Egram Based SVD Method for Gear Fault Diagnosis

Abstract

The performance of singular value decomposition (SVD) mainly relies on selection of the effective singular values. However, most of the existing methods for selecting the effective singular values have some problems such as unsatisfactory performance of denoising. For selecting the effective singular values more accurately, a novel energy diagram (Egram) based SVD method is proposed. Novelties of the proposed method are divided into two parts. Firstly, the form of the effective singular values is determined by selection criteria of embedding dimension of Hankel matrix in SVD. The selection criteria are defined based on the special relationship between the form of the effective singular values and the embedded dimension of Hankel matrix for the amplitude modulation-frequency modulation (AM-FM) signal, and the special relationship is found that, when appropriate embedding dimension is selected, the AM-FM signal is mainly decomposed into two adjacent singular values with approximately equal numerical magnitude, which are called singular value pairs ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SVP</i> ). Secondly, the Egram is developed to adaptively locate effective <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SVP</i> by estimating the energy of frequency band and to detect gear fault. The Egram-based SVD method is verified using the simulated signal and experiment signal that measured from the gearbox test bench, and analysis results show that the form and location of the effective singular values that contains gear fault can be determined. Comparisons with the difference spectrum, relative change rate of singular values, relative change rate of singular kurtosis and fast Kurtogram show that the Egram-based SVD has much better ability to detect gear fault.