COSTA BRANCO, P.J.; LORI, N; DENTE, J.A.; (1996) "New Approaches on Structure Identification of Fuzzy Models: Case Study in an Electro-Mechanical System". In Fuzzy Logic, Neural Networks, and EvolutionaryComputation, LNCS/Lecture Notes in Artificial Intelligence, Eds. T.Furuhashi and Y. Uchikawa, pp. 104-143, Springer-Verlag, Berlin. New Approaches on Structure Identification of Fuzzy Models: Case Study in an Electro-Mechanical System P.J. Costa Branco * , N. Lori ** and J.A. Dente * * Instituto Superior Técnico ** Washington University in Saint Louis CAUTL/Laboratório de Mecatrónica Physics Department Av. Rovisco Pais, 1096 Lisboa Codex, Portugal USA Fax Nº. 351-1-8417167 E-mail: lori@hbar.wustl.edu E-mail: pbranco@alfa.ist.utl.pt http://macdente.ist.utl.pt The main problem in design fuzzy models is to identify their structure. This means recognise the variables that better characterise the system dynamics, the number of membership functions partitioning each variable, as well as their distribution and fuzziness degree. This work presents two pre-processing methods for structure identification of fuzzy models. The first approach uses the statistical method of Principal Component Analysis (PCA). The second one uses a clustering technique called autonomous mountain-clustering method. The statistical method of Principal Component Analysis helps to select the variables that dominate the system dynamics. Besides, this method contributes to design fuzzy models with better performance. The second approach identifies the fuzzy model order. That is, the method identifies the number of membership functions attributed to each variable, as well as their position and width. So, the autonomous mountain-clustering eliminates the usual “trial-and-error” mechanism. The pre-processing methods can be used to initialize the neuro-fuzzy techniques and therefore accelerate their learning process. We test these methods using a simple learning process applied to extract the fuzzy model of an experimental electro-hydraulic system. The results show that a good modeling capability is achieved without employ any complicated optimisation procedure to structure identification. 1 Introduction The structure of a fuzzy model can be extracted from expert's knowledge by translating their information about the system to a linguistic description. An example is the knowledge representation of the human operator decisions in process control. Clearly, an identification of the system's structure based only in the expert’s description can be very poor. If the acquired information is wrong or not enough, the model will be bad. It is necessary to complement operator subjectivity with more objective knowledge using available numerical data from the system in question. Structure identification of fuzzy systems [6] consists in detect the variables that dominates the system dynamics, the identification of the number of membership functions partitioning each variable, their position in the respective universe of discourse, as well as their fuzziness degree indicated by each fuzzy set's width. In dynamical systems the number of variables is often very high. If the premise part of each fuzzy rule considers all variables, the model will have great complexity with high computational costs. However, in real situations only few variables dominate the process dynamics. The statistical technique of PCA helps to define these set of variables reducing the effective dimensionality of the system.