Reducing the number of local linear models in neuro-fuzzy modeling: A split-and-merge clustering approach

Abstract

In this paper, we propose a neuro-fuzzy modeling approach for identification of a generalized first-order Takagi–Sugeno (TS) fuzzy models with considerably low number of local linear models (LLMs). For this purpose, the main idea is to identify uneven linear operating regimes of a process by LLMs localized in rather flexible fuzzy subspaces (FSs). To this end, a split-and-merge clustering approach is introduced. Through the split procedure, a generalized TS model is identified whose LLMs are localized in simple FSs. Then, by merging these simple FSs, so to keep the generality of the model, more flexible FSs are produced to localize the LLMs. As an illustrative example, the proposed modeling method is utilized to approximate a benchmark nonlinear function. Moreover, the performance of our approach is compared with that of several well-known state-of-the-art approaches in identification of a steam generator. It is demonstrated that our identified model generalizes well, with considerable lower number of LLMs. Robustness of the proposed modeling method against additive noise and outliers is studied as well, where good resilience against noise and drop of performance in the face of frequent outliers is observed in prediction of Mackey–Glass time-series.