Correntropy Kernel Learning for Nonlinear System Identification with Outliers

One significant challenge in nonlinear system identification developed for industrial processes is that the modeling samples often contain outliers and noise. In this work, a novel general identification method, Correntropy Kernel Learning (CKL), is proposed for the identification of nonlinear systems with outliers and noise. Unlike the traditional mean squared error criterion adopted by almost all the existing identification methods, correntropy is introduced into the field of nonlinear system identification. A new correntropy-based index is proposed to evaluate the performance of identification models for nonlinear systems with outliers and noise. The CKL identification method can reduce the effects of outliers by the use of a robust nonlinear estimator that maximizes correntropy. Without resorting to unnecessary efforts, the outlier samples can be simultaneously detected once the CKL identification model is obtained. Moreover, an efficient two-level training procedure is proposed to implement the CKL method in a more practical manner. The superiority of the proposed CKL method is first demonstrated through a benchmark example in different situations. It is also compared with other KL methods for identification of an industrial process in Taiwan. The benefit of its more accurate and reliable performance indicates that CKL is promising in practice for the identification of nonlinear systems with outliers.