Interpretable Semi-Mechanistic Fuzzy Models by Clustering, OLS and FIS Model Reduction

Abstract

A semi-mechanistic fuzzy modeling technique is proposed to obtain compact and transparent process models based on small data-sets. Semi-mechanistic models are hybrid models that consist of a white box structure based on mechanistic relationships and black-box substructures to model less defined parts. First, it is shown that certain type of white-box models can be efficiently incorporated into a Takagi-Sugeno fuzzy rule structure. Next, the proposed models are identified from learning data and special attention is paid to transparency and accuracy aspects. The approach is based on a combination of (i) prior knowledge-based model structures, (ii) fuzzy clustering, (iii) orthogonal least-squares, and (iv) the modified Fisher’s interclass separability method. For the identification of the semimechanistic fuzzy model, a new fuzzy clustering method is proposed, i.e., clustering is achieved by the simultaneous identification of fuzzy sets defined on some of the scheduling variables and identification of the parameters of the local semimechanistic submodels. Subsequently, model reduction is applied to make the TS models as compact as possible, i.e., the most relevant consequent variables are selected by an orthogonal least squares method, and the modified Fisher’s interclass separability criteria is used for selection of relevant antecedent (scheduling) variables. The overall procedure is demonstrated by the development of a semimechanistic model for a biochemical process. Although the results do not carry over directly to other engineering fields, the main ideas and conclusions, will certainly hold for other application areas as well.