Structure selection for nonlinear input-output models based on fuzzy cluster analysis

Selecting the structure (the input variables or regressors) or an input-output dynamic model is a crucial step in system identification. In this paper, a method is proposed that uses fuzzy clustering to select the structure of a nonlinear input-output model. Clustering is applied to the product space or the input and output variables. The model structure is then estimated on the basis of the cluster covariance matrix eigenvalues. The main advantage of the proposed solution is that it is model-free. This means that no particular model needs to be constructed in order to select the structure, while most other techniques are 'wrapped' around a particular model construction method. This saves the computational effort and avoids a possible bias due to the particular construction method used. Two simulation examples are given to illustrate the proposed technique: estimation of the model structure for a polymerization reactor and the van der Vusse reactor.