FLEXFIS: A Robust Incremental Learning Approach for Evolving Takagi–Sugeno Fuzzy Models

In this paper, we introduce a new algorithm for incremental learning of a specific form of Takagi–Sugeno fuzzy systems proposed by Wang and Mendel in 1992. The new data-driven online learning approach includes not only the adaptation of linear parameters appearing in the rule consequents, but also the incremental learning of premise parameters appearing in the membership functions (fuzzy sets), together with a rule learning strategy in sample mode. A modified version of vector quantization is exploited for rule evolution and an incremental learning of the rules' premise parts. The modifications include an automatic generation of new clusters based on the nature, distribution, and quality of new data and an alternative strategy for selecting the winning cluster (rule) in each incremental learning step. Antecedent and consequent learning are connected in a stable manner, meaning that a convergence toward the optimal parameter set in the least-squares sense can be achieved. An evaluation and a comparison to conventional batch methods based on static and dynamic process models are presented for high-dimensional data recorded at engine test benches and at rolling mills. For the latter, the obtained data-driven fuzzy models are even compared with an analytical physical model. Furthermore, a comparison with other evolving fuzzy systems approaches is carried out based on nonlinear dynamic system identification tasks and a three-input nonlinear function approximation example.