1. Introduction
Rotating machinery is one of the most widely used equipment in the industrial field [
1]. As an important part of rotating machinery equipment, rolling bearings play a vital role in ensuring the normal operation of equipment. However, due to the harsh operating environment of the equipment and the highly variable workload, rolling bearing faces inevitable risks of wear and failure [
2]. The prediction of equipment’s remaining useful life is one of the key technologies in fault prediction and health management (PHM) [
3]. If the rolling bearing degrades to the required threshold, the machine will fail. How to accurately determine the RUL of rolling bearing based on monitoring data is crucial for developing a reasonable maintenance plan and reducing downtime and cost losses [
4]. For RUL prediction of rolling bearing under strong background noise, due to the complex degradation characteristics of vibration signals and the difficulty in extracting key features, it is difficult to obtain accurate prediction results based on non-stationary vibration signals. Therefore, it is necessary to explore RUL prediction methods based on multi-domain features, which have important practical significance in equipment maintenance management.
Currently, the remaining useful life (RUL) prediction methods for rolling bearing equipment can be mainly divided into two types: traditional methods based on physical models and data-driven methods [
5]. The remaining useful life prediction method based on physical models [
6] relies on degradation mechanisms, expert rules, and empirical knowledge, resulting in limited applicability of the model. In recent years, with the advancement of sensor technology and the development of deep learning [
7], data-driven remaining useful life prediction models have received widespread attention [
8]. This type of model learns degradation features and trends from data for prediction, reducing the need for prior knowledge and complex physical models. It can adapt to changes in different systems and environments, and has strong adaptability and scalability. Data-driven methods can be further divided into shallow machine learning-based methods and deep learning-based methods. Methods based on shallow machine learning include statistical regression analysis [
9], support vector machines [
10,
11], neural networks [
12,
13,
14], and so on. However, the hierarchical structure of shallow machine learning-based methods is relatively simple, which limits the model’s ability to extract deep-level structures and abstract features from the data. Life prediction methods based on deep learning typically perform better in feature extraction on large-scale data and can automatically learn feature representations that are suitable for tasks. The model-building process of this method generally requires three major steps: signal denoising, feature extraction and health indicator construction, and prediction model.
Signal noise reduction is an important prerequisite for predicting the remaining useful life prediction of rolling bearings. Yao et al. [
15] proposed a denoising network model based on convolutional denoising autoencoder. The noise component was removed from the original data by stacking convolutional autoencoders, and the RUL of rolling bearings was predicted by the bidirectional long short-term memory network model. Li et al. [
16] use a wavelet packet algorithm to denoise the direct current component of the gear pump pressure signal and then extract state evaluation indexes to predict the remaining useful life of the gear pump. Ren et al. [
17] proposed a joint denoising algorithm based on adaptive white noise complete set empirical mode decomposition and improved adaptive wavelet threshold to address the issue of wavelet threshold denoising algorithms not being able to adaptively select decomposition levels and wavelet bases. The processed intrinsic mode functions (IMF) components were reconstructed to better extract signal features from noisy signals. Zhao et al. [
18] proposed an improved stacked denoising autoencoder method, which extracts features from noisy signals through the encoder and reconstructs the signal using the decoder to achieve effective signal denoising. At present, the above method has the advantages of automatic feature extraction and improved prediction accuracy in signal noise reduction processing, but there are also challenges, such as high algorithm complexity and great demand for parameter adjustment, and it is difficult to determine the method parameters adaptively, resulting in increased sensitivity of the model to noise, and the effect of the remaining useful life prediction model needs to be further improved.
Feature extraction and health index construction are the key steps of remaining useful life prediction of rolling bearing. Zhou et al. [
19] proposed a depth feature extraction method based on multi-dimensional self-attention temporal convolutional networks and designed a pattern-weighted feature fusion method to obtain degradation indicators. She et al. [
20] proposed a health index construction method based on the canonical resolution autoencoder model and predicted the remaining useful life of rolling bearings through the RUL prediction model based on a particle filter. Zhao et al. [
21] proposed a data-driven feature extraction method, namely the fitting curve derivative method of maximum power spectrum density. This method extracts the performance degradation features of rolling bearings throughout the life cycle from historical data, thereby establishing a RUL prediction model. Peng et al. [
22] proposed a multi-sensor health indicator (HI) construction method based on reinforcement learning, which can realize automatic learning and find the best sensor combination rules, thereby improving the RUL prediction performance of the model. Li et al. [
23] proposed a method for constructing composite health indicators by weighted fusion of multi-source sensors to characterize the evolution trend of equipment degradation and achieve remaining useful life prediction. Zhang et al. [
24] used the self-organizing mapping method to extract features based on similar sample sets and proposed a health indicator construction method based on the minimum feature circle. The existing methods have achieved certain results in feature extraction and health indicator construction, with high efficiency and accuracy, but there are still some shortcomings, such as the single-domain feature is difficult to fully express the nonlinear degradation law of equipment in feature extraction, and the interaction between features is not fully considered in feature selection. Traditional feature dimensionality reduction methods based on linear models [
25,
26] cannot adequately capture complex dynamic characteristics in nonlinear and non-stationary vibration signals, which may lead to information loss and other problems during feature dimensionality reduction.
The construction of the remaining useful life prediction model has an important impact on the prediction effect. Cao et al. [
27] proposed a remaining useful life prediction method combining a self-attention mechanism with a long short-term memory neural network to solve the problem that the correlation between components was not fully considered in the RUL prediction of mechanical equipment. Zhang et al. [
28] proposed a remaining useful life prediction model based on a transformer, which can simultaneously extract features of different sensors and time steps in parallel and finally verify the model performance using turbofan engine data sets. Lin et al. [
29] proposed an attention-based gated recurrent unit neural network model to effectively use feature information to predict the remaining useful life of equipment. Liu et al. [
30] proposed an enhanced encoder-decoder framework, which inputs the time series feature data into the encoder-decoder network model based on LSTM and calculates the RUL value at the end of the acquired signal combined with the linear regression algorithm of the output layer. Cao et al. [
31] combined kernel principal component analysis and long short-term memory network method to predict the remaining useful life of rotating machinery in view of the difficulty in extracting degraded information caused by redundant data from multiple sensors. The above RUL prediction model has been applied in the field of intelligent fault diagnosis and remains useful for life prediction to a certain extent. However, traditional remaining life prediction models, such as the convolutional neural network model (CNN), recurrent neural network model (RNN) and, long short-term memory network model (LSTM), Transformer model are difficult to capture long-term temporal dependence effectively and have insufficient feature extraction ability for signal key information. The accuracy of model prediction still needs to be further improved.
In order to overcome the limitations of the above-mentioned method for predicting the remaining useful life of rolling bearings, the main contributions of this paper are as follows: (1) Dung Beetle algorithm optimized VMD combined with correlation coefficient method is proposed to reduce the noise of the original signal. It realizes automatic optimization of VMD initial parameters, reduces manual intervention, and captures degradation information in noisy signals more accurately. (2) A feature dimension reduction method based on a multi-domain mixed feature and isometric feature mapping (ISOMAP) algorithm is proposed. To capture the characteristics of vibration signals in different fields, obtain comprehensive information on signals, and combine the ISOMAP algorithm to better solve the problem of nonlinear vibration signal feature dimensionality reduction. (3) A remaining useful life prediction model of TCNMABG is proposed. Enhance the feature extraction ability of the model in the process of rotary machinery equipment degradation and improve the prediction accuracy of the remaining useful life prediction model.
The structure of this article is as follows.
Section 2 introduces the general framework of the remaining useful life prediction method for TCNMABG rolling bearing.
Section 3 introduces the implementation process of the proposed model in detail based on the XJTU-SY dataset, and the results of the comparison experiment and ablation experiment of the model are analyzed and discussed.
Section 4, the FEMTO-ST bearing dataset, is used to verify the performance of the model further. Finally, the whole research content is summarized, and the prospect is put forward.
4. Validation Analysis of TCNMABG Based on FEMTO-ST Dataset
In order to further verify the generalization performance of TCNMABG, the bearing dataset released by the French FEMTO-ST Institute is used for experimental verification. The FEMTO-ST dataset [
39] collects the full life cycle data of the test bearings through the PRONOSTIA experimental platform, which is capable of performing accelerated bearing degradation tests under different working conditions.
The platform is mainly composed of asynchronous motors, drive shafts, couplings, test bearings, pneumatic jack loading systems, and digital regulators, which are shown in
Figure 14. The adjustable working condition parameters are the radial force applied to the test bearings and the rotational speed. The vibration signals were collected by two Dytran 3035 B micro-accelerometers at 90 degrees to each other with a sampling frequency of 25.6 kHz. The specific parameters of the test bearing are shown in
Table 7.
In this paper, the bearings under the load of 4000 N and speed of 1800 rpm working conditions are selected to test the general performance of TCNMABG. Bearing1_1, Bearing1_2, and Bearing1_3 are set as training sets, and Bearing1_4 is set as a test set. According to the proposed framework of TCNMABG, the extraction of multi-domain mixed features can be obtained by the comprehensive index, and the extracted features of Bearing1_1 are shown in
Figure 15.
The FPT of the early degradation point is determined by KFCM, and the results of the FPT of the four bearings in working condition one are shown in
Table 8.
Based on the determined FPT, the segmented linear degradation labels are used to evaluate the RUL of bearings, which is shown in
Figure 16. To better analyze the error indexes of TCNMABG, RNN, GRU, LSTM, and BiLSTM are used to analyze the RMSE, MSE, MAE, and R
2 based on FEMTO-ST dataset, and the results are listed in
Table 9.
According to the results of Bearing1_4 in
Table 9, compared with RNN, GRU, LSTM, and BiLSTM, the mean square error of TCNMABG is reduced by 71.02%, 68.11%, 66.57%, and 57.52%, respectively, with an average reduction of 65.96%. The root mean square error of TCNMABG is reduced by 46.17%, 43.53%, 42.18%, and 34.83%, respectively, with an average reduction of 41.68%. The mean absolute error of TCNMABG is reduced by 37.33%, 39.71%, 30.70%, and 34.82%, respectively, with an average reduction of 35.64%. In addition, according to the
R2 results, the
R2 of TCNMABG is increased by 17.01% on average compared with the other four methods, and the RUL prediction curve fits the real remaining useful life label better, which improves the accuracy of RUL prediction results.