Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models

J. Abonyi1, R. Babuska2, F. Szeifert1
1Department of Process Engineering, University of Veszprem, Veszprem, Hungary
2Control Systems Engineering Group, Department of Information Technology and Systems, Delft University of Technnology, Delft, Netherlands

Tóm tắt

The construction of interpretable Takagi-Sugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the Gath-Geva (GG) algorithm. To preserve the partitioning of the antecedent space, linearly transformed input variables can be used in the model. This may, however, complicate the interpretation of the rules. To form an easily interpretable model that does not use the transformed input variables, a new clustering algorithm is proposed, based on the expectation-maximization (EM) identification of Gaussian mixture models. This new technique is applied to two well-known benchmark problems: the MPG (miles per gallon) prediction and a simulated second-order nonlinear process. The obtained results are compared with results from the literature.

Từ khóa

#Takagi-Sugeno model #Fuzzy sets #Fuzzy systems #Optimization methods #Clustering algorithms #Partitioning algorithms #Input variables #Multidimensional systems #Predictive models #Nonlinear systems

Tài liệu tham khảo

10.1007/978-3-642-60767-7 hoppner, 1999, Fuzzy Cluster Analysis&#x2014 Methods for Classification Data Analysis and Image Recognition 10.1109/FUZZY.1996.552396 jang, 1997, Neuro-Fuzzy and Soft Computing A Computational Approach to Learning and Machine Intelligence 10.1109/5.364486 10.1109/91.842154 johansen, 2002, on multi-objective identification of takagi-sugeno fuzzy model parameters, Preprints 15th IFAC World Congress 10.1109/91.855918 kambhatala, 1996, Local models and Gaussian mixture models for statistical data processing 10.1109/91.728458 10.1109/T-C.1975.224317 10.1007/978-3-642-60767-7_2 draper, 1994, Applied regression analysis bishop, 1995, Neural Networks for Pattern Recognition 10.1038/16873 10.1109/34.192473 babus˘ka babuska, 1998, Fuzzy Modeling for Control, 10.1007/978-94-011-4868-9 gustafson, 1979, fuzzy clustering with fuzzy covariance matrix, Proc IEEE CDC, 761 abonyi, 2000, local and global identification and interpretation of parameters in takagi-sugeno fuzzy models, Proc IEEE ICFS, 835 murray-smith, 1997, Multiple Model Approaches to Nonlinear Modeling and Control 10.1016/0165-0114(86)90010-2 10.1109/FUZZY.2000.839128 10.1109/TSMC.1985.6313399 10.1109/TFUZZ.1993.390281 10.1109/91.705503