The Application of Orthogonal Wavelet Transformation: Support Vector Data Description in Evaluating the Performance and Health of Bearings

Abstract

Support vector data description (SVDD) is common supervised learning. Its basic idea is to establish a closed and compact area with the objects to be described as integrity. The described objects are all included within the area or as far as possible. In contrast, other objects are excluded out of the area as far as possible. The inherent nature and laws of data are subsequently revealed, thereby distinguishing the operation state of the machine. In this paper, an orthogonal wavelet transformation-support vector data description (OWTSVDD) is proposed to evaluate the performance of bearings, where the peak-to-peak value of detail signal is extracted through orthogonal wavelet transformation as the set of test samples, thus solving the distance $R_z$ from the set of test samples to the center of the sphere. Based on $\text{HI}=R_z^2-R^2$ , its distance to the hypersphere is calculated to judge whether it belongs to the normal state training samples. Finally, the performance and health of bearings are evaluated with HI. According to the classification of two sets of experimental data of rolling bearings, the proposed method better reflects the degeneration of bearing’s performance compared with the (SVDD) HI value without extraction of characteristic value, being entirely able to evaluate the entire life cycle of bearings from normal operation to fault and degradation. The HI evaluation result based on experimental data in Xi’an Jiaotong University is consistent with the life-cycle vibration signal of bearings, providing a scientific basis for production and equipment management and improving the prognostics technology-centered prognostics and health management (PHM).