Incipient fault feature extraction of rolling bearings based on the MVMD and Teager energy operator

Highlights

• The modified variational mode decomposition method based on spectrum adaptive segmentation of scale space is proposed.

• An incipient fault feature extraction method of rolling bearings combined MVMD with Teager energy operator is presented.

• The validity of the presented MVMD-TEO method is verified by The experimental cases of three different data-sets.

Abstract

Aiming at the problems that the incipient fault of rolling bearings is difficult to recognize and the number of intrinsic mode functions (IMFs) decomposed by variational mode decomposition (VMD) must be set in advance and can not be adaptively selected, taking full advantages of the adaptive segmentation of scale spectrum and Teager energy operator (TEO) demodulation, a new method for early fault feature extraction of rolling bearings based on the modified VMD and Teager energy operator (MVMD-TEO) is proposed. Firstly, the vibration signal of rolling bearings is analyzed by adaptive scale space spectrum segmentation to obtain the spectrum segmentation support boundary, and then the number K of IMFs decomposed by VMD is adaptively determined. Secondly, the original vibration signal is adaptively decomposed into K IMFs, and the effective IMF components are extracted based on the correlation coefficient criterion. Finally, the Teager energy spectrum of the reconstructed signal of the effective IMF components is calculated by the TEO, and then the early fault features of rolling bearings are extracted to realize the fault identification and location. Comparative experiments of the proposed method and the existing fault feature extraction method based on Local Mean Decomposition and Teager energy operator (LMD-TEO) have been implemented using experimental data-sets and a measured data-set. The results of comparative experiments in three application cases show that the presented method can achieve a fairly or slightly better performance than LMD-TEO method, and the validity and feasibility of the proposed method are proved.

Introduction

Rolling bearings always rotate constantly in harsh industrial environment such as high temperature, variable rotational speed and big loads so that they have high breakdown frequency [1]. Its health condition directly determines the performance of the rotating machinery. Defects in rolling bearings may arise during operation or during the manufacturing process, which will cause vibration, noise, and even system failure. Therefore, it is important to detect the defects of rolling bearings at their incipient stage, to prevent the catastrophic damage or failures of the rotating machine [2].

To diagnose early fault of rolling bearings, vibration signal monitoring remains more effective than others for it can discriminate slight change in bearings operating status through signal processing [3]. It is crucial and difficult to extract characteristic information directly from vibration signal of rolling bearings which is non-stationary, nonlinear, and with strong noise interference [4]. The general way to extract fault features is based on adaptive time frequency transform. And then the effective decomposition components are selected in accordance with correlation coefficient and kurtosis criterion, etc.

Empirical Mode Decomposition (EMD) is a typical adaptive time frequency decomposition method which confronts negative instantaneous frequency, mode mixing problem and end effects [1,5]. Local Mean Decomposition (LMD) [6] is developed to analyze complicated data through time-varying frequency, phase and energy characteristics. And the implementation principle of LMD is similar with EMD. However, it has been proven that LMD is better than EMD in local characteristic, time-scale, suppression mode mixing problem and weakening end effects [7]. At the same time, LMD can ensure that the instantaneous frequency has physics meaning for each of product functions (PFs) and overcome the negative frequency problem of the decomposed components which cannot be interpreted with EMD [8]. A new subspace decomposition technique called non-negative matrix factorization (NMF) which imposes a non-negativity constraint is proposed to extract key features of data [9]. Moreover, it is also observed that EMD or LMD acts essentially as discrete wavelet transform (DWT) like filter bank or a variational framework [[10], [11], [12]]. Aiming at solving the fixed dyadic frequency partition problem in DWT and achieving EMD-like adaptively in WT, a novel wavelet transform, named empirical wavelet transform (EWT), is developed to extract meaningful modes from a signal [13]. The EWT method shows its effectiveness through successful application in area of mechanical fault diagnosis. Chen adopted EWT to diagnose the generator bearing fault of wind turbine, and compare the results of EWT with other adaptive methods [14]. Pan modified EWT by data-driven adaptive Fourier spectrum segment, and applied it to identify the bearing fault of locomotive [15]. But the binary band allocation of EWT may divide the characteristic signal into different mode [16,17].

In order to overcome the shortcomings of mentioned above signal decompostion methods, a new, adaptive and quasi-orthogonal signal decomposition method, named variational mode decomposition (VMD), is proposed by K. Dragomiretskiy [18]. And the mode mixing and misclassification of EMD or LMD can be effectively overcome using the VMD method [[19], [20], [21]]. Since the VMD method is proposed, it has received extensive attention and also played a successful role in fault diagnosis of rolling bearings [[22], [23], [24]]. However, the VMD method has some limitations mainly including two aspects: the first is that the number of IMFs must be set in advance, and remain unchanged; another one is that the selection of the penalty parameter α of VMD lacks of theoretical support. Due to various factors such as strong noise of working condition or vibration of other components of rolling bearings, the presetted number of IMFs may cause loss of information or excessive decomposition, and affect the subsequent analytical results of feature extraction [25]. In order to overcome these limitations of the VMD method, some improved methods are also reported. A fault diagnosis method for rolling bearings based on parameter optimized VMD using particle swarm optimization (PSO) is proposed [26]. PSO method is used to search for the quasi-optimal combination of the penalty parameter and the number of components of VMD. To diagnose the oil film instability of rotor systems, an improved VMD method is proposed based on mutual information criterion to match the waveform and extend the endpoints [27]. In addition, the energy criterion is introduced as the iteration terminal condition of VMD to improve the decomposition performance [28]. But, the parameter optimization is a process of iterative optimization. The optimization time of PSO sharply increases with the amount of data, which is not conducive to online application. And the PSO algorithm is easy to get the local optimal result. Therefore, one of the most important problems is how to rapidly and adaptively determine the number of IMFs of VMD method and improve the processing speed of subsequent signal analysis.

Inspired by Ref. [29], the scale space segmentation method is introduced to modify VMD, named MVMD. It can rapidly and adaptively select the number of IMFs and improve online processing ability of the algorithm. Then, TEO is superior to be chosen as a kind of envelope demodulation method, because it has such advantages as enhancing transient characteristics and detecting shock components of signals, high-resolution on time and low computational complexity. So, an incipient fault feature extraction method of rolling bearings combined MVMD with TEO is presented. The proposed method is then applied to diagnose rolling bearings fault based on two groups numerical simulated signals and actually measured signal. A comparison between the proposed MVMD-TEO method and the LMD-TEO method [36] has also been conducted to evaluate the effectiveness of identifying the rolling bearings fault.

The remainder of the paper is organized as follows. The principle of MVMD is investigated in Section 2. In Section 3, The realization process MVMD-TEO is described. The effectiveness of the proposed method for rolling bearings fault diagnosis is evaluated by comparison with LMD-TEO method in Section 4. The actual application performance of the proposed method is shown in Section 5. Discussion and conclusion are presented in Section 6.