A performance enhanced time-varying morphological filtering method for bearing fault diagnosis

Highlights

• A new MHPO is proposed to enhance impulse feature extraction.

• A new time-varying SE design strategy is proposed for morphological filtering.

• An ATVMF method is proposed for adaptive extraction of bearing fault features.

• An ATVMF-DSS method is developed to enhance bearing fault diagnosis.

• ATVMF-DSS exhibits excellent bearing fault diagnosis performance.

Abstract

Fault feature extraction and broadband noise elimination are the keys to weak bearing fault diagnosis. Morphological filtering is a typical fault feature extraction method. However, the parameter selection of structural element (SE) has an important influence on the filtering result. To solve this problem, an adaptive time-varying morphological filtering (ATVMF) is proposed. ATVMF adaptively determines the shape and scale of SE according to the inherent characteristics of vibration signal, effectively improving the fault feature extraction capability and computational efficiency. To solve broadband noise pollution, the diagonal slice spectrum (DSS) is applied to the resulting signal of ATVMF to further eliminate the fault-unrelated components. Finally, a weak bearing fault diagnosis method combining ATVMF and DSS is developed. Simulation and experimental results verify that the proposed method can effectively enhance fault-related impulse features and diagnose weak bearing faults. The comparison with several existing methods demonstrates the advantages of the proposed method.

Introduction

Nowadays, increasing attention is paid to the prognostics and health management of mechanical systems [1]. As a vital component of rotary machinery systems, rolling bearings are usually one of the key monitoring objects. Due to the rich information contained in vibration signals and their sensitivity to incipient faults, vibration analysis has become one of the commonly used techniques for bearing condition monitoring and fault diagnosis [2]. However, due to the harsh working environment, bearing vibration signals are often contaminated by background noise and external interferences, making it difficult to detect local defects on the bearing from the vibration signals. Therefore, broadband noise elimination and fault feature extraction for the monitoring vibration signals are the keys to weak bearing fault diagnosis.

For the elimination of broadband noise, the commonly used signal processing techniques include time series analysis [3], decomposition-based methods [4], [5], [6], [7], [8], [9], [10], and higher-order cumulant [11]. The decomposition-based method is a widely used denoising technique in vibration signal processing. This method decomposes a multi-component signal into a series of sub-signals with limited bandwidth, and then selects one or more sub-signals (other sub-signals are regarded as noise components) for reconstruction to achieve the purpose of reducing broadband noise pollution. The wavelet-based method [4], [5], singular value decomposition [6], empirical mode decomposition [7], local mean decomposition [8], instrinsic time-scale decomposition [9] and variational mode decomposition (VMD) [10], [12] have been widely employed to reduce the background noise of mechanical vibration signals. However, these decomposition-based methods have some limitations in practical application. The wavelet-based methods need to define the basis function in advance. For the singular value decomposition-based methods, it is still challenging to design appropriate criteria to reconstruct the signal. Empirical mode decomposition and local mean decomposition have the shortcomings of mode mixing and sensitivity to noise. The proper rotations obtained by instrinsic time-scale decomposition are not strict mono-components when confronted with strong interferences, which may cause erroneous instantaneous characteristics. VMD is a frequency-domain signal decomposition method, which estimates each signal component by solving a frequency-domain variational optimization problem [13]. However, its two key parameters, the number of modes and the penalty factor, need to be carefully selected. Other commonly used noise reduction techniques are autocorrelation function and third-order cumulant diagonal slice (TOCDS). The autocorrelation function is a well-known periodic detection tool, which uses correlation characteristics to eliminate aperiodic interference components in the vibration signal. In [14], [15], the autocorrelation function is applied to the signals obtained by wavelet packet transform to further eliminate the bearing fault-unrelated components. Since the TOCDS of Gaussian and symmetrically distributed noise is zero [16], the TOCDS can be used to eliminate Gaussian and symmetrically distributed noise in vibration signals [11]. Furthermore, the frequency spectrum of TOCDS, called diagonal slice spectrum (DSS), can detect the quadratic frequency coupling of the vibration signals [17]. The TOCDS has been successfully applied to vibration signal noise reduction in bearing fault diagnosis [17], [18], [19]. However, the autocorrelation function and TOCDS are sensitive to harmonic components. Therefore, they are often used in the post-processing of vibration signals in mechanical fault diagnosis.

For the fault feature extraction, at present, many feature extraction techniques have been developed and widely applied to fault diagnosis of rotating machinery, such as envelope analysis [20], [21], [22], deconvolution-based methods [23], [24], [25], cyclic spectral analysis [26], [27], [28], matching pursuit [29], modulation signal bispectrum [30], and morphological filtering (MF) methods [18], [31]. Among these techniques, MF is a nonlinear signal processing technique developed from integral geometry and random set theory, which aims to modify the geometric shape of the signal through its interaction with a structural element (SE) [32], [33]. Due to its remarkable performance in impulse feature extraction, the MF is often used to extract impulse features related to rotating machinery faults from vibration signals. However, the selection of the shape and scale of SE is crucial for obtaining good filtering results, especially the scale of the SE. Because it is difficult or even impossible to extract impulse features when using an inaccurate SE scale. The study in [31] showed that a flat SE length of 0.6–0.7 times the impulse repetition period can minimize the noise effects, whereas it is an empirical rule. The multi-scale MF (MMF) alleviates the influence of SE scale selection by calculating the weighted average of the filtering results at different scales as the final result [34], [35]. However, the filtered signals of inaccurate scales seriously contaminate the fault-related features and the analysis process is time-consuming due to the repeated execution of morphological operators [36]. To reduce the fault-unrelated components, the optimal scale MF (OSMF) methods [19], [37], [38], [39], [40] were developed. These methods focus on selecting the optimal signal from a set of filtered signals obtained from different SE scales for fault detection through an evaluation indicator. Although the OSMF reduces the residual noise in filtering results, its computational efficiency (similar to the MMF) is not improved, which is not conducive to online application. To improve computational efficiency, Zhang et al. [34] reduced the scale range of triangular SE for MMF based on the intervals of local maximum points of vibration signal. Their method greatly reduces the computation time compared with the traditional MMF, but another shortcoming of the MMF is not overcome. Another representative method is the time-varying MF (TVMF) proposed by Li et al. [36], which adaptively adjusts the shape and scale of SE according to the local extreme points of vibration signals to extract local impulse features. However, the above-mentioned MF methods all adopt the window function-based SEs, such as the flat SE, triangular SE, and Dolph-Chebyshev SE, which cannot match impulse features well under strong interference and lead to poor impulse feature extraction. Wang et al. [41] and Hu et al. [42] adopted the impulsive attenuation function and sinusoidal harmonic function, respectively, to construct SE and obtained better bearing fault impulse extraction effect than the traditional SEs based on window functions. However, their methods require prior knowledge of bearing fault signals, such as resonant frequencies, which limits their applications to some extent. Therefore, it is necessary to develop robust and adaptive SE for bearing fault feature extraction.

To improve the performance of MF methods in bearing fault feature extraction and weak bearing fault diagnosis, this paper explores the weak bearing fault diagnosis method based on the performance-enhanced MF algorithm. The main contributions of this paper are summarized as follows:

(1) An adaptive TVMF (ATVMF) algorithm is proposed for adaptive extraction of impulse features. The ATVMF uses a new time-varying SE strategy to adaptively determine the shape and scale of SE according to the inherent characteristics of the vibration signal, and adopts a new morphology hat product operator (MHPO) to extract fault-related impulse features from vibration signals. This design enables the ATVMF to exhibit stronger impulse feature extraction ability and higher computational efficiency compared with the traditional MMF and OSMF methods.

(2) A weak bearing fault diagnosis methodology that combines the merits of ATVMF and DSS, named ATVMF-DSS, is developed. The ATVMF is firstly employed to extract fault-related impulse features from bearing vibration signals. Then TOCDS is applied to the filtered signal to further remove broadband noise and highlight fault features. Finally, the DSS is used to detect the coupling characteristic frequencies for bearing fault diagnosis.

(3) The fault diagnosis performance of the proposed method and the comparison with two reported MF methods and two benchmark methods are investigated on the simulated signals and railway bearing experimental signals. Experimental results demonstrate that the proposed method can effectively enhance fault-related impulse features and diagnose rolling bearing faults under strong interference.

The remainder of this paper is arranged as follows. Section 2 introduces the basic theory of new MHPO, new time-varying SE design strategy, and DSS. In Section 3, the implementation procedure of the ATVMF-DSS method is described. In 4 Verification with numerical simulation, 5 Experimental verification, the simulated and experimental signals are analyzed to validate the proposed method, and comparisons with several existing methods are conducted. Section 6 presents further analysis results of the ATVMF-DSS. Finally, conclusions are summarized in Section 7.