Robust T-S Fuzzy Model Identification Approach Based on FCRM Algorithm and L1-Norm Loss Function

Abstract

The Takagi-Sugeno (T-S) fuzzy model identification is a very powerful tool for modelling of complicated nonlinear system. However, the traditional T-S fuzzy model typically uses the L2-norm loss function, which is very sensitive to outliers or noises. So an unreliable model may be obtained due to the presence of outliers or noises. In this paper, the outliers and noises robust T-S fuzzy model identification method based on the fuzzy c-regression model (FCRM) clustering and the L1-norm loss function is proposed. The hyper-plane-shaped clustering algorithm has been proved to be more effective than hyper-sphere-shaped clustering algorithm in T-S fuzzy model identification. Therefore the FCRM clustering algorithm is used in T-S fuzzy model identification for structure identification in the antecedent part. A mass of relevant researches have pointed out that the L1-norm loss function is more robust to outliers and noises than L2-norm loss function. In order to reduce the negative influence of outliers and noises, the L1-norm loss function is employed to enhance the robustness of T-S fuzzy model instead of the L2-norm loss function in the consequent part. Regression and classification applications have been used to demonstrate the validity of the proposed method. The experimental results show that the proposed method has significantly improved the modelling accuracy in dealing with data contaminated by outliers and noises compared with other algorithms. INDEX TERMS T-S fuzzy model, fuzzy c-regression model, L1-norm loss function, outliers and noises robustness.

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