Abstract
A novel interval-data based Takagi-Sugeno fuzzy system is proposed to identify uncertain nonlinear dynamic systems by endowing the classical TS fuzzy system with probability theory and symbolic data analysis. Such systems have variability in their outputs, that is they produce varying responses each time when the same stimuli is applied to them under the same condition. Interval data is generated by repeating the identification experiment multiple times and applying the probabilistic techniques to get soft bounds of output. The interval data is then directly used in the TS fuzzy modelling, giving rise to interval antecedent and consequent parameters. This method does not require any specific assumption on the probability distribution of the random variable that models the uncertainty. The developed procedure is demonstrated for a pneumatic drive system.
Zusammenfassung
In diesem Beitrag wird ein neues Verfahren zur Modellierung der Unsicherheit von Beobachtungen nichtlinearer dynamischer Systeme mittels spezieller Takagi-Sugeno- (TS-)Modelle vorgestellt. Dabei wird das gleiche Testsignal mehrfach auf das System geschaltet, so dass eine Schar von Zeitreihen der Ausgangsgröße entsteht. Mittels wahrscheinlichkeitstheoretischer Methoden wird diese Schar vorverarbeitet und auf eine intervall-wertige Zeitreihe abgebildet. Diese wird zusammen mit dem Testsignal genutzt, um Prämissen- und Konklusionsparameter eines TS-Modells in Form von Intervallen zu identifizieren. Das entwickelte Verfahren wird für die Modellbildung eines pneumatischen Linearantriebs demonstriert. Dabei werden auf den Einschrittprädiktions- oder den Simulationsfehler optimierte Modelle eingesetzt.
About the authors
Salman Zaidi (1984) is a research associate at the Department of Measurement and Control at the University of Kassel. His research areas are fuzzy identification, intelligent control, intelligent optimization techniques and machine learning.
Department of Measurement and Control, Institute for System Analytics and Control, Faculty of Mechanical Engineering, University of Kassel, Kassel, Germany
Univ.-Prof. Dr.-Ing. Andreas Kroll (1967) is head of the Department of Measurement and Control at the University of Kassel. His research areas are nonlinear identification and control methods, computational intelligence, and complex systems.
Department of Measurement and Control, Institute for System Analytics and Control, Faculty of Mechanical Engineering, University of Kassel, Kassel, Germany
Acknowledgement
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the article. The first author is also grateful to the German Academic Exchange Service (DAAD) for the financial grant.
©2016 Walter de Gruyter Berlin/Boston
