Probabilistic Weighted Support Vector Machine for Robust Modeling With Application to Hydraulic Actuator

An effective model of the hydraulic actuator is crucial for high-accuracy driving control. However, modeling this driving process is difficult due to strong nonlinearities in the hydraulic system and load as well as unknown influence from sources of noise including sampling, modeling, measurement, and operation errors in the process. In this paper, a probabilistic weighted least square support vector machine (LS-SVM) is proposed to model this kind of processes under noise. The proposed method can increase robustness and accuracy even with outliers or non-Gaussian noise. First, a distribution construction method is developed to extract the probabilistic distribution of the distributed LS-SVM models caused by outliers and/or noise samples. Then, a new objective function is constructed using this distribution information to negate outlier or noise influence. Since this method considers the probabilistic information of outliers and/or noise samples, it has greatly improved the LS-SVM modeling capabilities in a noisy environment. Successful application of the proposed method to artificial cases and practical hydraulic actuators as well as comparison to several common modeling methods further highlight its superiority in modeling the nonlinear processes with noise.