T–S Fuzzy Model Identification with Sparse Bayesian Techniques

This paper introduces a novel method for fuzzy modeling based on sparse Bayesian techniques. The sparse representation problems in the Takagi–Sugeno (T–S) fuzzy system identification are studied, which is to establish a T–S fuzzy system with a adaptive number of fuzzy rules and simultaneously have a minimal number of nonzero consequent parameters. The proposed method is called sparse Bayesian fuzzy inference systems (B-sparseFIS). There are two main procedures in the paper. Firstly, initial fuzzy rule of antecedent part is extracted automatically by an AP clustering method. By using the algorithm of adaptive block orthogonal matching pursuit, the number of rules is computed statistically then the main important fuzzy rules can be selected. In the algorithm, the redundant rules are eliminated for better model accuracy and generalization performance; secondly, an adaptive B-sparseFIS is exploited. The consequence of fuzzy system is identified and simplified with sparse Bayesian techniques such that many consequent parameters will approximate to zero. Four examples are provided to illustrate the effectiveness of the proposed algorithm. Furthermore, the performances of the algorithm are validated through the results of statistical analyses including parameter estimate error, MSE, NRMSE, etc.