Employment of Inverse Multiple Local Modeling Technique for Identification of Dynamic Systems With Outliers

Abstract

The growing complexity and prevalence of non-linear systems and processes, especially in industrial settings, have driven a significant increase in academic interest in developing advanced and more accurate techniques for Dynamic Systems Identification. Among these techniques, local modeling stands out due to its ability to represent complex systems through the generation of multiple local linear models. However, the presence of noise in the data, often caused by process-related factors, can introduce irrelevant information (outliers) that significantly impacts the accuracy of the identification process. In this study, the multiple local modeling algorithms D-MKSOM and P-MKSOM were modified to incorporate the M-estimation technique, enhancing their robustness in handling outlier-contaminated data. The resulting models, named RD-MKSOM and RP-MKSOM, were applied to datasets characterized by strong non-linearities. To evaluate their performance, the datasets were intentionally contaminated with noise, allowing for both qualitative and quantitative analyses of the algorithms’ robustness. The quantitative evaluation included the Normalized Mean Square Error (NMSE) and the coefficient of determination ( $R^{2}$ ), while the qualitative analysis employed cross-correlation, autocorrelation, and Gaussian distribution assessments via residual histograms. For comparative purposes, the Robust ELM global neural network (R-ELM) was also applied to the same datasets. Another type of robust local model is based on the classical Takagi-Sugeno-Kang (TSK) fuzzy system, called the Robust TSK (R-TSK) model, which is also compared with the proposed robust algorithms. The results demonstrated that the proposed robust algorithms offer improved generalization capabilities and enhanced resistance to outliers in test data, as evidenced by superior error metrics and robust behavior across varying test conditions.