Kernel scatter-difference-based discriminant analysis for nonlinear fault diagnosis

There are two fundamental problems with the kernel fisher discriminant analysis (KFDA) for nonlinear fault diagnosis. One is the singularity problem of the within-class scatter matrix due to the small sample size problem. The other is that the computational cost of kernel matrix becomes large when the training sample number increases. Aiming at these two problems, in this paper, a kernel scatter-difference-based discriminant analysis (KSDA) method is proposed for fault diagnosis. The proposed method cannot only produce nonlinear discriminant features of the process data, but also avoid the singularity problem of the within-class scatter matrix. When the training sample number becomes large, a feature vector selection (FVS) scheme based on a geometrical consideration is given to reduce the computational complexity of KSDA for fault diagnosis. Experimental results are given to show the effectiveness of the new method.