Research on rolling bearing fault diagnosis technology based on singular value decomposition

Abstract

To solve the difficulty of selecting the number of effective singular values in Singular Value Decomposition denoising, a new method to determine the number of effective singular values is proposed. The proposed method to determine the number of effective singular values is based on the non-zero singular value distribution law of the Hankel matrix constructed by the signal. Specifically, the number of effective singular values in the Hankel matrix is twice the number of frequencies contained in the signal, and the difference between the effective singular values of the noisy signal and the non-zero singular values of the pure signal is very small. The proposed method for determining the number of effective singular values is to perform differential processing on the singular values of the signal and normalize the difference obtained. An empirical parameter T is provided, and the number of effective singular values is determined by comparing them with the normalized results. The proposed method is applied to the simulated and measured rolling bearing signals, and the results are compared with the wavelet threshold denoising method. The results show that the proposed method for determining the number of singular values can effectively filter out the noise frequency contained in the signal while maintaining the characteristic frequency of the signal and achieving the purpose of mechanical equipment fault diagnosis.