1. Introduction
Rotating machinery is the predominant equipment type in applied sectors, such as electric power, petrochemicals, metallurgy, aerospace, and other industries. Bearings, being crucial components of these machines, play a particularly significant role in their monitoring and diagnosis [
1]. Research findings indicate that rolling bearing failures account for 30% of all rotating machinery failures [
2,
3,
4]. Therefore, fault diagnosis of rolling bearings holds immense importance.
In recent years, there has been a proliferation of fault diagnosis methods for rolling bearings. The research on early fault feature extraction of rolling bearings extensively utilizes wavelet transform, empirical mode decomposition (EMD), and machine learning techniques. He et al. [
5] proposed a novel deep neural network by integrating wavelet transform with deep learning techniques, which was successfully applied for fault diagnosis in rolling bearings. Xue et al. [
6] employed the combination of empirical wavelet transform and correlation kurtosis for fault diagnosis in rolling bearings. Ding et al. [
7] integrated the Markov method with a depth residual network to enhance fault diagnosis of rolling bearings. In a subsequent study, Xue et al. [
8] utilized the Markov transition field technique to transform the original vibration signal into a time-dependent image for fault diagnosis in rolling bearings under small sample conditions. The empirical mode decomposition (EMD) method is capable of decomposing the original signal and effectively eliminating Gaussian white noise. Building upon this research, Li et al. [
9] proposed a rapid adaptive EMD technique to extract fault features from rolling bearings.
In the field of deep learning, with the rapid advancement of artificial intelligence techniques, convolutional neural networks (CNN) have demonstrated remarkable capabilities in feature extraction and generalization. CNNs excel at processing images and other data types with translation invariance while reducing computational complexity. Over the past few years, numerous researchers have successfully applied CNN networks to mechanical fault diagnosis tasks. For instance, Xu et al. [
10] transformed bearing vibration signals into image representations using the continuous wavelet transform. They then developed a deep learning model based on CNN for accurate fault diagnosis of rolling bearings. Wen et al. [
11] proposed a novel approach based on LeNet-5 architecture within the CNN framework and achieved high classification accuracy when tested on a motor bearing dataset, self-priming centrifugal pump dataset, and axial piston hydraulic pump dataset. Ye et al. [
12] constructed a new deep neural network for feature learning from vibration signals and introduced a kernel selection method to fuse multi-branch features for transmission fault diagnosis. To address the limitations of traditional CNN models under unstable and complex working environments, Xu et al. [
13] proposed an improved multi-scale convolutional neural network model integrated with a feature attention mechanism. Subsequently, Zhang et al. [
14] combined one-dimensional convolutional neural networks (1DCNN) to propose a research methodology for gearbox-bearing fault diagnosis based on deep learning. The results demonstrate that this proposed method is effective for diagnosing wind turbine gearbox bearing faults. To solve the problem of insufficient global and local attention mechanisms, Jiang et al. [
15] proposed an adaptive sparse attention network for bearing fault diagnosis. Aiming at the multi-source information fusion conflict problem of industrial motor bearings, Wang et al. [
16] proposed a multi-local decision-making model. Fu et al. [
17] proposed a bearing fault diagnosis method based on wavelet denoising and machine learning.
Although the aforementioned methods have yielded favorable outcomes in bearing fault diagnosis, they solely rely on vibration signals for diagnostic purposes. Vibration signals are classified as contact measurements. This may present challenges if the bearing seat material is non-ferromagnetic and cannot be magnetically attached to the unit using a buckle. Moreover, excessive unit vibration may lead to sensor detachment, resulting in unnecessary complications during signal acquisition. Consequently, non-contact measurement methods are gradually being employed in bearing fault diagnosis, with increasing emphasis placed on experts and scholars within the field of fault diagnosis utilizing acoustic radiation signals as a non-contact measurement method [
18,
19,
20].
For acoustic fault diagnosis, Bai et al. [
21] successfully achieved weak fault detection of rolling bearings by extracting comprehensive status information from acoustic signals, thereby providing a novel approach for bearing condition monitoring. Glowacz et al. [
22] proposed a frequency component shortening method to classify the feature components of acoustic power tool fault diagnosis. He et al. [
23] utilized microphone-collected acoustic signals and employed small beamforming enhancement technology for rolling bearing fault diagnosis, ultimately diagnosing train bearing faults. However, due to significant background noise interference in the acoustic radiation signal, effectively filtering the collected signal becomes crucial. In the case of complex mechanical equipment operation, the collected signal contains substantial interference information and exhibits strong non-stationarity. Directly inputting the original collected signal into a neural network would reduce classification accuracy; hence, it is imperative to filter and denoise the acquired sound signal.
Mathematical morphology has been extensively applied in mechanical vibration signal processing, serving as an effective nonlinear and time-varying method for extracting fault characteristic information by directly operating on time domain signals. The mathematical morphology theory has been extensively investigated by scholars. Yan et al. [
24] employed grey correlation analysis (GCA) to determine the optimal scale of multi-scale mathematical morphology’s structural element, successfully achieving fault feature extraction for rolling bearings. Li et al. [
25] proposed a novel research approach for planetary gearbox fault diagnosis that combines adaptive multi-scale morphological filtering with improved hierarchical arrangement entropy. Numerical and experimental results demonstrate the capability of this method to identify various types of faults in planetary gearboxes. Deng et al. [
26] introduced a sparse envelope spectrum evaluation index factor called IESS to select the optimal scale for the AVG-Hat operator’s structural element, aiming at identifying different bearing faults effectively. Yi et al. [
27] presented a fault diagnosis research methodology based on multi-scale morphology to accurately distinguish between various types of bearing faults. Yu et al. [
28] put forward an average combined differential morphological filtering operator named ACDIF and a new index evaluation factor TEK to determine the optimal scale for selecting structural elements, effectively suppressing noise, and extracting shock pulses from vibration signals according to experimental results.
In summary, most scholars have concentrated on developing mathematical morphological operators and selecting appropriate structural elements for scaling purposes. Currently, there is a dearth of literature regarding the implementation of mathematical morphological filters in deep learning networks as well as fault diagnosis of acoustic signals. Therefore, this paper aims to address the challenge of constructing an end-to-end learning network that can effectively extract features from pulse signals.
The above research serves as the foundation for proposing a novel mathematical morphological network aimed at extracting shock features from acoustic array signals. The key contributions of this study are outlined as follows:
(1) The mathematical morphology layer is constructed using the multi-scale enhanced Top Hat morphology operator (MEAVGH), which generates new morphological branching channels by processing input signals with various structural elements.
(2) By incorporating channel attention and spatial attention mechanisms, we assign weights to the generated morphological branch channels to further enhance the screening of crucial feature information.
(3) We integrate the constructed mathematical morphological layer into a deep learning network for fault feature extraction in acoustic radiation signals emitted by rolling bearings.
The validity of the proposed model is only verified under laboratory conditions; thus, the diagnostic capability of the algorithm must be further verified under actual working conditions with complex background noise. The remaining sections of this paper are organized as follows: the second section provides a theoretical introduction, the third section presents experimental verification, and the concluding section offers an analysis of the findings.
4. Discussion and Conclusions
The acoustic sensor offers the advantages of non-contact measurement and easy installation. However, the acoustic array captures abundant fault characteristic information of rolling bearings and a significant amount of background noise. To address these issues, we propose embedding the multi-scale mathematical morphological operator into the convolutional neural network to create a novel mathematical morphological neural network named MMNet. Consequently, we have obtained the following conclusions:
(1) The proposed method effectively mitigates noise interference in acoustic signals and successfully extracts fault characteristic information from rolling bearings. The algorithm demonstrates rapid convergence speed, achieving a fault classification accuracy of 98.56%. Experimental results indicate that the proposed method maintains high sensitivity and stability even under strong background noise and limited training samples.
(2) Compared to ResNet, DenseNet, and LeNet-5, it is evident that the proposed method demonstrates superior t-SNE clustering efficacy with distinct separation among different fault types. Additionally, this method achieves higher accuracy rates than the other three methods. Regarding model training efficiency, the proposed method only takes 22.97 s for a 100-step iteration time, outperforming the other three methods. These comparative results further validate the exceptional accuracy of the proposed method in fault diagnosis.
The noise addition experiment demonstrates the effective noise removal capability of the proposed method, as the EAVGH operator can simultaneously extract positive and negative pulses in acoustic radiation signals. Furthermore, different structural element scales of EAVGH exhibit varying feature extraction performance, further validating the exceptional filtering ability of MMNet. Consequently, it is anticipated that the proposed method will also yield favorable results under real working conditions. Future work will further investigate the migration algorithm and lifetime prediction method based on mathematical morphological networks. Additionally, it will explore research on rolling bearing fault diagnosis in the presence of multi-source data. Moreover, we can consider addressing the fault diagnosis problem of multi-source field coupling and researching transfer learning based on mathematical morphological networks.