A new approach to nonlinear modelling of dynamic systems based on fuzzy rules
Łukasz Bartczuk; Andrzej Przybył; Krzysztof Cpałka
International Journal of Applied Mathematics and Computer Science (2016)
- Volume: 26, Issue: 3, page 603-621
- ISSN: 1641-876X
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topŁukasz Bartczuk, Andrzej Przybył, and Krzysztof Cpałka. "A new approach to nonlinear modelling of dynamic systems based on fuzzy rules." International Journal of Applied Mathematics and Computer Science 26.3 (2016): 603-621. <http://eudml.org/doc/286734>.
@article{ŁukaszBartczuk2016,
abstract = {For many practical weakly nonlinear systems we have their approximated linear model. Its parameters are known or can be determined by one of typical identification procedures. The model obtained using these methods well describes the main features of the system's dynamics. However, usually it has a low accuracy, which can be a result of the omission of many secondary phenomena in its description. In this paper we propose a new approach to the modelling of weakly nonlinear dynamic systems. In this approach we assume that the model of the weakly nonlinear system is composed of two parts: a linear term and a separate nonlinear correction term. The elements of the correction term are described by fuzzy rules which are designed in such a way as to minimize the inaccuracy resulting from the use of an approximate linear model. This gives us very rich possibilities for exploring and interpreting the operation of the modelled system. An important advantage of the proposed approach is a set of new interpretability criteria of the knowledge represented by fuzzy rules. Taking them into account in the process of automatic model selection allows us to reach a compromise between the accuracy of modelling and the readability of fuzzy rules.},
author = {Łukasz Bartczuk, Andrzej Przybył, Krzysztof Cpałka},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonlinear modelling; dynamic systems; fuzzy systems; interpretability of fuzzy systems; evolutionary algorithms},
language = {eng},
number = {3},
pages = {603-621},
title = {A new approach to nonlinear modelling of dynamic systems based on fuzzy rules},
url = {http://eudml.org/doc/286734},
volume = {26},
year = {2016},
}
TY - JOUR
AU - Łukasz Bartczuk
AU - Andrzej Przybył
AU - Krzysztof Cpałka
TI - A new approach to nonlinear modelling of dynamic systems based on fuzzy rules
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 3
SP - 603
EP - 621
AB - For many practical weakly nonlinear systems we have their approximated linear model. Its parameters are known or can be determined by one of typical identification procedures. The model obtained using these methods well describes the main features of the system's dynamics. However, usually it has a low accuracy, which can be a result of the omission of many secondary phenomena in its description. In this paper we propose a new approach to the modelling of weakly nonlinear dynamic systems. In this approach we assume that the model of the weakly nonlinear system is composed of two parts: a linear term and a separate nonlinear correction term. The elements of the correction term are described by fuzzy rules which are designed in such a way as to minimize the inaccuracy resulting from the use of an approximate linear model. This gives us very rich possibilities for exploring and interpreting the operation of the modelled system. An important advantage of the proposed approach is a set of new interpretability criteria of the knowledge represented by fuzzy rules. Taking them into account in the process of automatic model selection allows us to reach a compromise between the accuracy of modelling and the readability of fuzzy rules.
LA - eng
KW - nonlinear modelling; dynamic systems; fuzzy systems; interpretability of fuzzy systems; evolutionary algorithms
UR - http://eudml.org/doc/286734
ER -
References
top- Adjrad, M. and Belouchrani, A. (2007). Estimation of multicomponent polynomial-phase signals impinging on a multisensor array using state-space modeling, IEEE Transactions on Signal Processing 55(1): 32-45.
- Angelov, P.P., Filev, D.P. (2004). Flexible models with evolving structure, International Journal of Intelligent Systems 19(4): 327-340. Zbl1101.68747
- Babuska, R., Verbruggen, H. (2003). Flexible neuro-fuzzy methods for nonlinear system identification, Annual Reviews in Control 27(1): 73-85.
- Bagarinao, E., Matsuo, K., Nakai, T. and Sato, S. (2003). Estimation of general linear model coefficients for real-time application, NeuroImage 19(2): 422-429.
- Banerjee, A., Arkun, Y., Ogunnaike, B. and Pearson, R. (1997). Estimation of nonlinear systems using linear multiple models, AIChE Journal 43(5): 1204-1226.
- Bohlin, T.P. (2006). Practical Grey-Box Process Identification: Theory and Applications, Springer, London. Zbl1122.93059
- Boukezzoula, R., Galichet, S. and Foulloy, L. (2007). Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure, International Journal of Applied Mathematics and Computer Science 17(2): 233-248, DOI: 10.2478/v10006-007-0021-4. Zbl1119.93357
- Casillas, J., Cordón, O., Herrera, F. and Magdalena, L. (2003). Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: An overview, in J. Casillas et al. (Eds.), Interpretability Issues in Fuzzy Modeling, Springer, Berlin/Heidelberg, pp. 3-22. Zbl1048.93003
- Caughey, T.K. (1963). Equivalent linearization techniques, Journal of the Acoustical Society of America 35(11): 1706-1711.
- Cordón, O. (2011). A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: Designing interpretable genetic fuzzy systems, International Journal of Approximate Reasoning 52(6): 894-913.
- Cordón, O., Herrera, F., Hoffmann, F. and Magdalena, L. (2001). Genetic Fuzzy Systems, World Scientific Publishing Company, Singapore. Zbl1042.68098
- Cpałka, K. (2009a). A new method for design and reduction of neuro-fuzzy classification systems, IEEE Transactions on Neural Networks 20(4): 701-714.
- Cpałka, K. (2009b). On evolutionary designing and learning of flexible neuro-fuzzy structures for nonlinear classification, Nonlinear Analysis A: Theory, Methods and Applications 71(12): 1659-1672.
- Cpałka, K., Łapa, K., Przybył, A. and Zalasiński, M. (2014). A new method for designing neuro-fuzzy systems for nonlinear modelling with interpretability aspects, Neurocomputing 135: 203-217.
- Cpałka, K., Rebrova, O., Nowicki, R. and Rutkowski, L. (2013). On design of flexible neuro-fuzzy systems for nonlinear modelling, International Journal of General Systems 42(6): 706-720. Zbl1268.93016
- Czekalski, P. (2006). Evolution-fuzzy rule based system with parameterized consequences, International Journal of Applied Mathematics and Computer Science 16(3): 373-385. Zbl1144.68339
- DeHaan, D. and Guay, M. (2006). A new real-time perspective on non-linear model predictive control, Journal of Process Control 16(6): 615-624.
- Di Nuovo, A. and Ascia, G. (2013). A fuzzy system index to preserve interpretability in deep tuning of fuzzy rule based classifiers, Journal of Intelligent and Fuzzy Systems 25(2): 493-504.
- Eiben, A.E. and Smith, J. (2008). Introduction to Evolutionary Computing, Springer, Berlin/Heidelberg. Zbl1028.68022
- Fei, X., Lu, C.-C. and Liu, K. (2011). A Bayesian dynamic linear model approach for real-time short-term freeway travel time prediction, Transportation Research C: Emerging Technologies 19(6): 1306-1318.
- Fogel, D.B. (2006). Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, Vol. 1, John Wiley & Sons, Hoboken, NJ. Zbl0926.68052
- Fogel, D.B. and Atmar, J.W. (1990). Comparing genetic operators with Gaussian mutations in simulated evolutionary processes using linear systems, Biological Cybernetics 63(2): 111-114.
- Forst, W. and Hoffmann, D. (2010). Optimization Theory and Practice, Springer, New York, NY. Zbl1211.90002
- Gabryel, M. and Rutkowski, L. (2006). Evolutionary learning of Mamdani-type neuro-fuzzy systems, in L. Rutkowski et al. (Eds.), Artificial Intelligence and Soft Computing, Lecture Notes in Computer Science, Vol. 4029, Springer, Berlin/Heidelberg, pp. 354-359.
- Gacto, M., Alcala, R. and Herrera, F. (2011). Interpretability of linguistic fuzzy rule-based systems: An overview of interpretability measures, Information Sciences 181(20): 4340-4360. Zbl05947939
- Grabowski, P. and Callier, F.M. (2001). Circle criterion and boundary control systems in factor form: Input-output approach, Applied Mathematics and Computer Science 11(6): 1387-1403. Zbl0999.93061
- Háber, R. and Keviczky, L. (1999). Nonlinear System Identification-Input-Output Modeling Approach, Vol. 1: Nonlinear System Parameter Identification, Springer Netherlands, Dordrecht. Zbl0934.93004
- Homaifar, A. and McCormick, E. (1995). Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms, IEEE Transactions on Fuzzy Systems 3(2): 129-139.
- Horzyk, A. and Tadeusiewicz, R. (2004). Self-optimizing neural networks, Advances in Neural Networks, Springer, Berlin/Heidelberg, pp. 150-155.
- Huijberts, H., Nijmeijer, H. and Willems, R. (2000). System identification in communication with chaotic systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47(6): 800-808. Zbl0972.93017
- Ikonen, E. and Najim, K. (2001). Advanced Process Identification and Control, Vol. 9, CRC Press, New York, NY. Zbl1132.93048
- Ishibashi, R. and Lucio Nascimento, Jr., C. (2013). GFRBS-PHM: A genetic fuzzy rule-based system for PHM with improved interpretability, IEEE Conference on Prognostics and Health Management, 2013, Gaithersburg, MD, USA, pp. 1-7.
- Ishibuchi, H. and Yamamoto, T. (2004). Fuzzy rule selection by multi-objective genetic local search algorithms and rule evaluation measures in data mining, Fuzzy Sets and Systems 141(1): 59-88. Zbl1081.68091
- Jang, I.-S. R. and Sun, C.-T. (1995). Neuro-fuzzy modeling and control, Proceedings of the IEEE 83(3): 378-406.
- Johansen, T.A., Shorten, R. and Murray-Smith, R. (2000). On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models, IEEE Transactions on Fuzzy Systems 8(3): 297-313.
- Johansson, U., Sönströd, C., Norinder, U. and Boström, H. (2011). Trade-off between accuracy and interpretability for predictive in silico modeling, Future Medicinal Chemistry 3(6): 647-663.
- Jordan, A. (2006). Linearization of non-linear state equation, Bulletin of the Polish Academy of Sciences: Technical Sciences 54(1): 63-73. Zbl1194.78065
- Juang, C.-F. and Chen, C.-Y. (2013). Data-driven interval type-2 neural fuzzy system with high learning accuracy and improved model interpretability, IEEE Transactions on Cybernetics 43(6): 1781-1795.
- Kim, M.-S., Kim, C.-H. and Lee, J.-J. (2006). Evolving compact and interpretable Takagi-Sugeno fuzzy models with a new encoding scheme, IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics 36(5): 1006-1023.
- Kluska, J. (2009). Analytical Methods in Fuzzy Modeling and Control, Springer, Berlin/Heidelberg. Zbl1226.93002
- Kluska, J. (2015). Selected applications of P1-TS fuzzy rule-based systems, in L. Rutkowski et al. (Eds.), Artificial Intelligence and Soft Computing, Lecture Notes in Computer Science, Vol. 9119, Springer, Berlin/Heidelberg, pp. 195-206.
- Kristensen, N.R., Madsen, H. and Jørgensen, S.B. (2004). A method for systematic improvement of stochastic grey-box models, Computers & Chemical Engineering 28(8): 1431-1449.
- Kroese, D.P., Taimre, T. and Botev, Z.I. (2011). Handbook of Monte Carlo Methods, Vol. 706, John Wiley & Sons, Hoboken, NJ. Zbl1213.65001
- Li, C. and Chiang, T.-W. (2012). Intelligent financial time series forecasting: A complex neuro-fuzzy approach with multi-swarm intelligence, International Journal of Applied Mathematics and Computer Science 22(4): 787-800, DOI: 10.2478/v10006-012-0058-x. Zbl1286.91149
- Ljung, L. (2010). Approaches to identification of nonlinear systems, 9th Chinese Control Conference, Beijing, China, pp. 1-5.
- Łęski, J. (2003). A fuzzy if-then rule-based nonlinear classifier, International Journal of Applied Mathematics and Computer Science 13(2): 215-223. Zbl1048.93503
- Lughofer, E. (2013). On-line assurance of interpretability criteria in evolving fuzzy systems-achievements, new concepts and open issues, Information Sciences 251: 22-46.
- Malchiodi, D. and Pedrycz, W. (2013). Learning membership functions for fuzzy sets through modified support vector clustering, in F. Masulli et al. (Eds.), Fuzzy Logic and Applications, Springer, Cham, pp. 52-59. Zbl06344557
- Medasani, S., Kim, J. and Krishnapuram, R. (1998). An overview of membership function generation techniques for pattern recognition, International Journal of Approximate Reasoning 19(3): 391-417. Zbl0947.68555
- Miller, G.A. (1956 ). The magical number seven, plus or minus two: Some limits on our capacity for processing information, The Psychological Review 63: 81-97.
- Mrugalski, M. (2014). Advanced Neural Network-Based Computational Schemes for Robust Fault Diagnosis, Studies in Computational Intelligence, Vol. 510, Springer-Verlag, Berlin/Heidelberg. Zbl1280.68007
- Murray-Smith, R. and Johansen, T. (1997). Multiple Model Approaches to Nonlinear Modelling and Control, CRC Press, Boca Raton, FL.
- Nelles, O. (2001). Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models, Springer, Berlin/Heidelberg. Zbl0963.93001
- Ogata, K. (2004). System Dynamics, Pearson/Prentice Hall, Upper Saddle River, NJ.
- Patton, R.J., Korbicz, J., Witczak, M. and Uppal, F. (2005). Combined computational intelligence and analytical methods in fault diagnosis, IEE Control Engineering Series 70: 349. Zbl1267.93125
- Pedro, J.O. and Dahunsi, O.A. (2011). Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system, International Journal of Applied Mathematics and Computer Science 21(1): 137-147, DOI: 10.2478/v10006-011-0010-5. Zbl1221.93088
- Przybył, A. and Jelonkiewicz, J. (2003). Genetic algorithm for observer parameters tuning in sensorless induction motor drive, Proceedings of the 6th International Conference on Neural Networks and Soft Computing, Zakopane Poland, pp. 376-381.
- Puig, V., Witczak, M., Nejjari, F., Quevedo, J. and Korbicz, J. (2007). A GMDH neural network-based approach to passive robust fault detection using a constraint satisfaction backward test, Engineering Applications of Artificial Intelligence 20(7): 886-897.
- Quah, K.H. and Quek, C., (2006). FITSK: Online local learning with generic fuzzy input Takagi-Sugeno-Kang fuzzy framework for nonlinear system estimation, IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics 36(1): 166-178.
- Roffel, B. and Betlem, B.H. (2004). Advanced Practical Process Control, Springer, Berlin/Heidelberg. Zbl1042.93003
- Rüping, S. (2006). Learning Interpretable Models, Ph.D. thesis, Technical University of Dortmund, Dortmund.
- Rutkowski, L. (2008). Computational Intelligence: Methods and Techniques, Springer, Berlin/Heidelberg. Zbl1147.68061
- Rutkowski, L. and Cpałka, K. (2005). Designing and learning of adjustable quasi-triangular norms with applications to neuro-fuzzy systems, IEEE Transactions on Fuzzy Systems 13(1): 140-151.
- Salapa, K., Trawińska, A., Roterman, I. and Tadeusiewicz, R. (2014). Speaker identification based on artificial neural networks. Case study: The Polish vowel (a pilot study), Bio-Algorithms and Med-Systems 10(2): 91-99.
- Setnes, M. and Roubos, H. (2000). GA-fuzzy modeling and classification: Complexity and performance, IEEE Transactions on Fuzzy Systems 8(5): 509-522.
- Schröder, D. (Ed.) (2000). Intelligent Observer and Control Design for Nonlinear Systems, Springer, Berlin/Heidelberg.
- Shill, P., Akhand, M. and Murase, K. (2011). Simultaneous design of membership functions and rule sets for type-2 fuzzy controllers using genetic algorithms, 14th International Conference on Computer and Information Technology, Dhaka, Bangladesh, pp. 554-559.
- Shukla, P. and Tripathi, S. (2013). Interpretability issues in evolutionary multi-objective fuzzy knowledge base systems, 7th International Conference on Bio-Inspired Computing: Theories and Applications, Madhya Pradesh, India, pp. 473-484.
- Sivanandam, S. and Deepa, S. (2008). Genetic Algorithm Optimization Problems, Springer, Berlin/Heidelberg. Zbl1129.90001
- Starczewski, J.T., Bartczuk, Ł., Dziwiński, P. and Marvuglia, A. (2010). Learning methods for type-2 FLS based on FCM, in L. Rutkowski et al. (Eds.), Artificial Intelligence and Soft Computing, Springer, Berlin/Heidelberg, pp. 224-231.
- Tadeusiewicz, R. (2010). Using neural networks for simplified discovery of some psychological phenomena, in L. Rutkowski et al. (Eds.), Artificial Intelligence and Soft Computing, Springer, Berlin/Heidelberg, pp. 104-123.
- Tadeusiewicz, R., Chaki, R. and Chaki, N. (2014). Exploring Neural Networks with C#, CRC Press, Boca Raton, FL.
- Tadeusiewicz, R. and Figura, I. (2011). Phenomenon of tolerance to damage in artificial neural networks, Computer Methods in Materials Science 11(4): 501-513.
- Tan, Y. (2004). Time-varying time-delay estimation for nonlinear systems using neural networks, International Journal of Applied Mathematics and Computer Science 14(1): 63-68. Zbl1171.94386
- Wang, H., Kwong, S., Jin, Y., Wei, W. and Man, K.-F. (2005). Agent-based evolutionary approach for interpretable rule-based knowledge extraction, IEEE Transactions on Systems, Man, and Cybernetics C: Applications and Reviews 35(2): 143-155.
- Wang, H., Kwong, S., Jin, Y., Wei, W. and Man, K.-F. (2005). Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction, Fuzzy Sets and Systems 149(1): 149-186. Zbl1071.68550
- Wilamowski, B.M. (2005). Methods of computational intelligence for nonlinear control systems, ICCAE 2005 International Conference on Control, Automation and System, Gyeonggi-Do, Korea, pp. P1-P8.
- Witkowska, A. and Śmierzchalski, R. (2012). Designing a ship course controller by applying the adaptive backstepping method, International Journal of Applied Mathematics and Computer Science 22(4): 985-997, DOI: 10.2478/v10006-012-0073-y. Zbl1283.93156
- Wu, C.-J. and Liu, G.-Y. (2000). A genetic approach for simultaneous design of membership functions and fuzzy control rules, Journal of Intelligent and Robotic Systems 28(3): 195-211. Zbl1034.68701
- Xie, Y., Guo, B., Xu, L., Li, J. and Stoica, P. (2006). Multistatic adaptive microwave imaging for early breast cancer detection, IEEE Transactions on Biomedical Engineering 53(8): 1647.
- Zhou, S.-M., Gan, J. Q. (2008). Low-level interpretability and high-level interpretability: A unified view of data-driven interpretable fuzzy system modelling, Fuzzy Sets and Systems 159(23): 3091-3131.
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