Process fault diagnosis based on kernel regularized fisher discriminant

Abstract

Fisher discriminant analysis (FDA) is a widely used dimensionality reduction technique for fault diagnosis in industry process, whereas it is difficult to capture nonlinear relationship. Kernel FDA (KFDA) is nonlinear extension of FDA developed in the last ten years. Unfortunately, small sample size (3S) problem will be arisen in both FDA and KFDA. Regularized FDA (RFDA) is an effective solution for this problem. To obtain kernel form of RFDA is basis for solving both nonlinear and 3S problem. In this paper a novel kernel form of RFDA, which is transformed to equation solving problem and expressed in the dual form, is deduced and implement procedure for fault diagnosis is given. Experimental results on the Tennessee Eastman (TE) process show validity and effectivity of the proposed kernel algorithm for 3s problem. Several relationships between regularization parameter and diagnosis effect are derived at last.