<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

A new approach to nonlinear modelling of dynamic systems based on fuzzy rules

Institute of Computational Intelligence, Częstochowa University of Technology, ul. Armii Krajowej 36, 42-200 Częstochowa,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A new approach to nonlinear modelling of dynamic systems based on fuzzy rules"}

For many practical weakly nonlinear systems we have their approximated linear model. Its parameters are known or can be determined by one of typical...

A new approach to nonlinear modelling of dynamic systems based on fuzzy rules

Published Online: Sep 29, 2016

Page range: 603 - 621

Received: Jun 27, 2015

Accepted: Jun 15, 2016

DOI: https://doi.org/10.1515/amcs-2016-0042

Keywords
nonlinear modelling, dynamic systems, fuzzy systems, interpretability of fuzzy systems, evolutionary algorithms

© 2016 Łukasz Bartczuk et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A new approach to nonlinear modelling of dynamic systems based on fuzzy rules

Published Online: Sep 29, 2016

Page range: 603 - 621

Received: Jun 27, 2015

Accepted: Jun 15, 2016

DOI: https://doi.org/10.1515/amcs-2016-0042

Keywordsnonlinear modelling, dynamic systems, fuzzy systems, interpretability of fuzzy systems, evolutionary algorithms

© 2016 Łukasz Bartczuk et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nonlinear modelling, dynamic systems, fuzzy systems, interpretability of fuzzy systems, evolutionary algorithms