed clockwise when viewed from the interior of the area. 2.2 The Extended PLA-Database, PLAX We want to modify the PLA-Model in a way that also directed and weighted graphs can be stored in the model easily. Our idea on simple, directed and (edge) weighted graphs does not differ from the standard scientific and informal meaning. That is, in a directed graph each edge has an orientation, namely each has its head and tail. A weighted graph is one having directed or undirected edges with labels, these labels are the weights. In our research we restrict our investigation only to non-negative weights, which restriction leads to an appropriate model, hugging together directed and weighted graphs. In this model weighted graphs also are seen as directed graphs. An example for the practical use of this type of graph is a traffic network where the roads are oriented either in both direction or only in one way. The capacities of the roads may also be different, and can be modelled by weights. For our general purpose, which is; to represent graphs in a regular way in the extended PLA-Model, we give the formal definition of graphs. Formally, by a graph we mean an ordered quartet @ 7KH PDLQVWUHDP GDWD PLQLQJ WHFKQLTXHV DWWHPSW WR ILQG DQG GHVFULEH VWUXFWXUDO SDW WHUQVLQGDWD7ZREDVLFDOO\GLIIHUHQWVW\OHVDUHSUHYDOHQW>@,QFODVVLILFDWLRQOHDUQLQJ V\VWHP OHDUQV WR FODVVLI\ XQVHHQ H[DPSOHV E\ DQDO\VLQJ VHW RI DOUHDG\ FODVVLILHG H[DPSOHV,QDVVRFLDWLRQOHDUQLQJDQ\DVVRFLDWLRQVEHWZHHQGDWDSURSHUWLHVDUHVRXJKW %RWK DSSURDFKHV DUH LWHUDWLYH ± GLIIHUHQW PRGHOV DUH UHSHDWHGO\ EXLOW DQG HYDOXDWHG LQ RUGHU WR REWDLQ FUHGLWDEOH UHVXOWV 7KH SDSHU GHSLFWV DQ LQWHJUDWHG GDWD FODVVLILFDWLRQ 199

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Business Rules Modeling by Means of F-logic, UML and Ontologies (problems and possible solutions) Mirko ýubrilo1, Mirko Malekoviü1 1

Faculty of Organization and Informatics Zagreb University, Zagreb, Croatia {mcubrilo,mmalekov}@foi.hr

Abstract — The application framework, supporting the modern way of doing business, especially e–business, increasingly adopts the formal tools and techniques developed in symbolic logic framework. One of the most recent examples are agent theories and tools, used as computational models of economies, modeled as evolving systems of autonomous interacting agents (Tesfatsion, [12]), sometimes accompanied with the simulating software, such as Trade Network Game Laboratory (McFadzean and all, [8]). An appropriate formalization, however, does not yet exist in the domain of "classical" business rules. In this paper we shall analyze the questions and problems concernig the proper formalization of the R. G. Ross's business rule system and argue that the F-logic system of Kifer and all ([4]), as implemented through Flora-2 system ([13]), being a part of the XSB Prolog development environment (including the second order logic programming language HiLog), could serve as such symbolic logic framework.

1 Introduction Business rules are the backbone of business transactions between enterprises. Because of the great organizational disparity, law legislature and the ways of doing business, business rules are very difficult to formalize appropriately. The first, up to a considerably high level consistent catalogization (or systematization, but not a formalization!) of the business rules was developed by R. G. Ross in [10]. His ideas were incorporated through the implementation of the so-called business rules handling systems (such as the Rule Track). Despite of that, such catalogization of business rules system missed an appropriate formalization in the sense of a logic system. R. G. Ross, being aware of that problem, attracted some very famous scientists from the data bases theory domain to it, as a result of which they tried to formalize the business rules systems with the aid of the relational database theory and some rudiments of constraints handling theory, but without considerable success. The main goal of this paper is to analyze difficulties on the way towards appropriate business rules formalization and to suggest the proper theoretical and programming tools for the solution to that problem. There are two aspects which have to be unified here. On one side, the business subjects, systems and transactions (incorporating

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ýUBRILO, MALEKOVIû business rules), are objects in a sense of object-oriented programming paradigm. On the other side, the business rules also display some features of logic calculi (consistency, completeness, soundness, context dependency, nonmonotonicity, etc.). Having all this in mind, and for reasons we shall explain later in this paper, we see F-Logic of Kifer and all ([4]) as the appropriate framework, capable of formalizing business rule systems. F-logic also represents the logic calculus, which combines the advantages of deductive databases with rich modeling capabilities (objects, methods, class hierarchy, nonmonotonic inheritance, signatures) of the object-oriented data model.

2 R. G. ROSS's business rules system In his book ([8]), R. G. Ross explained one rather complete catalogization of the business rules. He started with the question "What are rules?" ([10], p. 11). We quote his answer (ibid.): A rule may be defined as a constraint or a test exercised for the purpose of maintaining integrity (i.e., correctness) of data. The purpose of a rule generally is to control the updating of persistent (i.e., stored) data – in other words, the results that the execution of actions (processes) are permited to leave behind. Such control reflects desired patterns for business behavior. A rule thus embodies a formal, implementable expression of some "user requirement", usually stated in textual form using a natural language (e. g., English). This textual form is called a business rule statement. Two paragraphs later Ross says: Unfortunately, business rule statements often are ambiguos, and cannot be translated directly into an actual implementation, (i.e., into running code). The task of the rule analyst thus is to translate business rule statements into formal, precise (and implementable) rules. R. G. Ross's approach to the business rules handling is really precise, a bit less formal, but hardly directly implementable. It gives natural and sound catalogization of business rules and that represents its most valuable feature. In his method of cataloguing business rules R. G. Ross has used a kind of graphical language. On the following two pictures we can see a few of its most elementary building elements. On the picture corresponding to the Rule 14 ([10], p. 21) we can see the integrity constraint on some data. Rule 14 has an anchor, the source data type (but it could be another rule too), providing the point of reference for interpretation of the rule (here it is a customer data type) and the rule correspondent, the "target" of the rule. Rule correspondent may also be another rule. What differs rule 15 from rule 14 is symbol p instead of r. The first one always yields the value true (or undefined) (every instance of the customer anchor must have an address). The second presents a test (does the given instance of the customer anchor have an address?).

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BUSINESS RULES MODELING IN F-LOGIC, UML AND ONTOLOGIES

A customer must have an address

Figure 1: Rule 14 – integrity constraint ([10], p. 21)

If a customer has an address, then…

Figure 2: Rule 15 – test, ([10], p. 21) Business rules in Ross's catalogization are divided in seven atomic types. These are: − − − − − − −

Instance verifiers Type verifiers Position verifiers Functional verifiers Comparative evaluators Mathematical evaluators Projection controllers

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ýUBRILO, MALEKOVIû The core idea here is that the rules of each given type compute something. For example, the rules of the subtype FLUCTUATING of the rule type FUNCTIONAL VERIFIERS (type IV in Ross's classification) check if all instances of a type are different from one to the next. Each business rule class consists of many rule subtypes. On the following two pictures we can see one sample rule of the Type verifiers and Comparative evaluators types. The last rule yields a sample rule of the MUTUALLY-INCLUSIVE (MI) rule subtype, which prescribes a test to determine whether one or more correspondent types are true. In addition to seven atomic business rule classes, Ross's catalogization knows of twelve derivative rule types. They are simply composite rule types, but not from anywhere, so that they are worth of additional catalogization. For example, subtype F consists of derivatives for testing recursion in composition structures.

A team must have either a manager or a budget (or both) at all times.

Figure 3: Rule 224 – Type verifiers type, ([10], p. 96)

An employee must not manage himself, even indirectly.

Figure 4: Rule 653 – Comparative evaluators type, ([10], p. 163)

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BUSINESS RULES MODELING IN F-LOGIC, UML AND ONTOLOGIES It is irrefutable that R. Ross's business rule catalogization possesses many good features, like the following ones: − Catalogization parameters are reasonably natural, combining some object-oriented and logic features of its constituents (primarily data types, their values and some simple constraints on values). − The whole catalogization possesses a high level of granularity, resulting in the possibility of precise and detailed decomposition of every (we don't know of any counterexample!) business rule statement. But, from the theoretical, and partly implementational point of view, Ross's business rule catalogization has some disadvantages, such as: − Nonexistence of a unique (minimal) canonical structure for every business rule type and its subtypes (insufficient level of uniformity in rule abstraction) − A lack of an explicitly stated inheritance mechanism between business rule types and their subtypes − Nonexistence of the business rule equivalence checking mechanism, or on a higher level, nonexistence of the business rule deduction mechanism (perhaps the composition of several complex rules could be reduced to one simple rule), or on the highest level, the nonexistence of the mechanism for reasoning about the business rules. In the rest of the paper we consider the mentioned disadvantages in the light of F-logic and point out the possible solutions in that framework. The explanation of F-Logic is given according to [3], and its implementation of Flora-2 according to [13]. For the full explanation of F-logic the reader is referred to [4]. We shall also mention another, very good implementation of F-Logic, namely the FLORID system ( [6] and [7]).

3 F-logic and its implementations 3.1 F-logic syntax The alphabet of an F-Logic language consists of a set of object constructors, playing the role of function symbols, a set of variables, several auxiliary symbols like ), (, j, J, 1, S,l,L, :, :: and the usual first-order logic connectives 5, 6 and 7. For convention, object constructors start with lowercase letters whereas variables start with uppercase letters. Object constructors play the role of F-logic function symbols. Each function symbol has an arity-a nonnegative integer that determines the number of arguments this symbol can take. Symbols of arity 0 are also called constants; symbols of arity > 1 are used to construct larger terms out of simpler ones. An id-term is a usual first-order term composed of function symbols and variables, as in first order predicate calculus. The set

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ýUBRILO, MALEKOVIû of all ground (i.e., variable-free) id-terms is commonly known as F-logic Herbrand Universe.. Conceptually, ground id-terms play the role of logical object identifiers – which are the logical abstraction of the implementational concept of physical object identity. They serve as names of objects, classes and methods. In the sequel, let o, c, c1, c2, m, p1, . . . , pn and r be id-terms for n > 0. − An is-a atom is an expression of the form o:c (o is a member of class c) or c1 :: c2 ( c1 is a subclass of c2). The following expressions are data atoms: − jo(m@( p1, . . . , pn) 1 rJ: applying the scalar method m with parameters p1, . . . , pn to o - as an object - results in r, − jo(m@( p1, . . . , pn ) S rJ: o - as a class - provides the inheritable scalar method m to its members, which, if called with parameters p1, . . . , pn, results in r, − jo(m@( p1, . . . , pn ) l rJ and jo(m@( p1, . . . , pn ) L rJ as 1 and S above for a multivalued method m. − An eq-atom is an expression of the form p1 = p2 with the meaning that p1 and p2 denote the same object. − A rule h :- b1, . . . , bk, with k ≥ 1, is a logic rule over atoms h, b1, . . . , bk. A fact is a formula h. for an atom h. − A query is a formula ?- b1, . . . , bk. for atoms b1, . . . , bk, k ≥ 1. − A program is just a set of facts and rules (like in Prolog). Many sample F-logic programs one can find in [3], [4], [5], [6] and [13]. 3.2 F-logic semantics According to the well known result of J. Herbrand, questioning the logical consequences of the given set of first order sentences can be reduced to questioning Herbrand interpretations on Herbrand Universe of that set of sentences. Therefore, in considering semantics of F-logic one can restrict herself/himself to Herbrand interpretations, where the universe consists of all ground id-terms. An H-structure is a set of ground atoms describing an object world, which means that it has to satisfy several closure axioms, related to general object-oriented properties. Let H be a (possibly infinite) set of ground atoms. Then H is an H-structure if the following conditions hold for arbitrary ground id-terms u, uo,. . . , un, ur, ur', and um:

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BUSINESS RULES MODELING IN F-LOGIC, UML AND ONTOLOGIES − u :: u ∈H (subclass reflexivity), − If u1 :: u2 ∈H and u2 :: u3 ∈H then u1 :: u3∈H (subclass transitivity), − If u1 :: u2 ∈H and u2 :: u1 ∈H then u1= u2 ∈H (subclass acyclicity), − If u1 : u2 ∈H and u2 :: u3 ∈H then u1 : u3∈H (instance-subclass dependency), − If [uo(um@(u1, ..., un„)1ur]∈H and [uo(um@(u1, ..., un)1ur']∈H, then ur = ur'∈H. The same holds for S (uniqueness of scalar methods). On the ground of F-logic H-structure, the meaning of atoms and formulas is given in the usual way. Furthermore, the well known free equality axioms for = have to hold. In reasoning about knowledge in general, and in reasoning about the business rules in particular, one cannot avoid the problem of handling inheritance. The axioms above describe the so called structural inheritance (inheritance in the context of classes, subclasses and their elements). But F-logic knows of another kind of inheritance, the so called behavioral inheritance. The problem with behavioral inheritance is that it is non-monotonic, meaning that adding new facts might obviate previously established inference. Behavioral inheritance in F-logic is discussed at length in [4]. One shorter, but very interesting explanation could be found in [3]. In general, behavioral inheritance is handled through some kind of trigger semantic, which itself is implemented through socalled inheritance-canonic models [4]. The idea is to derive a minimal model of a program (as an intersection of all of its models) first, without considering inheritance at all, and then to decompose each inheritance step into a pair of steps: 1) a "pure" inheritance step, which may introduce new facts but whose output may no longer be a model of the program; and 2) a new fixpoint derivation (as a model of F-logic program) which extends the result of the previous step to a model. These operations are repeated until no more inheritance can be done. As already mentioned, a detailed explanation, including some interesting nontrivial examples, could be found in [4]. In a very recent time, Guizhen Yang, in his dissertation [14] completely solved multiple value and code inheritance problem in object-oriented knowledge bases, the Ross's business rules system shurely is a kind of. 3.3 F-logic as a programming language There are two main implementations of F-logic, the Flora-2 system ([13]) and FLORID ([7]). Flora-2 is a part of the XSB Prolog system ([11]), now in version 2.5, which also includes the higher order logic programming language HiLog. Moreover, the Flora-2 system uses the HiLog syntax as its default syntax. The whole XSB system is still in a developing process. On the Windows platform the XSB Prolog could be compiled as a DLL library and connected with other programming languages and development environments, such as that of Visual Basic, which has very good means of implementing R. G. Ross's business rule graphical language. FLORID is another very good implementation of F-logic, constantly competing on a friendly basis of exchanging ideas and programming solutions, etc. with Flora-2 (earlier it was just Flora). The FLORID system is primarily designed for UNIX operating system.

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ýUBRILO, MALEKOVIû Here you can see the sample program in F-Logic, coming from the official Flora-2 distribution and consisting of main F-Logic program constructs and modeling persons from German TV serial The Fallers and their relationships. Here we cannot comment the program in detail. /* File: family_obj.flp ** Author(s): Bertram Ludaescher ** Contact: [email protected] ** ** Copyright (C) Bertram Ludaescher, 1998 %%%=================================================================== %%% QUERYING THE PEDIGREE OF ``THE FALLERS'' %%% (German TV serial; see: www.swf.de/diefallers/stammbaum/index.html) %%% An OBJECT-ORIENTED version of family_rel.flp %%%=================================================================== %%%=================================================================== %%% SCHEMA DATA: CLASSES & SIGNATURES %%%=================================================================== male :: person. % subclass relation female :: person. % subclass relation person[ mother=>person; father=>person; spouse=>person; husband=>person; son=>>person; daughter=>>person; brother=>>person; sister=>>person; uncle=>>person; aunt=>>person; ancestor=>>person; parent=>>person].

% some SINGLE-valued... % ... methods % some MULTI-valued... % ... methods...

%%%=================================================================== %%% INSTANCE DATA (aka EDB/BASE FACTS) %%% (partially) define mother, father, spouse, (fe)male info %%%=================================================================== wilhelm:male[spouse->rita]. rita:female. franz:male[mother->rita;father->wilhelm]. heinz:male[mother->rita;father->wilhelm]. hermann:male[mother->rita;father->wilhelm;spouse->johanna]. johanna:female. monique:female. bernhard:male[mother->johanna;father->hermann]. karl:male[mother->johanna;father->hermann;spouse->christina]. christina:female. kati:female[mother->johanna;father->hermann]. albert:male[mother->monique;father->bernhard]. eva:female[mother->kati]. %%%=================================================================== %%% RULES (aka IDB/DERIVED RELATIONS) %%%=================================================================== X[spouse->Y] :- Y[spouse->X]. % spouse is symmetric!

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BUSINESS RULES MODELING IN F-LOGIC, UML AND ONTOLOGIES X[parent->>{Y}] :- X[father->Y]. X[parent->>{Y}] :- X[mother->Y]. X[son->>{Y}] :- Y[parent->>{X}], Y:male. X[daughter->>{Y}] :- Y[parent->>{X}], Y:female. X[brother->>{Y}] :- X..parent[son->>{Y}], not X=Y. X[sister->>{Y}] :- X..parent[daughter->>{Y}], not X=Y. X[brother_in_law->>{Y}] :- X..sister[spouse->Y]. X[brother_in_law->>{Y}] :- X.spouse[brother->>{Y}]. X[sister_in_law->>{Y}] :- X..brother[spouse->Y]. X[sister_in_law->>{Y}] :- X.spouse[sister->>{Y}]. X[uncle->>{Y}] X[uncle->>{Y}] X[aunt->>{Y}] X[aunt->>{Y}]

::::-

X..parent[brother->>{Y}]. X..parent[brother_in_law->>{Y}]. X..parent[sister->>{Y}]. X..parent[sister_in_law->>{Y}].

X[ancestor->>{Y}] :- X[parent->>{Y}]. X[ancestor->>{Y}] :- X..ancestor[ancestor->>{Y}]. X:illegitimate :- X[father->F; mother->M], M[spouse -> S], S\=F. %%%=================================================================== %%% QUERIES %%%=================================================================== ?- albert:C. ?- albert[M->X]. ?- albert[M->>{X}]. ?- _.S[]. ?- _..M[]. ?- _:C[].

% which classes... % ... and methods... % ... are known for Albert?

% show SINGLE-valued and... % ... MULTI-valued methods... % ... and classes

?- albert..parent..uncle[sister_in_law ->> {Y}]. % a path expression ?- X[sister_in_law->>{Y}].

4 Business Rules Modeling in F-Logic After the relatively simplified descriptions of the R.G.Ross business rule system and F-logic have been presented, we may state the main question here: What can F-logic offer to the modeling of business rules? Modeling the individual business rules in F-logic is a rather simple task. Here we formalize (already mentioned) Rule 224 in a Flora-2 notation: team:teams. % object team is an element of the class teams manager:managers. % object manager is an element of the class managers team[mustHave -> manager]. team[mustHave -> budget].

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ýUBRILO, MALEKOVIû But, modeling the individual business rules by far is not a main point here. It is a necessary, but by no means a sufficient task to do. The main point is reasoning about business rules. Here we propose an answer to the question stated above in a form of a scenario for the systematical analysis of the Ross’s business rule system and its reduction into canonic form using the means of F-logic and its respective programming tools. After that we discuss some existing software which can be used for rapid development of such a system. The proposed scenario consists of the following steps: STEP 0 (visual, object-oriented implementation of the module for the purpose of designing, editing and manipulating Ross's business rules). Although STEP 0 is not a necessity, it could be very useful. It would consist of implementing a graphical language for the purpose of designing, editing and manipulating Ross's business rules in one of the "visual" programming languages (environments), such as Microsoft Visual C++, Microsoft Visual Basic, Borland Delphi, PDC Visual Prolog,...). All these languages support object oriented programming (using a paradigm of objects, events and object's reactions to the events), so that they could, without any doubt, serve well for the purpose of modeling every aspect of Ross's business rules. STEP 1 (modeling the busines rules in Flora -2) Supposing the STEP 0 is realized successfully, a module should be developed (in XSB Prolog), which shall call Flora-2 and transform the visual (graphical) implementation of a single business rule into its Flora-2 implementation. In the case of Step 0 being skipped, it would be necessary to execute Step 1 directly. STEP 2 (developing the programming environment for reasoning about business rules) In the programming environment of XSB Prolog, HiLog and Flora-2, the modules serving the following purposes should be developed: − Composition and decomposition of complex rules − Business rules equivalence check − Reasoning on business rules The final goal of the realization of the proposed scenario, which is a subject of further research and development, would be a generative grammar of business rules, implemented using the means and the tools of F-logic. A possibility of its complete realization is, however, in a certain measure disputable. What can be achieved beyond any doubt, is a reconstruction of the extant Ross business rule type and subtype classification, which could potentially result in a reformulation of the present structure of Ross business rule system. The proposed scenario gives us some general plan for implementing the system almost from scratch. The question is what of existing (commercial or academic) software someone

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BUSINESS RULES MODELING IN F-LOGIC, UML AND ONTOLOGIES could use to accelerate the development of the system. Generally speaking, we see the two main possibilities for that. The first one is to use some implementation of the UML (Unified Modeling Language), such as Visual UML, or Rational Rose, or any other UML modeling software, for the purpose of mapping the Ross’s business rules model into the UML model. The newest specification of the UML modeling language (version 1.5 of March 2003, as presented in [2]), gives us a complete set of tools for modeling the Ross's business rules (and much more). For example, the stereotype construct from UML could immediately model (at static level) the anchor type as a construct from the domain of Ross’s business rules. Further, the Object Constraint Language as a part of the UML specification, can be used for a number of different purposes, such as: − to specify invariants on classes and types in the class model − to describe pre- and post conditions on operations and methods − to specify constraints on operations which, beyond the shadow of doubt, should be more than enough for formal specification of behavioral aspects of Ross’s business rules. An executable LL(1) version of this grammar is available on the OCL web site. (See http://www.software.ibm.com/ad/ocl) and could easily be implemented as F-Logic (Flora, FLORID) program. The benefits of using the F-Logic formalism in tandem with UML should reflect itself in the possibility of reasoning about the Ross’s business rules, stating queries about theirs properties, methods, structural components, etc.). Second possibility, which does not express such a rich set of modeling capabilities, but would satisfy all the modeling needs, consists of using some kind of ontology modeling software, such as Protege-2000 (http://protege.stanford.edu/index.shtml).

Figure 5: Protege-2000 Window

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ýUBRILO, MALEKOVIû Ontology is a model of a particular field of knowledge - the concepts and their attributes, as well as the relationships between the concepts. In Protégé-2000 ([9]), an ontology is represented as a set of classes with their associated slots. Besides classes, the other building elements of an ontology are slots, forms, instances and queries. Slots represent class attributes, while instances model the real data. In general, ontologies are capable of modeling the static aspect of business rules (anchors, constraints, etc.) but are pretty short in doing deduction for the purpose of reasoning about them. For that purpose Protege is strengthen with a plug-in, called Flora tab, which implements the fragment of F-logic, used for reasoning needs of Protege itself. In that environment Protege knowledge base can be exported as F-Logic program (including axioms), queries can be executed in an XSB/Flora “sub-process”, list of answers to queries are shown in Protégé (if answers are instances). Further, F-Logic tab can also be used to model constraints (queries must/must not fail if knowledge base is consistent/inconsistent) and views can be defined in a pretty powerful way.

Acknowledgments We would like to thank our reviewer for many valuable suggestions.

References [1] M. ýubrilo. Formalization of the Business Rules Systems, scientific project proposal to Ministry of Science and Technology Republic of Croatia, October, 2001. [2] G. Booch, I. Jacobson, J. Rumbaugh: OMG Unified Modeling Language Specification, http://www.omg.org/cgi-bin/apps/doc?formal/03 -03-01.pdf). [3] P. T. Kandzia. Nonmonotonic Reasoning in Florid, 4th International Workshop on Logic Programming and Nonmonotonic Reasonong (LPNMR'97), July 1997, Dagstuhl Castle, Germany. [4] M. Kifer, G. Lausen and J. Wu. Logical Foundations of Object-Oriented and Frame Languages, Journal of the ACM, 42(4):741-843, July, 1995. [5] W. May, P.T. Kandzia. Nonmonotonic Inheritance in Object-Oriented Deductive Database Languages, Technical Report 1843-1998., Technical University Vienna. [6] W. May. FLORID, How to Write F-logic Programs in Florid. A Tutorial for the Database Language F-Logic, Version 3.0 (FLOXML), Institut fur Informatik, Universitat Freiburg, Germany, October, 2000. [7] W. May, W. FLORID, User Manual, Version 3.0 Informatik, Universitat Freiburg, Germany, October, 2000.

(FLOXML), Institut fur

[8] D. McFadzean, D. Stewart and L. Tefatsion. A Computational Laboratory for Evolutionary Trade Networks", IEEE Transactions on Evolutionary Computation, vol. XX, 2001. [9] N. F. Noy, R. W. Fergerson and M. A. Musen. The knowledge model of Protege2000: Combining interoperability and flexibility. 2th International Conference on

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BUSINESS RULES MODELING IN F-LOGIC, UML AND ONTOLOGIES Knowledge Engineering and Knowledge Management (EKAW'2000), Juan-les-Pins, France, 2000. [10] R. G. Ross. The Business Rules Book: Classyfying, Defining and Modeling Rules, second edition, Database Research Group, Inc., Boston, Massachusetts, 1996. [11] K. Sagonas and all. The XSB System, Version 2.5, Volume 1: Programmer's Manual. [12] L. Tesfatsion. Agent-Based Computational Economies: Growing Economies from the Bottom Up, Iowa State University Economics Working Paper No. 1., March 2002. [13] G. Yang and M. Kifer. Flora-2: User's Manual, Department of Computer Science, State University of New York at Stony brook, 2001. [14] G. Yang. A Model Theory for Nonmonotonic Multiple Value and Code Inheritance in Object-Oriented Knowledge Bases, Ph. D. Thesis, State University of New York at Stoni Brook, 2002.

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Document Clustering Using Concept Set Representation László Kovács1, Péter Baranyi 2 1

Department of Information Technology, University of Miskolc, Miskolc, Hungary [email protected]

2

Dep. of Telecommunication and Telematics, Budapest University of Technology and Economics, Budapest, Hungary baranyi@ ttt-202.ttt.bme.hu

Abstract — There is in our days an increasing interest on application of concept lattices for data mining, for representation of the concept hierarchy generated from the underlying data set. The paper presents a document query system that clusters the documents into groups using a generated concept lattice. To reduce the computational costs, the word set is reduced using frequency filtering and clustering. The concepts are calculated from the reduced word set. The users can use the reduced concept lattice to perform queries with relevance feedback. The users start the query by entering a set of keywords. The system returns the concepts closest to the query vector. The users get a list of neighboring concepts too, thus they can select the way to navigate to reach the result document set.

1 Introduction Concept lattices are used in many application areas to represent conceptual hierarchies stored in a hidden form in the underlying data. The field of Formal Concept Analysis [1] introduced in the early 80ies has grown to a powerful theory for data analysis, information retrieval and knowledge discovery. There is nowdays an increasing interest on application of concept lattice for data mining especially for generating association rules [8]. One of the main characteristics of this application area is the large amount of structured data to be analyzed. Beside this area another important application field is the program analysis inside a compiler using concept lattices of very large size. A technical oriented application field of Formal Concept Analysis is the area of production planning where the concept lattices are used to partition the products into disjoint groups yielding an optimal processing cost [6]. As the cost of building concept lattice is a super-linear function of the corresponding context size, the efficient computing of concept lattices is a very important issue investigated for long years [5]. In the information systems, the data can be stored in structured databases, in semistructured documents or in some kind of un-structured text documents. Although, the storage in databases provides a very secure and flexible way, it requires additional costs including hardware, software and organizational costs. Due to these extra costs, most of the information is stored in non-structured or in semi-structured data sources. 225

KOVACS, BARANYI The importance of this kind of data storage is unbroken increasing. The data management and the query of the non-structured documents means a large challenge to develop new efficient, human oriented methods. The most important purpose of the document or text database is to provide an efficient and flexible query system for the non-technical users. The query operation usually includes some kinds of filtering or selection. The query systems based on relevance feedback, start the query process using a list of initial keywords. Next, the system returns the documents close enough to the keyword set. The users give feedback with the relevance value for each resulted document. Based on the feedback, the system alters the query condition and performs a new query phase. The new result set is presented to the user who can make a new refinement feedback to improve the accuracy of the query. One of the key problems of this approach is that the result set can be very large, and so requires a large amount of work from the users too. Considering these problems, it seems reasonable to offer a more flexible query interface for document processing. The new method can perform the grouping of documents automatically, and provides a flexible way for the users to refine their query conditions and the users should not process a large amount of document sets during the navigation steps. In our approach, the concept lattice provides a tool to perform an automatic clustering. The users can navigate among the document sets traversing along the edges of the concept lattice. The users can select based on the neighboring concepts which way to proceed next. The proposed method is independent from the actual problem area. The paper presents first the basic notations of Formal Concept Analysis and then the most known methods proposed in the literature so far will be introduced. The next chapters introduce the algorithms for generating the concept sets and for building the concept lattice including some optimization methods for better efficiency. The paper contains the detailed description for the query algorithm with comments on the efficiency considerations.

2 Formal Concept Analysis This section gives only a brief overview of the main basic notations of theory for Formal Concept Analysis. For a more detailed description, we refer to [1]. A K context is a triple K(G,M,I) where G and M are sets and I is a relation between G and M. The G is called as set of objects and M is the set of attributes. The cross table T of a context K(G,M,I) is a matrix form description of the I relation: tij = 1 , if giIaj and (1) 0 otherwise where gi  G, aj  M. For every A Ž G is defined a derivation operator: (2) A' = { a  M | g I a for  g A } and for every B Ž M (3) B' = { g  G | g I a for  a B } The pair C(A,B) is a concept of the K context if (4) - A Ž G, B Ž M, - A' = B, B' = A hold. In this case, the A is called as the extent and B is the intent of the C concept. Considering the ) set of all concepts for the K context, an ordering relation can be introduced for the concept set on the following way:

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DOCUMENT CLUSTERING USING CONCEPT SET REPRESENTATION C1 d C2

(5)

if A 1 Ž A2 where C1 and C2 are arbitrary concepts. It can be shown that for every (C1,C2) pairs of concepts, the following rules hold: (6) C 1 š C2  ) C1 › C2  ). Based on this properties, the (), d) is a lattice, called as concept lattice. According to the Basic Theorem of concept lattices, the (), d) is a complete lattice, i.e., the infinum and suprenum exist for every set of concepts. The following rules hold for every concept: (7) ›i (Ai, Bi) = (ˆiAi,(‰iBi)'') ši (Ai, Bi) = ((‰iAi) '',ˆiBi) where A'' denotes the closure of the set A and it is defined as derivation of the derivated set: A'' = (A')' (8) The structure of concept lattice can be used not only to describe the concepts hidden in the underlying data system, but it shows the generalisation relation among the objects and it can be used for clustering purposes too. A good description on the related chapters of the lattice theory can be found among others in the [1].

3 Algorithms for Generating the Concept Set and Concept Lattice As for every concept, the extend part is determined unambiguously by the intent part, we will investigate the generation of the intent parts only. In most data mining applications, the intent parts are enough to generate the rules. The rules define a relation, an implication among the attributes, i.e. on the intent part. The actual support set for the rules are usually not important. Among the sophisticated concept set generation algorithms is the Ganter's next closure algorithm [1] probably the most widely known method. It is widely accepted by the experts, that this algorithm is not only the best known but the most effective one, too [4]. The concepts are generated according to an ordering relation. This method calculates the extent part first; the intent part is generated from the intent part. The key function element, the next extent routine, tests several extent variants until it finds an appropriate one. The total asymptotic cost of the algorithm is equal to O(CN2o + CN2M) (9) where C is the number of concepts in the concept set. Considering our objectives, we may have some concerns regarding the efficiency of this algorithm: 1. The disk IO cost may be very high if N is high 2. The total cost is proportional with N2, so it will be resulted in high cost for contexts of large number of objects, as it is assumed in our investigation. A different kind of approach is presented by Godin[2]. His proposal is an incremental concept formation method, where the concept set is updated in incremental manner, i.e. the set is updated when the context table is extended by a new object instance. In this kind of methods, every context table element is accessed only once, yielding a minimal IO cost. The building the concept set in incremental mode is based on the following rule: Every new concept intent after inserting a new 227

KOVACS, BARANYI object into the context, will be the result of intersecting the new objects' attribute set with some intent set already present in the concept set. The Godin's method can be used for updating the concept set after insertion a new object into the context. The algorithm consists of the following main steps. First, the concepts are partitioned into buckets based on the cardinality. Next, the buckets are processed in ascending cardinality order. All the intents in the current bucket are intersected with the intent set of the new object. If the result set is not present in the concept set, it will be added. The cost estimation for the algorithm can be given by O(No + CNDM) (10) This formula assumes a linear existence testing. The linear testing was implemented in the algorithm as the testing can be reduced to the subset of so-called marked elements. The marking test can be performed only in linear mode. In the cost estimation formula the D denotes the number of element with mark. The mark is assigned to the elements generated in the current phase. Comparing this cost function with the cost estimation of the next closure method, we can see, that incremental method will be more efficient if 1. The o cost unit is high 2. or N is high. On the other hand, the cost of Godin's method is more sensitive to the C size of the concept set. In our proposal, the concept set generation phase is based on an optimized incremental method presented in [10]. To implement the cost reduction elements into the concept set building algorithm, the following modifications of the basic incremental method were developed: 1. Before the testing loop for the new incoming object, it is tested whether is equal with an already existing intent part. The test for existence checking is performed using a B-tree structure, resulting in a test cost of O(log(C)) 2. Before the intersects of the elements would be inserted into the concept set, the candidate elements (the results of the intersections) are stored in a hash table, so the sets generated repeatedly can be detected in a cost effective way. 3. To reduce the redundant intersection tests, the elements of the concept set are stored in a special pointer list where the elements containing a given attribute value are connected to each other. The intersection operation should be performed only for elements having at least one common attribute. Thus the intersection test for disjoint elements can be eliminated. 4. To eliminate the insertion testing for intents already present in the concept set, during the intersection phase, a special marker is used in the hash table. In most of the cases, the existence can be detected in the hash table-building phase, before the insertion phase. The total cost of the new algorithm can be given by O(No + NmlogC + N'MlogC + N’C''MlogC) (11) One of the benefits of this algorithm is that it can reduce the computation cost if the new object has an attribute set contained in the context yet. A brief comparison of the new method with the basic methods is given in Table 1. In the concept lattice, the neighbor concepts are connected to each other by an edge. The main task of the concept lattice-building phase is to determine the neighboring concepts. An L  ) is a lower neighbor of C if 228

DOCUMENT CLUSTERING USING CONCEPT SET REPRESENTATION (12) L < C and ™ X  ) : L < X < C The upper neighbor can be defined on the similar way. In a lattice an element may have several upper and lower neighbor elements. We denote the set of lower (upper) neighbors for C by Low(C) and Upp(C). For building the lattice the Low(C) and Upp(C) must be known for every C. Method Elapsed time Size of concept set naive 245 3865 Ganter 14 Godin 6 proposed 3 naive 796 37344 Ganter 170 Godin 83 proposed 42 Table 1: Comparison of lattice building methods In the literature, we can find several approaches addressing this problem. We will describe here only the most recent ones. The proposal of Ky Hu [3] was published in 1999. The first phase of this method is based on the Godin's incremental lattice generation method. The algorithm generates the concepts in increasing cardinality order of the intent part. According to this principle, the parents are generated first, and only after that the children. The lower neighbors will be determined during the insertion of the children elements. The cost estimation of the algorithm can be given by O(CCnCaM) (13) where Ca is number of ancestor nodes and Cn is the number of neighbor nodes Another current approach is the algorithm of Lindig presented in [4]. The proposed concept set and lattice-building algorithm is related to the Ganter's method in many aspects. The concepts from the concept set are processed in total order to make sure all concepts that are inserted into the lattice are also considered for their neighbors. The lexical order used in Ganter's method is an appropriate ordering. Due to this processing order only the upper neighbor set is needed to build here too. The test for upper neighbor is based on extending the extent part with a new element and performing a closure operation. The cost estimation for this algorithm can be given by O(CN2M) (14) i.e. it has the same asymptotic cost value as the next closure method has. In our tests, we implemented an optimized concept lattice-building algorithm that is described in detail in [9]. This algorithm is strongly related to the Godin’s incremental concept set generation method. The key element of the optimization is that in a search processes for upper or lower neighbor elements, the cost of lattice traversing depends on the number of nodes to be processed and not on the number of ancestors or descendants. The number of tested nodes is more than the number of ancestors or descendants as there are a large number of nodes with negative test results. These nodes are located on the border of the ancestor or descendants sub-lattice. According to our test results, the cost to process these border elements can be very high and it depends dominantly on the position and insertion ordering of the X nodes. The aim of our investigation was to find an optimal order of concept insertion yielding a low computational cost.

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4 Overview of Existing Approaches in Document Categorization Traditionally, the document categorization tasks are performed manually. The main limitations of this approach are the cost and efficiency. To cope with a larger number of documents, some automatic categorization methods are applied. If the available classes are known, the categorization can be regarded as a classification process. If no classes are known in advance, the groups are determined during the categorization process. This process is called clustering. The document categorization can be performed from different viewpoints regarding from the volume and type of information included into the categorization process. The following levels can be defined: - statistical - semantical - ontological. In the simplest case, the documents can be regarded as set of words. The words are simple character strings, without any semantic or meaning. In this case, only the statistical behavior of the words is used to create the different groups of the documents. The documents containing the same words will belong to the same group. In the next level, the semantic similarity between the words is also considered during the categorization process. In our communication, we use different words for the same or similar meaning. The best-known relationship among the words is the generalization link. The words can be organized into thesauri based on the generalization relationship. A thesaurus is a tree or lattice where the nodes are the words or terms and the sub-tree or sub-lattice of a node are the specialization of the given node. Using the thesauri, the original documents representation can be converted into a reduced representation where the words are replaced by the more general terms. An important characteristic of the human speech and of human thinking is that the same words may be used for different meanings in different situations. Another aspect is that sometimes a given chain of words may carry a new meaning. In this case, the whole context of the document should be understood and the special word sequences should be located and transformed into meaningful unit. In our investigation, we were focusing on the simplest method that can be carried out without any additional information; we selected the statistical way for categorization. The main directions in the statistical classification methods are summarized in the followings. The Bayes-classification [11] method calculates the conditional probabilities for the different class memberships. The class probability value depends on the attribute values of the documents. The main restriction of this method is, that the different attributes are supposed to be independent from each other. In the real word, this assumption is very rarely met. Thus, the yielded result can be treated as an approximation of the real probability values. In the case of a decision tree [12] method, every node in the tree is assigned to an attribute. This attribute may have several values for the different documents. Every possible attribute values have an edge starting from this node. Every document traverses along the path, corresponding the attribute values. If each documents moving to a given node, belong to the same class, the node becomes a leaf assigned to the current class. 230

DOCUMENT CLUSTERING USING CONCEPT SET REPRESENTATION The K-nearest neighbor method [13] uses a metric function to measure the distance or similarity between the different documents. It assumed that the documents lying close to each other belong to the same class. A new document is assigned to the class of its neighbor documents. The main efficiency problem of this method is the large number of comparison during the classification phase. To improve the efficiency, the selected codebook vectors are structured into a hierarchy.

5 Application of Concept Lattices in Document Clustering Our investigation focuses on the clustering problem of documents. There are lots of application areas like new agencies or discussion forums, custom services where there are a lot of documents collected during the normal operation activities. The elements of this large pool of documents may belong to different topics. Due to efficiency considerations, it is desirable to use an automatic clustering method instead of a manual clustering. The automatic clustering method should apply an appropriate reduction algorithm to convert the document description into a manageable size. In our approach, we combine different reduction methods to provide a better and more compact representation form. The reduction process includes the following techniques: stop word elimination, clustering and relevance based filtering. The proposed clustering algorithm contains the following modules in execution order: - Stop word elimination - Word elimination based on word frequency - Word reduction based on correlation of words - Creating document description using codebook words - Performing concept generation - Selection of characteristic concepts for documents categorization The first step is the usual attribute elimination method. The complexity of this step depends on the current language. In the initial phase the root (the dictionary form) of the words are determined. The un-important words are contained in a dictionary. Every words found in this dictionary are removed from the document description. The complexity of this step is (15) O(D L log(W)) where D : number of documents L : average length of a document W : length of the dictionary. In the next step, the words with too low or too high frequency are eliminated. The frequency of a word is equal to the number of documents containing the word. The reason of this step is that these words are not appropriate words to determine the grouping of the documents. The cost of frequency filtering is equal to (16) O(D L) In the next step the remaining words are clustered. The clustering is based on the distances between the words. The distance between two words is calculated as the correlation value. The correlation value id high if the words occur in the same documents and low if they occur in different documents. (17) Dis(w1,w2) = (|W1\W2| + |W2\W1|) / |W1 U W2|

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KOVACS, BARANYI The distance value lies in the [0,1] interval. Calculating these distance values, we get a distance of correlation matrix. The cost of generating the correlation matrix is (18) O(D2 L’2 G) where L’ denotes the average length of documents after the previous reduction step. The G denotes average number of documents a word occurs in. Due to the high value of D and L’, this step is the most costly one. The clustering of the words is performed using a simple hierarchical method. At beginning, every word is considered as a cluster. In every iteration step, the word pair having the smallest distance value, are merged together to cerate a common cluster. So, in every iteration step, the total number of clusters decreases by one. The termination conditions are the followings - the total number of clusters sink below a threshold or - the minimal distance value is greater than a threshold. The cost of this step is not dominant if we assume, that the pairs are ordered by the distance value (19) O(L) In the next step, every cluster is denoted by a representing word. The words are then replaced with the corresponding representing word. As a result, the number of attributes to describe the documents can be reduced drastically. In the next step, the concept lattice is generated. The context matrix contains the documents as objects and the representing words as attributes. Using a simple lattice generation algorithm, the cost value is equal to (20) O(C N2 M) After generating the concept lattice, the lattice will be reduced by eliminating the concepts with low support values. The support value is equal to the number of documents supporting this concept. This value is equal to the size of the extension of the concept. At the end, a reduced concept lattice is generated. This reduced lattice can be used in the information retrieval component. Every concept denotes a group of documents. Every group can be described by a set of representing words. The accuracy of the lattice generation is tested by comparison of the manual and the statistical categorization results. As all of the training Reuters documents are manually classified, the accuracy of the statistical categorization can be tested directly with the training data.

6 Experimental Results For test purposes, the Reuter Corpus Volume 1 (English Language, 1996-08-20 to 1997-08-1)[14] was selected as training document pool. The Reuters Corpus is an archive of more than 800000 news stories. All of the stories are fully annotated using category or class codes for topic, region and industry sector. The stories cover a range of content typical of an English language newswire and can vary from a few hundred to several thousand words in length. The number of used topic codes is about 100; the number of industry codes is about 380. The number of region codes is about 370. The main benefits of the Reuters Corpus can be summarized in the following points: - standard set of documents, - large amount of training documents, - standard XML format, - accurately classified documents. 232

DOCUMENT CLUSTERING USING CONCEPT SET REPRESENTATION In our first investigation, we have selected only a subset of the full corpus (see Table 2). The frequency distribution of the words is shown in Figure 1. Number of documents Number of words Number of different words Min. frequency Max. frequency

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KOVACS, BARANYI contains only one word, the largest cluster has 228 words. The average cluster size is 3. The population distribution function is shown in Figure 3. 250 200 150 100 50 0 1

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Figure 3: Cluster size distribution The next step of processing is the generation of the concepts. To reduce the lattice size, the concepts with low support values are eliminated from the concept set. After the reduction step, the resulted set contains only X concepts. These concepts will be presented to the users during the information retrieval procedure. In the last step, the resulted categorization was compared with the manual classification. From the available classification systems, the topic classification was selected. This classification seems the most suitable for statistical categorization as to a topic belongs a larger pool of words. In the case region, it has very little possibility that two city names belonging to the same region, occur in the same document. Analyzing the clusters, we can see, that every cluster contained words having similar meanings. Thus the statistical clustering provides a real and correct categorization of the words. Regarding the second larger cluster, the contained words have meaning close to war and fighting. Comparing the manual Reuters classification with our grouping, we can see a good correlation between the two categorizations method. For example, the dominating part of the documents containing words from cluster ‘war’, the Reuters classification also uses a similar category notation: Government 1508 War 746 Domestic Politics 397 International Relations 273 Corporate 265 Markets 220 Economy 167 Table 4: Dominating classification codes for cluster No 2. Testing the other clusters, we can find a similar good correlation between the Reuters classification and our statistical test results. These results are on the other hand, only the first steps to implement an efficient automatic categorization system. In the next phases of the research project, the clustering method should be extended with other statistical and heuristic methods to involve more outlier words into the clustering than in the current version. The current results shows that it is useful to develop a document categorization method based on the proposed methods.

Acknowledgement This research is supported by FKFP 180/2001.

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References [1]

B. Ganter and R. Wille: Formal Concept Analysis, Mathematical Foundations, Springer Verlag, 1999

[2]

R. Godin and R. Missaoui and H. Alaoui: Incremental concept formation algorithms based on Galois lattices, Computational Intelligence, 11(2), 1995, 246-267

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K. Hu and Y. Lu and C Shi: Incremental Discovering Association Rules: A Concept Lattice Approach, Proceedings of PAKDD99, Beijing, 1999, 109-113

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C. Lindig: Fast Concept Analysis, Proceedings of the 8th ICCS, Darmstadt, 2000

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L. Nourine and O. Raynaud: A Fast Algorithm for Building Lattices, Information Processing Letters, 71, 1999, 197-210

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S. Radeleczki and T. Tóth, Fogalomhálók alkalmazása a csoporttechnológiában, Kutatási jelentés, OTKA kutatási jelentés, Miskolc, Hungary, 2001.

[7]

G. Stumme and R. Taouil and Y. Bastide and N. Pasquier and L. Lakhal: Fast Computation of Concept Lattices Using Data Mining Techniques, 7th International Workshop on Knowlegde Representation meets Databases (KRDB 2000), Berlin, 2000

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M. Zaki and M. Ogihara: Theoretical Foundations of Association Rules, Proceedings of 3 rd SIGMOD'98 Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD'98), Seattle, Washington, USA, June 1998.

[9]

L. Kovacs: Efficiency Analysis of Building Concept Lattice, Proceedings of 2nd ISHR on Computational Intelligence, Budapest, 2001

[10]

L. Kovacs: A Fast Algorithm for Building Concept Set, Proceedings of MicroCAD2002, Miskolc, Hungary 2002

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D. Lewis and M. Ringuette. A comparison of two learning algorithms for text classification, In Third Annual Symposium on Document Analysis and Information Retrieval, pp. 81-93, 1994

[12]

S. Weiss and C. Apte, F. Damerau, D. Johnson, F. Oles, T. Goetz, T. Hampp. Maximizing text-mining performance. IEEE Intelligent Systems, 14(4):2-8, July/august 1999

[13]

Y. Yang. An evaluation of statistical approaches top text categorization. Information retrieval 1(1-2):69-90, 1999

[14]

Reuters Corpus Vol. 1, English Language, 1996-08-20 http://about.reutres.com/researchandstandards/corpus/

to

1997-08-19,

About the Authors László Kovács received M S. degree in natural sciences in 1985 and the PhD. degree in mechanical sciences in 1998. His meain research areas are intelligent database systems, document classification, nearest neighbor queries. Péter Baranyi received M. S. degree in electrical engineering in 1994 and the PhD. degree in electrical sciences in 1999. His main research areas are fuzzy controlling, information retrieval systems, neural networks.

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Text Mining for Documents Annotation and Ontology Support Jan Paralic and Peter Bednar Department of Cybernetics and Artificial Intelligence, Technical University of Kosice, Letná 9, 041 20 Kosice, Slovakia {Jan.Paralic,Peter.Bednar}@tuke.sk

Abstract — This paper presents a survey of basic concepts in the area of text data mining and some of the methods used in order to elicit useful knowledge from collections of textual data. Three different text data mining techniques (clustering/visualisation, association rules and classification models) are analysed and its exploitation possibilities within the Webocracy project1 are showed. Clustering and association rules discovery are well suited as supporting tools for ontology management. Classification models are used for automatic documents annotation.

1 Introduction In order to get some new, useful information (or knowledge) from (possibly large) collection of textual documents, text data mining methods can be applied. As the concept of knowledge discovery in texts (KDT) is quite new, in the following section 2 the basic process of KDT and its particular steps are described. The process of KDT can be divided into two main phases. Within the first phase, (free-form) text documents are transformed into an internal or intermediate form, which presents already structured data suitable for text data mining, i.e. the second phase of the whole process. Internal representation forms of a text document collection as well as some important pre-processing steps necessary to achieve an efficient and useful internal representation are described in section 3. Different text data mining approaches and algorithms supporting them are analysed in section 4. As first, clustering/visualisation and association rules as unsupervised text mining approaches are presented. Next, supervised approaches used for building classification models are described. In section 5 the possible use of some of the described text mining methods within the WEBOCRAT system is sketched.

2 Knowledge Discovery in Texts Knowledge discovery in texts (KDT) or text data mining can be defined in the same way as knowledge discovery in databases (KDD), though here the data are textual. This implies significant difference in comparison to KDD, which uses as a source of data well 1

IST-1999-20364 Webocracy: “Web Technologies Supporting Direct Participation in Democratic Processes”

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PARALIC, BEDNAR structured databases. In KDT usually plain textual documents are used. There are also some minor attempts to use (partially or fully) structured textual documents as HTML or XML documents in order to make use not only of plain textual parts but also of additional structural information. Despite this simple approximation of the KDD definition, there is quite a lot of confusion, what KDT really is. For example, Marti Hearst [2] claims that it is important to distinguish between text data mining and information retrieval. The goal of information retrieval is to help users find documents that satisfy their information needs. Marti Hearst describes information retrieval as “a way to pull out the documents you are interested in and push away the others“. Which means, that information retrieval is the process of finding information that is already known and has been inserted into document by an author. In text data mining in contrast, a collection of documents is examined with the aim to discover information (knowledge) not contained in any individual document in the collection. Yves Kodratoff [1] distinguishes between inductive and deductive text mining. The better-known deductive text mining is called Information Extraction, and amounts to finding instances of a predefined pattern in a set of texts. On the other hand, inductive text mining looks for unknown patterns or rules to discover inside a set of texts. We further on refer always to inductive text mining, when we are speaking about text data mining. 2.1 Particular steps of the KDT process Text data mining is much more complex task than data mining [7], because it involves text data that is inherently unstructured and fuzzy. KDT process can be divided into two main phases. 1. Transformation of (free-form) text documents into an internal or intermediate form (this is an analogy of data pre-processing techniques in KDD process. 2. Text mining itself (A. H. Tan in [7] calls it knowledge distillation) that deduces patterns or knowledge from the intermediate form. In greater detail we can compare the KDT approach and its particular steps against the KDD process steps [8]. 1. Understanding the application domain and the goals of the KDT process: user must define which concepts are interesting. 2. Acquiring or selecting a target data set: texts must be gathered using information retrieval tools or in manual way. 3. Data cleaning, pre-processing and transformation: concepts must be described and texts need to be analyzed and stored in the internal representation form, usually after eliminating stop-words and possibly after stemming and exclusion of too frequent. 4. Model development and hypothesis building: identifying concepts in the collection 5. Choosing and execution of suitable data mining algorithms: e.g. the application of the statistical techniques (text data mining task). 6. Result interpretation and visualisation: human must interpret the results. 2.2 Text Data Mining Tasks Mining internal representation form of a document collection induces patterns and relationship across documents [7]. Some examples of unsupervised text mining tasks are:

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TEXT MINING FOR DOCUMENTS ANNOTATION AND ONTOLOGY SUPPORT  Clustering/visualisation of documents  Association rules Typical example of supervised text mining task is  Predictive modelling (classification models)

3 Representation of Textual Documents For internal representation of textual documents we can use some information retrieval model (see formal definition in [2]). The classic models in information retrieval consider that each document is described by a set of representative keywords called index terms. An index term is simply a (document) word whose semantics helps in remembering the documents’ main themes [2]. It is quite obvious that different index terms have varying relevance when used to describe document contents in particular document collection. This effect is captured through the assignment of numerical weights to each index term of a document. Let tj be an index term, di be a document, and wij • 0 be a weight associated with the pair (di, tj). This weight quantifies the importance of the index term tj describing the document di semantic contents. Based on how these weights are calculated and treated, there are three classic information retrieval models, namely the Boolean, the vector [5], and the probabilistic models [2]. 3.1 Classical information retrieval models The Boolean model is a simple retrieval model based on set theory and Boolean algebra. This model considers that index terms are present or absent in a document. As a result, the index term weights are assumed to be binary, i.e. wij  {0,1}. A query is composed of index terms linked by three logical connectives: not, and, or. Thus a query is essentially a Boolean expression with precise semantics. As a result this model is unable to recognise partial matches, which frequently leads to poor performance. Another weakness is that by considering only the presence or absence of term, the binary weighting scheme ignores information inherent in the frequencies of terms. A related problem concerns document length. As a document gets longer, the number of distinct terms used will in general increase. Many of these terms usages in very long documents will be unrelated to the core content of the document, but are treated as being of the same significance as similar occurrences in short documents. The vector model removes this disadvantages by assigning non-binary weights to index terms in queries and in documents. The term frequency of occurrence (tf) [5] [6] in document is a common weighting scheme here and is generally used as the basis of the weighted document vector. Document frequency can be combined with the collection frequency factor, which is used to discriminate one document from the other. Most of the used schemes for this factor, e.g. the inverse document frequency (idf), assume that the importance of a term is proportional to the number of documents the terms appear in. As a combination of these two factors we can obtain tfidf scheme, which is the most widely used weighting scheme, defined as: C (1) w(i, j ) tfidf (d i , t j ) Nd i , t j . log Nt j

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PARALIC, BEDNAR where Ndi,tj denotes the number the term tj occurs in the document di (term frequency factor), Ntj denotes the number of documents in collection C in which tj occurs at least once (document frequency of the term tj) and |C| denotes the number of the documents in collection C. This weighting scheme includes intuitive presumption that:  the more often a term occurs in a document, the more it is representative of the content of the document, and  the more documents the term occurs in, less discriminating it is. In order to fit weights into the interval ¢0, 1² and documents be represented by vectors of equal length, the document vector resulting from tfidf weighting are often normalized to length equal to 1, so final normalized term weight can be computed as: w(i, j )

tfidf (d i , t j ) norm

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where T is the set of terms used for the vector representation of the document i. The probabilistic model attempts to capture the IR problem within a probabilistic framework [2]. The index term weights are all binary and a query is a subset of index terms. Given a user query, there is a set of documents which contains exactly relevant documents and no other (so called ideal answer set). The querying process can be seen as a process of specifying the properties of an ideal answer set. Since these properties are not known at query time, an effort has to be made at initially guessing what they could be. This initial guess allows then to generate a preliminary probabilistic description of the ideal answer set which is used to retrieve a first set of documents. An interaction with the user is then initiated with the purpose of improving the probabilistic description of the ideal answer set. Through several different measures, Salton and Buckley in [6] showed that the vector space model is expected to outperform the probabilistic model with general collections. This also seems to be dominant thought among researchers, practitioners, and the Web community, where popularity of the vector model runs high [2]. 3.2 Term selection/reduction Documents can be described by thousands of terms and this high dimensionality of document space can cause problem with efficiency. Terms that do not describe content of documents induce noise, which can degrade performance of created text mining model. For these reasons, selection of relevant terms is very important text processing. Appropriate method for term selection is generally dependent on used text mining algorithm. Either it will be a supervised text data mining algorithm (i.e. the information about classes of particular documents is available), or an unsupervised one (i.e. no information about classes of particular documents is available). Main difference is that methods for supervised learning can use information about document category, and relevance of the term can be determined by how it separates documents into categories. The classification accuracy of the generated model (classifier) estimated on the testing examples can be used as a guide to find optimal set of terms. Note that unsupervised term selection methods can be generally used also for the supervised learning.

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TEXT MINING FOR DOCUMENTS ANNOTATION AND ONTOLOGY SUPPORT From unsupervised term selection methods two can be mentioned: Document frequency threshold [7] is the simplest technique for term selection. In this method, document frequency for all terms on training collection is computed and terms, which have document frequency lower than specified threshold, are removed from the resulting set of terms used for document representation. Over years, alternative modelling paradigms for each type of classic model have been proposed. Regarding vector model, as a representative of algebraic models, a very interesting extension the latent semantic indexing (LSI) has been proposed in [13]. From supervised term selection methods, e.g. Information gain is frequently employed. Other approach uses F2 statistic measures.

4 Text Mining Methods 4.1 Clustering/visualization For clustering of textual documents in vector representation the self-organizing map (SOM) [9] is used very often. SOM is an unsupervised neural network, which provides a mapping from high-dimensional feature spaces onto a two-dimensional space such that similar data are mapped close to each other. This allows a very intuitive cluster representation and analysis. A comparison of the SOM approach with a statistical one, on one particular domain can be found in [12]. The comparison has shown that statistical approach was not powerful enough to deal with larger text collections and the interpretation of results has been quite difficult. Very interesting for text mining purposes is the combination of the basic SOM algorithm with the LabelSOM method to automatically extract classification from the trained SOM [10]. This method has been used e.g. within the SOMLib system [11]. The SOMLib Digital Library System provides methods for organizing of large collections of electronic documents to allow topic-oriented browsing and orientation. SOM provides only flat, i.e. two-dimensional representation of documents’ clusters, which might be blind for interpretation when document collection is very large. Moreover, this representation of clusters has usually very irregular coverage with documents due to unbalanced topic distribution. To overcome these limitations the Growing Hierarchical SOM (GHSOM) [11], which automatically creates a hierarchical organization of a set of documents has been developed. This allows the network architecture to determine the topical structure of the given document repository during the training process, creating a hierarchy of self-organizing maps, each of which provides a topologically sorted representation of a topical subset. Starting from a rather small high-level SOM, which provides a coarse overview of the various topics present in the collection, subsequent layers are added where necessary to display a finer subdivision of topics. Each map in turn grows in size until it represents its topic in sufficient degree of granularity. Since usually not all topics are present equally strongly in a collection, this leads to an unbalanced hierarchy, assigning more “mapspace” to topics that are more prominent in a given collection. This allows the user to approach and intuitively browse a document collection in a way similar to conventional libraries.

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PARALIC, BEDNAR Visualization by this system is provided by means of web interface. An HTML page represents each map with links to lower level (expanded) maps, or particular documents associated with a cell at the lowest –leaves level (see Figure 1).

Figure 1: A partial view of the 2nd layer map for a text collection from Austrian newsletter Standard 4.2 Association Rules This text data mining task discovers associations between concepts and expresses these findings as rules in the format B Ÿ H [support, confidence], where B as well as H may be a set of concepts or a unique concept [8]. The rule means, “if B is present in a text, then H is present with a certain confidence and a certain support”. Following the usual definition (e.g. in [4]), confidence is the proportion of texts that have B AND H in relation to number of texts that have only B and support is the proportion of texts that have B AND H in relation to number of all texts in the collection. Such rules allow predicting the presence of (a) concept(s) according to the presence of another one(s). Moreover, complex rules may be discovered, when combination of concepts and/or words is allowed in discovered rules. E.g. WORD_1 AND WORD_2 AND CONCEPT_1 AND CONCEPT_2 Ÿ CONCEPT_3. This kind of rule can be used to select sub-collections of text documents where some words are present.

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TEXT MINING FOR DOCUMENTS ANNOTATION AND ONTOLOGY SUPPORT The most often used approach to mine associations is Apriori algorithm [4], which is running in two steps. 1. Finds all frequent itemsets (i.e. tuples of concepts or terms). Each of these itemsets must occur at least as frequently as a pre-defined minimum support count. 2. Generates strong association rules from the frequent itemsets. These rules must satisfy pre-defined minimum support and minimum confidence. The name of the Apriori algorithm is based on the fact, that the algorithm uses prior knowledge of frequent itemset properties in the following way. It employs an iterative approach known as level-wise search, where k-itemsets are used to explore (k+1)itemsets, starting with k=1 until no more frequent k-itemsets can be found. For each new k one full scan of the database is needed. To improve the efficiency of Apriori algorithm, anti-monotone property is applied which means that all subsets of a frequent itemset must be frequent itemsets. This reduces the number of candidate itemsets generated for k+1 (from already identified frequent itemsets of size k and less). Even so the performance of Apriori algorithm does not scale well for large databases, which is the case of document collections as well. An interesting method that generates the set of frequent itemsets without candidate generation is called frequent-pattern growth, or simply FP-growth [4], which adopts a divide-and-conquer strategy. 4.3 Classification Models The term classification can cover any procedure in which some decision or forecast is made on the basis of currently available information. In the context of data mining a more restrictive interpretation is considered. At first, we may aim of establishing existence of classes (or clusters) in the data according to a set of observations. Or we may know for certain that there are some classes, and the aim is to establish a rule by use of which we can classify a new observation into one (or more) of the existing class(es). The first case is known as unsupervised learning (clustering). In this chapter we use the term classification for the second case - supervised learning. Rule induction algorithms. Any form of inference in which the premises do not imply deductively the conclusions, can be thought of as an induction. In the case of the text categorisation, it is one special form of the inductive inference, supervised concept learning or classification learning. To learn a concept means to infer its general definition from a number of specific examples of it. A concept can be formally considered as a function from the set of all examples (in our case from the set of all documents) to the Boolean set {true, false} or equivalently to the set {document is assigned to category; document is not assigned to category}. For text categorization, the concept is equivalent to some category, so the problem is to find a definition of this category from a number of documents. Rules induction algorithms are characterized by representing the target category as a set of "if-then" rules. These rules have the form "if then predict where is the conjunction of the attribute tests (selectors). Rule induction algorithms have several advantages; the most noteworthy one is that these rules are best understandable for humans from all representations currently in use in concept learning.

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PARALIC, BEDNAR Examples of rule induction algorithms are CN2 [15] (see Figure 2 with visualisation of the results in KDD Package* [12]), REP, IREP [16], RIPPER [17]. Other possibility is to mine decision trees, e.g. using Quinlan’s algorithm C4.5

Figure 2: Example of a visual representation of decision rules produced by the CN2 implementation within the KDD package.

5 Exploitation of KDT in Webocracy Webocracy project responds to an urgent need for establishment of efficient systems providing effective and secure user-friendly tools, working methods, and support mechanisms to ensure the efficient exchange of information between citizens and the administrations. The project addresses the problem of providing new types of communication flows and services from public institutions to citizens, and improves the access of citizens to public administration services and information. The new types of services will increase the efficiency, transparency and accountability of public administration institutions and their policies toward citizens. Within this project a WEBOCRAT system is being designed and developed. WEBOCRAT system is a Web-based system comprising Web publishing, computer-mediated discussion, virtual communities, discussion forums, organizational memories, text data mining, and knowledge modeling. The WEBOCRAT system will support communication and discussion, publication of documents on the Internet, browsing and navigation, opinion polling on questions of public interest, intelligent retrieval, analytical tool, alerting services, and convenient access to information based on individual needs. 5.1 Clustering/visualisation We think, that clustering/visualisation does not fit the functionality of the WEBOCRAT system as defined in [3], because documents in WEBOCRAT system are primarily organ*

We have developed KDD Package within the EU funded INCO Copernicus project No. 977091 GOAL Geographic Information On-Line Analysis (GIS – Data Warehouse Integration)

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TEXT MINING FOR DOCUMENTS ANNOTATION AND ONTOLOGY SUPPORT ized by their links to knowledge model so that primarily knowledge model is used for document retrieval and topic-oriented browsing On the other hand, it could be useful to use techniques like GHSOM, because of its hierarchical structure that is tailored to the actual text data collection, as a supporting tool within the initial phase, when the knowledge model of a local authority is being constructed. This is true in such a case when local authority has a representative set of text documents in electronic form available for this purpose. It is assumed that these documents will be later on published using the WEBOCRAT system and linked to the knowledge model for intelligent retrieval purposes. But users must be aware of the fact, that GHSOM does not produce any ontology. It is just a hierarchical structure, where documents are organized in such a way that documents about similar topics should be topologically close to each other, and documents with different topics should be topologically far away from each other. Particular node in this hierarchical structure is labelled by (stemmed) words – terms, which occur most often in cluster of documents presented by this node. This list of terms can provide some idea about concept(s), which can be (possibly) represented in the designed knowledge model. Finally, particular documents represent leave nodes of this hierarchical structure. It is in our opinion necessary to look carefully through the whole structure, including particular documents in order to make reasonable conclusions about particular concepts proposed for the knowledge model and relations among them. 5.2 Association rules Association rules as presented in previous section have been used e.g. in [8] in two different experiments. The first one tried to analyse political newspaper articles from two different periods in order to analyse what there are saying about a mayor in a big Brazil city (first period was before corruption scandal and the other one after it). The second experiment tried to analyse articles about various text mining tools as competitive intelligence analysis. In both experiments firstly, concepts were defined by different approaches. To identify concept terms, natural language processing is commonly required. Instead of that, ontology provides this information in the WEBOCRAT system, and we can represent documents directly as a binary vector. This vector has one element for each concept, equal to 1 if document is linked to the particular concept. Another advantage is, that within the WEBOCRAT system a hierarchy of concepts from particular domain (local authority’s area of work) is available. We can make use of it for mining of associations, not only at the level of leaves concepts, but also at the higher levels of the hierarchy, getting so called multi-dimensional association rules [4]. Association rules can be exploited e.g. for automatic improvements of the knowledge model in the following way. When we use as input attributes for association rules mining algorithm only concepts to which documents are linked that means that we are looking for frequently occurring linking patterns. These patterns can be confronted with the actual ontology. When e.g. our algorithm finds association between concepts X, Y, and Z and in our ontology no relation between concepts X, Y and Z is presented, we can expect a missing relation between them. This approach is suitable mainly for documents that were not linked automatically, using a pre-defined template.

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PARALIC, BEDNAR 5.3 Classification models In the WEBOCRAT system, ontology is used as a knowledge model of the domain, which is composed from concepts occurring in this domain and relationships between these concepts. Information is stored in the system in the form of text documents, which are annotated by set of concepts relevant to the document content. One strategy for document retrieval is based on concepts. User selects interesting concepts and asks for information related to them, is used for information retrieval. The decision about document relevance to the user query is based on a similarity between set of query concepts and a set of concepts, which are annotated to the document. This task of document retrieval can be viewed as a classification task when the decision is made, whether the document is relevant for the user or not. With appropriate ontology which models domain well, use of this knowledge model can yield better results than e.g. retrieval based on vector representation of documents. Retrieval accuracy depends on the quality of documents annotation. Data mining methods can be very useful to guide user at annotating new document. Annotation of the new document is the classification task (text categorization task) when we need to make decision which concept (concept represents category) is relevant to the content of the document. The system must propose relevant concepts for new document in real time, so important requirement to used algorithm is execution time efficiency. User can add or delete some link between new document and concepts, and these changes can be immediately integrated into classifier. This requires ability of incremental learning. Relevance weighting of the concepts to the new document is better than simple binary decision. Concepts can be ordered by weight of the relevance to the new document and user can search for additional relevant concept according to this ordering.

Acknowledgments This work is done within the Webocracy project, which is supported by European Commission DG INFSO under the IST program, contract No. IST-1999-20364; within the TEXAS Project supported by Austrian Institute for East- and Southeast Europe and within the VEGA project 1/8131/01 ”Knowledge Technologies for Information Acquisition and Retrieval” of Scientific Grant Agency of Ministry of Education of the Slovak Republic. The content of this publication is the sole responsibility of the authors, and in no way represents the view of the European Commission or its services.

References [1] Kodratoff, Y. (2001) Rating the Interest of Rules Induced from Data and within Texts. In Proc. of the 12th IEEE - International Conference on Database and Expert Systems Applications DEXA 2001, Munich. (Long version of the paper, submitted for publication in Knowledge and Information Systems: An International Journal). [2] Baeza-Yates, R. and Ribeiro-Neto, B. (1999) Modern Information Retrieval. Addison-Wesley Longman Publishing Company [3] Mach, M., Furdik K. (2001) Webocrat system architecture and functionality. Webocracy deliverable R2.4, Technical University of Kosice, April 2001

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TEXT MINING FOR DOCUMENTS ANNOTATION AND ONTOLOGY SUPPORT [4] Han, J., Kamber, M. (2000) Data Mining – Concepts and Techniques. Morgan Kaufmann Publishers [5] Salton, G., Wong, A., Yang, C. (1975) A Vector Space Model for Automatic Indexing. Communications of the ACM, 18(11), 613-620. [6] Salton, G.,Buckley, C. (1988) Term Weighting Approaches in Automatic Text Retrieval. Information Processing & Management, 24(5), 513-523. [7] Ah-Hwee Tan (1999) Text Mining: The state of the art and the challenges. In Proc. of the PAKDD'99 workshop on Knowledge Disocovery from Advanced Databases, Beijing, pp. 65-70 [8] Loh, S., Wives, L. K., and Palazzo, J. (2000) Concept-Based Knowledge Discovery in Texts Extracted from the Web. SIGKDD Explorations, Vol. 2, Issue 1, July 2000, pp. 29-39 [9] Kohonen, T. Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 1982. Springer Verlag, Berlin, Heidelberg, New York. [10] Rauber, A. (1999) On the labeling of self-organizing maps. In Proc. of the International Joint Conference on Neural Networks, Washington, DC [11] Rauber, A., Dittenbach, M. and Merkl, D. (2000) Automatically Detecting and Organizing Documents into Topic Hierarchies: A Neural Network Based Approach to Bookshelf Creation and Arrangement. In: Proc. of the 4th European Conference on Research and Advanced Technologies for Digital Libraries (ECDL2000), Springer LNCS 1923, Lisboa, Portugal [12] Rauber, A., and Paralic, J. (2000) Cluster Analysis as a First Step in the Knowledge Discovery Process. In Journal of Advanced Computational Intelligence, Fuji Technology Press Ltd., ISSN 1343-0130, Vol. 4, No. 4, pp. 258 – 262 [13] Deerwester, S., Dumais, S. T., Landauer, T. K., Furnas, G. W. Harshman, R. A. (1990) Indexing by latent semantic analysis. Journal of the Society for Information Science 41(6), 391-407. [14] Lewis, D. D. (1998) Naive (Bayes) at Forty: The Independence Assumption in Information Retrieval. In Proceedings of ECML-98, 10th European Conference on Machine Learning, 415, Chemnitz. [15] Clark, P., Niblett, T. (1989) The CN2 induction algorithm. Machine Learning Journal, 3(4), 261-283. [16] Fürnkranz, J., Widmer, G. (1994) Incremental Reduced Error Prunning. Machine Learning: Proceedings of the 11th Annual Conference, New Brunswick, New Jersey. [17] Cohen, W. W. (1995) Fast effective rule induction. Proceedings of the 12th International Conference (ML95), Morgan Kaufmann, San Mateo, California.

About the Authors Jan Paralic received his Master’s degree in technical cybernetics in 1992 and PhD’s degree in artificial intelligence in 1998 from Technical University of Kosice. His research currently focuses mainly on knowledge discovery (from databases as well as from texts) and knowledge management. Peter Bednar received a Master’s degree in cybernetics 2001 from Technical University of Kosice. His research interests include text categorisation, data and text mining.

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Fuzzy Relational Thesauri in Information Retrieval: Automatic Knowledge Base Expansion by Means of Classified Textual Data∗ Domonkos Tikk1,2,3 , Jae Dong Yang3 , P´eter Baranyi1,2 , and Anik´o Szak´al4 1 Dept.

of Telecommunications & Telematics Budapest University of Technology and Economics, Budapest, Hungary [email protected], [email protected] 2 Intelligent

Integrated Systems Japanese–Hungarian Laboratory Budapest, Hungary 3 Department

of Computer Science Chonbuk National University Chonju, Korea [email protected] 4 Budapest

Polytechnic Budapest, Hungary [email protected]

Abstract — In our ongoing project we develop a tool which provides domain engineers with a facility to create fuzzy relational thesauri (FRT) describing subject domains. The created fuzzy relational thesauri can be used as knowledge base for an intelligent information agent when answering user queries relevant to the described domains, or for textual searching on the web. However, the manual creation of (fuzzy) thesauri is quite tedious process if the source of data from which the domain engineer may select concepts and instances for the thesaurus is not well organized or structured. That is the typical case of textual data bases. In order to ease FRT creation process we make use of a small starting FRT and our text categorization technique that temporarily expands FRT while doing the supervised learning part of text categorization. This by-product of categorization is then used for enlarging automatically or semi-automatically the final FRT. ∗

Research supported by the National Scientific Research Foundation (OTKA) Grant No. D034614, and by the Hungarian Ministry of Education Grant No. FKFP 0180/2001. A part of this work was done while D. Tikk was visiting at Department of Computer Science, Chonbuk National University.

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1 Introduction Information agent technology emerged as a major field of interest among practitioners and researchers of various fields with the immense grow of available information on the internet since the early 90s. The vast amount of heterogeneous information source available on the internet demands advanced solutions for acquiring, mediating, and maintaining relevant information on behalf of users or other agents. In general, intelligent information agents are autonomous computational software entities that are developed to provide proactive resource discovery, create a link between information consumers and providers, and offer value-added information services and products [1]. The agents are assumed to deal with difficulty associated with the enormous amount of information overload of users, preferably in real-time. There are different approaches to build information agents including user programming, machine learning, and knowledge engineering. When using knowledge engineering for the construction, the agent is set out a large deal of domain specific knowledge about the application and the user. However, a significant drawback of this method is that it requires substantial efforts from the knowledge engineer to build up and maintain knowledge bases. Moreover, the agent is highly domain-specific and its knowledge is relatively fixed [1]. In order to facilitate the construction and maintenance of the agent’s knowledge our project aims to assist domain experts (and possible users) with a useful tool. This tool helps to create fuzzy relational thesauri which describe the subject domain by means of its major concepts/instances and the various kind of relationship between these concepts/instances. In our approach the concepts in the fuzzy relational thesauri are represented by keywords of the subject domain. The build-up of a fuzzy relational thesaurus (FRT) is considerably tedious process when the knowledge engineer has to take into account all the important concepts (in our approach: keywords) of the actual domain, together with their possible synonyms and associated words. In order to facilitate this procedure we retrieve the keywords from a sample text archive, and then apply text categorization in this text retrieval method. he text archive can be the collection of documents selected by a domain expert, or obtained as the result of web searches. The next step is the categorization of the archive by means of our FRT based hierarchical (or structured) text categorization method [2]. This approach requires – a small starting FRT typically consisting of the major concepts of the subject domain; – labelling the documents for the supervised learning with category names corresponding to the concepts of the starting FRT; – one-to-one correspondence between category names and FRT terms. he categorization process uses FRT as the implementation of the hierarchical category system (often called taxonomy), i.e. the categories are represented by terms (concepts) in FRT. In order to prevent FRT from being incoherent and far from the view of its creator, categorization is proceeded on a copy of the starting FRT. The approach assigns to every category a set of terms, so-called local dictionaries, which contains words being typical for the category in the text corpus and are stored in FRT. From the aspect of categorization local dictionaries are useful to discriminate documents belonging to different categories.

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From the aspect of FRT creation, local dictionaries, being in fact a by-product of the categorization approach, collect the most frequent words of categories and so describe them efficiently. The size, contents and the preparation technique of the local dictionaries vary depending on various parameters of the categorization. For the final expansion of the starting FRT, elements of local dictionaries can be inserted permanently to FRT. We provide an option for the knowledge engineer (maintaining the FRT) to supervise, filter and modify elements of local dictionaries before added to the thesaurus. In such a way the FRT is maintained in accordance with the knowledge of the domain expert and reflects his/her view on the subject domain the best. This paper is organized as follows. Section 2 describes the role of FRT in information retrieval systems. Section 3 describes the FRT management system developed we utilize in next. Section 4 provides a brief description of our FRT based text categorization approach with special emphasize on the creation of local dictionaries. In section 5 we present the utilization of the local dictionaries, and finally section 6 summarizes the paper.

2 Fuzzy relational thesaurus in information retrieval A thesaurus in an information retrieval system (IRS) can be considered as a knowledge base that represents the conceptual model of certain subject domain [3]. The thesaurus has similar role in an IRS as a knowledge base in expert systems. In IRS’s the query may be seen as a concept, and documents as objects. An object is in the answer to the query to the degree it is an instance of the concept. With the above terminology, a document satisfies a query to the degree to which it is classified as that query. In what follows we assume that the knowledge base represented by the thesaurus is in term-centered form which is maintained by the domain expert. A fuzzy relational thesaurus (FRT) [3], is a particular representation form, which is an extension of traditional thesauri schemes enriched by the strength of the term relationships and a richer set of binary relations. In FRT every term relation has a strength represented by a number of the unit interval. Formally: Definition 2.1 [3] Let X be the set of all terms, and R(X, X) is an arbitrary fuzzy term relation. Then for an ordered pair of terms, (x, y) ∈ X 2 , R(x, y) ∈ [0, 1] is the belief (or certainty) that x implies y. This strength can be considered as the membership degree of (x, y) in the fuzzy term relation R(X, X). Note that since (x, y) is an ordered pair, the symmetry of the relation is not a necessary condition. The term relation may comprise the following possibilities: – General relations: RT – related term; ST – synonym term; BT – broader term; N T – narrower term. – Abstraction relations: KO – kind of (specialization of, subclass of); IO – instance of; F O – has feature object (e.g. F O(IA, CM)) where IA = information agent, CM = construction method. – Domain specific relations of the form f o(x, y), where f o is the name of the feature object associated with x, and y is the concepts f o-feature object of y, e.g. CM (IA1 , knowledge engineering).

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These relations are organized in a partial ordering based on their specificity (see Figure 1). The ordering is exploited in the construction of the FRT and in query answering. The strength of actual term relations is determined by the domain engineer, but a default value is assigned for each relation type in order to ease and reduce the engineer’s work (for details see section 3). RT BT KO

FO

ST

F ON T = (BT  ) IO

IO

KO

Figure 1: Partial ordering of relations.  means inverse. The lower a relation in the tree, the more specific it is (redrawn from [3]). The answer to a query is determined by the relation of the query terms and the document terms. In order to calculate the strength of relation between an arbitrary pair of terms, the transitive closure [4] of the term relations are computed using the partial ordering of the relations depicted on Figure 1. The transitive closure is computed with respect to a specified t-norm, e.g. the minimum or the algebraic product. In [3] the authors proposed an effective way for this computation, with time complexity of order O(m log m), where m is the pairs of terms being in relation in the knowledge base.

3 Project description In [3] the authors assumed that the domain expert is assisted by a software tool, a kind of “FRT management system” which help him in the construction task. In the next we describe one of our ongoing project which aims at developing this software. Because of the lack of space for this description is relatively brief. For further details we refer to our paper [5], which is available also on the internet. We propose a new approach for managing domain specific thesauri, where objectoriented paradigm is applied to thesaurus construction and query-based browsing. This approach provides an object-oriented mechanism to assist domain experts in constructing thesauri; it determines a considerable part of relationship degrees between terms by inheritance and supplies domain experts with information available from a thesaurus being constructed. It enables domain experts to incrementally construct the thesaurus as well, since the automatically determined degree of relationships can be refined whenever a more sophisticated thesaurus is needed. It may minimize domain expert’s burden caused from the exhaustive specification of individual relationship. This approach also provides a query-based browsing, which allows users to easily verify thesaurus terms before they are used in usual boolean queries. Our thesaurus is called object-based thesaurus. All its relationships are represented in terms of two levels: concept level and instance level. The former defines the relationships between concepts, and the latter specifies the relationships between instances. The relationships in the object-oriented paradigm are employed to directly implement the object-based thesaurus, providing a formal specification in the construction of the thesaurus. For example, BT/NT relationship is redefined as a generalization hierarchy, while

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a vague relationship, RT is refined into aggregation and association which have more concrete semantics. The aggregation and association of a concept acts here as a property in the generalization hierarchy that its sub-concept inherits. Such an inheritance of the relationship turns out to be a useful mechanism to structurally specify semantics between concepts. We assign a default strength to each relationship type. For example we assign 0.7 as to every association relation, 0.8 to every part-of relation, and 0.9 to every sub-concept-of relation. We worked out a mechanism to calculate the strength of a relationship between any arbitrary pair of concepts based on object-oriented paradigm. We also have a technique to resolve multiple inheritance situation. For more details we refer to [5].

4 Text categorization for fuzzy thesaurus creation Without any facility for preprocessing the domain engineer should create the domain descriptive FRT based on raw textual data and/or his/her experience. Our goal is to facilitate this work thereby providing categorized textual data and the set of frequent keywords assigned to each category. Automated text categorization is a thriving research topic in the area of information retrieval. The objective is to assign a document to an appropriate category selected from a finite set. This task was traditionally made manually by domain expert, but in last decades the exponential increase of online available textual data various stimulated developments of automated approaches. For a survey see [6]. These methods are usually based on a probabilistic model or various kind of learning strategies. For learning purpose a set of training documents with manually assigned class labels is assumed to be available. As we mentioned earlier, our FRT based approach is applicable if categories are organized in topic hierarchy, also called taxonomy. Document categorization in taxonomy is a recently emerged field of text mining (see also [7, 8, 9]. On the internet topics are often organized in hierarchy (see, e.g., www.yahoo.com, www.ibm.com/patents), because it improves the perspicuity of the subject domain if the number of categories at a level is kept under a certain threshold. This is also the principle when inserting e-mails in a prescribed folder system. Now we describe shortly our FRT based text categorization method [2]. The FRT is basically the implementation of the taxonomy which stores and maintains adaptive local dictionary for each category. For categorization the type relationship is uniform, but their strength has importance when learning. In graph theory, term hierarchy of FRT and taxonomy can be represented by digraphs. An FRT can be applied to categorize documents belonging to the topic hierarchy of a taxonomy, if there exist a subgraph of the FRT which is isomorphic with the digraph of the taxonomy. Therefore each category is represented by an FRT term. We use the most common representation framework, the vector space model, where a document D is described by a vector of word frequency values, W D , and vector of FRT terms appearing in the document TD , respectively: WD = (w1D , · · · , wpD );

D TD = (tD 1 , . . . , tq ),

(1)

where p is the total number of unique terms appearing in the document collection, and q is the number of terms in the FRT.

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The set of unique terms is determined automatically by removing the function words from the total term set (like e.g. “the” in English) and then applying stemming on the remaining set. There are numerous possible weighting schemes in the literature to determine the values of weights wiD and tD i . The best and most sophisticated method is the entropy weighting, which was found to outmatch 6 others in [10], but perhaps the most popular is the tf×idf weighting [11] and its versions, which defines w iD in proportion to the number of occurrence of the term i in the document, fiD , and in inverse proportion to the number of documents in the collection for which the term occurs at least once: wiD

=

fiD





N · log . ni

For tj , we use the number of appearance of jth FRT-term in the document D. The vectors in (1) are normalized before any further processing is done. We remark that the available raw text can also be processed by other approaches for FRT refinement. The set up of association relationship can be supported by measuring the cooccurrence of keywords in training documents [12]. This may overcome the creation of erroneous relations between term and also helps to discover the synonyms terms. The categorization is done in iteratively, alternating two phases. First, the vector T D is used to infer the category (or categories) of D (see [2]). In the beginning of the categorization process FRT contains only few terms, therefore the categorization is usually not efficient. In order to endow FRT with good categorizing ability, in the second (learning) phase terms being typical for the category/ies of D are added to the FRT. These two phases are proceed alternatively, while the performance of categorization achieves a certain level or cannot be improved significantly. For the purpose of FRT expansion one of the most important issue of the categorization is the determination of terms assigned to a category of a document, called local dictionary LD (C), inserted to FRT in the learning phase. The selection employs the K-nearest neighbour technique. First, the K nearest neighbours of D is selected in the sense of a similarity measure (usually cosine). Let then J denote the index set of documents among the neighbours of D being classified also in C, and containing common words with C. LD (C) is an importance ordered set of words appearing in D and in the documents of J, DJ . The importance value of the ith word is determined as the sum of frequency value  in D and in DJ : j∈DJ ∪D wij . The size of LD (C) can be controlled by two parameters, p1 the maximum number of words, and α1 the minimum (cumulated) frequency value of a word (p1 ∈ N, α1 ∈ [0, 1]). Thus, the final LD (C) is an ordered set with cardinality at most |p1 |, where every word has at least α1 weight. The performance of the categorization focusing on a single category is usually measured by two quantities: recall and precision. Let a and b be the number of documents correctly or incorrectly assigned to the given category, respectively, while c be the number of documents incorrectly rejected from the given category. With this terminology: recall =

a ; a+c

precision =

a a+b

Usually only one of these measures does not give realistic result about the performance,

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therefore the F-measure, their combination is usually applied: Fβ =

(β 2 + 1)precision · recall (β 2 · precision) + recall

where the parameter β is commonly set to 1. The classifier can commit two kinds of mistake. It can incorrectly assign a category to a document and hence reduce the precision, or it can reject incorrectly a category and hence degrade the recall of the classifier. The performance of the categorization depends on the above two quantities to be maximized. In the first case our approach decreases the relationship wait along the topic path, i.e. between the erroneously selected category C and the terms in TD which supported C. In the latter case new terms are inserted to FRT in order to enhance the classification performance. The insertion is proceeded in such a way that the new terms are forced to be as deep in the taxonomy as possible. This is because a term deep in the hierarchy supports all the categories along the path between the term and the root. For more details see [2].

5 Expansion of the FRT The text categorization helps the knowledge engineers to create an FRT describing the subject domain efficiently in two ways. First, local dictionaries are provided to each category. The user is offered options to filter the words, modify the weight and to specify the kind of relationship according to his/her view about the subject domain. Second, new documents can be classified and thus new data are provided for further investigation and consideration. We illustrate the described method on a simple example. We collected documents in the domain of electronic appliances from the web. The created a 211 and a 327 element document sets. We proceeded tests on both document sets. The unique term set (p in Eq. (1)) consisted of 3731, and 5793 words, respectively. The FRT was created by a semi-automatic thesaurus construction software [5]. In our application the depth of the taxonomy is three. The collected documents were classified into the following six top level topic: Audio, Computer, Computer Components, Computer Peripheral Device, House-Hold Appliances, Office Communications Appliances. We had 30 (31) 2nd level, and 40 (58) 3rd level topics in the case of 211 (327) document set. Each category had at least two training examples. The size of the total number of inserted terms depends on the parameter p 1 and α1 . The content of the local dictionaries can be modified if the stemming is omitted, or if other preprocession is performed on the corpus. The classifier applies different methods assigning categories which may also influence the size and contents of the local dictionaries. Table 1 shows the total number of inserted words in terms of the above parameters. The starting FRT contains 584, and 1779 terms in case of 211 and 327 element document set, resp. The total number of inserted words is comparable with these quantities. When stemming is proceeded in the preparation phase, a list of original versions is also provided to the user as synonyms of stemmed words. This option allows the user to select the best possible term to be inserted. The presented facility greatly reduces the required time for FRT creation even at the final insertion the user is prompted at each word.

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´ TIKK, YANG, BARANYI, SZAKAL

327 element document set p1 α1 inserted words it 5 0.1 1069∼1198 10 5 0.25 630 3 5 0.2 796 15 7 0.05 1139∼1204 12

211 element document set p1 α1 inserted words it 7 0.05 766∼769 12 5 0.1 708∼723 10 10 0.02 860 10 7 0.05 1139∼1204 12

Table 1: Total number of inserted words in terms of p1 , α1 and the number of iteration it

6 Conclusion We develop a fuzzy relational thesaurus management system. The aim of the system is to create a knowledge base for intelligent agent. FRT creation is a tedious process, which may be ease if the majority of data for the construction is supplied in a structured form. Therefore, we provide categorized textual data and local dictionaries assigned to categories to help the knowledge engineer in the build-up. The information is retrieved by means of an FRT based text categorization approach, that classifies documents into hierarchical topic taxonomies. The categorization process creates local dictionaries as a by-product while improving its classification performance.

References [1] M. Klusch. Information agent technology for the Internet: A survey. Data & Knowledge Engineering, 36:337–372, 2001. [2] D. Tikk, J. D. Yang, and S. L. Bang. Hierarchical text categorization using fuzzy relational thesaurus. Submitted to Kybernetika. [3] H. L. Larsen and R. R. Yager. The use of fuzzy relational thesaurus for classificatory problem solving in information retrieval and expert systems. IEEE Trans. on Systems, Man, and Cybernetics, 23(1), 1993. [4] L. A. Zadeh. Similarity relations and fuzzy orderings. Inform. Sci., pages 171–200, 1971. [5] J. H. Choi, J. J. Park, J. D. Yang, and D. K. Lee. An object-based approach to managing domain specific thesauri: semiautomatic thesaurus construction and query-based browsing. Technical Report TR 98/11, Dept. of Computer Science, Chonbuk National University, 1998. http://cs.chonbuk.ac.kr/∼jdyang/publication/techpaper.html. [6] L. Aas and L. Eikvil. Text categorisation: A survey. Raport NR 941, Norwegian Computing Center, 1999. [7] S. Chakrabarti, B. Dom, R. Agrawal, and P. Raghavan. Scalable feature selection, classification and signature generation for organizing large text databases into hierarchical topic taxonomies. The VLDB Journal, 7(3):163–178, 1998. [8] A. McCallum, R. Rosenfeld, T. Mitchell, and A. Ng. Improving text classification by shrinkage in a hierarchy of classes. In Proc. of the ICML-98, 1998. http://www2.cs.cmu.edu/∼mccallum/papers/hier-icml98.ps.gz. [9] W. Chuang, A. Tiyyagura, J. Yang, and G. Giuffrida. A fast algorithm for hierarchical text classification. In Proc. of the 2nd Int. Conf. on Data Warehousing and Knowledge Discovery (DaWaK’00), pages 409–418, London–Greenwich, UK, 2000. [10] S. T. Dumais. Improving the retrieval information from external soures. Behaviour Research Methods, Instruments and Computers, 23(2):229–236, 1991.

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[11] G. Salton and M. J. McGill. An Introduction to Modern Information Retrieval. McGraw-Hill, 1983. [12] L. T. K´oczy and T. D. Gedeon. Fuzzy tolerance relations based on hierarchical co-occurrence of words for intelligent information retrieval. Technical Report, University of New South Wales, 2000.

About the Authors Domonkos Tikk received his B.Sc. and M.Sc. degree in computer science both from E o¨ tv¨os L´or´and Science University in Hungary in the years 1993 and 1995, respectively. He received his doctoral degree in engineering in 2000 from Budapest University of Technology and Economics in Hungary. His research interests include data mining, text mining, automatical categorization methods, fuzzy systems, and soft computing techniques. Jae Dong Yang received the B.E. degree in computer engineering from Seoul National University, Seoul, Korea, and the M.S. and Ph.D. degrees in computer science from the Korea Advanced Institute of Science and Technology (KAIST) in 1985 and 1991, respectively. His research area includes fuzzy information retrieval, fuzzy reasoning, automatic document categorization, and databases. P´eter Baranyi received degrees M.Sc. in electrical engineering (1994), M.Sc. in Education of Engineering Sciences (1995) and Ph. D. (1999) from the Technical University of Budapest. His research focuses on fuzzy and neural network techniques. Anik´o Szak´al received her B.Sc. degree in information technology from Budapest Polytechnic, Hungary in 2000, and she is doing her M.Sc. studies at E o¨ tv¨os L´orand University, Budapest. She has twelve publications at proceedings of international conferences and workshops on the field of soft computing.

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How to Combine Various Factors to Select Appropriate Knowledge Elicitation Technique? Sandra Lovrenþiü Faculty of organization and informatics, University of Zagreb, Varaždin, Croatia [email protected]

Abstract — This paper presents well-known factors that influence the knowledge elicitation (KEL) technique selection combined with psychological factors. Those factors can be considered as crisp or fuzzy. Also, additional elements that influence on the determination of factors are proposed. This approach to the KEL technique selection, using elements, is implemented in a rule-based application with fuzzy reasoning that gives a list of ranked techniques as a result. Application research results were evaluated against research results obtained according to prior knowledge of research subjects in this field. The aim was to see whether there is a need to develop more complex and systematic methods for the KEL technique selection or simpler ones that can be easily made using excerpts from literature can give the same results quality. Proposals for other methods of the KEL technique selection are made.

1 Introduction There are many different approaches for solving the bottleneck problem of knowledge acquisition (KA) and knowledge elicitation (KEL), as its part. Nowadays, most of authors are occupied with automated knowledge acquisition and data mining. Those approaches solved many problems of acquiring and representing knowledge. Still, there is always a certain amount of knowledge that needs to be elicited from a domain expert. In that part of the knowledge elicitation still exists a problem of psychological factors that are involved on expert and knowledge engineer's side. Most of books regarding a KEL were published in late 1980’s and early 1990’s [1,2,3,4,5]. They covered the subject generally, mostly concentrating on interview and giving common guidelines about the elicitation process and when to use a certain technique. Articles published in last 15 years covered different aspects of KEL: a KEL technique classification [6,7], a comparison of KEL techniques [8,9,10,11,12] and various KEL tools [13,6,14,15,16,17,18,19]. Over years, different authors covered different techniques and different factors that influence on the technique selection. This article tries to unite the most often used techniques (sixteen of them) with eleven influence factors and additional elements that determine values of factors. Most factors are well known, as knowledge type, and they are combined with psychological factors, as expert’s verbal expression. It is obvious that in

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LOVRENýIû the real world each factor can have more than one value at a time, but with a different degree of confidence. Furthermore, it is obvious that the determination of values of those factors represents a subjective and uncertain estimation of a knowledge engineer (KE). The same can be applied to elements, so both factors and elements can be considered as fuzzy. As such, they are implemented in an application, where factors and technique values are obtained using fuzzy rules. Usage of both fuzzy factors and fuzzy elements is aimed precisely at overcoming the mentioned subjectivity of a KE’s judgement. To this proposed approach is opposed a classic way, mostly used in books that give guidelines about the selection process, which uses knowledge engineer’s knowledge, mostly without explicitly specifying factors.

2 Factors and Elements Ten influence factors that the author gave in [20] are now divided into eleven factors and each of them can obtain three possible values. Values of those factors can be determined:  directly, when a KE determines a value of a certain factor, or  indirectly, when a KE determines values of intermediary elements which then deter-mine factor values. For reasons of a KE’s uncertainty and subjectivity, for each factor two or three elements that should characterize a particular factor are proposed. 2.1 Factors Factors that influence on the KEL technique selection are divided into three groups. With each influence factor references that mention all or some parts of that factor are given:  Factors related to the problem domain x

knowledge type (procedural, declarative, combination) [2,6,7,8,9,10,15,21,22],

x

domain width (narrow, medium, broad) [6,21],

x

knowledge scope (common or special knowledge, or combination) [2,4,6,15 ];

 Factors related to participants in the elicitation process x expert type (verbal, non-verbal, in between) [2,4,6,7], x expert’s availability (good, medium, bad) [6], x relations between KE and expert (good, medium, bad) [6], x KE’s experience (good, medium, bad) [6], x KE’s knowledge of the problem domain (good, medium, bad) [2,6,10];  Factors related to elicitation techniques (short, medium, long) x preparation time [6], x training time[6],

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HOW TO COMBINE VARIOUS FACTORS TO SELECT APPROPRIATE ... x elicitation realization time [2,6,21]. 2.2 Elements Additionally to fuzzy factors, fuzzy elements for each factor, according to assumption of their influence on factor values, are proposed. Those elements for individual factors are as follows:  Knowledge type x procedures – the percentage of procedures in domain knowledge that a KE is ac-quainted with: the low percentage means that required knowledge will be more procedural, x concepts – the percentage of concepts in domain knowledge that a KE is acquainted with, x strategies, decisions, goals (SDG) - the percentage of strategies, decisions and goals in domain knowledge that a KE is acquainted with: the low percentage means that required knowledge will be more conceptual;  Domain width x subdomains – the number of subdomains of a problem domain, x solutions – the number of solutions that are required as an output from the system;  Knowledge scope x common knowledge - the percentage of common knowledge in domain knowledge that a KE is acquainted with: the low percentage means that required knowledge will be more common, x special knowledge - the percentage of special knowledge in domain knowledge that a KE is acquainted with;  Expert type x eloquence – a grade from one to ten that designates expert’s eloquence when he expounds his domain knowledge, x making conclusions - a grade from one to ten that designates expert’s explicitness when he expounds his conclusions and problem solving strategies, x prop-words - a grade from one to ten that designates expert’s stammer and usage of prop-words;  Expert’s availability x meetings – the number of KEL meetings that an expert has time for, x hours – the number of hours per one meeting that an expert has time for;  Relations between KE and expert

261

LOVRENýIû x cooperation – a grade from one to ten that designates expert’s readiness to cooper-ate in a KEL, x complaisance – a grade from one to ten that designates expert’s complaisance when a KE solves knowledge problems that occurred during the knowledgebased system (KBS) development;  KE’s experience x the number of techniques - the number of KEL techniques that a KE has practical experience with, x gathered knowledge - the percentage of success that a KE had in prior KEL cases;  KE’s knowledge of the problem domain x common knowledge - the percentage of common knowledge in domain knowledge that a KE is acquainted with (the same as for knowledge scope), x procedures knowledge – a grade from one to ten that designates a KE’s knowledge of characteristic domain procedures independently of the current problem, x concepts knowledge - a grade from one to ten that designates KE’s knowledge of characteristic domain concepts independently of the current problem;  Preparation time x the number of hours – the number of hours that a KE can spend to prepare himself for the elicitation;  Training time x the number of hours - the number of hours that an expert can spend to get acquainted with the technique and to prepare himself for the KEL;  Elicitation realization time x the number of hours - the number of hours that an expert and a KE can spend on the KEL process itself.

3 Selection Method Fifteen techniques used in this selection method are mentioned in [20]. The only difference is that real-time protocols are now divided into verbal and non-verbal. All sixteen techniques are: unstructured interview, semi-structured interview, structured interview, focused discussion, laddering, 20 questions, teach back, critique, construct elicitation (Repertory Grid Analysis), card sorting, matrices, verbal real-time protocols, non-verbal real-time protocols, retrospective protocols, role playing and simulation. The application, using only factors without elements, is also described in [20]. The final application is made in XpertRule tool [23], where each element and each factor is fuzzified using graphs on which functions for confidence degrees, or membership values (MV) are denoted for all element and factor values.

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HOW TO COMBINE VARIOUS FACTORS TO SELECT APPROPRIATE ... A classic way of the technique selection is, of course, used without an application. 3.1 Determining Factor Values To determine membership values for all factor values, a KE must estimate grades for all elements. Those grades are then fuzzified and used in fuzzy rules. For each factor exist three rules for each influence element (since each factor can have three different values). The process of fuzzy inference is made according to the MAX-MIN composition [23,24] described in [20] and the process of defuzzification is made according to the Centre-ofgravity (COG) method [23,24], also described in [20]. Obtained defuzzified factor values are then used as input for determining technique ranks. 3.2 Determining Technique Ranks The process of determining technique grades is the same as for factor values. A final solution is a list of ranked KEL techniques, as shown in Figure 1. The application offers the following knowledge elicitation technique list: Technique Semi-structured interview Focused discussion Structured interview Unstructured interview 20 questions Teach back Laddering Critique Simulation Role playing Construct elicitation Matrices Retrospective protocol Card sorting Non-verbal real-time protocol Verbal real-time protocol

Points 7,26 7,24 7,18 6,54 6,31 6,29 6,23 5,97 5,59 5,46 5,39 5,28 5,28 5,23 5,03 4,91

Figure 1: Application results Factor values obtained in the prior step are again fuzzified and used in fuzzy rules for each of sixteen techniques. Each technique has 33 rules (eleven factors with three possible values). Rules for determining technique grades are developed from textual descriptions in various literatures [2,4,6,7,8,9,10,15,21,22,25]. As a final solution is taken a result from COG formula, rounded on two decimal places for better distinction among technique ranks.

4 Research The aim of the evaluation was to prove the hypothesis that results of fuzzy rule-based approach (using the application) are better than those gained by a KE according to his/her

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LOVRENýIû prior knowledge in this field. The research was conducted at University of Zagreb, Faculty of organization and informatics in Varaždin, among third year students. 4.1 Knowledge Engineer Subjects Fourteen students and former students that already had a course in knowledge-based systems and developed demo-versions of KBS represented KE-s. Materials about techniques and influence factors were given to those KE subjects to study for a week. After that they had a short ten-question test about influence factors. Ten of them had 50% or more accurate answers and were included in further research. Six of them were female and four of them male. The year in which they took course in KBS is shown in Table 1. The average grade that subjects achieved on test was 6,10 out of 10. Course Year 1996/1997 1997/1998 1998/1999 1999/2000 2000/2001

Number of KE subjects 1 1 2 3 3

Table 1: The year of a KE subjects’ KBS course KE subjects were also asked to read two KEL problems and to rank KEL techniques from 1 to 16, where rank 1 denotes the most appropriate technique. The first problem was the appropriate wine selection for a certain meal and the second one was a cardiac infarct diagnosis. In both problem descriptions information about all factors was incorporated. Technique ranks were transformed into 1 to 10 grades, where the best technique obtained grade 10 and the worst 0,625. After that, pondered arithmetic mean was calculated from each technique grades, where ponders were grades that students gained on test. This mean was considered as final technique grade. According to those final grades, techniques were ranked so that a technique with the highest grade was put on the first place. 4.2 Evaluation Subjects 73 third grade students had lesson in knowledge elicitation as a normal part of their course in KBS and after that they received additional materials to study for a week. During the research, they were divided into two groups of 36 and 37 subjects. One group was the test group and the other the control group. They were tested with two tenquestion tests, one for influence factors and one for factor elements. They were also asked to read two KEL problems, the same as KE subjects. After that, lists of techniques and their grades for both problems, which were obtained by KE subjects, as described previously, were presented to the test group. Also, lists of techniques and their grades for both problems, which were obtained by application, were presented to the control group. Groups had to grade those lists according to seven criteria that will be described in the next section. The process of the hypothesis evaluation is shown in Figure 2. Only 30 students in each group had 50% or more accurate answers on test (28 in test group, so two students with 45% accurate answers were added) and their list grades were

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HOW TO COMBINE VARIOUS FACTORS TO SELECT APPROPRIATE ... taken into consideration. In the first group were 24 male and 6 female subjects. The second group consisted of 23 male and 7 female subjects. The average test grade was 6,43 for the first group and 6,08 for the second. Problem

Knowledge

Elements & Factors

10 students

Fuzzy rules

Technique list

Technique list

Test group

Control group

Figure 2: The hypothesis evaluation 4.3 Evaluation Criteria The application evaluation involved seven different criteria that comprised all eleven influence factors:  knowledge type,  domain width,  knowledge scope (with KE’s knowledge of the problem domain),  expert type,  relations and KE’s experience,  time limits (expert’s availability, preparation, training and elicitation realization time),  combination of all criteria. Evaluation subjects had to grade both problems technique lists for each criterion on one-to-five Likert-type scale. The grading form is shown in Figure 3.

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LOVRENýIû Please grade proposed solution with grades from 1 to 5 (1 - it doesn’t satisfy at all, 5 - completely satisfies) according to how it satisfies following characteristics of the problem (circle only 1 number): Characteristics 1. knowledge type (concepts, procedures, strategies) 2. domain width (subdomains, solutions) 3. knowledge scope (general, special, concepts, procedures) 4. expert type (eloquence, prop-words, stammer) 5. relations and experience (cooperation, successfully used techniques) 6. time limits (preparation, training, KEL) 7. all characteristics together

Solution 1

2

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Figure 3: The grading form 4.4 Results The research hypothesis was that the combination of eleven factors along with elements and implementation of fuzzines in the appropriate KEL technique determination would give better results than the determination of techniques by KE subjects’. To prove the hypothesis, for each criterion should have been proven the same. If we denote the average grade of the list obtained by KE subjects as X KE and the average grade of the list obtained by the application as X A , following hypotheses can be made: H 0 ... X A d X KE

H 1 ... X A ! X KE Hypotheses testing were made at 5% (Į.05) confidence level with one-tailed t-test. Results for the problem one are shown in Table 2 and for the problem two in Table 3. As it can be seen in results, the average grade for the technique list obtained by the application is significantly greater than the average grade of the technique list obtained by KE subjects according to all seven criteria and for both problems. Therefore, H0 should be rejected and H1 accepted. The proposed hypothesis is fully proven. According to the results, it is obvious that a systematic way of using relevant factors can give more satisfying proposal of a KEL technique that should be used in the KEL process than mostly non-systematic direct proposal of a knowledge engineer.

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HOW TO COMBINE VARIOUS FACTORS TO SELECT APPROPRIATE ... Criteria Knowledge Solution 1 type Solution 2 Domain Solution 1 width Solution 2 Knowledge Solution 1 scope Solution 2 Solution 1 Expert type Solution 2 Relations & Solution 1 experience Solution 2 Solution 1 Time Solution 2 Solution 1 All criteria Solution 2

X

3,100 3,700 3,133 3,633 3,367 3,767 3,500 4,000 3,433 4,033 2,900 3,733 3,367 3,733

į 0,978 0,737 0,763 0,482 0,752 0,844 1,057 1,183 0,920 0,795 0,746 0,964 0,605 0,573

t-test

p

2,683 p h/2 is given by [30]: N(X ) =

kª 2kh( X − h / 2) § X / h ·º 1− Ns¨ ¸» − j « 2¬ © 1 − X / h ¹¼ πX 2

(4a)

N s ( z) =

2 ª −1 1 1 § −1 1 ·º sin + cos¨ sin ¸ z z z ¹»¼ 𠫬 ©

(4b)

The classical backlash model corresponds to the DF of a linear system of a single mass M1+M2 followed by the geometric backlash having as input and as output the position variables x(t) and y(t), respectively, as depicted in Figure 2. For a sinusoidal input force f(t) = F cos(ωt) the condition X = h/2 leads to the limit frequency ωL applicable to this system: 1

ª2 º2 F ωL = « » ¬ h (M 1 + M 2 ) ¼

(5)

Figure 3 shows the Nyquist plot of –1/N(F,ω) = –1/[G(jω)N(X)] for several values of the input force F. Linear system

Backlash y

f(t)

1 (M1 + M 2 )s 2

x(t)

slope k

-h/2 h/2

G(s)

N(X)

Figure 2: Classical backlash model

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BARBOSA, MACHADO 6000

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Figure 3: Nyquist plot of −1/N(F,ω) for the system of Figure 2, F = {10, 20, 30, 40, 50} N, 0 < ω < ωL, M1 = M2 = 1 kg and h = 10−1 m This approach to the backlash study is based on the adoption of a geometric model that neglects the dynamic phenomena involved during the impact process. Due to this reason often real results differ significantly from those predicted by that model. 3.1 Dynamic Backlash In this section we use the DF method to analyse systems with backlash and impact phenomena, usually called dynamic backlash [33−34]. The proposed mechanical model consists on two masses (M1 and M2) subjected to backlash and impact phenomenon as shown in Figure 4. A collision between the masses M1 and M2 occurs when x1 = x2 or x2 = h+x1. In this case, we can compute the velocities of masses M1 and M2 after the impact ( x1′ and x 2′ ) by relating them to the previous values ( x1 and x 2 ) through Newton’s rule:

(x´′1 − x´′2 ) = −ε (x1 − x 2 ),

0 ≤ ε ≤1

(6)

where ε is the coefficient of restitution. In the case of a fully plastic (inelastic) collision ε = 0, while in the ideal elastic case ε = 1. x1 , x1

x 2 , x 2

f(t)

M2 M1 Side A

h

Side B

Figure 4: System with two masses subjected to dynamic backlash

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ANALYSIS OF SYSTEMS WITH BACKLASH AND IMPACTS... By application of the principle of conservation of momentum M 1 x1′ + M 2 x 2′ = M 1 x1 + M 2 x 2 and of expression (6) we can find the sought velocities ( x1′ and x 2′ ) of both masses after an impact, given by: x1 (M 1 − εM 2 ) + x 2 (1 + ε)M 2 x1 (1 + ε)M 1 + x 2 (M 2 − εM 1 ) , x 2′ = M1 + M 2 M1 + M 2

x1′ =

(7)

For the system of Figure 4 we calculate numerically the Nyquist diagram of −1/N(F,ω) for an input force f(t) = F cos(ωt) applied to mass M2 and considering the output position x1(t) of mass M1. The values of the parameters adopted in the subsequent simulations are M1 = M2 = 1 kg and h = 10−1 m. Figures 5 and 6 show the Nyquist plots for F = 50 N and ε = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9} and for F = {10, 20, 30, 40, 50} N and ε = {0.2, 0.5, 0.8}. The Nyquist charts of Figures 5−6 reveal the occurrence of a jumping phenomenon, which is a characteristic of nonlinear systems. This phenomenon is more visible around ε ≈ 0.5, while for the limiting cases (ε → 0 and ε → 1) the singularity disappears. Moreover, shows also that for a fixed value of ε the charts are proportional to the input amplitude F. 3000

2500

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Figure 5: Nyquist plot of −1/N(F,ω) for a system with dynamic backlash, for F = 50 N and ε = {0.1, .., 0.9} and F = {10, 20, 30, 40, 50} N and ε = 0.2 1200

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Figure 6: Nyquist plot of −1/N(F,ω) for a system with dynamic backlash, for F = {10, 20, 30, 40, 50} N and ε = {0.5,0.8}

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BARBOSA, MACHADO The validity of the proposed model is restricted to frequencies of the exciting input force f(t) higher than a lower-limit frequency ωC. On the other hand, there is also an upper-limit frequency ωL determined by application of Newton’s law to mass M2 and considering that the amplitude of the displacement is within the clearance h/2. In the middlerange frequency, ωC < ω < ωL, the jumping phenomena occurs at frequency ωJ. These frequencies are given by the following expressions: 1

1

1

2 ª§ º4 § F ·2 § F ·2 F · ¸¸ ¸¸ ⋅ (1 − ε)5 » , ω L = 2 ⋅ ¨¨ ¸¸ , ω J ~ ¨¨ ωc ≈ «¨¨ 2 «¬© M 2 ⋅ h ¹ »¼ © h ⋅ M2 ¹ © h⋅ M2 ¹

(8)

Figures 7 and 8 illustrate the variation of the Nyquist plots of −1/N(F,ω) for the cases of the static and dynamic backlash and shows the log-log plots of Re{−1/N} and Im{−1/N} versus ω for a coefficient of restitution ε = 0.5 and F = {10, 20, 30, 40, 50} N and for an input force F = 50 N and ε = {0.1, 0.3, 0.5, 0.7, 0.9}, respectively. 4

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2

ω (rad/s)

Figure 7: Log-log plots of Re{−1/N} and Im{−1/N} versus the exciting frequency ω, for ε = 0.5 and F = {10, 20, 30, 40, 50} N 10

4

10

4

Static

Static 10

3

ε =0.7, 0.9 ε =0.5 ε =0.3

10

10

10

ε =0.1

1

10

10

Dynam ic 10

10

Dynam ic

1

0

-1

0

10

10

ε =0.1 ε =0.3 ε =0.5 ε =0.7 ε =0.9

2

2

Im (-1/N)

Re(-1/N)

10

3

-1

10

10 0

1

10 ω (rad/s)

10

2

-2

-3

10

0

10

1

10

2

ω (rad/s )

Figure 8: Log-log plots of Re{−1/N} and Im{−1/N} versus the exciting frequency ω, for F = 50 N and ε = {0.1, 0.3, 0.5, 0.7, 0.9}

416

ANALYSIS OF SYSTEMS WITH BACKLASH AND IMPACTS... Comparing the results for the static and the dynamic backlash models we conclude that: − The charts of Re{−1/N} are similar for low frequencies (where they reveal a slope of +40 dB/dec) but differ significantly for high frequencies. − The charts of Im{−1/N} are different in all range of frequencies. Moreover, for low frequencies, the dynamic backlash has a fractional slope inferior to +80 dB/dec of the static model. A careful analysis must be taken because it was not demonstrated that a DF fractional slope would imply a fractional-order model. In fact, in this study we adopt integer-order models for the system description but the fractional-order slope is due to continuous/discrete dynamic variation that results due to the mass collisions. Figure 9 presents the Fourier transform of the output displacement of mass M1, F{x1(t)}, namely the amplitude of the harmonic content of x1(t) for an input force f(t) = 50 cos(ωt), ωC < ω < ωL, and ε = {0.2, 0.8}. The charts reveal that the fundamental harmonic of the output has a much higher magnitude than the other higher-harmonic components. This fact enables the application of the describing function in the prediction of limit cycles for this system. Nevertheless, for high values of ε, there is a significant high-order harmonic content, and by consequence, a lower precision of the limit cycle prediction. Figures 10−14 show the time response of the output velocity x1 (t ) of a system with dynamic backlash for ω = {15, 20, 25, 35, 40} rad/s and ε = {0.2, 0.5, 0.8}. The charts reveal that we can have chaotic or periodic responses according with the values of ω and ε. A complementary perspective is revealed by Figure 15 that depicts the number of consecutive collisions on side A (or B), nA (or nB), versus the exciting frequency ω and the coefficient of restitution ε for an input force f(t) = 50 cos(ωt). From Figure 15 we can distinguish two kinds of regions. The first, for ωC < ω < ωJ, where the system is characterized by an irregular number of impacts and a chaotic dynamics. The second, for ωJ < ω < ωL, where the motion is characterized by a regular behaviour corresponding to one alternate collision on each side of M1. The conclusions are similar to those obtained from Figures 10−14. ε=0.2

ε=0.8

Log(|F(x (t))|)

0

1

1

Log(|F(x (t))|)

2 0

−5

−10

−2 −4 −6

40

−8 30

ω (rad/s)

50 20 10 0

0

1

2

3

4

5

6

7

8

9

10

40 ω (rad/s)

30 20

harmonic index k

10 0

0

1

2

3

4

5

6

7

8

9

10

harmonic index k

Figure 9: Fourier transform of the output displacement x1(t), F{x1(t)}, over 20 cycles, versus the exciting frequency ω and the harmonic index k, for ε = {0.2, 0.8}

417

BARBOSA, MACHADO ε =0 .5 2

1.5

1.5

1

1

0.5

0.5 dx /dt

0

0

1

1

dx /dt

Model not applicable. For ε = 0.2 it results a lower-limit frequency ωC = 23.9 rad/s.

ε =0 .8

2

-0.5

-0.5

-1

-1

-1.5

-1.5

-2 1.65

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

-2 1.65

2.05

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

2.05

Figure 10: Plot of the output velocity x1 (t ) for ω = 15 rad/s and ε = {0.2, 0.5, 0.8} ε =0 .8 2

1.5

1.5

1

1

0.5

0.5 dx /dt

0

0

1

1

Model not applicable. For ε = 0.2 it results a lower-limit frequency ωC = 23.9 rad/s.

dx /dt

ε =0.5 2

-0.5

-0.5

-1

-1

-1.5

-1.5

-2 1.65

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

-2 1.65

2.05

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

2.05

Figure 11: Plot of the output velocity x1 (t ) for ω = 20 rad/s and ε = {0.2, 0.5, 0.8} ε =0.5

ε =0.8 2

1.5

1.5

1.5

1

1

1

0.5

0.5

0.5

0

1

1

0

-0.5

dx /dt

2

dx /dt

1

dx /dt

ε =0 .2 2

-0.5

0

-0.5

-1

-1

-1

-1.5

-1.5

-1.5

-2 1.65

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

-2 1.65

2.05

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

-2 1.65

2.05

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

2.05

Figure 12: Plot of the output velocity x1 (t ) for ω = 25 rad/s and ε = {0.2, 0.5, 0.8} ε =0.5

ε =0.8 2

1.5

1.5

1.5

1

1

1

0.5

0.5

0.5

0

1

1

0

-0.5

dx /dt

2

dx /dt

1

dx /dt

ε =0 .2 2

-0.5

0

-0.5

-1

-1

-1

-1.5

-1.5

-1.5

-2 1.65

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

-2 1.65

2.05

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

-2 1.65

2.05

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

2.05

Figure 13: Plot of the output velocity x1 (t ) for ω = 35 rad/s and ε = {0.2, 0.5, 0.8} ε =0.5

ε =0.8 2

1.5

1.5

1.5

1

1

1

0.5

0.5

0.5

0

1

1

0

-0.5

dx /dt

2

dx /dt

1

dx /dt

ε =0 .2 2

-0.5

0

-0.5

-1

-1

-1

-1.5

-1.5

-1.5

-2 1.65

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

2.05

-2 1.65

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

2.05

-2 1.65

1.7

1.75

1.8

1.85 1.9 time (s)

1.95

2

2.05

Figure 14: Plot of the output velocity x1 (t ) for ω = 40 rad/s and ε = {0.2, 0.5, 0.8}

418

ANALYSIS OF SYSTEMS WITH BACKLASH AND IMPACTS...

Figure 15: Number of consecutive collisions on side A (nA ) versus the exciting frequency ω and the coefficient of restitution ε, for an input force f(t) = 50 cos(ωt). For the side B (nB ) the chart is of the same type

4 Conclusions This paper addressed several aspects of the phenomena involved in systems with backlash and impacts. The dynamics of a two mass system was analysed through the describing function method and compared with standard models. The results revealed that these systems might lead to chaos and to fractional order dynamics. These conclusions encourage further studies of nonlinear systems in the perspective of the fractional calculus since integer order dynamical models are not capable to take into account many phenomena that occur.

References [1]

K. B. Oldham and J. Spanier. The Fractional Calculus. Academic Press, New York, 1974.

[2]

S. G. Samko, A. A. Kilbas and O. I. Marichev. Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, Amsterdam, 1993.

[3]

K. S. Miller and B. Ross. An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons, New York, 1993.

[4]

I. Podlubny. Fractional Differential Equations. Academic Press, San Diego, 1999.

[5]

R. Hilfer. Applications of Fractional Calculus in Physics. World Scientific, Singapore, 2000.

[6]

A. Gemant. A Method of Analyzing Experimental Results Obtained from Elasto-Viscous Bodies. Physics, 7: 311−317, 1936.

[7]

R. L. Bagley and P. J. Torvik. Fractional Calculus-A Different Approach to the Analysis of Viscoelastically Damped Structures. AIAA Journal, 21(5): 741−748, 1983.

419

BARBOSA, MACHADO [8]

L. Rogers. Operators and Fractional Derivatves for Viscoelastic Constitutive Equations. Journal of Rheology, 27(4): 351−372, 1983.

[9]

R. C. Koeller. Applications of Fractional Calculus to the Theory of Viscoelasticity. ASME Journal of Applied Mechanics, 51: 299−307, 1984.

[10] N. Makris and M. C. Constantinou. Fractional-Derivative Maxwell Model for Viscous Dampers. Journal of Structural Engineering, 117(9): 2708−2724, 1991. [11] L. Gaul and M. Schanz. Dynamics of Viscoelastic Solids Treated by Boundary Element Approaches in Time Domain. European Journal of Mechanics, A/Solids, 13(4) – suppl.: 43−59, 1994. [12] Åsa Fenander. Modal Synthesis when Modeling Damping by Use of Fractional Derivatives. AIAA Journal, 34(5): 1051−1058, 1996. [13] T. T. Hartley, C. F. Lorenzo and H. K. Qammer. Chaos in Fractional Order Chua’s System. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 42(8): 485−490, 1995. [14] B. Mandelbrot. The Fractal Geometry of Nature. W. H. Freeman and Company, New York, 1983. [15] A. Méhauté. Fractal Geometries: Theory and Applications. Penton Press, London, 1991. [16] Fernando B. Duarte and J. A. Tenreiro Machado. Chaotic Phenomena and Fractional-Order Dynamics in the Trajectory Control of Redundant Manipulators. Nonlinear Dynamics, 29(1−4): 315−342, July 2002. [17] T. J. Anastasio. The Fractional-Order Dynamics of Brainstem Vestibulo-oculomotor Neurons. Biological Cybernetics, 72: 69−79, 1994. [18] H. M. Ozaktas, Z. Zalevsky and M. A. Kutay. The Fractional Fourier Transform. John Wiley & Sons, Chichester, 2001. [19] B. Mathieu, L. Le Lay and A. Oustaloup. Identification of Non Integer Order Systems in the Time Domain. In Proceedings of the IEEE SMC/IMACS Symposium on Control, Optimization and Supervision, pages 952−956, Lille, France, 1996. [20] F. Mainardi. Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena. Chaos, Solitons & Fractals, 7(9): 1461−1477, 1996. [21] R. Gorenflo and F. Mainardi. Random Walk Models for Space-Fractional Diffusion Processes. FCAA Fractional Calculus and Applied Analysis, 1(2): 167−191, 1998. [22] N. Engheta. On the Role of Fractional Calculus in Electromagnetic Theory. IEEE Antennas and Propagation Magazine, 39(4): 35−46, 1997. [23] A. Méhauté. From Dissipative and to Non-dissipative Processes in Fractal Geometry: The Janals. New Journal of Chemistry, 14(3): 207−215, 1990. [24] A. Oustaloup. La Commande CRONE: Commande Robuste d’Ordre Non Entier. Hermes, Paris, 1991. [25] J. A. Tenreiro Machado. Analysis and Design of Fractional-Order Digital Control Systems. SAMS Journal Systems Analysis, Modelling, Simulation, 27: 107−122, 1997. [26] J. A. Tenreiro Machado. Discrete-Time Fractional-Order Controllers. FCAA Fractional Calculus and Applied Analysis, 4(1): 47−66, 2001.

420

ANALYSIS OF SYSTEMS WITH BACKLASH AND IMPACTS... [27] B. M. Vinagre, I. Podlubny, A. Hernández and V. Feliu. Some Approximations of Fractional Order Operators Used in Control Theory and Applications. FCAA Fractional Calculus and Applied Analysis, 3(3): 231−248, 2000. [28] I. Podlubny. Fractional-Order Systems and PIλDμ-Controllers. IEEE Transactions on Automatic Control, 44(1): 208−213, 1999. [29] J. A. Tenreiro Machado, Ramiro S. Barbosa, and N. M. Fonseca Ferreira. Fractional-Order Position/Force Control of Mechanical Manipulators. In Proceedings of the CIFA’2002 Conférence Int. Francophone d'Automatique, pages 641−646, Nantes, France, July 2002. [30] C. L. Phillips and R. D. Harbor. Feedback Control Systems. Prentice-Hall, New Jersey, 2000. [31] J. E. Slotine and W. Li. Applied Nonlinear Control. Prentice-Hall, New Jersey, 1991. [32] M. Nordin and P. Gutman. Controlling Mechanical Systems with Backlash−a Survey. Automatica, 38: 1633−1649, 2002. [33] Ramiro S. Barbosa and J. A. Tenreiro Machado. Describing Function Analysis of Systems with Impacts and Backlash. Nonlinear Dynamics, 29(1−4): 235−250, July 2002. [34] A. Azenha and J. A. T. Machado. On the Describing Function Method and the Prediction of limit Cycles in Nonlinear Dynamical Systems. SAMS Journal of Systems analysis, Modelling and Simulation, 33: 307−320, 1998. [35] G. Tao and P. V. Kokotovic. Adaptive Control of Systems with Unknown Output Backlash. IEEE Transactions on Automatic Control, 40(2): 326−330, 1995. [36] Y. S. Choi and S. T. Noah. Periodic Response of a Link Coupling with Clearance. ASME Journal of Dynamic Systems, Measurement and Control, 111(2): 253−259, 1989. [37] S. Dubowsky, J. F. Deck and H. Costello. The Dynamic Modelling of Flexible Spatial Machine Systems with Clearance Connections. ASME Journal of Mechanisms, Transmissions and Automation in Design, 109(1): 87−94, 1987. [38] Y. Stepanenko and T. S. Sankar. Vibro-Impact Analysis of Control Systems with Mechanical Clearance and Its Application to Robotic Actuators. ASME Journal of Dynamic Systems, Measurement and Control, 108(1): 9−16, 1986.

About the Authors Ramiro S. Barbosa was born in January 7, 1971. He graduated in Electrical Engineering - Industrial Control from Institute of Engineering of Polytechnic Institute of Porto, Portugal, in 1994 and received the Master’s degree in Electrical and Computer Engineering from the Faculty of Engineering of the University of Porto, Portugal, in 2000. Presently he teaches at the Institute of Engineering of the Polytechnic Institute of Porto, Department of Electrical Engineering. His research interests include modelling, control, fractional-order systems, and nonlinear systems. J. A. Tenreiro Machado was born in October 6, 1957. He graduated and received the Ph.D. degree in electrical and computer engineering from the Faculty of Engineering of the University of Porto, Portugal, in 1980 and 1989, respectively. Presently he is Coordinator Professor at the Institute of Engineering of the Polytechnic Institute of Porto, Department of Electrical Engineering. His main research interests are robotics, modelling, control, genetic algorithms, fractional-order systems and intelligent transportation systems.

421

422

Mathematical Model of the Half Bridge Resonant Converter Zoltán Puklus Széchenyi István University GyĘr Hungary [email protected] Abstract - The paper shows the topology of the symmetrical half bridge resonant converter (HBRC) which has been developed in our laboratory. Typical wave forms, simulation and measuring results are also presented. Operation boundaries are analyzed using energy considerations as well. The mathematical model (transfer function) of HBRC was developed. The obtained results point out that the same transfer function can be used for both the continuous and the discontinuous conduction modes.

1 Introduction Symmetrical resonant buck, boost and buck-boost converters are known from [1, 2, 3, 4, 9]. Transformer isolated belonging to this converter family has recently been developed in laboratories [6, 7, 8, 10]. The paper shows the topology of the symmetrical half bridge resonant converter (HBRC) (Fig.1)

Figure 1: Half bridge resonant converter (with D3) The important advantage of the resonant topology is the fact, that the switch on time of the switching elements (transistors) is determined by the operation of the main circuit part of the converter and not by the control circuit. The main task of the control circuit is the alternative switching of the two switches in the primary side with a duty factor of ca. 50%. 423

PUKLUS It is typical for the circuit that a transformer having a turn ratio of N1/N2 is connected in series with the resonant L and C elements. The turn ratio of this transformer changes the natural resonant frequency of the original L-C resonant circuit, but in this case, the value of the output voltage is not influenced by the turn ratio. The constant power operation is also characteristic for the circuit at a given frequency, which means that the power transferred is independent of the load resistor R0. The results obtained involve that the same transfer function belongs to both the continuous, and the discontinuous conduction modes.

2 Circuit analysis The half bridge resonant converter (Fig. 1) contains two voltage supplies (V1=V2=Vi) and 2 controlled switching elements (T1 and T2) in the primary part, furthermore a transformer with one primary and 2 secondary windings (L1 and L2= L3 ) as well as 2 (or 3) output diodes D1, D2 (D3) and a current choke (L=L4). Capacitor C=C1 and current choke L determine the resonant frequency, however it is modified by transformer winding ratio.

3 Operation of the converter This type of converters has two operation modes: the discontinuous conduction mode (DCM) and the continuous conduction mode (CCM) depending on the currentless condition of the current choke L. 3.1 DCM operation Investigating the steady state condition it can be supposed that at the beginning of the switching period the capacitor C is charged on the voltage (-Vi ) and the current choke L has no energy. Switching on T1, a sinusoidal current will flow through the elements Vi -T1-Tr-D1L-Vo-Tr-C-Vi. Taking into consideration the turn ratio of the transformer (N1:N2), the maximum value of this current is: I p max

2Vi  V 0 N1

N2

Z 0 L N1 N 2

(1)

where Ȧ0=(LC)-1/2 is the natural resonant angular frequency of the transformerless L-C circuit. The current increases the voltage of the capacitor C, then the capacitor charges to opposite polarity (+Vi ). The natural angular frequency of the sinusoidal current is as follows: Z 0tr

N2 Z 0 L 2 L1 Z 0 N1

the instantaneous primary current

424

(2)

MATHEMATICAL MODEL OF THE HALF BRIDGE RESONANT CONVERTER N1 N 2 sin § Z N 2 t · ¸ ¨ 0 N1 N1 ¹ © Z0L N2

2Vi  V0 ip

(3)

the secondary current is

N1 ip N2

(4)

the instantaneous voltage of current choke L is vL

N1 · § N2 · N2 § t¸ ¨ 2Vi  V0 ¸ cos¨ Z 0 N1 © N2¹ © N1 ¹

(5)

The process of charging to opposite polarity will finish at (t=tD), when the voltage of the capacitor C is equal to (+Vi ). When t = tD, then vC = Vi , vp = vsec = 0, vL= -V0 by using (5) we obtain  V0

N2 § N1 · § N2 · tD ¸ ¨ 2Vi  V0 ¸ cos¨ Z 0 N2¹ N1 ¹ N1 © ©

(5)

and N1 V0 N2 N1 2Vi  V0 N2 

N2 · § cos¨ Z 0 tD ¸ N1 ¹ ©

(6)

where cos D

V0 N2 V0  2 Vi N1

(7)

N2 tD N1

(8)

D Z0

The energy stored in the current choke L (W LI D2 / 2 ) dippers at the output. The current iL will decrease linearly, the slope is (-V0 /L). The current iL will commutate to the diode D1, D2 and D3 and the resonant process will be cut. The magnetizing current of the transformer flows through the diodes D1 and D2 to the output (via current choke L). The current iL decreasing linearly will reach zero before switching on the transistor T2. The circuit can operate without the diode D3, in this case the role of it is taken over by the diodes D1 and D2 in the ratio of 50 - 50%. It is normal that the diode D3 can not be used. In this cause get a practical half bridge resonant converter (Fig. 4) Using ultrafast rectifiers, the diode D3 will increase the efficiency by 1 or 1.5% based on our measurements (V1 = 20 - 30V, V0 = 2 - 5V). The current components (Fig. 3) of current choke L in Ts/2 period can be seen in Fig. 2 (two diode configuration).

425

PUKLUS

Figure 2: The currents of the L coil (DCM) In the second half period of the switching period Ts, the transistor T2 will be switched ON and the whole process will be repeated in the circuit containing the diode D2. 3.1.1 Energy considerations In the first half period of the switching period Ts, the voltage of the capacitor C changed from (-Vi) to (+Vi). This fact can be interpreted in such a way that the transferred amount of energy (energy parcel) to the output is: C 2Vi 2

2

W Ts i

2

2CVi 2

(9)

In the next half period the same amount of energy comes to the output, thus WiTs

4CVi 2

(10)

which shows, that the energy drawn by the converter does not depend on the value of the load resistor R0. Supposing constant output voltage V0 during the period Ts the output energy during the period Ts is as follows: W0Ts

Ts

V02 R0

1 V02 f s R0

(11)

Relation (10) show that the converter provides constant power at a given switching frequency and the output voltage can be determined using (10) and (11). V0

2Vi CR0 f s

(12)

4CVi 2 f s

(13)

The output power is P0

substituting (12) into (1) the maximum current will be I p max

2Vi § N1 · CR0 f s ¸ ¨1  N1 © N 2 ¹ Z0 L N2

426

(14)

MATHEMATICAL MODEL OF THE HALF BRIDGE RESONANT CONVERTER sinusoidal current will only be developed, when Ip max > 0 1!

N1 CR0 f s N2

(15)

i.e. energy transfer can only be developed, when the primary current ip exists, thus for R0,max R0,max 

1 2

§ N1 · ¨ ¸ Cf s © N2¹

(16)

using (12) and (16) V0

2Vi

N2 N1

R0 R0,max

(17)

N2 N1

(18)

obtain V0 max

2Vi

if the parameters are R0 and fs we’ll obtain the V0-I0 characteristic of the converter (Fig. 3)

Figure 3: V0-I0 characteristic 3.2 CCM operation It has been proved that P=const. in DCM. Though in CCM the charge current of the capacitor C has two components (19), the transferred energy amount will be constant during a switching period. This holds true because the voltage change on the capacitor C will be the same in both cases (2 Vi). In CCM the primary current can be given by (19), where IL0 is the value of iL when the transistor turns ON. N1 V0 N 2 sin Z N 2 t  I N1 cos Z N 2 t 0 L0 0 N1 N2 N1 N1 Z0 L N2

2Vi  ip

Figure 5 shows the iL current and the iD2 current.

427

(19)

PUKLUS

Figure 4: Half bridge resonant converter

Figure 5: Current iL in CCM

4 Mathematical Model The injected-absorbed current method [11] will be used to the identification of the HBRC’s transfer function. For this we have to determine the average current which is injected to the output. The general case (DCM or CCM): In case of the lossless converter we can write WiTs

W0

V0 Q0

(20)

where Q0 is the output charge on the V0 output voltage. By using (10) it is true that Q0

4CVi 2 V0

I 0 Ts

(21)

where I0 is the average injected current in general case. It is

I0

4Cf s

Vi 2 V0

(22)

The partial differentiation of the injected current is GI 0

GI 0 GI GI Gv i  0 Gv 0  0 f s v Gv i Gf s

428

(23)

MATHEMATICAL MODEL OF THE HALF BRIDGE RESONANT CONVERTER V GI 0 8Cf s i V0 Gv i GI 0 V 2i 4Cf s 2 Gv 0 V0

GI 0 Gf s

(24) (25)

2

4C

Vi V0

(26)

The total differential of the injected current GI0 is then 2

GI 0

8Cf s

Vi V V 2i Gvi  4Cf s 2 Gv0  4C i Gf s V0 V0 V0

(27)

After taking the Laplace transform of (27), we obtain an equation for the injected current I0(s). The s model of the R0-C0 output is V0 ( s ) I 0 ( s)

R0 1  sR0 C 0

(28)

The complete transfer function model of HBRC is shown in Fig5.

Figure 5: The transfer function model of a HBRC (the same as in DCM and CCM) Fig. 6 illustrates the control block diagram for closed loop control of the converter (VFO - Variable Frequency Oscillator )

Figure 6: Converter with closed loop control

429

PUKLUS

5 Conclusions A lot of HBRC equations were determined. The possible modes of operation of the converter were identified. Boundary conditions for critical mode (R0,max) were found. The converter designed by the above mentioned procedure was built and tested. All timing information, currents and voltages can be read from the attached waveforms, and compared to simulated values. The designed and the measured parameters are rather close to each other. P=const. operation is also characteristic for the circuit at a given frequency which means that the power transferred is not depending on the value of resistor R0 . It has been pointed at that the transfer function model of the converter is identical in the DCM and CCM. The PSpice simulation and the laboratory measurements confirm the viability of this topology.

References >1@ Nagy I.: Resonant DC-DC Configurations. 3rd European conference on Power Electronics and Applications, 1989 pp.1495-1500. vol. III. Aachen, Germany

[2] Z. Puklus: The Resonant flyback converter -PEMC'98 8th International Power Electronics & Motion Control Conference 8-10 September 1998 Prague Proceedings volume Last minute papers pp. 2.229-2.234 and CD-ROM 2.229-2.234 >3@ Z. Puklus, L. Hodossy, P. Cs. Szilagyi: Contribution to the Development of a New Type of DC/DC Converters-IECON'97- The 23rd Annual International Conference of the IEEE Industrial Electronics Society, New Orleans, Louisiana USA November 9-14, 1997, Proceedings Volume 2 of 4 pp 581-586 >4@ Z. Puklus, L. Hodossy, P. Cs. Szilagyi,: Analysis and test results of double buck and buck/boost quasi-resonant converters-EPE'97-7th Europen Conference on Power Electronics and Applications 8-10 September 1997, Trondheim, Norway Proceedings volume 2 pp. 2.196-2.201 >5@ M. Kazmierczuk,D. Czarkowski: Resonant Power Converters, John Wiley & Sons Inc. New York 1995 >6@ Z. Puklus, P. Cs. Szilagyi L. Hodossy, L. Gyimesi : Resonant flyback converter, PECIM'98 Power Electronics,- Automation, Motion,- Drives & Control Power QualityInternational Conference-, May 26-28 1998, Nuremberg, Germany Proceedings volume 38 pp 495-500 >7@ Z. Puklus: The (quasi) Resonant flyback converter, IECON'98- The 24th Annual International Conference of the IEEE Industrial Electronics Society, Aachen, Germany August 31-Sept. 4, 1998 Proceedings volume 2 pp. 1066-1071 >8@ J. Hamar, I. Nagy: New Topologys of a Resonant Converter Family Electromotion’01 June 2001 Bologna, Italy >9@ Z. Puklus, P. Cs. Szilagyi, P. Korondi: Sliding Mode Controlled Dual-buck Resonant Converter- INES’2000 IEEE International Conference on Intelligent Engineering Systems, 17-19 September, 2000, Portoroz, Slovenia, Proceedings pp.345-349. >10@ Z. Puklus, L. Hodossy, Z. Szikál, T. Szaif: Synchronous Half Brige Resonant Converter. Proceedings of the 5th IEEE International Conference on Intelligent Engineering Systems (INES 2001), Helsinki, Finland, September 16-18, 2001, pp. 501-505, ISBN 952-15-0689-X >11@ A.S.Kislovski, R. Redl, N.O. Sokal: Dynamic Analysis of Switching-Mode DC/DC Converters Design Automation Inc. Lexington, MA, U.S.A. 1996

430

MATHEMATICAL MODEL OF THE HALF BRIDGE RESONANT CONVERTER

About the Author Zoltán Puklus received doctoral degree in technical sciences in 1998 from the Technical University of Cluj.Napoca in Romania. His research includes switch mode power supplies and its controls, motion control, and EC motor control.

Appendix: Laboratory and Pspice Results The half bridge resonant converter from fig 1 was built and its Pspice and laboratory results are as follows: Vo-Io With D3 Diode

Vi=40 V C=47nF L=210μH

20

100

18

70

50

40

16

30

14 Vo [V]

12

35 KHz

20

50 KHz

10

62,5 KHz 8

83,3 KHz

6

10

4 2 0 0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

Io [A]

(measurement) Vo-Io output characteristic

With & without D3 Diode 80 78

? [%]

76 74

With Diode

72

Without Diode

70 68 66 0

0,1

0,2

0,3

0,4

0,5

Io [A]

(measurement) Efficiency

431

0,6

PUKLUS

(measurement) A1 – D3 diode current; A2- D1 diode current

(Pspice) H1-D1+D2+D3=L current; H2-D1 current; H3-D3 current

(PSpice) E1– D3 diode current; E2- D1 diode current

432

UML Statechart-Based Verification and Testing of Embedded Systems Balázs Benyó Department of Informatics Széchenyi István University, GyĘr, Hungary [email protected]

Abstract  This paper introduces the use of statechart models for the verification of the design and implementation process of embedded software systems. The proposed system verification process includes automated design verification and automated testing phases to encourage the development of fault-free systems. All the phases of the statechart-based verification are fully integrated into the development process which allows the automated execution of the verification and testing steps. This paper presents the proposed verification and testing algorithms. The algorithms have been implemented in a common development environment. This environment combines both self-developed and off-the-shelf components. The environment works with standard UML models shared with the system under development. The paper deals with the details of the proposed design and development process and also introduces an application example.

1 Introduction Validation and verification are essential phases of the development of computer-based systems. With the enlargement of the size and complexity of the systems under development the importance of these tasks has increased. The system development process, regardless of the applied methodology, can be divided into two main phases (Figure 1):  analysis & design  implementation. The system development process is typically accompanied by the occurrence of design and implementation faults. To avoid these faults the different phases of the system development are supplemented by verification and validation steps. These steps are intended to discover the faults that may arise in the design and implementation by finding any differences between the requirements and the design or the requirements and the implemented system.

433

BENYÓ The verification and validation are very time-consuming parts of system development. The time consumption of these phases can run up to 40% of the total development time, depending on the size and complexity of the system under development.

Requirements

1. Analysis & Design verification

Design (statechart model)

2. Design Verification Verified Design (statechart model)

3. Implementation

Implemented System (C code) 4. Testing

Tested System

Figure 1: Main phases of the development process The verification and validation can be done by testing. Testing is the process when the behaviour of the system is compared with the requirements when the system is activated by a given input stimulus. Testing includes different activities:  test case definition (the definition of the input data to use and other conditions of the testing)  test case execution and the evaluation of the results. In order to accelerate the otherwise time-consuming verification of large systems, the automation of these activities is essential. In modern software development environments, system development is supported by CASE tools. The CASE tools allow the use of formal or semi–formal models of the system under development to accelerate the design and implementation. These design models can be efficiently used for the acceleration of testing activities as well. The definition of test cases and the evaluation of the test results can be easier when they are based on the

434

UML STATECHART-BASED VERIFICATION AND TESTING OF EMBEDDED … design models. In the case of formal design models these activities can even be automated [1]. Implementation faults can be discovered by testing the implemented system. However, design faults may remain undiscovered. In order to recognize these faults, the development process has to be completed by the design verification step. The goal of design verification is to find faults in the design itself. The design faults may be instantiated as an  inconsistent design (i.e. there are contradictions in the design itself) or as  contradictions between the design and the original requirements. In the case when the requirements are not defined formally, the consistency between the requirements and the design can be verified only manually. However, as mentioned above, in the modern software development environments (supported by CASE tools) the design can be generated in the form of a formal description. This allows us to verify the consistency of the design itself by automated tools [2]. 1.1 Goal of the research The goal of our research work was to develop a system development process that includes automated design verification and automated testing steps. In our work the UML statechart diagram has been selected as a common formal description format of the system under development. Statecharts are a widely used modeling language of embedded systems containing digital hardware and software components [3]. Statechart diagrams are frequently used in the field of embedded system design [4] and in process automation [5]. The designers of communication systems traditionally use statecharts (e.g. in protocol design) for the description of the behavior of communicating objects.

2 Integrated Development Environment 2.1 Design Verification Subsystem The design verification in the proposed development process is implemented by the design verification subsystem [2]. The design verification subsystem includes the SPIN model checker [6], and a self-developed intelligent data converter unit. The verification subsystem is able to recognize design faults in the statechart models, e.g. inaccessible or deadlock states. The internal structure of the design verification system is introduced in Figure 2. The UML statechart diagrams are transformed to a model checker compatible format in two steps. In the first step the XML representation of the diagrams is extracted and then the models are converted to a model checker specific description. The format of this description is defined by a formal modeling language called Promela (Process Meta Language) [6]. Promela is the input format of the SPIN model checker used in the design verification subsystem. The Promela language allows the description of concurrent objects and the communication between them. The details of the conversion and the model checker are described in detail in [7] and [8].

435

BENYÓ Design statechart model

2. Design verification 2.1 XML converter

occurrent corrections

XML description

model checker specific description

2.2 Of-the-shelf model checker

Verified Design statechart model

Figure 2: Automated design verification 2.2 Testing Subsystem The automated testing of the system under verification is implemented by the integration of a previously developed testing system [1], [9].The integrated system is a state diagram based automated testing system. It is able to execute test cases with the implemented system and compare the behavior of the system under test with the behavior defined by state diagrams in the design. The system is able to derive different metrics (e.g. state coverage) to control the testing process. The testing system uses state diagrams to describe the behavior of the system under test. The mapping between the model elements of UML statecharts and state diagrams had to be defined in order to integrate the state diagram based testing to the UML-based development process [10]. The UML statechart model allows several sophisticated description opportunities to describe the system behavior [11]. The equivalent state diagram representation of many of these constructs results in a complicated state diagram model. Because of this, the set of UML constructs allowed for use in the statechart model is limited in order to simplify the model conversion. The allowed modeling constructs are as follows:  states,  events (without guard conditions),  actions. This subset will be the subject of extension in a further phase of the research. The steps of the testing process are shown in Figure 3. The testing process will be introduced in detail by an example in the following section.

436

UML STATECHART-BASED VERIFICATION AND TESTING OF EMBEDDED …

Implemented System C code

Verified Design statechart model

4. Test 4.2 State diagram converter

4.1 Code annotation

state diagram

annotated C code occ. corrections 4.3 Test case execution

Tested System

Figure 3: Automated testing 2.3 Example The system under development in the introduced example is the controller software of an ASI Master card. The ASI is a fieldbus standard widely used in process automation. The software was designed to control the Master node of the fieldbus network. The ASI Master Firmware is an interrupt driven system. In the example, the behavior of its interrupt controller is verified (together with the behavior of the environment that generates the signals). The statechart diagram of the core behavior of the interrupt controller is presented in Figure 4. The state transitions are initiated by one or more events and could result in the generation of other events. The dependencies are modeled by statechart diagrams as well. In Figure 5 an example of this conditional event generation is presented. The condition for the generation of the event Interrupt_AnyError_NoRes is the occurrence of all of the following three events: NoResetInterruptReceivePointer, AnyError, and Interrupt. The model of the full system consists of 7 statechart diagrams containing 39 states and 82 transitions.

437

BENYÓ

Interrupt_AnyError_NoRes / PointerIs1_AnyError0

Interrupt_FatalError_NoRes / PointerIs1_FatalError0

Interrupt_AnyError_NoRes / PointerIs2_AnyError1

Interrupt_GeneralError_NoRes / PointerIs1_GeneralError0

Interrupt_FatalError_NoRes / PointerIs2_FatalError1

Interrupt_NoError_NoRes / PointerIs1_NoError0

Interrupt_GeneralError_NoRes / PointerIs2_GeneralError1

Interrupt_AnyError_NoRes / PointerIs3_AnyError2 Interrupt_FatalError_NoRes / PointerIs3_FatalError2 Interrupt_GeneralError_NoRes / PointerIs3_GeneralError2

ResetInterruptReceivePointer ISRBuffer2

ISRBuffer1

ISRBuffer0

Interrupt_NoError_NoRes / PointerIs2_NoError1

ISRBuffer3

Interrupt_NoError_NoRes / PointerIs3_NoError2

ResetInterruptReceivePointer ResetInterruptReceivePointer ResetInterruptReceivePointer

Interrupt_AnyError_NoRes / PointerIs0_AnyError3

Interrupt_FatalError_NoRes / PointerIs0_FatalError3

Interrupt_GeneralError_NoRes / PointerIs0_GeneralError3

Interrupt_NoError_NoRes / PointerIs0_NoError3

Figure 4: Statechart of the interrupt controller of the ASI Master A nyE rror

IT

IT +Error

N oRese tInterrup tRecei vePoi nte r Interrupt

I nterrupt

AnyE rror

N oR es etI nterrupt Rec eiv ePoin ter ^ISR _Ev entQueue. Int errupt_Any Error_NoRes

N oR es et I nterrupt Rec eiv ePoin ter

Error

NoRes et Int errupt Rec eiv ePointer

Erro r+N RI RP

I nterrupt ^I SR_Ev ent Queue.I nterrupt _A ny Error_N oR es

End

AnyE rror Any Error ^I SR_Ev e nt Queue.I nt erru pt _Any Error_NoRes

NR IR P

Interru pt

IT +NRIRP

Figure 5: Statechart of the event generation The description of the state diagram model of the interrupt controller of the ASI Master is shown in Figure 6. The state diagram model is described by a formal language defined in [12]. In order to generate this description, the state diagram converter extracts the XML representation of the state chart model, and then translates the state chart model elements to the corresponding state diagram construct. The mapping between the state chart elements and the state diagram constructs is defined in [10].

438

UML STATECHART-BASED VERIFICATION AND TESTING OF EMBEDDED … BEHAVIOUR ISR; AUTOMATON ControlISR: ISRBuffer0, ISRBuffer1, ISRBuffer2, ISRBuffer3; FROM FROM FROM FROM FROM

ISRBuffer0 ISRBuffer0 ISRBuffer0 ISRBuffer0 ISRBuffer0

ON ON ON ON ON

ResetInterruptReceivePointer Interrupt_AnyError_NoRes Interrupt_FatalError_NoRes Interrupt_GeneralError_NoRes Interrupt_NoError_NoRes

TO TO TO TO TO

ISRBuffer0; ISRBuffer1 ISRBuffer1 ISRBuffer1 ISRBuffer1

WITH WITH WITH WITH

PointerIs1_AnyError0; PointerIs1_FatalError0; PointerIs1_GeneralError0; PointerIs1_NoError0;

FROM FROM FROM FROM FROM

ISRBuffer1 ISRBuffer1 ISRBuffer1 ISRBuffer1 ISRBuffer1

ON ON ON ON ON

ResetInterruptReceivePointer Interrupt_AnyError_NoRes Interrupt_FatalError_NoRes Interrupt_GeneralError_NoRes Interrupt_NoError_NoRes

TO TO TO TO TO

ISRBuffer0; ISRBuffer2 ISRBuffer2 ISRBuffer2 ISRBuffer2

WITH WITH WITH WITH

PointerIs2_AnyError1; PointerIs2_FatalError1; PointerIs2_GeneralError1; PointerIs2_NoError1;

FROM FROM FROM FROM FROM

ISRBuffer2 ISRBuffer2 ISRBuffer2 ISRBuffer2 ISRBuffer2

ON ON ON ON ON

ResetInterruptReceivePointer Interrupt_AnyError_NoRes Interrupt_FatalError_NoRes Interrupt_GeneralError_NoRes Interrupt_NoError_NoRes

TO TO TO TO TO

ISRBuffer0; ISRBuffer3 ISRBuffer3 ISRBuffer3 ISRBuffer3

WITH WITH WITH WITH

PointerIs3_AnyError2; PointerIs3_FatalError2; PointerIs3_GeneralError2; PointerIs3_NoError2;

FROM FROM FROM FROM FROM

ISRBuffer3 ISRBuffer3 ISRBuffer3 ISRBuffer3 ISRBuffer3

ON ON ON ON ON

ResetInterruptReceivePointer Interrupt_AnyError_NoRes Interrupt_FatalError_NoRes Interrupt_GeneralError_NoRes Interrupt_NoError_NoRes

TO TO TO TO TO

ISRBuffer0; ISRBuffer0 ISRBuffer0 ISRBuffer0 ISRBuffer0

WITH WITH WITH WITH

PointerIs0_AnyError3; PointerIs0_FatalError3; PointerIs0_GeneralError3; PointerIs0_NoError3;

Figure 6: State diagram of the interrupt controller During the test execution, the testing subsystem traces the state of the system based on the annotation inserted to the original code. In the current system setup the annotation is done manually, however theoretically it can be automated. The code annotations are special comments in the source code as can be seen in Figure 7. These comments are valid C statements separated by comment symbols from the original code.

/*@ ISR_InterruptReceivePointer */ // BTH_OnPoint("ISR: ISR_InterruptReceivePointer", // 12, __FILE__, __LINE__,0, 4, // (MDS->p_uee_receive == 0), // (MDS->p_uee_receive == 1), // (MDS->p_uee_receive == 2), // (MDS->p_uee_receive == 3) );

Figure 7: Code annotation example

439

BENYÓ In the release version of the system these comments are discarded by the compiler but during the test phase the test environment processes these comments as well. During the execution of the test cases, based on the annotation statements, the test environment can trace the current state of the system. In each test case the actual state transitions of the system are compared to the state transitions defined by the state diagram. Based on the comparison, the behaviour of the implemented system can be verified. More detailed description of the automated test case execution is described in [9].

3 Conclusion The process of statechart model based design and implementation of embedded systems has been introduced. The main benefits of the proposed process are fast and fault-free system development. The avoidance of faults is supported by including design verification and testing steps in the development process. In order to reduce the time demand of these otherwise time-consuming phases of the system development the verification and testing steps are automated. The proposed development process is implemented in a common software development environment. The environment efficiently integrates self-developed and off-the-self components. The proposed development and verification process uses the same standard UML statechart model as used for the development of the system.

4 Further Work The primary goal of further research work is the development of the fully- or semiautomated code annotation algorithm. We are also targeting the integration of an automated test case generator to the development environment. This test case generator will traverse the paths in the state chart model and generate test cases for each traversed path.

Acknowledgments This research was supported by the Hungarian National Research Fund (grant No. OTKA F029739, T029830) and by the Hungarian Ministry of Education (grant No. FKFP 0200/2001). The research work of Balázs Benyó is supported by the Hungarian Ministry of Education (Békésy György Scholarship).

References [1]

B. Benyó. Verification of complex object oriented systems. In Proceedings of the 4th IEEE International Workshop on Design and Diagnostics of Electronic Circuits and Systems 2001, pp. 289-290, GyĘr, Hungary, April 18-20, 2001

[2]

Á. Darvas, I Majzik, and B. Benyó. Verification of UML Statechart Models of Embedded Systems. In Proceedings of the 5th IEEE International Workshop on Design and Diagnostics of Electronic Circuits and Systems 2002, pp.70-77, Brno, Czech Republic, April 16-19, 2002, ISBN 80-214-2094-4

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UML STATECHART-BASED VERIFICATION AND TESTING OF EMBEDDED … [3]

Cs. Szász and J. Sziray. Run-Time Verification of UML State-Chart Implementations. In Proceedings of the 4th IEEE International Conference on Intelligent Engineering Systems, pp. 355-358, Portoroz, Slovenia, Sept 17-19, 2000, ISBN 961-6303-23-6

[4]

D. Bursky: Embedded-Controller Architectures Suit All Needs. Electronic Design, pp. 5364, January 8, 1996

[5]

P. Várady, Z. Benyó, and B. Benyó. An Open Architecture Patient Monitoring System Using Standard Technologies. IEEE Transaction on Information Technology in Biomedicine, Vol. 6, No. 1, pp. 95-98, March 2002, ISSN 1089-7771

[6]

G. J. Holzmann: The Model Checker SPIN. IEEE Trans. on Software Eng, pp. 279-295, Vol. 23, No. 5, 1997

[7]

D. Latella, I. Majzik, and M. Massink. Automatic Verification of UML Statechart Diagrams using the SPIN Model-Checker. Formal Aspects of Computing, pp. 637-664, Vol. 11, No. 6, Springer Verlag, Berlin, 1999

[8]

J. K. Tar, I. J. Rudas, and J. F. Bitó. Group Theoretical Approach in Using Canonical Transformations and Symplectic Geometry in the Control of Approximately Modeled Mechanical Systems Interacting with Unmodelled Environment, Robotica, pp. 163-179, Vol.15, 1997

[9]

P. Várady and B. Benyó. A Systematic Method for the Behavioural Test and Analysis of Embedded Systems. In Proceedings of the 4th IEEE International Conference on Intelligent Engineering Systems, pp.177-180, Portoroz, Slovenia, Sept 17-19 2000, ISBN 961-630323-6

[10] V. Lévai. Verification of software systems based on state transition diagrams. BSc Thesis (in Hungarian), Széchenyi István University, GyĘr, 2000 [11] Zs. Pap, I. Majzik, A. Pataricza, and A. Szegi. Completeness Analysis of UML Statechart Specifications. In Proceedings of the 4th IEEE International Workshop on Design and Diagnostics of Electronic Circuits and Systems 2001, pp. 83-90, GyĘr, Hungary, April 18-20, 2001 [12] P. Várady: Konzeption und Entwicklung einer Analysebibliothek zum Test des Verhaltens eingebetteter Software, MSc Thesis (in German), FZI-MRT, Karlsruhe, 1997

441

442

Author’s Index Akama, Kiyoshi, 299 Arat´o, P´eter, 311, 373

Ishikawa, Takahiko, 299 Jakobovi´c, Domagoj, 121

Baranyi, P´eter, 15, 225, 249 Barbosa, Ramiro S., 41, 411 Bednar, Peter, 237 Bencsik, Attila L., 169 Beny´o, Bal´azs, 433 Berger, Ulrich, 145 Bit´o, Jan´os F., 3 Bogunovic, Nikola, 199 Brumnic, Antun, 397 Budin, Leo, 121

Kand´ar, Tibor, 373 Kem´eny, Zsolt, 323 Kirner, Raimund, 67 Kov´acs, L´aszl´o, 225 Laczay, B´alint, 349 Lendvay, Marianna, 169 Lepratti, Raffaello, 145 Lopes, Ant´onio, 87 Lovrenˇci´c, Sandra, 259

Catrina, Gheorghe, 79 Cs´ak, Bence, 373 ˇ Cubrilo, Mirko, 211, 283

Mabuchi, Hiroshi, 299 Machado, J. A. Tenreiro, 41, 87, 109, 411 Malekovi´c, Mirko, 211, 283 ´ am, 311, 349 Mann, Zolt´an Ad´ Martins, J. F., 29 Mazilu, Dumitru, 79 Megyeri, Csaba, 349 Mendes, R. Vilela, 29 Michelberger, P´al, 15

Dente, J. A., 29 Dong Yang, Jae, 249 Duarte, Fernando, 41 Elmenreich, Wilfried, 67, 335 Ferreira, Nuno, 41 Friedler, Ferenc, 157

Nagy, Istv´an, 99 ´ Nov´ak, Agnes B., 189

Glavinic, Vlado, 271 Golda, Bence, 349 Gyapay, Szilvia, 157

Oliveira, P. B. de Moura, 109 Orb´an, Andr´as, 311 Paralic, Jan, 237 Pataricza, Andr´as, 157 Patriciu, Alexandru, 79 Penya, Yoseba K., 135 Peti, Philipp, 335

Horv´ath, L´aszl´o, 179, 363 Imecs, M´aria, 53 Incze, J´anos J., 53 Iordachita, Iulian, 79

443

Pires, A. J., 29 Pires, E. J. Solteiro, 109 Puklus, Zolt´an, 423 Recski, Andr´as, 349 Rosic, Marko, 271 Rudas, Imre J., 3, 179, 363 Sauter, Thilo, 135 Silva, Manuel F., 87 Stankov, Slavomir, 271 Stoianovici, Dan, 79 Szab´o, Csaba, 53 Szak´al, Anik´o, 249 Sziray, J´ozsef, 157, 385 Tar, J´ozsef, 3 Tikk, Domonkos, 15, 249 Tuza, Zsolt, 189 Ujevic, Filip, 199 V´as´arhelyi, J´ozsef, 53 Yam, Yeung, 15 Yamamoto, Yuichi, 299

444