Kernel Regression Residual Decomposition Method to Detect Rolling Element Bearing Faults

Xiaoqian Wang,Wei Zhang,Jiawei Xiang,Weisheng Zhao,Jie Cai,Jinlian Deng,Dali Sheng,Zhifeng Dai

doi:10.1155/2021/5523098

Abstract

The raw vibration signal carries a great deal of information representing the mechanical equipment's health conditions. However, in the working condition, the vibration response signals of faulty components are often characterized by the presence of different kinds of impulses, and the corresponding fault features are always immersed in heavy noises. Therefore, signal denoising is one of the most important tasks in the fault detection of mechanical components. As a time-frequency signal processing technique without the support of the strictly mathematical theory, empirical mode decomposition (EMD) has been widely applied to detect faults in mechanical systems. Kernel regression (KR) is a well-known nonparametric mathematical tool to construct a prediction model with good performance. Inspired by the basic idea of EMD, a new kernel regression residual decomposition (KRRD) method is proposed. Nonparametric Nadaraya–Watson KR and a standard deviation (SD) criterion are employed to generate a deep cascading framework including a series of high-frequency terms denoted by residual signals and a final low-frequency term represented by kernel regression signal. The soft thresholding technique is then applied to each residual signal to suppress noises. To illustrate the feasibility and the performance of the KRRD method, a numerical simulation and the faulty rolling element bearings of well-known open access data as well as the experimental investigations of the machinery simulator are performed. The fault detection results show that the proposed method enables the recognition of faults in mechanical systems. It is expected that the KRRD method might have a similar application prospect of EMD.

Highlights

Academic Editor: Zhifeng Dai e raw vibration signal carries a great deal of information representing the mechanical equipment’s health conditions
Nonparametric Nadaraya–Watson Kernel regression (KR) and a standard deviation (SD) criterion are employed to generate a deep cascading framework including a series of high-frequency terms denoted by residual signals and a final low-frequency term represented by kernel regression signal. e soft thresholding technique is applied to each residual signal to suppress noises
Like the empirical mode decomposition (EMD) method, the kernel regression residual decomposition (KRRD) method is used to decompose a signal into a number of residual signals at different scales

Summary

Kernel Regression Residual Decomposition Methodology

Regression model-based methods will be applied to decompose signals, according to the basic idea of EMD. The soft thresholding technique and SD criterion are applied to obtain noise-suppressed residual signals. Where f 􏽐, 2(t) denote the summation of all residual signals at scale [2,n] In this step, estimating f 􏽐, 2(t) by given. Since the residual signal at scale n can be obtained by equation (4), a deep cascading framework can be expressed as follows: rj(t) f 􏽘, j(t) − f 􏽘, j + 1(t) sj − sj+1, (5). The signal decomposed realization of KRRD via kernel regression at each scale is completed, and the KRRD is the summation of all residual signals r1(t), r2(t), . Considering some unusual data in the signal, we use the median absolute deviation function to estimate the noise threshold θj at scale j, using adaptive noise estimate. Compared the theoretical feature frequencies of faults in bearings with demodulation frequencies, the type of bearing faults could be determined

Simulation Analysis

Experimental Evaluation

Conclusion