1. Introduction
With the enhancement of rotating equipment in complexity and reliability, prognostics and health management of equipment attract widespread attention. As a crucial component of rotating equipment, rolling bearings can cause the entire equipment to shut down and even lead to serious safety accidents once they fail. Therefore, “timely” bearing weak fault detection is quite important for the safe operation of high-end mechanical equipment. The vibration signal contains abundant operation status information on mechanical equipment, and early fault detection based on the vibration signal has been widely researched [
1,
2,
3,
4].
Early weak faults are usually represented as tiny changes in vibration signals, which tend to be blended in a large amount of strong noise interference, making it difficult to accurately extract and recognize. Therefore, to address these problems, some high-efficiency signal processing techniques and advanced characteristics extraction methods have been adopted to overcome signal weakness and strong background noise interference. Wang et al. proposed different low-rank and sparse estimation models for weak fault characteristics extraction of bearings under different conditions [
5,
6,
7]. Zhao et al. [
8] developed a high-concentration TFA technique, termed frequency-chirprate synchrosqueezing-based scaling chirplet transform (FCSSCT) for analyzing nonstationary and close-spaced fault frequencies of wind turbines. Li et al. [
9] proposed a novel time-frequency ridge estimation (TFRE) method for extracting weak fault characteristics of bearings under variable speed conditions. Kumar et al. [
10] proposed a dynamic degradation monitoring method based on variational mode decomposition (VMD) and based on trigonometric entropy measurements for early fault detection of rolling bearings. Zhang et al. [
11] proposed a fast nonlinear blind deconvolution algorithm for early fault diagnosis of rotating machinery. Bin et al. [
12] proposed a method combining wavelet packet decomposition (WPD) and empirical mode decomposition (EMD) for rotating machinery early fault diagnosis. Li et al. [
13] proposed a new method for extracting the bearing fault characteristic frequency based on improved singular value decomposition (ISVD). Pan et al. [
14] proposed a newly intelligent diagnosis method based on a semi-supervised matrixized graph embedding machine (SMGEM), which can use a few labeled samples to obtain better identification accuracy. Zhao et al. [
15] proposed a novel frequency matching demodulation transform (FMDT) technique extending the generalized demodulation transform for bearing weak fault feature extraction and diagnosis under variable speeds. However, current signal processing and characteristics extraction methods for early weak faults mainly focus on dealing with single-channel signals.
With the popularity of multichannel/multisensory in the Industry 4.0 era, multichannel signals, which contain an abundance of condition information on equipment, show greater potential for weak fault characteristics extraction and early fault detection. Li et al. [
16] studied composite fault diagnosis based on multi-source signals, and the compression sensing technique was utilized to process signals. Wu et al. [
17] proposed a new deep long-short-term memory model to fuse multisensory monitoring signals and improve the prediction accuracy. Long et al. [
18] researched the multi-sensor signals processing method with an attention mechanism and improved AdaBoost for motor fault diagnosis. In addition, to solve the multichannel and multidimensional signal processing problem, multidimensional signal processing technology has also been further developed. Multivariate empirical mode decomposition (MEMD) can realize synchronous processing and adaptive decomposition of multichannel signals [
19]. Lv et al. [
20] applied MEMD to synchronously analyze multivariate signals for bearing fault diagnosis. Similarly, Rehman et al. [
21] extended the variational mode decomposition algorithm and proposed multivariate variational mode decomposition (MVMD) to process multivariate or multichannel data. Song et al. [
22] studied the multichannel mode extraction based on MVMD and self-adaptive MVMD to realize the multichannel fault diagnosis. Zhang et al. [
23] proposed a novel weighted sparsity index based on multichannel fused graph spectra for machine health monitoring. Lang et al. [
24] proposed the direct MITD (DMITD) algorithm for the adaptive processing of multi-loop data, which outperforms traditional techniques in capturing both the regularity and evolution of the plant-wide oscillation from noisy signals in the nonlinear and nonstationary process. Yan et al. [
25] proposed a new approach based on multivariate singular spectrum decomposition (MSSD) and improved Kolmogorov complexity (IKC), which demonstrates good performance in extracting fault information and health condition identification. In fact, in addition to containing more fault characteristic information, the potential structural information between each channel can effectively assist in weak fault characteristics extraction and fault diagnosis [
26]. However, the current high-dimensional signal processing methods tend to preprocess data into matrix or vector form. This preprocessing destroys the potential structural information between channels for multichannel data, weakening the inherent advantages of multichannel signals in characteristics extraction and fault diagnosis. Thus, how to effectively utilize the advantages of multichannel signals with their information richness and explore the correlation features between multichannel structural information and fault characteristics synchronously has become the key to achieving effective fault characteristics extraction for weak fault detection.
Tensors, as a natural and direct form of data representation for high-dimensional data, can maximize the preservation of data information and structure [
27]. Recently, tensor and tensor decomposition-related research work has been widely carried out in various fields and has broad application prospects in pattern recognition [
28], speech processing, computer vision [
29] and fault diagnosis. The structure correlation between multichannel signals and the fault modes has a certain mapping relationship, which can assist in the fault characteristics extraction from multichannel signals effectively. Based on this assumption, the multichannel processing method based on tensor decomposition has been widely researched in fault diagnosis. Hu et al. [
30] proposed a tensor-based method to realize the fault diagnosis of rotating equipment. To utilize multisensory signals for the gear fault diagnosis, Cheng et al. [
31] proposed a nearest neighbor convex hull tensor classifier. Yuan et al. [
32] proposed a novel multichannel signal denoising method based on a high-order singular value decomposition. The multichannel signal processing methods based on tensor decomposition can fully utilize the topological structure and correlation between different channels and more effectively extract the structural correlation features from high-dimensional datasets, which has been a new way for weak fault characteristics extraction of multichannel signals.
Tensor singular value decomposition (TSVD), as one of the tensor decomposition methods, has a promising application in signal characteristics extraction under multichannel conditions. Zeng et al. [
33] proposed a multispectral image denoising method based on TSVD and tensor nuclear norm (TNN). Liu et al. [
34] presented a tensor train-TSVD algorithm for data reduction. Song et al. [
35] proposed a transformed TSVD-based method for tensor completion. TSVD-based methods have achieved excellent applications in image denoising and data recovery, and TSVD is theoretically fully applicable to the processing of mechanical fault signals. Ge et al. [
36] studied tensor robust principal component analysis (TRPCA) based on TSVD and achieved good applications in bearing fault diagnosis. Therefore, the TSVD-related method provides a promising way for multichannel signal processing in the tensor domain. To deal with the weak fault characteristics extraction from multichannel signals under strong background noise, an adaptive low-rank tensor estimation model based on multichannel weak fault detection for bearings is investigated in this paper. The major contributions consist of the following three aspects.
- (1)
To tackle weak fault characteristics extraction from multichannel signals under strong background noise, an adaptive threshold function is introduced, and an adaptive low-rank tensor estimation model is constructed.
- (2)
A new sparsity metric-oriented parameter optimization strategy is provided for the adaptive low-rank tensor estimation model to further improve the estimation accuracy of weak fault characteristics extracted from multichannel signals.
- (3)
The effectiveness and superiority of the proposed method were verified through multichannel data from the repeatable simulation, the publicly available XJTU-SY whole lifetime datasets and an accelerated fatigue test of rolling bearings.
The structure of this paper is arranged as follows.
Section 2 introduces the tensor-related theory and tensor characterization method. The proposed method is described in
Section 3. In
Section 4, the effectiveness and superiority of the proposed method are validated through multichannel simulation signals. The proposed method is also verified for its superiority through public bearing accelerated fatigue life datasets, and laboratory bearing accelerated fatigue test datasets in
Section 5.
Section 6 summarizes the main work and significance of this paper.
5. Experiment Verification
Early faults are usually very weak and masked by strong surrounding background noise. Therefore, it is difficult to detect. Timely fault detection in the early fault stage could undoubtedly provide more time and possibility, for preventive maintenance of equipment, more reference basis for further life prediction, and effectively reduce maintenance costs and machine downtime. The proposed method is applied for early fault detection in real scenarios to further validate its superiority in multichannel weak fault characteristics extraction under strong background noise. Two different bearing whole lifetime datasets, the publicly available XJTU-SY bearing whole lifetime dataset from Xi’an Jiaotong University [
50] and the rolling element bearing dataset of an accelerated fatigue test, are utilized for validation.
5.1. Case 1: XJTU-SY Bearing Lifetime Dataset
The bearing accelerated fatigue testing platform of XJTU-SY is shown in
Figure 16. The testbed consists of an AC induction motor, hydraulic loading system, motor speed controller, support bearings, and support shaft. The type of tested bearing is an LDK UER204. Datasets of Bearing1_1 and Bearing1_3 are selected for further analysis, whose rotating speed and radial force are 2100 rpm and 12 kN, respectively. The sampling frequency is 25.6 kHz. A total of 1.28 s of data were recorded per minute. Two accelerometers were installed to collect the vibration signals through two channels.
Figure 17 displays the root mean square (RMS) of the vibration signals throughout the whole lifetime for both bearings. A distinct rise in the RMS value, especially when followed by a continuous increase, usually indicates the occurrence of fault for bearings as highlighted by the red rectangular box in
Figure 17. The signals sampled around these time points are further analyzed to study the state of the bearings. The envelope spectra of the signal at 81 min in Bearing1_1 and 61 min in Bearing1_3 are displayed in
Figure 18, from which the rotating frequency and the characteristic frequency of bearing outer race fault can be clearly observed in both channels from these two bearings. It indicates that a local fault has occurred in the outer race during the degradation processes.
Due to the low sensitivity of the RMS metrics to early faults, more detailed fault information cannot be obtained from the RMS plots. Instead, the proposed method is capable of exactly extracting early weak fault characteristics that are submerged by the strong background noise. To detect the early fault as quickly as possible, the signals sampled before the obvious fault stage are analyzed using the proposed method.
Firstly, a third-order tensor with the size of 138 × 245 × 2 is constructed by multichannel signals. Then, the observation tensor is processed through the MGISES-oriented parameter optimization strategy, the weak fault characteristics extraction by the adaptive low-rank tensor estimation model, inverse phase space reconstruction, and envelope spectrum analysis of the denoised signals. The early faults can be detected at 63 min in Bearing1_1 and 43 min in Bearing1_3 at the earliest. The envelope spectra of the original signals are displayed in
Figure 19. It is only possible to observe the rotating frequency of the bearings, while almost all fault characteristic frequencies of both bearings and their harmonics are drowned out by the strong background noise. Then, the envelope spectra of the finally extracted fault characteristic signals are shown in
Figure 20. It is observed that the fault characteristic frequencies of both bearings and their harmonics can be distinctly identified after noise reduction by the proposed method. It indicates that these two bearings start to undergo a weak degradation phenomenon at this point, producing early faults. After this moment, both bearings gradually began to show obvious faults. Finally, the testing bearings run to failure. Then, it was found through disassembly and inspection that these two bearings did indeed have outer race faults. Therefore, the early faults of both bearings can be clearly and timely identified based on the proposed method.
With the aim of validating the superiority of the “very early” detection of the proposed method, the earliest time points at which faults can be clearly identified are also analyzed by the proposed method for Bearing2_1 and Bearing3_1. The results are listed in
Table 3. Furthermore, early fault detection results from the relevant references are also listed in
Table 3 for comparison. It is obvious that the proposed method has a distinct advantage in early fault detection.
Then, the signals sampled at 63 min in Bearing1_1 and 43 min in Bearing1_3 are also processed by the methods in
Table 1 for comparative analysis.
Figure 21 shows the envelope spectra of the denoised signals by
Method 1. From
Figure 21a, it can be found that only the fault characteristic frequency in Channel#1 can be observed in the extracted signal for Bearing1_1. In
Figure 21b, the fault characteristic frequency and two times the fault characteristic frequency can be seen in both channels for Bearing1_3. However, obvious background noise is still visible in the envelope spectra of both channel signals.
Figure 22 and
Figure 23 show the envelope spectra of the denoised signals by
Method 2 and
Method 3. The fault characteristic frequency and its harmonic frequencies are clearly seen in the signals denoised by
Method 2 and
Method 3, which are attributed to the utilization of the fault characteristics extraction method based on the adaptive threshold function and the adaptive low-rank tensor estimation model. However, compared to
Figure 20, their fault characteristics extraction capabilities, as well as their energy retention effects, are relatively poor.
Figure 24,
Figure 25,
Figure 26 and
Figure 27 show the envelope spectra of the denoised signals of the two bearings by the other four methods in
Table 1 (i.e.,
Method 4,
Method 5,
Method 6, and
Method 7) through selecting the appropriate number of decomposition layers and intrinsic mode functions (IMFs). The best noise reduction was achieved by
Method 7. The results for the two bearings show clear fault frequencies but still suffer from noise interference. The remaining three methods can see little fault-related information in the result plots. Compared to
Figure 20, these four methods are generally unable to effectively extract early weak fault characteristics from strong background noise.
The proposed method can effectively utilize the structural correlation between multichannel signals to enhance the low-rank characteristics extraction ability. At the same time, under the guidance of the sparsity metric, it can maintain superior fault characteristics extraction ability in the presence of strong background noise. Therefore, for the “very early” fault stage, the proposed method achieves much better performances compared with the other four methods.
5.2. Case 2: An Accelerated Fatigue Test of Rolling Element Bearings
To further verify the superiority of the proposed method in multichannel weak fault characteristic extraction and early fault detection, an accelerated fatigue test was conducted on the accelerated bearing life tester (ABLT-1A), as shown in
Figure 28a. The experimental platform consisted of a lubrication system, transmission system, data acquisition system, AC motor, and loading system. Four bearings typed 6307 were synchronously installed at four locations for the accelerated life test. To accelerate the bearing fatigue process, a radial load of 12.744 kN was applied. The data acquisition system of the test bench included three PCB348A acceleration sensors to collect vibration signals generated by four bearings. The position of the sensors and the load are shown in
Figure 28b. The type of data acquisition card was NI PCI-6023E. The sampling frequency was 25.6 kHz, and 0.8 s of data were recorded per minute. The corresponding parameters of the testing bearings are provided in
Table 4. During the test, the rotating speed of the shaft was 3000 rpm. The fault characteristic frequencies of the bearings are calculated, as shown in
Table 5.
Furthermore, the signals sampled from the three channels contain significant differences. As seen from
Figure 29, the signal from Channel#3 is more sensitive to the degradation process and contains larger fluctuations caused by noise interference compared with the other two channels. However, it has been found that signals from Channel#2 and Channel#3 contain much clearer fault frequency characteristics from
Figure 30a. For signals at 1871 min in
Figure 30b, the amplitude at the rotating frequency is more pronounced in Channel#1. However, peaks at the fault characteristic frequency only can be visualized from the other two channels, although they are masked under strong interference noise. Therefore, multichannel signals contain richer fault characteristic information and can effectively assist the fault characteristics extraction under strong background noise.
Then, the 3-channel signals sampled at 1871 min are processed by the proposed method to extract the early fault characteristics. The size of the constructed observation tensor size is 196 × 114 × 3. Processed by the proposed method, the envelope spectra of the final extracted fault signals are shown in
Figure 31. To verify the superiority of the proposed method, methods in
Table 1 are also utilized to process these multichannel signals. The final results are displayed in
Figure 32 and
Figure 33.
In
Figure 31, the rotating frequency and its harmonics can be identified in the low-frequency range. More importantly, significant inner race fault characteristic frequencies and their harmonics can be distinctly observed without any background interference. It indicates that the bearing starts to undergo a weak degradation phenomenon at this point, producing an early fault. Therefore, the early fault can be detected at 1871 min with the proposed method. Then, an early warning can be provided before the fault worsens.
Figure 30a confirms that a distinct inner race fault indeed occurs in the later stage of the bearing lifetime. The proposed method achieves satisfying results on the early fault characteristics extraction in the presence of strong background noise in this application.
From the results of the comparative methods in
Figure 32a,
Method 1 has a relatively poor ability for fault characteristics extraction. As shown in
Figure 32a, the fault characteristics of the inner race fault are relatively obvious in Channel#1. However, the fault characteristic frequency cannot be clearly observed in the other two channels. There are still obvious interference components in the extracted signals. The envelope spectra of the denoised signal by
Method 2 and
Method 3 are shown in
Figure 32b,c, and it can be found that there are obvious fault characteristic frequencies in all three channels. But the amplitudes of the fault characteristic frequency in the extracted signals are much smaller than that in
Figure 31, which validates the important role of the proposed MGISES-oriented parameter optimization strategy in energy retention. The results of the other four methods in
Table 1 (i.e.,
Method 4,
Method 5,
Method 6, and
Method 7) are shown in
Figure 33. The results of
Method 4 and
Method 6 have fault-related information, but there is a large amount of noise, which fails to achieve good noise reduction. The results of
Method 5 and
Method 7 have obvious fault-related information. However, they fail to maintain the energy of the fault characteristics, and the noise still affects the extraction results.
In conclusion, the proposed method has achieved excellent performance in multichannel weak fault characteristics extraction under strong background noise. With the advantage of multichannel synchronous processing based on tensor decomposition, it can effectively remove the interference of strong background noise. In addition, it can better preserve the energy of fault characteristic components while removing strong background noise interference.
6. Conclusions
In this study, a weak fault detection framework is proposed as an effective method for multichannel signals under strong background noise. Firstly, the multichannel signals are transformed into a tensor by phase space reconstruction, which has obvious advantages in characterizing fault information for multichannel signals. And the low-rank property of multichannel fault signals in the tensor domain is revealed. Secondly, an adaptive threshold function is formulated according to the singular value distribution of the fault component and an adaptive low-rank tensor estimation model is constructed for weak fault characteristics extraction from multichannel signals under strong background noise. Thirdly, a new sparsity metric-oriented parameter optimization strategy is provided for the adaptive low-rank tensor estimation model to further improve the accurate estimation of weak fault characteristics from multichannel signals. Finally, an effective weak fault detection framework based on an adaptive low-rank tensor estimation model is formed for multichannel signals under strong background noise.
It is demonstrated by simulated multichannel signals and experimental analysis that the proposed method exhibits much better performance than other multichannel signal processing methods. First, the proposed method is compared with the traditional tensor estimation method. Results verify the superiority of the proposed adaptive threshold function and adaptive low-rank tensor estimation model in dealing with strong background noise. Second, compared to the Kurtosis/Negative entropy-oriented adaptive low-rank tensor estimation method, the proposed MGISES-oriented adaptive low-rank tensor estimation method is more helpful for weak fault characteristics extraction under strong background noise. Third, compared to advanced multichannel signal analysis methods (i.e., MEMD, MVMD, MITD, and MSSD), the proposed method verifies once again that the tensor-based characteristics extraction method is able to achieve better fault characteristics extraction results. In summary, this work can provide a reference for the research of multichannel/multisensory signal processing in the Industry 4.0 era. However, this method is based on a sole low-rank assumption, which will encounter difficulties in handling compound fault situations. In the future, to enrich and accelerate the development of intelligent diagnosis for compound fault, more in-depth studies for mechanical equipment not confined to bearings (e.g., gears, shafts, and other rotating parts) will be conducted on multichannel signal processing and feature extraction.