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.
Highlights
With the rapid development of artificial intelligence techniques, the data-driven modelling method [1]–[7] is playing an important role for modelling of complicated nonlinear system in the age of big data, where the performance of these methods crucially rely on the quality of given training data
ROBUST T-S FUZZY MODEL IDENTIFICATION In order to improve the robustness of T-S fuzzy model to outliers and noises, the robust T-S fuzzy model identification approach based on the fuzzy c-regression model (FCRM) algorithm and L1-norm loss function (RTS-L1) is proposed in this paper
WORKS In this paper, we have proposed the outliers and noises robust T-S fuzzy model identification method based on FCRM clustering algorithm and L1-norm loss function
Summary
With the rapid development of artificial intelligence techniques, the data-driven modelling method [1]–[7] is playing an important role for modelling of complicated nonlinear system in the age of big data, where the performance of these methods crucially rely on the quality of given training data. The traditional T-S fuzzy model identification approach with L2-norm loss function is very sensitive to the outliers or noises because the L2-norm. N. Zhang et al.: Robust T-S Fuzzy Model Identification Approach Based on FCRM Algorithm and L1-Norm Loss Function loss function is prone to be badly affected by outliers and noises [20]. A robust T-S fuzzy model identification approach based on the FCRM clustering algorithm and L1-norm loss function is proposed. With the obtained antecedent parameters, the L1-norm loss function which has more strong outliers or noises robustness is introduced to estimate the output error instead of the traditional L2-norm loss function in the consequent part. The experimental results show that the proposed method has significantly improved the modelling accuracy in handling data with outliers and noises. Where vij, σji represent the center and width of the membership function respectively
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