Parameter Optimization for Takagi-sugeno Fuzzy Models — Lessons Learnt

This article describes an approach to automatically build a Takagi-Sugeno fuzzy model (TSK-model) based on a set of input-output data (system identification). Identifying rule-based fuzzy models consists of two parts: structure modeling, i. e. determining the number of rules and input variables involved respectively, and parameter optimization, i. e. optimizing the rules consequences and the location and steepness of the fuzzy sets. For structure modeling, we investigate several search heuristics, also proposed by Takagi, Sugeno, and Kang in [1, 2, 3] or by Nelles in [4]. In order to find a good model structure, such search heuristics make it necessary to optimize and then evaluate a large number of different candidate models. To be applicable to real world problems, the parameter optimization must be highly efficient. For this, we investigate the use of two gradient descent algorithms: standard gradient descent (backpropagation) and resilient propagation (RPROP) [5, 6]. The combination of a structure search with a fast parameter optimization yields a powerful modeling algorithm that is capable to identify large real world systems. Several preceding publications showed the applicability of TSK fuzzy models to real world problems, e. g. [4, 7, 8]. In this paper we evaluate a number of varieties of TSK-like fuzzy models by performing a nonlinear regression benchmark of I. Frank [9]. We compare several types of fuzzy models that are constructed as combinations of different fuzzy sets, structuring algorithms, and parameter optimization techniques.