Regularized kernel function parameter of KPCA using WPSO-FDA for feature extraction and fault recognition of gearbox

Abstract

Gearbox is subject to damage or malfunctions by complicated factors such as installation position and operation condition, meanwhile, accompanied by some nonlinear behaviors, which increase the difficulty of fault diagnosis and identification. Kernel principal component analysis (KPCA) is a commonly used method to realize nonlinear mapping via kernel function for feature extraction. However, choosing an appropriate kernel function and the proper setting of its parameter are decisive to obtain a high performance of the kernel methods. In this paper, we present a novel approach combining PSO and KPCA to enhance the fault classification performance. The standard particle swarm optimization (WPSO) was used to regularize kernel function parameter of KPCA instead of the empirical value. In particular, in view of the thought of Fisher Discriminate Analysis (FDA) in pattern recognition, the optimal mathematical model of kernel parameter was constructed, and its global optimal solution was searched by WPSO. The effectiveness of the method was proven using the Iris data set classification and gearbox faults classification. In the process, gearbox fault experiments were carried out, and the vibration signals in different conditions have been tested and processed, and the fault feature parameters were extracted. At last the analysis results of gearbox fault recognition was obtained by KPCA and compared with PCA. The results show that the separability of failure patterns in the feature space is improved after kernel parameter optimized by WPSO-FDA. The problems of single failure and compound fault recognition have been effectively solved by the optimized KPCA.