Integration of weighted LS-SVM and manifold learning for fuzzy modeling

In this paper, a robust fuzzy modeling method is proposed for strongly nonlinear systems in the presence of noise and/or outliers. The proposed method integrates the advantages of the fuzzy structure, the manifold learning, and the weighted least squares support vector machine (LS-SVM). First, the Gustafson-Kessel clustering algorithm (GKCA) is applied to split the training data set into several subsets to determine the fuzzy rules and premise parameters. Then, a new objective function is constructed based on the fuzzy structure, the weighted LS-SVM, and the manifold regularization, which takes into account robustness and the intrinsic geometry of the data. A solving method is further developed, from which the fuzzy model is achieved and can effectively approximate a nonlinear system with various types of random noise. The proposed method is applied to an artificial case as well as a practical hydraulic actuator, demonstrating its effectiveness in modeling of a nonlinear system even under noise.