Computational Intelligence Applied to Nonlinear

International Journal of Computational Intelligence Systems, Vol.2, No. 2 (June, 2009), 99-103

Computational Intelligence Applied to Nonlinear Dynamics and Synchronization Abdelhamid Bouchachia, Kyandoghere Kyamakya Preface In general, to efficiently deal with modeling of complex nonlinear dynamical systems three essential tasks amongst others are involved, namely understanding, predicting, and explaining. The understanding task aims at developing mathematical models of systems relying on available data, measurements and observations in a bottom-up fashion. This allows identifying the system’s dynamics including the external interactions that affect the system’s behavior. Such identification should specify the set of functions (rules or equations) that captures the factors that control the change of the system’s behavior. Often, the identification task is reduced to choosing a certain parameterized model for which an estimation of the unknown parameters is to be performed. Identification as a process may be part of a more general task that is control whose aim is to equip the system with regulation mechanisms that provide stability and the desired performance in presence of feedback and disturbances from the environment. There is no doubt that the identification and control tasks are typical computational tasks that involve various algorithmic paradigms. The second task in system modeling is prediction which in broad terms is the process of predicting the outcome or the next system state at some future point of time. For this as well appropriate algorithmic models are necessary. Often the understanding stage is supplemented by the prediction task. The underlying idea is to develop a prediction model that reflects the system’s functionality like in understanding, but additionally, the model’s parameters must be tuned to observe and monitor the system’s behavior. This process is usually referred to as the learning stage. Once it is exhausted, the system goes through validation and deployment for prediction purposes. The third task is explaining and aims at comprehending the evolution of the system’s behavior from past states to the current state or eventually explaining the output of the system. This process is known as diagnosis and can also be involved in the analysis of the system being examined. The core issue here concerns the development of computational models that allow checking whether the system behaves correctly and consistently and, whenever incorrect behavior is observed, determining the faulty part(s) in the system. Clearly, all these tasks have common roots and require computational models. Hence the relevance of computational intelligence (CI) techniques in the context of cybernetics modeling becomes manifest. The application of such computational models is prompted by the optimization and computational speed requirements of the different tasks. However, since modern algorithmic models for system analysis and design are inspired from biological and natural intelligence, one often refers to these models as computational intelligence models. Computational intelligence techniques generally include the following: -

Evolutionary computing is a set of metaheuristics inspired from biological evolution and based on natural selection and genetic inheritance. It is mainly applied for optimization purposes in the various systems’ engineering and modeling of nonlinear dynamic systems 2,5,13,21,22,36. Neurocomputing is the set of problem-solving techniques that are based on principles and mechanisms of information processing in the brain. Neural networks have shown their efficiency in various identification, prediction, and diagnostic cases 25,34,35,38. Granular computing is the set of techniques that are based on the notion of information granulation to represent and process data. The most visible theories behind granular computing

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International Journal of Computational Intelligence Systems, Vol.2, No. 2 (June, 2009), 99-103

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are fuzzy sets and rough sets. In particular, fuzzy logic has been intensively applied in modeling nonlinear dynamic systems 1,20,29,37. Immune systems represent a collection of techniques inspired from natural immune systems that involve the biological immune principles and processes such as learning and memory. Their application in dynamic systems’ modeling has been investigated in much research work 6,7,8,9,19,28. Swarm intelligence is a set of techniques used to model collective behaviors of distributed and autonomous agents that communicate between each other and with the environment. It has been used in modeling various dynamic systems 2,3,30. Chaos and fractal theory stems from dynamic nonlinear modeling and has been used in various applications that exhibit chaotic and fractal behavior 17,18,23,26,32. Machine learning includes the set of techniques having various computational roots including the probabilistic and statistical reasoning to design and develop intelligent and complex systems based on the notion of learning 11,12,14,24,27,31.

Manifestly, the appropriateness of CI in modeling and simulating complex nonlinear dynamical systems has become indubitable as attested by the large number of studies reporting on the successful application of CI models especially in adaptive control applications, fault diagnostic, signal processing, medical diagnostic, etc. as outlined previously. The present special issue sheds light on the application of selected computational intelligence techniques to different facets of complex nonlinear dynamic systems, in particular those pertaining to the tasks mentioned earlier, namely identification, prediction and diagnostic. This issue consists of seven papers which are ordered according to these tasks. The first 5 papers are closely related to identification, the sixth paper pertains to prediction and the last one pertains to diagnostic. In each paper, one of the computational techniques is applied. In the following a brief summary of each of the papers is presented. The first paper, “The influence of the update dynamics on the evolution of cooperation”, by Grilo and Correia, investigates spatial evolutionary games which are examples of non-linear dynamical systems. Game is a metaphor that represents any type of interaction between entities of an environment. In fact, a spatial evolutionary game assumes the existence of a structured population of agents which interact during the game and which can change their strategy depending on the update dynamics. The paper discusses two update alternatives: synchronous and asynchronous (eventually sequential). In particular, the paper introduces formal statistical properties of the update methods and introduces various measures to analyze the simulations results. Moreover, the paper suggests studying various games for a better understanding of the conditions that allow the evolution of cooperation and of the update policy. The paper conclude with clear and consistent statements about this multi-faceted study. The second paper, “Optimal IP assignment for efficient NoC-based system implementation using NSGA-II and MicroGA”, by Da Silva, Nedjah and Mourelle, suggests an approach for addressing the problem of selecting the most adequate set of hardware components/libraries, called intellectual properties (IPs), from a set of available ones to build a network-on-chip (NoC). Since the optimization of the “IP selection” is driven by the minimization of the covered hardware/chip area/surface, the total execution time and the power consumption, the relationship between these features is very likely to be nonlinear due to the conflicting (i.e., concurrent and collaborative) objectives. To formulate this optimization task, two multiobjective evolutionary algorithms are proposed and evaluated. The experimental evaluation shows the various types of relationship that exists between the studied features. The third paper, “CNN-based genetic algorithm for optimizing the behavior of an unstructured robot”, by Fasih, Chedjou, and Kyamakya, suggests a cellular neural networks concept for dynamically controlling

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International Journal of Computational Intelligence Systems, Vol.2, No. 2 (June, 2009), 99-103

the motion of robots. The CNN processors, which can be connected to the robot actuators, require a selfadaptive the definition of their feedback and control templates. For this purpose, a genetic algorithm approach is proposed. It consists of searching the optimal configuration of the templates that allow a smooth motion of the robot. The evaluation of the approach has been conducted on structured and unstructured robots moving in different environments by tuning the fitness function showing that the hybrid approach CNN-GA successfully achieves the purpose of this study. The fourth paper, “Global approximations to cost and production functions using artificial neural networks”, authored by Tsionas, Michaelides and Vouldis, is about the application of nonlinear neural networks for estimating the cost and production functions in economics. A detailed description of the procedures to determine the parameters and relevant economic measures (such as Returns to Scale (RTS) and Total Factor Productivity (TFP)) from the neural cost function is provided. Moreover, a numerical evaluation of the approach on a large data set is discussed. Note that such an application of neural networks in this context is appealing since cost and production functions in economics are commonly estimated by means of linearised multifactor models which are less than satisfactory in numerous situations. The fifth paper, “Networks of mixed canonical-dissipative systems and dynamic Hebbian learning”, by Rodriguez and Hongler, investigates the dynamics of a network consisting of diffusively coupled, stablelimit-cycle oscillators on which individual frequencies are parameterized. In particular, a Hebbian learning rule is applied in order to train the proposed model with the overall aim to produce a consensual oscillatory state in which all oscillators share a common frequency. A detailed description of the proposed network is provided and an empirical evaluation is presented to show and demonstrate the learning mechanism. The sixth paper, “Radial basis function nets for time series prediction”, by Bouchachia, proposes an ensemble learning approach based on recurrent radial basis function networks (RRBFN) for chaotic time series prediction. The recurrent network proposed is based on the nonlinear autoregression with exogenous input model (NARX) and works according to a multi-step (MS) prediction regime. The ensemble learning technique combines various MSNARX-based RRBFNs which differ in the set of controlling parameters. The evaluation of the approach includes a discussion on the performance of the individual predictors and their combination. The last paper, “Feature extraction for the prognosis of electromechanical faults in electrical machines through the DWT”, by Antonino-Daviu et al., is concerned with the problem of electromechanical faults diagnostic in induction electrical machines. Two common faults are considered: broken rotor bars and mixed eccentricities. The presence of these faults results in frequency components that give birth to some particular patterns. To identify these patterns, the Discrete Wavelet Transform (DWT) is used. The extensive experiments demonstrate that the proposal outperforms another approach that relies on Fast Fourier Transform (FFT) in presence of faulty situations. We hope that this special issue sheds light on the application of a selected set of computational intelligence techniques to modeling and simulation issues in a set of nonlinear dynamical systems with focus on identification, prediction and diagnostics. At the end, we would like to gratefully acknowledge and sincerely thank all the reviewers for their insightful comments and criticism of the manuscripts. Our thanks go also to the authors for their contributions and collaboration. Finally, we are grateful to the Editor-in-chief of the International Journal of Computational Intelligence Systems, D. Ruan, for his suggestive and insightful editorial comments which greatly helped us producing this special issue. The editors A. Bouchachia, K. Kyamakya

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References 1. J. Augusto et al., “Management of Uncertainty and Spatio-Temporal Aspects for Monitoring and Diagnosis in a Smart Home”, International Journal of Computational Intelligence Systems, 1(4), pp. 361-378, 2008 2. J. Branke, “Evolutionary Optimization in Dynamic Environments”, Kluwer Academic Publishers, 2001 3. C. Bertelle, G. Duchamp, and H. Kadri-Dahmani (Eds.), “Complex Systems and Self-organization Modelling”, Series: Understanding Complex Systems, Springer, 2009 4. E. Bonabeau, M. Dorigo and G. Theraulaz, “Swarm Intelligence : From Natural to Artificial Systems”, Oxford University Press, 1999 5. W. Cedeno, V. Vemuri, “On the use of niching for dynamic landscapes”, IEEE International Conference on Evolutionary Computation, pp. 361-366, 1997 6. V. Cutello and G. Nicosia, “An Immunological Approach to Combinatorial Optimization Problems”, Lecture Notes in Computer Science, vol. 2527, pp. 361-370, 2002, Springer. 7. D. Dasgupta, Artificial Immune Systems and Their Applications, Springer-Verlag, 1999 8. L. de Castro and F. Von Zuben, “Learning and Optimization Using the Clonal Selection Principle”, IEEE Transactions on Evolutionary Computation, Special Issue on Artificial Immune Systems, 6 (3), pp. 239-251,2002. 9. D. Djurdjanovic, L. Liu, K. Marko and N. Jun, “Immune Systems Inspired Approach to Anomaly Detection and Fault Diagnosis for Engines”, International Joint Conference on Neural Networks, pp. 1375-1382, 2007 10. D. Dutkay and P. Jorgensen, “Wavelet constructions in non-linear dynamics”, Electron. Res. Announc. Amer. Math. Soc. 11, pp. 21-33, 2005 11. J. Hines, A. Usynin, “Current Computational Trends in Equipment Prognostics”, International Journal of Computational Intelligence Systems, 1(1), pp. 94-102, 2008 12. Hong, X. et al.,“Model selection approaches for non-linear system identification : a review”, International journal of systems science, 39(10), pp. 925-946, 2008 13. J, Juang and B. Lin, “Nonlinear system identification by evolutionary computation and recursive estimation method”, 2005. Proceedings of the American Control Conference, pp. 5073-5078, 2005 14. Y. Kawahara, T. Yairi, and K. Machida, “A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems”, Advances in Neural Information Processing Systems 18, pp. 665-672, 2006 15. Y. Kitada, “Identification of Nonlinear Structural Dynamic Systems Using Wavelets”, Journal of Engineering Mechanics, 124(10), pp. 1059-1066, 1998 16. C. Lin, “Nonlinear systems control using self-constructing wavelet networks ”, Applied Soft Computing, 9(1), pp. 71-79, 2009 17. H. Leung, “System identification using chaos with application to equalization of a chaotic modulation system”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45(3), pp. 314-320, 1998 18. L. Li, Y. Yang and H. Peng, “Fuzzy system identification via chaotic ant swarm”, Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2008.01.011, 2009 19. C. Luh, “Non-linear system identification using an artificial immune system”, Journal of Systems & Control Engineering; 215(6), pp. 569-585, 2001 20. M. Marseguerra, E. Zio, P. Baraldi and A. Oldrini, “Fuzzy logic for signal prediction in nuclear systems”, Progress in Nuclear Energy, 43(1), pp. 373-380, 2003. 21. L. Minzhong and K. Lishan, “Reconstructing the nonlinear dynamical systems by evolutionary computation techniques”, Wuhan University Journal of Natural Sciences, 11(3), pp. 520-524, 2008

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22. N. Mori, H. Kita, and Y. Nishikawa. “Adaptation to a changing environment by means of the feedback thermodynamical genetic algorithm”, Parallel Problem Solving from Nature, LNCS vol. 1498, pp. 149-158, 1998 23. F. Morrison, “The Art of Modeling Dynamic Systems: Forecasting for Chaos, Randomness and Determinism”, Multiscience Press, Inc., 1991 24. J. Nakanishi, J. Farrell and S. Schaal, “Composite adaptive control with locally weighted statistical learning Source”, Neural Networks, 18(1), pp. 71-90, 2005 25. O. Nelles (Ed.), “Nonlinear system identification”, Springer, 2000 26. F. Nelwamondo, U. Mahola, and T. Marwala, “Improving Speaker Identification Rate Using Fractals”, International Joint Conference on Neural Networks, pp. 3231-3236, 2006 27. A. Rahimi and B. Recht, “Unsupervised Regression with Applications to Nonlinear System Identification”, Advances in Neural Information Processing Systems 19, pp. 1113-1120, MIT Press, 2007 28. A. Ramaswamy, Venayagamoorthy, G. and S. Balakrishnan, “Optimal Control of Class of Non-linear Plants Using Artificial Immune Systems: Application of the Clonal Selection Algorithm”, the 22nd International Symposium on Intelligent Control, pp. 249-254, 2007 29. P. Rodjito, J. Atkins and R. Jones, “Motion tracking and prediction using fuzzy logic”, Journal of Computing Sciences in Colleges, Volume 21(6), pp. 308-308, 2006 30. A. Rodríguez, A. Grushin and J.Reggia, “Swarm intelligence systems using guided self-organization for collective problem solving”,Advances in Complex Systems, 10(1), pp. 5-34, 2007 31. S. Roweis and Z. Ghahramani, “Learning Nonlinear Dynamical Systems using the EM Algorithm”, in S. Haykin, Ed. Kalman Filtering and Neural Networks, pp. 175-220, 2001 32. K. Sakai, “Nonlinear Dynamics and Chaos in Agricultural Systems”, Elsevier, 2001 33. A. Sen, G. Litak, A. Syta, “Cutting process dynamics by nonlinear time series and wavelet analysis”, Chaos 17, 023133, 2007 34. Suykens, J. Artificial Neural Networks for Modeling and Control of Non-Linear Systems, SpringerVerlag, 1995 35. Y. Tan, “Time-varying time-delay estimation for nonlinear Systems using neural networks”, Int. J. Appl. Math. Comput. Sci., 14(1), pp. 63-68, 2004 36. R. Tinos and S. Yang, “A Self-Organizing Random Immigrants Genetic Algorithm for Dynamic Optimization Problems”, Genetic Programming and Evolvable Machines, 8(3), pp. 255-286, 2007 37. C. Tseng, B. Chen and H. Uang, "Fuzzy tracking control design for nonlinear dynamic systems via TS fuzzy model," IEEE Transactions on Fuzzy Systems, 9(3), pp. 381-392, 2001 38. D. Wang et al., “Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics”, Mathematics and Computers in Simulation,79(5), pp. 1745-1753, 2009

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