RTCA-Net: A New Framework for Monitoring the Wear Condition of Aero Bearing with a Residual Temporal Network under Special Working Conditions and Its Interpretability

Abstract

The inter-shaft bearing is the core component of a high-pressure rotor support system of a high-thrust aero engine. One of the most challenging tasks for a PHM is monitoring its working condition. However, considering that in the bearing rotor system of a high-thrust aero engine bearings are prone to wear failure due to unbalanced or misaligned faults of the rotor system, especially in harsh environments, such as those at high operating loads and high rotation speeds, bearing wear can easily evolve into serious faults. Compared with aero engine fault diagnosis and RUL prediction, relatively little research has been conducted on bearing condition monitoring. In addition, considering how to evaluate future performance states with limited time series data is a key problem. At the same time, the current deep neural network model has the technical challenge of poor interpretability. In order to fill the above gaps, we developed a new framework of a residual space–time feature fusion focusing module named RTCA-Net, which focuses on solving the key problem. It is difficult to accurately monitor the wear state of aero engine inter-shaft bearings under special working conditions in practical engineering. Specifically, firstly, a residual space–time structure module was innovatively designed to capture the characteristic information of the metal dust signal effectively. Secondly, a feature-focusing module was designed. By adjusting the change in the weight coefficient during training, the RTCA-Net framework can select the more useful information for monitoring the wear condition of inter-shaft bearings. Finally, the experimental dataset of metal debris was verified and compared with seven other methods, such as the RTC-Net. The results showed that the proposed RTCA-Net framework has good generalization, superiority, and credibility.

1. Introduction

Aero engines are praised as the “flower of industry” and are the core components that provide power, while the bearing rotor system is praised as the “heart” of the engine [1]. Condition monitoring is the key to their good function and a basic task of aero engine condition prediction. Accurately predicting the service condition of bearings can not only eliminate a potential safety hazard but also improve the economy during the use of an aero engine [2]. Affected by engine high speeds, high temperatures, heavy loads, and other harsh working conditions, bearings under extreme working conditions for a long time can experience extreme fatigue and internal extreme wear failure, which will directly cause engine failure, aircraft loss of power, etc., endangering people’s lives and property [3]. Therefore, it is of great significance to monitor the wear condition of aero engine bearings and provide warnings about their failure to support the stable operation of the engine.

The condition monitoring and wear prediction technologies of mechanical equipment can be mainly divided into physical model-driven methods [4,5], statistical model-driven methods [6,7], and machine learning-driven methods [8,9]. Among them, the methods based on physical models are limited by the complex and changeable operating conditions of modern industrial equipment systems, making it difficult to establish accurate models of complex dynamic systems [10]. The methods based on statistical models rely on a large amount of historical data and are difficult to apply to different systems and failure modes. The nonlinear expression ability of the methods driven by machine learning is weak, and their prediction effect depends largely on the quality of the extracted features [11]. With the continuous development of artificial intelligence and deep learning, data-driven bearing condition monitoring has become the mainstream direction of research [12,13].

A deep learning neural network provides an efficient and feasible solution for bearing condition monitoring and remaining service life prediction with excellent nonlinear expression ability. For example, Y. Zhao et al. [14] proposed such a system to enhance the recognition performance of HAR by a 1DCNN recognition algorithm that utilizes a single triaxial accelerometer. Shuzhi Gao et al. [15] proposed a rolling bearing fault diagnosis model based on adaptive modified complementary ensemble empirical mode decomposition and a one-dimensional convolutional neural network. Zhang, X et al. [16] proposed a methodology for predicting the remaining usability of rolling bearings. Qin, S et al. [17] proposed a new type of long short-term memory neural network with macroscopic–microscopic attention. Y. Qin et al. [18] proposed a new kind of gated recurrent unit neural network with dual attention gates, namely, a gated dual attention unit. Although the above models based on LSTM architecture and their model variants have achieved good prediction accuracy, these models are prone to overfitting due to their many parameters and long training time. Peng, Huachao et al. [19] proposed a novel multiscale temporal convolutional transformer to simultaneously extract long-term degradation features and local contextual associations directly from raw monitoring data. Cao, Yudong, et al. [20] proposed a new deep learning framework, a temporal convolutional network with a residual self-attention mechanism, which can learn both time frequency and temporal information from signals. However, a TCN network uses a fully connected neural network to extract the output features, which will lead to parameter redundancy and an increase in computation, thus increasing the complexity and training difficulty of the model.

Vaswani et al. [21] proposed the famous sequence model called Transformer, which raised the attention mechanism to a new level. Transformer, as an improved attention-based model, greatly exploited the potential of attention in processing serial data. For example, Liu Jie et al. proposed [22] a feature fusion-based method for bearing RUL prediction. Wei Yupeng et al. [23] proposed a Siamese LSTM network, which was first introduced to classify degradation stages before predicting the RUL of bearings. Chang Yuanhong et al. [24] proposed an efficient end-to-end Temporal Flow Transformer for RUL prognostics of rolling bearings.

Bearing wear state monitoring is an effective means to achieve a working state assessment of a machine. Vibration, sound, and temperature are mainly used to monitor the working conditions of rolling bearings [25]. The change in the key analysis index of a vibration signal indicates a change in the working state of mechanical equipment, but the vibration information is often interfered with by the noise of the mechanical equipment, so it cannot be used to effectively evaluate the bearing wear state in real time [26]. In addition, because bearing temperature changes are not noticeable when bearing wear faults occur, bearing wear faults cannot be monitored and judged in many cases [27]. Other methods, such as acoustic or acoustic emission monitoring, can also reflect bearing wear and working conditions, but there are specific limitations to engineering feasibility. In recent years, the field of aero engines began to use many chip sensors for online monitoring of bearing wear, which has the unique advantage of occurring in real time and being fast, comprehensive, and so on. However, due to weak signal fault characteristics and intense background noise of aero engine bearing wear fault, the current popular bearing wear monitoring methods have certain limitations, which are mainly manifested in the following aspects. ① In the high-thrust aero engine bearing rotor system, the bearing installation skew causes the system to appear unbalanced or misaligned failure, resulting in bearing wear failure quickly, especially in harsh environments, such as high load and high speed; bearing wear is apt to evolve into a serious fault and then affect the rotor support system and the whole machine safety and reliability. ② In engineering, the earlier the bearing wear state is found, the possibility of rotor support system failure and equipment shutdown will be significantly reduced. Compared with aero engine fault diagnosis and RUL prediction, there are relatively few studies on condition monitoring. ③ Considering that bearing performance changes are often accompanied by specific nonlinear and non-stationarity characteristics, the secondary redundant feature information in the data will interfere with the feature extraction of the TCN network. It cannot show the ability to make the actual final prediction. In addition, the current deep neural network state monitoring model has the inherent “black box” characteristic, and the mapping relationship between input and output is difficult to accurately describe by the existing model, and there are technical challenges of poor interpretability. Therefore, to solve the above problems, the major novelty points of this study are concluded as follows.

(1) In this paper, a new framework of the residual spatiotemporal feature fusion feature focusing module, named RTCA-Net, is developed in a new way, which focuses on solving the critical problem that it is difficult to accurately monitor: the wear state of aero engine intermediate bearings under special working conditions in practical engineering. This research significantly broadens the application of deep learning models to aircraft-bearing condition monitoring tasks.

(2) Considering the strong time variability of metal scrap particle data of the bearing wear state in a high-thrust aero engine bearing rotor system, a feature extraction module of the residual spatiotemporal structure was innovatively designed and introduced into the proposed RTCA-Net framework, thus improving the framework’s ability to mine the characteristics of the intermediate bearing wear state.

(3) Considering that the wear state data of aero engine intermediate bearings are highly nonlinear, unstable, and susceptible to interference from redundant information, a feature-focusing module is designed in this paper. By adjusting the weight coefficient changes in the training process, the RTCA-Net framework can focus on the more helpful information for monitoring the wear state of inter-shaft bearings from a wealth of information. Thus, the negative influence of redundant information on network learning can be reduced.

(4) Comparative analysis was conducted based on the measured dataset of the same metal debris particles, and the results showed that the proposed RTCA-Net framework achieved good results regarding the RMSE, MAE, and score. Among them, compared with the RTC-Net model, the proposed RTCA-Net framework has improved by 53% and 66% in two indicators, the RMSE MAE. At the same time, compared with the RTC-Net model, the proposed RTCA-Net framework has improved by 59%, 39%, 48%, and 67%, respectively, in four indicators, the e_MAE, e_RMSE, e_NMAE, and e_MAPE. Compared with the TCA-Net model, the proposed RTCA-Net framework has improved by 46%, 41%, 59%, and 52%, respectively, regarding the e_MAE, e_RMSE, e_NMAE, and e_MAPE. The proposed RTCA-Net framework has good generalization, superiority, and credibility.

2. Basic Theory

2.1. Space–Time Module

The temporal convolutional network (TCN) [28] is a network structure that can effectively process time series data. Using a residual layer to enhance and expand causal convolution, the TCN has a better ability to adaptively extract features from original vibration signals [29].

The TCN mainly consists of three modules: (1) dilated causal convolution (DCC), (2) a residual module, and (3) a 1D fully convolutional network. To accept long-distance historical information, the TCN takes a one-dimensional sequence input x∈Rn and a filter.

$$f:\{0,1,\dots ,k-1\}\to R$$

(1)

The following dilated convolution is performed on the element s.

$$F(s)=(x\times df)(s)=\sum k-1i=0f(i)·xs-di$$

(2)

where $\times d$ is the dilatative convolution operator and $d$ is the dilated factor. The comprehensive process of one-dimensional full convolution, causal convolution, and dilated convolution represented by dilated causal convolution is shown in Figure 1. The input sequence is

$$X=\{x1,x2,\dots ,xt-1,xt\}$$

(3)

The output sequence after the three-layer one-dimensional dilated causal convolution operation with a convolution kernel size of 3 is

$$Y=\{y1,y2,\dots ,yt-1,yt\}$$

(4)

The dilated coefficient d∈N* in convolution calculation is generally 2.

The receptive field v is related to the size of the convolution kernel, the number of layers computed by the convolution, and the dilated coefficient, and the formula is

$$v=1+\sum l-1i=0\left(k-1\right)·bi$$

(5)

where $k$ is the size of the convolution kernel; $l$ is the number of convolutional layers in the network; and $b$ is the base of the dilated coefficient, which is usually set to $b=2$. In the TCN, let the one-dimensional input sequence be $X\in R^n$ and the convolution kernel be $f:\{0,1,\dots ,k-1\}\to R$; then, the calculated result of the dilated causal full convolution at the sequence s position is

$$F\left(s\right)=\sum k-1i=0f\left(i\right)·xs-d·i$$

(6)

In the formula, $xs-d·i$ is the $s-d·i$ element in the previous layer, and other parameters have the same meanings as before. The residual block structure is used to replace the simple connection between layers in order to improve the generalization ability of the model, and its function expression is

$$o=Activation\left(x+F\left(x\right)\right)$$

(7)

2.2. Focusing Module

The self-attention mechanism is the embodiment of human visual attention. Compared with recurrent neural networks and their deformation, the self-attention mechanism has a shorter path length and less time complexity when it performs arbitrary combination operations of input and output sequences [30]. The self-attention mechanism can not only quickly screen out key information and reduce attention to other irrelevant information but also reduce dependence on external information and make it easier to capture the internal correlation of input data [31]. The introduction of a self-attention mechanism in the neural network model not only solves the problem of information overload but also improves the accuracy and robustness of the network. Therefore, once proposed, it has shined brightly in computer vision.

Figure 2 shows that the query matrix Q, key matrix K, and value matrix V are the core components of the self-attention mechanism and are used to calculate the importance of each element in the input sequence in its preceding and succeeding sequences. The query matrix Q, key matrix K, and value matrix V are all obtained by a linear transformation of the input vector X. Among them, the function of the query matrix Q is to represent the importance of a certain element in the sequence to all other time steps. The function of the key matrix K is to represent the characteristics of each element in the sequence. When calculating attention, the dot product of the query matrix Q and the key matrix K are used to determine their correlation and thus determine the importance of this element to the query element. The value matrix V contains the actual information content of each element. The final attention output is the weighted sum of the weight coefficients and the value matrix V.

Self-attention is calculated in two steps.

Step 1: Calculate the weight of attention between any vector in the input sequence;

Step 2: Calculate the weighted average of the input sequence based on the attention weight.

The self-attention mechanism is shown in Figure 2, $a^i(i=1,2,3,\dots ,t)$ indicates the input sequence; $v^i(i=1,2,3,\dots ,t)$ represents the value vector generated from the input sequence; ${\alpha }_{ti}(i=1,2,3,\dots ,t)$ represents the result after the input sequence is computed with the respective vectors Q and K and passed through the Softmax function; and $b^i(i=1,2,3,\dots ,t)$ represents the result of the attention mechanism operation between the i th position information in the input sequence and all the position information.

The specific operation of self-attention is as follows:

$$Q=X{W}^q$$

(8)

$$K=X{W}^k$$

(9)

$$V=X{W}^{\nu }$$

(10)

$$Attention(Q,K,V)=Soft \max \left({\displaystyle \frac{Q{K}^T}{\sqrt{\dim }}}\right)V$$

(11)

where Q, K, and V are query matrix, key matrix, and value matrix, respectively, which are obtained by multiplying input X with the corresponding weight matrices $W^q$, $W^k$, and $W^v$, respectively; and dim represents the dimensions of Q, K, and V.

3. Models

3.1. The Proposed Framework Process

In order to achieve high precision monitoring and health management of bearing and rotor system wear, a new bearing condition monitoring framework based on a spatiotemporal model and self-attention mechanism is proposed in this paper. The framework comprises five parts: bearing wear monitoring data acquisition, data preprocessing and dataset construction, model structure design, model offline training, and bearing wear state monitoring. The specific flowchart of the proposed framework is shown in Figure 3. The detailed steps are as follows.

(1) Bearing data acquisition: In the aero engine bearing rotor system, under actual special working conditions, the metal chip sensor is used to collect the metal chip data of the bearing wear state, and a large number of normal and abnormal state data are collected as much as possible to build a complete dataset.

(2) Data preprocessing and dataset construction: First, the min–max normalization method is used to preprocess the data of the bearing wear state. Second, the bearing data are divided by a fixed length to build a dataset for monitoring the wear state of the aero engine bearing rotor system. Finally, the dataset is divided into a training set and a test set. The training set is used to train the proposed RTCA-Net framework, and the test set is used to test the prediction accuracy of the proposed RTCA-Net framework.

(3) RTCA-Net framework design: To fully use the advantages of the TCN network and self-attention mechanism for processing time series and extracting data characterization features, a self-attention mechanism module based on the TCN network is developed to extract bearing wear state features.

(4) Model offline training: Based on the data of the wear state of the aero engine bearing rotor system measured, the model is input into the proposed RTCA-Net framework for training. The RTCA-Net framework is trained using the gradient descent method. Forward propagation calculates losses, and backpropagation is used to update model parameters. The trained RTCA-Net framework weights and biases are saved when the maximum training period is reached.

(5) Health state assessment: First, the test set data of wear state is used as the input of the trained RTCA-Net framework to calculate the classification probability and obtain the condition monitoring results. Then, the extracted characterization features are comprehensively evaluated and input into the RTCA-Net framework to obtain the predicted value that can reflect the bearing health state and indicate the degree of performance degradation in the bearing wear state.

3.2. RTCA-Net Framework Structure

In order to deeply mine the characteristics of wear state data of the aero engine bearing rotor system, this paper designs a new framework of spatiotemporal feature extraction with residual structure integrated with an attention mechanism (RTCA-Net), which mainly consists of two parts: a spatiotemporal feature extraction module and a feature focusing module. The structure of the proposed RTCA-Net framework is shown in Figure 4.

(1) Feature extraction module: Considering that aero engine bearings work in harsh environments, such as high loads and high speeds, especially in high-thrust aero engine bearing rotor systems with complex and variable loads, the degradation characteristics of bearing wear faults are weak and difficult to excavate. Therefore, a spatiotemporal feature extraction module is designed, which consists of five parts: a wide kernel convolution layer, a pooling layer, a residual block, a flattening layer, and a fully connected layer. Among them, the function of the convolution layer is to extract a local feature of the input data. Each convolution kernel in the convolution layer is a feature extractor with multiple convolution cores inside it. Each element of the convolution kernel contains a weight coefficient and deviation. Specific calculations are as follows:

$$X_{i,j}^{l+1}=f({\displaystyle \sum _{j=1}^L{\displaystyle \sum _{i=1}^m(X_{i,j}^l*w_{i,j}^l)}}+b_j^L)$$

(12)

where the input data represent the $X_{i,j}^l$ eigenvalue of the $i$-th dimension of the $l$-th layer of the network and the $X_{i,j}^{l+1}$ eigenvalue of the $i$-th dimension of the $j$-th layer of the network; $w_{i,j}^l$ and $b_j^L$, respectively, represent the weight and bias of the $j$-th convolution kernel in the L-th convolution layer; * represents the discrete convolution operator; and $f(·)$ is the activation function. The primary function of the pooling layer is to reduce the parameters of the neural network. The mathematical expression for maximum pooling is as follows:

$$p_{MP}^{l(i,j)}=\underset{(j-1)W+1\le t\le jW}{\max }\left\{a^{l(i.t)}\right\}{b}_i$$

(13)

where $W$ indicates the width of the pooling area; $p^{l(i,j)}$ represents the activation value of the t neuron of the i frame in layer l; and $a^{l(i.t)}$ indicates the result of pooling.

The actual metal chip data of the bearing wear state is taken as the input. A time convolutional network was introduced to model the monitoring data of airborne intermediate bearings, and a wide kernel convolutional layer was used to extract local features. Then, the structure of the residual block with a small convolution kernel is constructed. The residual connection can realize cross-layer information transfer between the various levels of the network. Then, the output is expressed as a linear superposition of a nonlinear transformation of the input to eliminate the leakage of future information from the convolution operation and strictly implement the constraints on the time direction of the data sequence. Further, extract the deep discernable feature information. Finally, the module can read the data faster, utilizing parallel solid computing capability. It can capture the long-term dependencies in the time series more accurately, thus improving the prediction accuracy of the bearing rotor system of the aero engine.

(2) Feature focusing module: The module consists of four parts: a permute layer, a dense layer, a multiply layer, and a flatten layer. The core idea of this module is to automatically learn the contribution of different degradation features of intermediate bearing wear status to state monitoring during network training. Furthermore, further screening of time series data information is conducted to selectively learn the intermediate features during the training process of the RTCA-Net framework. At the same time, this module employs a weight allocation approach, assigning corresponding weights to each input information based on their significance, enabling the RTCA-Net framework to emphasize further those features that significantly contribute to the output. This module can quickly filter out more valuable critical information and reduce dependence on external information. The RTCA-Net framework not only extracts richer and deeper bearing degradation feature information, reducing the difficulty of subsequent model training, but also solves the problem of model information overload, improving the anti-overfitting ability of the RTCA-Net framework. Ultimately, it can better model time series data, capture internal correlations of input data, and further improve model accuracy and robustness. In summary, the dilated factor in the space–time feature module is set to [1,2,4,8,16,32], the dropout rate in the RTCA-Net framework is 0.3, and the filters are the number of filters in the network, whose value is 56. The maximum number of iterations is 1150 to prevent the model from overfitting. All models in this article were trained and tested on the same computer with the Core i9-10900K CPU and the GeForce RTX3080Ti graphics card. The software version number used by all models is python3.8. The critical parameter settings of the proposed RTCA-Net framework are shown in

Table 1. Structure parameters of the proposed RTCA-Net framework.

Order	Optimization Parameter	Value1
1	Learning rate	0.0001
2	Activation function	ReLU
3	Train epochs	1150
4	Batch size	64
5	Dropout	0.3
6	Optimizer	Adam
7	Weight decay	0.01
8	Loss function	MAE

.

4. Experiment

4.1. Bearing Wear Failure Test

In the actual industrial environment, the change in working conditions is complex and challenging to predict, especially in the bearing. In the rotor system of the high-thrust aero engine, the bearing wear of the intermediate bearing can quickly evolve into a severe fault in a harsh environment, such as high loads and high speeds, which affects the safety and reliability of the rotor support system and the whole machine. However, in the actual working environment, due to various conditions, the time series data of bearing condition monitoring will have insufficient information, especially since the intermediary bearing is a vital component of the aero engine rotor system. It has been in harsh environments, such as high temperatures, high speeds, and significant load changes, for a long time. The time series data of intermediate bearing monitoring will have low availability and value density. Specifically, on the one hand, because the intermediary bearing is in the fault state for less time, there are more samples in the healthy state in the monitoring data, and the time from showing damage characteristics to failure is short, resulting in sample imbalance. On the other hand, due to some unique spatial structures, sensor installation difficulties, test costs, and other objective factors, obtaining the timing signal acquisition of intermediary bearings is complicated, and thus, the time series data of aero engine bearing health monitoring will be limited.

To monitor the wear failure of cylindrical roller bearing with pivot intermediate support in a high-pressure rotor support system with a high-thrust aero engine during installation deflection, a simulation test bench for an aero engine cylindrical roller bearing and a high-pressure rotor system were developed for verification and analysis. This test system is mainly composed of five parts: a drive system, a control system, a rotor support system, a data acquisition system, and a lubrication system. The physical diagram of the cylindrical roller bearing high-pressure rotor system simulation test bench is shown in Figure 5.

(1) Rotor support system: The bearing seat is fixed on the horizontal platform through a bolt connection, a sliding guide rail is installed on both sides of the bearing seat, and the guide rail is fixed on the platform to restrict the axial freedom of the bearing. The central part of the rotor in the rolling bearing high-pressure rotor system is constrained by two bearing seats at both ends of the high-pressure rotor shaft, and then the rolling bearing high-pressure rotor system is supported.

(2) Drive system: The frequency conversion control system is used to drive the motor to provide power for the rolling bearing high-pressure rotor system, and diaphragm coupling is connected with the high-pressure rotor to make the high-pressure rotor and the rolling bearing rotate together and then provide power for the rolling bearing high-pressure rotor system.

(3) Dust signal acquisition: The dust sensor is installed in the lubrication system of the aero engine bearing and the high-pressure rotor system, and the metal dust sensor is used to obtain the dust data in the oil sample for the bearing wear failure state, and then the correlation between the bearing wear state and the dust particle data is analyzed, which can effectively monitor the lubricating oil dust data in real time. The metal chip sensor of the ZXMS model was used in the test, and its physical picture is shown in Figure 6. The ZXMS series electromagnetic oil wear particle online monitoring sensor can measure the number, size, and properties of metal wear particles in the oil (ferromagnetic and non-ferromagnetic); ferromagnetic particle values are intermediate. By connecting it in series to the oil circuit in the lubrication system, the particle data from the metal chips in the hydraulic and lubrication system can be displayed online in real time. The cylindrical roller bearing mounted on the right side of the rolling bearing high-pressure rotor system is tested. The basic structural parameters of cylindrical roller bearings under test are shown in

Table 2. Basic parameters of the tested bearings.

Structure Name	Parameter	Structure Name	Parameter
Bearing type	N209	Roller diameter	10 mm
Pitch diameter	42.5 mm	Roller length	11 mm
Bearing outside diameter	85 mm	Number of rollers	13
Bearing bore diameter	45 mm	Contact Angle	0°
Inner and outer ring width	19 mm

.

(4) Lubrication system: The lubrication system in the rolling bearing high-pressure rotor system simulation test bench mainly includes five parts: a supply oil pump, a return oil pump, an oil tank, a flow-regulating valve, and an oil pipe. In order to facilitate better measurement of the number of metal particles of rolling bearings in lubricating oil, it can be clearly found in Figure 6 that forced lubrication is adopted in the test process so that the lubrication system in the simulation test bench of the rolling bearing high-pressure rotor system has the characteristics of forced oil intake and oil return.

(5) The setting of test conditions: To better simulate the wear failure of cylindrical roller bearings and obtain the wear failure data of cylindrical roller bearings in a short time, the high-pressure rotor system is set to two different states of unbalanced and unbalanced on the simulation test bench of the aero engine rolling bearing high-pressure rotor system. Among them, the bearing far away from the drive end is the test bearing, and the unbalance of 40 g·mm is added to the unbalance disc of the high-pressure rotor. The left bearing seat is raised by 0.75 mm, and the bearing installation tilt angle is 35°. This chapter selects the cylindrical roller bearing, with the right end as the test bearing. The test conditions are shown in

Table 3. Test conditions of rolling bearing and a high-pressure rotor.

Working Condition	Rotational Speed	Unbalance	Height Adjustment	Offset Angle
1	3900 rpm	0 g·mm	0 mm	0°
2	3900 rpm	40 g·mm	0.75 mm	35°
3	3900 rpm	40 g·mm	0.75 mm	35°
4	4500 rpm	35 g·mm	0.5 mm	35°
5	4500 rpm	35 g·mm	0.5 mm	35°

below.

First, let the rotor run continuously at a speed of 2000 r/min for no less than 15 min to avoid the impact of low speed and large current on the motor and ensure that the oil and gas lubrication supply is smooth and stable during operation. The chip sensor can work and collect data. Then, the bearing wear failure and evolution monitoring test was carried out, and the bearing was run for a long time at 3900 r/min. After stopping, wait until the speed is 0, adjust the speed to 4500 r/min, and then run for a long time; wait until the speed is 0 after stopping. The specific test process is as follows:

(a)

Turn on the power supply and turn on the oil mist lubrication system;

(b)

Start the motor at 2000 r/min and run stably for 15 min;

(c)

Increase the rotational speed to the test speed of 3900 r/min, keep the operation for 5 min, and check whether the data of the vibration, temperature, and metal particle dust data collection system are normal.

(d)

Set the sampling frequency of the vibration acquisition system to 5120 Hz for real-time data acquisition, analysis, and monitoring;

(e)

Increase the speed to 4500 r/min and continue to collect;

(f)

Turn off the motor, stop the system, and export the test data.

4.2. Bearing Wear Fault State

According to the test plan, when all the test tests of the aero engine bearing high-pressure rotor system are completed, the aero engine rolling bearing high-pressure rotor system is disassembled, and the surface wear state of the components of the cylindrical roller bearing is shown in Figure 7.

It can be found in Figure 7 that, in part of the roller of cylindrical roller bearing, there is an apparent bright band on the surface of the roller of cylindrical roller bearing, and there is also a clear, bright band on the surface of the outer ring of cylindrical roller bearing; the wear marks on the surface of the rolling body are relatively straightforward. At the same time, the inner surface of the outer ring of cylindrical roller bearing has undergone tremendous changes. Small spalling pits were found, indicating that the cylindrical roller bearing had suffered apparent wear failure during the test.

4.3. Bearing Metal Chip Data

The data collection method of metal dust particles is once every 10 s, and the collection time is 5 s. The collected data were constructed into a dataset of 3000 samples and divided into a training set and a test set according to a ratio of 8:2. That is, the first 2400 samples and the remaining 600 samples were, respectively, composed of the training set and the test set of the prediction model. The degradation dataset of the bearing wear state under two special working conditions of an aero engine bearing high-pressure rotor system is shown in Figure 8.

As can be seen in Figure 8, after high-speed operation of the aero engine bearing high-pressure rotor system, the accumulation of dust particles will increase linearly with the increase in bearing service time and the continuous change in the bearing wear state. In the two special working conditions of the bearing rotor system, the number of metal particles in the lubricating oil changes obviously, and the number of metal particles increase sharply, which verifies that the status monitoring of lubricating oil particles is in real time. At the same time, it can be found that although the degradation trend of the bearing high-pressure rotor is manifested as a fluctuating state of up and down oscillation, it shows a monotonically increasing trend on the whole and has a certain monotonicity, which can be used as a fundamental feature of bearing health monitoring for trend prediction.

4.4. Metal Scrap Data Training

The metal scrap particle data of the bearing wear state in the aero engine bearing high-pressure rotor system were input into (a) the proposed RTCA-Net framework and (b) the Residual Temporal Convolutional Network (RTC-Net), (c) the Temporal Convolutional Network-Self-Attention Mechanism (TCA-Net), (d) the temporal convolutional network (TCN-Net), (e) the One-dimensional Convolutional Neural Network–Gated Recurrent Unit (1DCNN-GRU-Net), (f) the Bi-directional Gated Recurrent Unit (Bi-GRU-Net), (g) Support Vector Regression (SVR-Net), and (h) Gaussian Process Regression (GPR-Net) and were trained.

The training cycles of the eight models were all set to 1150 cycles, and the loss value transformation curves of the eight model training processes are shown in Figure 9.

As seen in Figure 9, the loss value of the proposed RTCA-Net framework tends to converge after the first few iterations and is flat and 0 after 30 iterations. After 1150 training rounds, the training loss value stabilized at about 0.5. It shows that the proposed RTCA-Net framework has a good training effect, and the training time of the model is short. After several iterations, the time sequence characteristic information of the metal scrap particle data can be learned. At the same time, it can be seen that the loss values of the seven models, including RTC-Net, all show a trend of convergence during the training process, but the loss values of the seven models fluctuate considerably. After 1000 training rounds, the loss values of the seven models are not in a state of convergence, and the loss value of TCA-Net is the smallest, which can reach about two values. This shows that the seven models cannot learn the characteristic information of the metal scrap particle data well.

The datasets of metal scrap particles based on the same bearing wear state were input into the eight models, such as the proposed RTCA-Net framework for training. The RMSE value curves of the eight kinds of model training processes are shown in Figure 10.

As shown in Figure 10, with the increase in the iteration cycle, the RMSE value of the proposed RTCA-Net framework presents a rapid decline trend. After 50 cycles, the RMSE value gradually tends to 0; after 1150 cycles, the RMSE value stabilizes below one value. Compared with RTC-Net and the other seven models, the proposed RTCA-Net framework has the fastest convergence rate on the verification set. The main reason is that the RTCA-Net framework can extract both the time and frequency domain information faster, so it can converge faster. When the seven models, such as RTC-Net, were trained on the dataset of bearing wear, the RMSE value showed a downward trend as a whole. However, after 1150 cycles, the RMSE value of RTC-Net was relatively low and stable at about 2.5. In summary, compared with the seven models, such as the RTC-Net, the proposed RTCA-Net framework has a faster convergence speed, good model stability, and strong generalization ability. This shows that the proposed RTCA-Net frame used in this paper is more consistent with the actual results and can better solve the problem of bearing wear state evaluation.

5. Analysis of the Prediction Results for the Unbalanced Operating Conditions of Rotors

5.1. Bearing Health Monitoring and Evaluation Index

The RMSE (root mean square error) and the MAE (mean absolute error) are commonly used evaluation metrics [32] in the field of bearing health monitoring and remaining life prediction. The RMSE represents the square root of the ratio of the sum of the squares of the error between the expected value and the actual value to the duration n. The MAE represents the average of the absolute differences between the predicted and actual values. This paper uses the RMSE and MAE to make it easy to compare with other studies. Their calculation methods are shown in Equations (14) and (15).

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{t=1}^n{(e{r}_t)}^2}}$$

(14)

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{t=1}^n\left|e{r}_t\right|}$$

(15)

Among them, $e{r}_t=RU{L}_{act}-RU{L}_{pret}$ is the error between the actual RUL and the predicted RUL at time t, and n is the duration.

In order to evaluate the predictive model objectively and comprehensively, this study employs a scoring function, score, which considers underestimation, overestimation, and the impact of operational phases on the entire life cycle. Its calculation method is shown in Equation (16).

$$Score={\omega }_1{\displaystyle \frac{1}{m}}{\displaystyle \sum _{t=1}^m{A}_t}+{\omega }_2{\displaystyle \frac{1}{n-m}}{\displaystyle \sum _{m+1}^n{A}_t}$$

(16)

Among them, m is the duration of the early stage of the fault, ${\omega }_1$ and ${\omega }_2$ are the weight percentages of the early and late stages. In this article, $m=n/2$, ${\omega }_1=0.35,{\omega }_2=0.65$. The calculation method for the accuracy rating function is shown in Formula (17).

$$A_t\{\begin{array}{l}\exp (-\ln (0.6)\times (e{r}_t/10)), e{r}_t\le 0\\ \exp (\ln (0.6)\times (e{r}_t/40)), e{r}_t>0\end{array}$$

(17)

Among them, $e{r}_t$ is the prediction error, which represents the difference between the predicted remaining life and the actual remaining life, explicitly referring to the difference between the expected value and the actual value at the t-th time point. $A_t$ is an accuracy scoring function that represents the accuracy of predictions at a particular time point t. The calculation result is determined based on the value of $e{r}_t$, with the aim of quantitatively evaluating the prediction error and measuring the predictive performance of the model at that time point. The values of 10 and 40 are used for different scalings to $e{r}_t$. Specifically, when $e{r}_t\le 0$, the error was divided by 10, which meant that the impact of the negative error on the rating would be amplified, making the model more conservative in underestimating lifespan. When $e{r}_t\ge 0$, the error was divided by 40, which meant that the positive error had a relatively small impact on the rating, and the model had a higher tolerance for overestimating lifespan.

5.2. Stability of State Monitoring

Due to the impact of special operational conditions in actual engineering, verifying the generalization ability and prediction stability of the proposed RTCA-Net framework under these conditions is necessary. When setting the high-pressure rotor system to an imbalanced state, datasets of aerospace engine bearing wear states were collected and input into (a) the proposed RTCA-Net framework, (b) RTC-Net, (c) TCA-Net, (d) TCN-Net, (e) 1DCNN-GRU-Net, (f) Bi-GRU-Net, (g) SVR-Net, and (h) GPR-Net for comparative analysis. The comparison of the bearing wear state prediction for these eight different models is shown in Figure 11.

In Figure 11a, it can be shown that the proposed RTCA-Net framework predicts bearing wear states in aerospace engine bearings, and high-pressure rotor systems very closely to the valid values. The predicted values at specific time points are nearly identical or have minimal differences, showing only slight deviations that minimally impact the overall results. Moreover, it is noted that the RTCA-Net framework achieves relatively low residual error values for each bearing sample, averaging around 0.5, which indicates that the predictive models established by the RTCA-Net framework can accurately predict the degradation trends of bearings in the bearing rotor system.

In Figure 11b–f, it can be observed that the prediction effectiveness of the Figure 11b RTC-Net, Figure 11c TCA-Net, Figure 11d TCN-Net, Figure 11e 1DCNN-GRU-Net, and Figure 11f Bi-GRU-Net, which are based on five deep neural network models, is relatively poor. Their predicted curves for bearing wear states in aerospace engine bearings high-pressure rotor systems moderately align with the actual values, with varying degrees of fluctuation in the prediction curves. Figure 11g,h show a significant deviation between the predicted curve of the bearing wear state in the bearing rotor system and the actual value of the wear state using two traditional prediction models, Figure 11g SVR-Net and Figure 11h GPR-Net. At the same time, it can be seen that the prediction results for each bearing sample by models, such as Figure 11b RTC-Net, and the other seven models show relatively high residual error values. Particularly, the average residual value of traditional forecasting models, such as Figure 11g SVR-Net and Figure 11h GPR-Net, is around 8.

To further validate the superior predictive performance of the proposed RTCA-Net framework for bearing wear states in the bearing rotor system and to ensure the stability of the experimental results against randomness, the framework was run ten times under identical initial conditions. This paper calculates the MAE, RMSE, and score metrics for each run and compares the average accuracy of these metrics from the ten tests.

Table 4. The prediction results of the bearing wear state by the eight models under unbalanced working conditions.

Dataset	Methods	RMSE	MAE	Score
The unbalanced bearing rotor system	The RTCA-Net framework	1.687	1.2864	0.9162
	RTC-Net	3.561	3.829	0.6015
	TCA-Net	3.892	3.271	0.7136
	TCN-Net	5.833	4.281	0.6281
	1DCNN-GRU-Net	6.821	5.761	0.5219
	Bi-GRU-Net	5.732	6.512	0.5567
	SVR-Net	9.057	8.879	0.3831
	GPR-Net	8.926	9.381	0.3925

shows the prediction results of bearing wear states for the eight models under an imbalance in the high-pressure rotor system.

Table 4 indicates that the proposed RTCA-Net framework achieves the highest fitting accuracy in predicting bearing wear states, resulting in excellent performance across three metrics: the RMSE, MAE, and score. Specifically, compared to the RTC-Net model, the proposed RTCA-Net framework improves by 53% in the RMSE and 66% in the MAE. Compared to the TCA-Net model, the RTCA-Net framework shows improvements of 57% in the RMSE and 61% in the MAE. Comparative analysis based on the more critical score metric shows that the proposed RTCA-Net framework outperforms RTC-Net and the other seven models. Specifically, compared to RTC-Net, the RTCA-Net framework improves the score by 34%, 22%, 31%, 43%, 39%, 58%, and 57%, respectively, across these models. Through this comparison, the RTCA-Net framework demonstrates superior advantages in predicting bearing wear states under the specific condition of actual rotor imbalance. It is primarily because the residual structure of the TCN model aligns better with continuous time series signals, facilitating the extraction of internal wear features within the bearings. Additionally, this structure helps the RTCA-Net framework avoid gradient vanishing issues, achieving more stable prediction results.

5.3. The Interpretability of State Monitoring

To uncover the “black box” nature of the proposed RTCA-Net framework, it becomes possible to explain better the reasons behind the decisions made by the model in predicting bearing wear states under actual non-ideal conditions in rotor systems. Based on the same dataset, feasibility interpretations of the features provided by the eight models were conducted using standard distribution P-P plots. The lognormal P-P plots for predicting bearing wear states by the eight models are shown in Figure 12.

The typical distribution P-P plot of the features extracted from the bearing wear state data by the proposed RTCA-Net framework is shown in Figure 12a under the special conditions of actual misalignment. It is observed that the exact distribution of the feature samples of bearing wear state data approximates the theoretical distribution. Although there are some fluctuations in the residuals in the descending standard P-P plot, most absolute differences are slight, which indicates that the original data of the feature samples for the bearing wear state follow a normal distribution. Additionally, the PIT points of the features extracted by the proposed RTCA-Net framework are all within the 5% significance range of Kolmogorov, with a relatively high correlation coefficient and fitting accuracy, which demonstrates the high reliability of the prediction results for bearing wear states by the proposed RTCA-Net framework. In contrast, Figure 12b–h show that for RTC-Net and the other seven models, most of the feature distributions extracted from the bearing wear state data fall outside Kolmogorov’s 5% significance range, with lower correlation coefficients and fitting accuracy. So, this indicates that the prediction results for bearing wear states by RTC-Net and the other seven models are less reliable.

6. Analysis of the Prediction Results for the Misalignment Operating Conditions of Rotors

6.1. Evaluating Indicator

This paper calculates the following metrics: the absolute mean error (e_MAE), root mean square error (e_RMSE), normalized mean absolute error (e_NMAE), and mean absolute percentage error (e_MAPE) to compare the prediction errors of the proposed RTCA-Net framework and the other seven models for bearing wear states. The calculation is shown in Equation (18).

$$\{\begin{array}{l}{e}_{MAE=}{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|{\mathrm{y}}_i-{\widehat{y}}_l\right|}\\ e_{RMSE=}\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{({\mathrm{y}}_i-{\widehat{y}}_l)}^2}}\\ e_{NMAE=}{\displaystyle \frac{1}{n{\sigma }^2}}{\displaystyle \sum _{i=1}^n{({\mathrm{y}}_i-{\widehat{y}}_l)}^2}\\ e_{MAPE=}{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left|\frac{{\mathrm{y}}_i-{\widehat{y}}_l}{y_i}\right|}^2}\end{array}$$

(18)

6.2. The Effectiveness of Wear Condition Monitoring

Since special operating conditions in actual engineering projects affect model accuracy, this study needs to verify the generalization ability and stability of the prediction results of the proposed RTCA-Net framework under actual special conditions. When the high-pressure rotor system is set to a misaligned state, the collected dataset of bearing wear states in the aircraft engine bearing high-pressure rotor system is input into the following eight models for comparative analysis: (a) the proposed RTCA-Net framework, (b) RTC-Net, (c) TCA-Net, (d) TCN-Net, (e) 1DCNN-GRU-Net, (f) Bi-GRU-Net, (g) SVR-Net, and (h) GPR-Net. The comparison of bearing wear state predictions by the eight different models is shown in Figure 13.

As is shown in Figure 13a, the proposed RTCA-Net framework’s prediction results for the bearing wear state in the high-pressure rotor system of an aircraft engine fit closely with the actual values, almost overlapping with the actual bearing degradation trend curve. This indicates that the training set for the bearing wear state in the bearing rotor system has been effectively learned and trained within the proposed RTCA-Net framework. At the same time, the RTCA-Net framework proposed in this article has relatively low residual error values for each bearing sample, with an average of around 0.45. Figure 13b,c show that although the RTC-Net and TCA-Net models can roughly predict the bearing wear state, they exhibit significant fluctuations in the later stages of the prediction process. There are still issues with large local prediction deviations, preventing them from effectively tracking the degradation trend and facing sudden changes in the bearing degradation state.

In summary, the prediction results of RTC-Net and the other seven models exhibit relatively large prediction errors during specific periods. The main reason is that the dataset for bearing wear states is relatively large and complex, leading to insufficient utilization of feature information by RTC-Net and the other seven models, which results in significant discrepancies between the predicted and actual values at certain times. In contrast, the proposed RTCA-Net framework performs better in predicting the bearing wear degradation trend.

This research calculates four evaluation metrics: the absolute mean error (e_MAE), root mean square error (e_RMSE), normalized mean absolute error (e_NMAE), and mean absolute percentage error (e_MAPE) and compares the average accuracy of 10 tests to verify further the stability of the proposed RTCA-Net framework in predicting bearing wear states. The prediction results of bearing wear states under the misaligned condition of the high-pressure rotor system for the eight models are shown in

Table 5. The error of prediction of the bearing wear state by the eight kinds of models.

Dataset	Methods	eMAE	eRMSE	eNMAE	eMAPE
The misalignment of the bearing rotor system	The RTCA-Net framework	0.0219	0.00361	0.000216	0.0056
	RTC-Net	0.0538	0.00592	0.000415	0.0168
	TCA-Net	0.0403	0.00607	0.000536	0.0119
	TCN-Net	0.0612	0.00756	0.000482	0.0307
	1DCNN-GRU-Net	0.0817	0.00693	0.000621	0.0362
	Bi-GRU-Net	0.0753	0.00727	0.000597	0.0331
	SVR-Net	0.1014	0.00891	0.000831	0.0507
	GPR-Net	0.0978	0.00962	0.000853	0.0532

.

Table 5 shows that the proposed RTCA-Net framework significantly reduces the prediction errors for bearing wear states compared to RTC-Net and the other seven models, resulting in more stable predictions. Specifically, compared to the RTC-Net model, the RTCA-Net framework improves by 59% in the e_MAE, 39% in the e_RMSE, 48% in the e_NMAE, and 67% in the e_MAPE. Compared to the TCA-Net model, the RTCA-Net framework shows improvements of 46% in the e_MAE, 41% in the e_RMSE, 59% in the e_NMAE, and 52% in the e_MAPE across these four metrics. Therefore, the test results validate the improvement of the proposed RTCA-Net framework in prediction accuracy and generalization ability. The main reason for this result is that the RTCA-Net framework possesses superior learning capability and nonlinear feature extraction. It can deeply explore features within the data of bearing wear states and accurately map them to reflect the health status of bearings, thereby enhancing prediction accuracy. To sum up, the proposed RTCA-Net framework has advantages in predicting bearing wear states under the specific operating conditions of actual rotor misalignment. The main reason is that the residual structure reduces the number of parameters that need to be trained and optimized in the entire framework, which prevents the occasional occurrence of gradient vanishing or exploding during actual training, thereby enhancing the feature learning capability of the RTCA-Net framework and resulting in more accurate prediction ability.

6.3. The Interpretability of Wear Condition Monitoring

In special working conditions where the actual rotor system is misaligned, to explain further the basis of the proposed RTCA-Net framework for making specific decisions in predicting bearing wear status, the paper uses a standard distribution P-P diagram to explain the stability of the features proposed by the eight models based on the same dataset. Figure 14 shows the logarithmic normal P-P diagram for predicting bearing wear status using the eight models.

As is shown in Figure 14a, the PIT point distribution of the proposed RTCA-Net framework for bearing wear state data mining is relatively close to the diagonal, tightly clustered around the diagonal, and within the range of [0, 1]. This distribution follows the trend of a uniform distribution layer, thus satisfying the basic assumptions of linear regression analysis. It indicates that the proposed RTCA-Net framework’s prediction results for bearing wear state remain highly reliable under the special conditions of actual rotor system misalignment. The PIT points of RTC-Net and the other seven models are mainly distributed outside the 5% significance range of Kolmogorov, with low correlation coefficients and lower fitting accuracy in Figure 14b–h, which indicate a significant difference between the actual distribution of samples of bearing wear states and the theoretical distribution. Furthermore, in the descending typical P-P plot, there are substantial fluctuations in the residuals, with most absolute differences more significant than 0.10. As a result, the raw data of bearing wear status samples cannot approximately follow a logarithmic normal distribution at a 90% confidence level. In conclusion, the comprehensive comparative analysis above indicates that the proposed RTCA-Net framework demonstrates superior feasibility, reliability, and interpretability in predicting bearing wear states under specific operating conditions where deviations in actual rotor systems occur.

To further verify the superiority of the proposed RTCA-Net framework in predicting the wear state of aero engine intermediate bearings, the dataset collected by working condition 5 in Figure 3 in Section 4.1 was selected for analysis. The measured metal chip data of the bearing wear state were input into five advanced models, such as the RTCA-Net framework and Figure 15B GRU-Net, for training. Then, the bearing wear state prediction results were obtained using the six models, such as the proposed RTCA-Net framework. The comparison of the bearing state prediction results of the six advanced models is shown in Figure 15.

It can be seen in Figure 15 that the predicted curve of the proposed RTCA-Net framework for the wear state of the aero engine intermediary bearing is the most consistent with the natural wear state curve, indicating that the RTCA-Net framework can better fit the real degradation value of the wear state of the intermediary bearing. It, in turn, can provide more accurate predictions. The interval between 600 and 800 is used as an example; it can be found that when the bearing degradation curve fluctuates, the predicted curve of the RTCA-Net framework is closer to the actual wear state curve. The main reason is that the feature attention module is introduced into the RTCA-Net framework, which can strengthen the attention of essential features in the bearing wear state so that the prediction accuracy is improved to a certain extent. However, in Figure 15B, the prediction curve of the bearing wear state of the five advanced models, such as GRU-Net, is highly volatile, and the prediction curve cannot be well consistent with the real wear state curve. At the same time, there is a big difference between the predicted results of the five models and the observed bearing absolute values, and the output curve fitting rate is higher. To more clearly analyze the predictive performance of the proposed five advanced models, such as the RTCA-Net framework and Figure 15B GRU-Net, on intermediary bearings, the results of the six models were selected in this paper for comparative tests, and the results are shown in Figure 16.

As shown in Figure 16, the proposed life prediction curve of the RTCA-Net framework is closer to the natural lifeline. At the same time, the average residual error of the RTCA-Net framework is relatively low, reaching about 0.2. In addition, it can be shown that the RTCA-Net framework has a relatively high prediction accuracy for the bearing wear state under the extreme working conditions of an unbalanced aero engine rotor. Compared with the other five advanced models, the proposed framework is superior to them. At the same time, when the five models, such as (B) GRU-Net, (C) MCA-DTCN-Net, (D) RCDAN-Net, (E) MHT-Net, and (F) AGATT-Net, are used to predict the bearing wear state, the average residual error is relatively high, reaching about five or above, which means that the curve coincidence degree is shallow, the robustness is poor, and the prediction accuracy is very low. The results show that the five advanced models have the worst prediction accuracy and robustness. To sum up, the prediction accuracy of the RTCA-Net framework proposed in this paper is the highest, and the prediction curve of bearing life is the closest to the real curve, which indicates that the RTCA-Net framework bearing condition evaluation has good accuracy.

To further explain the extraction effect of the proposed RTCA-Net framework on bearing wear state features, a Pearson correlation scatter plot was introduced into the RTCA-Net framework. The distribution of bearing wear state characteristics obtained by the six advanced models is shown in Figure 17.

It can be seen in Figure 17 that the proposed RTCA-Net framework is significantly superior to (B) GRU-Net and the five other advanced models in extracting the wear state data features of engine intermediary bearing. Among them, it can be found in Figure 17A that the clustering of data points in the metal scraps is relatively evenly distributed near the main diagonal, and the histogram of data point mapping presents a relatively symmetrical distribution. It is further explained that the RTCA-Net framework has thoroughly mined the data characteristics of the aero engine intermediary bearing, which makes the predicted characteristics consistent with the actual characteristics. Furthermore, the proposed RTCA-Net framework enhances the understanding of high accuracy and good bearing wear state prediction stability. At the same time, it can be found in Figure 17B–F that (B) GRU-Net and the other advanced five models cannot effectively mine the data characteristics of the bearing wear state, resulting in the relatively scattered distribution of predicted metal scrap features, and some data features are far from the main diagonal. At the same time, the histogram distribution is not uniform, indicating that (B) GRU-Net and the other advanced five models have large randomness in predicting the bearing wear state. It is worth noting that data points predicted by the (E) MHT-Net and AGATT-Net models for the bearing wear state deviate more significantly from the main diagonal, indicating that these models may not be able to capture all the key factors affecting the observed values, resulting in variability in the model’s underlying pattern in the captured data. It is further explained that the RTCA-Net framework performs excellently in predicting the wear state of aero engine intermediate bearing.

As seen in

Table 6. Different models evaluate data on the unbalanced dataset.

Methods	RMSE	MAE	Score	t/s
The RTCA-Net framework	0.1576	0.1175	0.8951	305.32
GRU-Net [31]	0.3675	0.3829	0.3925	382.51
MCA-DTCN-Net [28]	0.4403	0.2125	0.6723	418.35
RCDAN-Net [32]	0.3813	0.5176	0.5236	406.27
MHT-Net [33]	0.5361	0.3973	0.3817	469.58
AGATT-Net [34]	0.5024	0.6261	0.5725	517.63

, the proposed RTCA-Net framework has the best mean value for predicting the wear state of aero engine intermediate bearings, with a score of 0.8951, an MAE of 0.1175, and an RMSE of 0.1576. The RMSE and MAE were higher by 0.5026, 0.2228, 0.3715, 0.5134, and 0.3226. This indicates that the proposed RTCA-Net framework has the highest prediction accuracy and good prediction performance for the intermediate bearing wear state. Meanwhile, the proposed RTCA-Net framework can more comprehensively monitor the bearing rotor system degradation process of a high-thrust aero engine. It can extract the data features of the intermediate bearing wear state more effectively. At the same time, it can be seen in Table 6 that the training time of the proposed RTCA-Net framework on the bearing metal chip data is the shortest, and the calculation time is 305.32 s. It is relative to the other five kinds of advanced models and was reduced by 77.19, 113.03, 100.95, 164.26, and 212.31. The results show that the proposed RTCA-Net framework has advantages and strong robustness in predicting the wear state of intermediate bearings. More petite MAE and RMSE values were obtained on E and score, which significantly improved compared to the five advanced models. Taking the score index as an example, the proposed RTCA-Net framework is compared with the other five advanced models. The mean absolute error (MAE) and root mean square error (RMSE) were used to analyze the predicted data quantitatively, and scores were obtained according to these indicators. Among them, the RMSE and MAE of model a were 0.1576, 0.1175, and 0.8951. Model b has an RMSE of 0.3675, an MAE of 0.3829, and a score of 0.3925. The RMSE and MAE of model c were 0.4403, 0.2125, and 0.6723. Model d has an RMSE of 0.3813, an MAE of 0.5176, and a score of 0.5236. Model e has an RMSE of 0.5361, an MAE of 0.3973, and a score of 0.3817. Model a has an RMSE of 0.5024, an MAE of 0.6261, and a score of 0.5725.

7. Conclusions

The intermediate bearings in high-thrust aircraft engines are prone to wear and tear faults, and the current deep neural network models make it difficult to monitor the wear status of bearings accurately. This paper takes a unique approach and develops a new framework for a residual spatiotemporal feature fusion feature focusing module named RTCA-Net. It provides theoretical and technical support for fault monitoring and health management of aircraft engine rotors and bearings. The main conclusions are as follows.

(1) Considering that aviation intermediate bearings operate in harsh environments, such as high loads and high speeds, especially in special operating conditions where the rotor system is unbalanced or misaligned, the proposed RTCA-Net framework achieves accurate prediction of the wear status of intermediate bearings. This study significantly expands the application of deep learning models in aviation-bearing condition monitoring tasks.

(2) Considering the solid time-varying nature of metal debris particle data in the bearing rotor system of high-thrust aircraft engines, an innovative feature extraction module for a residual spatiotemporal structure is designed. The residual idea is introduced into the proposed RTCA-Net framework, which improved the framework’s ability to mine intermediate bearing wear state features and reduced computational resource consumption.

(3) Considering the strong nonlinearity, instability, and susceptibility to redundant information in the wear status data of intermediate bearings in aircraft engines, this paper designs a feature-focusing module that can enhance essential features in the debris particle data of intermediate bearings and suppress the influence of non-important features. The accuracy and generalization performance of the proposed RTCA-Net framework is further improved by weighing the spatiotemporal information in the intermediate bearing data.

(4) Based on comparative analysis of the same metal chip particle dataset measured, the proposed RTCA-Net framework exhibits superior performance compared to previous studies, with high superiority, generalization, and robustness. By introducing the interpretable RTCA-Net framework, the reliability and credibility of mining the wear state characteristics of intermediate bearings in aircraft engines have been achieved.