End-to-End Intelligent Fault Diagnosis of Transmission Bearings in Electric Vehicles Based on CNN

Abstract

Environmental noise and transmission components can cause significant interference in vibration signals, rendering the extraction of bearing fault features challenging in service scenarios. Traditional fault diagnosis methods rely heavily on professional domain knowledge, prior models, and signal preprocessing methods. The accuracy of fault diagnosis depends on the quality of the fault-sensitive features extracted by vibration signal preprocessing methods. An improved convolutional neural network (CNN) end-to-end intelligent fault diagnosis model based on raw vibration data (RVDCNN) is proposed. The time-domain vibration signal of the transmission bearing is converted into a continuous two-dimensional numerical matrix, and a two-dimensional CNN model is constructed through network structure optimization. The original time-domain vibration signal numerical matrix of the bearing is trained and tested to extract and learn abstract fault features of different fault types, and then the fault classification of the bearing is achieved. To verify the generalizability of the RVDCNN intelligent fault diagnosis model, it is applied to the recognition of rolling bearings in the two-speed mechanical automatic transmission of electric vehicles, achieving recognition accuracy of 99.11% for seven types of bearings.

1. Introduction

In recent years, prognostic and health management (PHM) has become an important field in the intelligent manufacturing industry [1]. As an additional external excitation source for electric vehicle transmission, the drive motor adds tangential electromagnetic force, axial electromagnetic force, and electromagnetic torque fluctuations and excitations during transmission. These excitations act on the bearings and gears through the rotor and have an undeniable impact on the working conditions and vibration characteristics of the bearings [2]. The working speed of the motor is significantly higher than that in traditional internal combustion engines. In addition, the rapid power response of the motor increases the impact excitation of the gear, and the recovery of the braking energy also causes frequent changes in the direction of the load borne by the gear. The multi-level factors brought by driving motors accelerate the fatigue damage and fault evolution of the gears and bearings, which creates higher requirements for the early fault identification and classification diagnosis of bearings.

The vibration characteristics of transmission bearings exhibit complex features, such as nonstationarity and nonlinearity, and their vibration signals are often disturbed by the vibration or noise of other components, making it difficult to accurately identify and extract fault features directly from the original vibration signals.

Guo et al. [3] proposed a modulation signal bispectrum analysis method based on non-Gaussian noise suppression, using autoregressive filters as preprocessing units to effectively process non-Gaussian noise while retaining the advantage of suppressing Gaussian noise, achieving efficient and accurate performance in extracting fault features. Ziani et al. [4] achieved the detection of bevel gears under variable load conditions by successfully integrating EMD, the Teager–Kaiser energy operator, and an impact detector. This method effectively extracts the fault features from complex vibration signals and has important reference value for the fault feature extraction of rolling bearings. In their research on the fault diagnosis of rolling bearings, Zhang et al. [5] adopted the ensemble empirical mode decomposition technique and selected the singular value entropy as the key criterion; this enabled the accurate identification and classification of different fault characteristics of rolling bearings through the in-depth analysis of vibration signals. Zhen et al. [6] introduced a fault detection technique for the analysis of nonstationary vibration signals. This method leverages weighted average ensemble empirical mode decomposition and modulation signal bispectrum analysis to effectively reduce Gaussian noise and decompose the intrinsic modulation components within the vibration signal. Consequently, it enables the detection of faults in both the inner and outer races of rolling bearings.

The feature extraction diagnostic method performed through signal processing heavily relies on the professional experience and knowledge of engineers or advanced manual signal processing methods. Due to the rapid advancements in machine learning within the vision and speech recognition domains, intelligent fault diagnosis techniques for PHM have gained widespread adoption in mechanical fault diagnosis. These methods are favored for their adaptive learning capabilities, automated feature extraction processes, and robust nonlinear regression abilities.

The existing fault diagnosis approaches based on traditional machine learning usually combine signal processing methods, and the diagnosis process is as follows: first, the fault features are extracted and enhanced; then, traditional machine learning algorithms are used to identify bearing faults.

In their research on the fault diagnosis of rolling bearings, Amar et al. [7] converted the vibration signals of rolling bearings into spectral images. In order to enhance the key features in the images, a two-dimensional average filter was applied to process the spectral images. Finally, an ANN was used to successfully classify the spectral images of bearings with different fault types. Lei et al. [8] proposed an improved distance evaluation technique and selected six sensitive features from the temporal and spectral characteristics of bearing signals as the input dataset for an adaptive neural fuzzy inference system, achieving bearing fault classification. Liu et al. [9] used the multi-scale entropy feature index of rolling bearings and implemented fault detection using BPNN. Muruganatham et al. [10] used singular values of the bearing condition as characteristic indicators and implemented the fault diagnosis of bearings using BPNN. Khazaee et al. [11] collected the vibration and sound signals of planetary gearboxes and then used wavelet analysis to extract features from the temporal to time–frequency domains. After signal processing, the data from each sensor were used as input to the ANN classifier for primary fault diagnosis. The output of the classification was used as input for the Dempster–Shafer rule, which was used for the fusion of classifiers, thus achieving high accuracy in the final classification. Li et al. [12] extracted 10 temporal features from the vibration signals of bearings and then conducted fault diagnosis research on the bearings using an ANN optimized with the firefly algorithm. In their study of the early fault diagnosis of rotors, Bin et al. [13] first used a wavelet packet transform (WPT) to process the original vibration signal; they then reconstructed the wavelet coefficients obtained through WPT processing using EMD to obtain the energy characteristics of each component; finally, they used BPNN to achieve the efficient and accurate diagnosis of early rotor faults.

With the significant achievements in bearing fault diagnosis research utilizing signal processing and traditional machine learning techniques, it has been possible, to some extent, to reduce the dependence on factors such as fault mechanisms and knowledge experience models and improve the accuracy of fault diagnosis. However, there are also certain limitations, which mainly include the following.

(1)

The precision of fault diagnosis largely depends on the choice of feature indicators and the design of the feature components. However, in the case of strong background noise and weak fault features, selecting sensitive feature indicators is a challenging research task [14].

(2)

Due to the presence of weak early fault signals, low signal-to-noise ratios, and the varying operational conditions of transmission bearings, there is a complex mapping relationship between the sensitive features that characterize the degrees of faults. However, the nonlinear feature learning ability of traditional machine learning is limited, making it difficult to fully explore the fault information contained in the vibration signals of transmission bearings [15].

Cheng et al. [16] proposed a data-driven intelligent fault diagnosis method for rotating machinery based on a new continuous wavelet transform local binary CNN, and they established an end-to-end diagnostic mechanism. Li et al. [17] proposed a feature fusion algorithm for bearing fault diagnosis based on an integrated deep CNN and the improved Dempster–Shafer theory. Their algorithm used the root mean square of the spectral features of two sensors as input data and achieved good results on the open-source CWRU bearing dataset. Miao et al. [18] converted the vibration signal into an angle domain. Then, the corner domain signal was converted into corresponding envelope and squared envelope spectral features and fused into a red–green–blue color image to enhance the sample features and expand the differences between various health states. Finally, a CNN was constructed to complete fault identification. Pang et al. [19] proposed an intelligent diagnosis method for planetary gear faults based on a deep CNN and vibration bispectrum. Raouf et al. [20] introduced a feature aggregation network into a two-dimensional CNN and used scale map images to detect faults in the servo motor bearings of industrial robots.

Transfer learning has shown great potential in dealing with data scarcity problems and has become a new research hotspot. Pan et al. [21] proposed a residual service life prediction method combining a multi-head attention network and adaptive meta-transfer learning, which achieved the accurate residual service life prediction of low-temperature bearings in rocket engines during the steady-state stage. Chen et al. [22] proposed an online unsupervised anomaly detection framework that did not rely on professional knowledge or labeled historical data. To address the issue of data scarcity, they proposed an adaptive self-transfer learning algorithm based on Gaussian processes, which modeled monitoring data using uncertainty information and achieved the fault diagnosis and monitoring of steam turbines. Fang et al. [23] proposed a method based on transfer learning and deep transfer clustering, which achieved the high-precision diagnosis of unknown faults. The application of transfer learning in various fields provides new ideas in solving the problem of rocket engine fault diagnosis. Li et al. [24] proposed an extreme learning machine based on transfer learning to align the distribution differences in data from turbofan engines, and they verified the effectiveness and feasibility of the method through fault diagnosis experiments on turbofan engines. Jamil et al. [25] proposed an instance-based weight deep transfer learning method that could update source and target machine training samples separately, thereby achieving the high-precision fault detection of wind turbine gearboxes.

However, in service scenarios, environmental noise, electromagnetic excitation, and other transmission components of the gearbox can cause significant interference in vibration signals, making it difficult to extract clear fault features. Traditional fault diagnosis methods rely heavily on professional domain knowledge, prior models, and signal preprocessing methods. The accuracy of fault diagnosis relies on the quality of fault-sensitive feature extraction by vibration signal preprocessing methods. Here, given sufficient sample data, a novel intelligent diagnosis approach is proposed, which leverages the original time-domain vibration signal for end-to-end fault diagnosis, using a convolutional neural network (CNN) as the underlying model framework. This study constructs a two-dimensional CNN network structure with strong feature extraction abilities and optimizes the hyperparameters to achieve the high-precision fault diagnosis and classification of transmission bearings.

This study proposes the RVDCNN intelligent fault diagnosis model based on raw vibration data. The time-domain vibration signals of transmission bearings are converted into continuous two-dimensional numerical matrices. A two-dimensional CNN model is constructed through network structure optimization to train and test the original time-domain vibration signal numerical matrices of bearings, extract and learn abstract fault features of different fault types, and then achieve the fault classification of bearings. To verify the generalization capacity of the RVDCNN intelligent fault diagnosis model, it is utilized for the diagnosis and identification of faults in rolling bearings within a two-speed mechanical automatic transmission system in an electric vehicle, achieving multi-type and high-precision diagnosis and recognition and overcoming the difficulties associated with advanced signal preprocessing technology and professional diagnostic experience.

2. Methodology

2.1. Data Reconstruction

Moving away from signal processing methods based on professional knowledge or expert experience, and using the original time-domain vibration signals of bearings as training data, the original time-domain signals are reorganized into a two-dimensional numerical matrix, and abstract numerical feature information is extracted and mined from the time-domain signals through a two-dimensional deep convolutional kernel. In order to reduce the number of training samples and improve the diagnostic efficiency, the size of the input matrix is defined by periodically sampled data points.

The calculation of the data collection volume within one cycle is as follows:

$$M=f_s\times {\displaystyle \frac{60}{N}}$$

(1)

where M is the number of signal data in one cycle. f_s is the sampling frequency of the vibration signals. N is the rotation speed of the rotating machinery.

The process of segmenting and reassembling the original vibration signal data is shown in Figure 1. Divide one-dimensional raw vibration data into several signal segments based on the size of the model input samples as shown in the red dot box. After segmentation, independent one-dimensional signal segments are obtained, as shown in the red line box. Assuming that the size of the input numerical matrix is n and the number of samples is y, n² data points are extracted by sliding in sequence from a signal of length y × n². The n² original time-domain vibration data are flattened from left to right and top to bottom into a matrix in sequence, and the one-dimensional original vibration signal is reset to obtain a y two-dimensional numerical matrix of size n.

2.2. Model Theory

The convolutional layer contains multiple convolutional kernels, which constitute a matrix, also known as a convolutional filter. In the convolutional layers, a convolution operation is performed on the local area of the input signal to obtain a corresponding two-dimensional feature map. Different features are extracted using different kernels for each convolutional layer.

The convolution is defined as follows:

$$Y_j^l=f\left(\sum _{i=1}^j{Y}_j^{l-1}\times W_{ij}^l\right)$$

(2)

where $Y_j^{l-1}$ is the (l − 1)th layer’s jth element. $W_{ij}^l$ is the convolutional kernel weight matrix. f(*) is the activation function, which is defined as the ReLu function.

$$f(x)=\left\{\begin{array}{c}0,x\le 0\\ x,x>0\end{array}\right.$$

(3)

After the operation of the convolutional layer, the number of feature maps increases rapidly. It is imperative to establish a pooling layer to reduce the dimensions of the feature maps and the parameters of the network after the convolutional layer. There are two methods commonly used in the pooling layer, namely average pooling and max pooling. In this study, average pooling is applied to process each feature map.

The pooling layer is calculated as follows:

$$Y_j^l=avgdown\left(Y_j^{l-1}\right)$$

(4)

There is a fully connected layer after the combination of two convolutional layers and two pooling layers. The fully connected layer is similar to the convolutional layer and applies different classification steps. The neuron nodes of the fully connected layer are connected to all of the neuron nodes of the feature maps from the former pooling layer. If the number of output labels is k, the output of softmax regression can be represented as follows:

$$output=\left[\begin{array}{l}p\left(1\right|x;W_1,b_1)\\ p\left(2\right|x;W_2,b_2)\\ \cdots \\ p\left(K\right|x;W_K,b_K)\end{array}\right]={\displaystyle \frac{1}{{\sum }_{j=1}^K\mathit{exp}(W_{j}x+b_j)}}\left[\begin{array}{l}\mathit{exp}(W_{1}x+b_1)\\ \mathit{exp}(W_{2}x+b_2)\\ \cdots \\ \mathit{exp}(W_{K}x+b_K)\end{array}\right]$$

(5)

where W_j is the weight matrix and b_j is the bias.

2.3. Intelligent Fault Diagnosis Method

A CNN is a type of deep feedforward neural network that has been widely used in fields such as visual image recognition, natural language processing, and fault diagnosis due to its unique network structure, unique computing principles, and powerful nonlinear feature extraction capabilities. It is currently one of the most widely used deep learning models. A CNN has the characteristics of local connections, weight sharing, pooling operations, and a multi-level structure. Different hierarchical structures can be used to mine numerical features from different dimensions. This study focuses on the LeNet-5 model, further simplifying the network structure by removing one convolutional layer and a fully connected layer. In addition to the characteristics of bearing vibration signals, appropriate convolutional kernel sizes and quantities are selected to construct a high-precision fault diagnosis model that is suitable for electric vehicle transmission bearings.

A two-dimensional CNN is a deep learning structure composed of convolutional layers, pooling layers, and fully connected layers. The convolutional kernel of the convolutional layer is a two-dimensional structure that has excellent feature extraction abilities due to its ability to capture the shift characteristics of the input data [26]. CNNs have great potential and abilities in complex nonlinear numerical feature extraction and high-precision recognition [27], providing new ideas for the end-to-end fault diagnosis of transmission bearings.

The intelligent fault diagnosis process is shown in Figure 2. Firstly, bearings with different fault types are embedded into the transmission, and acceleration vibration signal data are collected under the same operating conditions. Then, the time-domain vibration data are sequentially segmented and reassembled into a fixed-size two-dimensional numerical matrix. By constructing a CNN network structure and optimizing the network’s hyperparameters, a model with strong adaptive feature extraction capabilities is obtained. Finally, the original two-dimensional numerical matrix of vibration signals is used as the sample set to achieve the high-precision diagnosis and recognition of rolling bearings in electric vehicle transmission.

3. Analysis and Selection of CNN Model Parameters

Based on the advantages of CNNs in adaptive feature learning, a two-dimensional deep CNN intelligent diagnostic model is constructed using the framework of “convolutional layer–pooling layer–convolutional layer–pooling layer–fully connected layer”.

We optimize the CNN’s hyperparameters using fault bearing data from the open-source Case Western Reserve University (CWRU) Bearing Data Center. The CWRU fault bearing sampling frequency is f_s = 12 kHz. The minimum speed in the experiment is 1730 r/min and the maximum speed is 1797 r/min, so the number of data acquired in one rotation is M_bearing = 400~416. The input speed of the electric vehicle transmission is significantly increased, leading to a substantial decrease in the quantity of data points collected after one rotation of the gears and bearings and a decrease in the data volume required for a single training sample in the end-to-end intelligent diagnostic model. Each sample’s data size should include at least one vibration signal of the bearing rotation cycle to ensure that the sample contains the characteristics of the bearing cycle sampling point data. Therefore, the input numerical matrix size of the model is designated as 24 × 24, which means that each sample contains 576 data points.

In order to exploit the potential of deep learning, improve the diagnostic accuracy, and obtain better CNN models, the selection of the model’s structural parameters is crucial. Research in the literature has shown that the network layer structures and hyperparameters of CNN models have a complex impact on the diagnostic accuracy [28]. Shallow network layers can lead to insufficient feature information extracted by the convolutional layers and low classification accuracy. When the depth of the network layers is too great, the weight of the convolutional kernel increases, which not only increases the time cost but may also cause overfitting. If the convolutional kernel size is too small, it can lead to fragmented features after pooling and reduce the sensitivity of feature recognition. If the convolutional kernel size is too large, it will also increase the number of weights, the computational time, and the probability of overfitting. Therefore, in order to obtain a better deep CNN structure, it is necessary to define a reasonable range of hyperparameters.

Using the CWRU rolling bearing fault dataset as the training and test set, we explore the influence of the convolutional kernel number and size and the pooling function on the diagnostic results.

The datasets used for training and testing are presented in

Table 1. CWRU rolling bearing outer race failure dataset.

Fault Location	Fault Size (mm)	Working Condition (r/min, hp)	Number of Samples	Sample Size
outer race	0.18	1730, 12	625	24 × 24
outer race	0.18	1750, 8	625	24 × 24
outer race	0.18	1772, 4	625	24 × 24
outer race	0.18	1797, 0	625	24 × 24

. Considering the deep feature extraction abilities of the CNN model, the data type is selected as a weak fault diameter of 0.18 mm located on the outer race, and it is divided into four labels under different working conditions. The original time-domain signal of each label is taken for 9.6 s, with a total of 115,200 data points, forming 200 samples, with 576 data points per sample. The fault forms are the same, but the working conditions are different, and the feature recognition of the model is refined and sensitive to small differences.

3.1. Determining the Quantity of Convolutional Kernels

Adopting a structure consisting of a convolutional layer, pooling layer, another convolutional layer, another pooling layer, and a fully connected layer, a two-dimensional deep CNN model is constructed, where the activation function is ReLU, the pooling function is average pooling, the quantity of neurons in the fully connected layer is set to 4, the step size is set to 1, and the learning rate is set to 0.01, with weight decay of 0.005, momentum value of 0.9, and a dropout rate of 0.8. The batch processing volume is 10, and 50 iterations are performed. The first convolutional layer has a kernel size of 5 × 5, with numbers of 6, 8, and 10, respectively. The size and quantity of the second convolutional layer are both 5 × 5 × 24, with 80% of the sample size used as training data and 20% as testing data. After conducting five diagnoses, the average value is computed. The outcomes of these diagnoses are displayed in

Table 2. Effect of the number of convolutional kernels in convolutional layer 1.

Type	1	2	3
Convolutional Layer	5 × 5 × 6	5 × 5 × 8	5 × 5 × 10
Activation Function	ReLU
Pooling Layer	average pooling 2 × 2
Convolutional Layer	5 × 5 × 24
Activation Function	ReLU
Pooling Layer	average pooling 2 × 2
Fully Connected Layer	10
Result	87.00%	94.20%	94.20%

.

With six convolutional kernels, the diagnostic accuracy is 87.00%, which is lower than the 94.20% achieved with eight convolutional kernels. However, further increasing the number to 10 does not enhance the diagnostic results. Therefore, eight convolutional kernels in the first layer is the optimal choice.

After determining the optimal number of convolutional kernels for the first layer, five experiments are carried out to assess the effect of varying the number of convolutional kernels in the second layer on the diagnostic outcomes. In the second layer, the number of convolutional kernels is set to 10, 16, 20, 24, and 30, respectively, while all other parameters remain constant. The diagnostic accuracy results are summarized in

Table 3. Impact of varying the number of convolutional kernels in the second convolutional layer.

Type	1	2	3	4	5
Convolutional Layer	5 × 5 × 8
Activation Function	ReLU
Pooling Layer	average pooling 2 × 2
Convolutional Layer	5 × 5 × 10	5 × 5 × 16	5 × 5 × 20	5 × 5 × 24	5 × 5 × 30
Activation Function	ReLU
Pooling Layer	average pooling 2 × 2
Fully Connected Layer	10
Result	83.80%	88.40%	90.40%	94.20%	89.60%

, revealing a similar trend to that observed with the first layer’s convolutional kernels.

As the number of convolutional kernels increases, the fault recognition rate improves to a certain point. Specifically, the diagnostic accuracy is gradually enhanced as the number of convolutional kernels increases from 10 to 24, suggesting that an increased number of convolutional kernels aids in the better extraction of fault features. However, when the number reaches 30, the recognition accuracy declines to 89.60%. Consequently, for the second layer, a more suitable choice for the number of convolutional kernels is 24.

3.2. Selection of Convolutional Kernel Size

To investigate the influence of the convolutional kernel size on the model’s diagnostic results, experiments were conducted based on a configuration with eight convolutional kernels in the first layer and 24 in the second layer. The size of the first convolutional kernel was varied as follows: 5 × 5, 7 × 7, 9 × 9, 11 × 11, and 13 × 13. Corresponding to each of the first convolutional kernel sizes, the second convolutional kernel size was also varied.

When the size of the first convolutional kernel was 5 × 5, the tested sizes for the second convolutional kernel were 3 × 3, 5 × 5, 7 × 7, and 9 × 9. When the size of the first convolutional kernel was 7 × 7, the tested sizes for the second convolutional kernel were 2 × 2, 4 × 4, 6 × 6, and 8 × 8. When the size of the first convolutional kernel was 9 × 9, the tested sizes for the second convolutional kernel were 3 × 3, 5 × 5, and 7 × 7. When the size of the first convolutional kernel was 11 × 11, the tested sizes for the second convolutional kernel were 2 × 2, 4 × 4, and 6 × 6. When the size of the first convolutional kernel was 13 × 13, the tested sizes for the second convolutional kernel were 3 × 3 and 5 × 5.

A total of 16 deep convolutional neural network models were evaluated, and their fault diagnosis results are presented in

Table 4. The influence of different convolutional kernel sizes on the diagnostic results.

Type	1	2	3	4	5	6	7	8
Convolutional kernel	5 × 5				7 × 7
Pooling layer	average pooling 2 × 2
Convolutional kernel	3 × 3	5 × 5	7 × 7	9 × 9	2 × 2	4 × 4	6 × 6	8 × 8
Pooling layer	average pooling 2 × 2
Output size	4 × 4	3 × 3	2 × 2	1 × 1	4 × 4	3 × 3	2 × 2	1 × 1
Result	90.30%	94.20%	92.80%	92.40%	91.80%	95.40%	92.50%	95.60%
Type	9	10	11	12	13	14	15	16
Convolutional kernel	9 × 9			11 × 11			13 × 13
Pooling layer	average pooling 2 × 2
Convolutional kernel	3 × 3	5 × 5	7 × 7	2 × 2	4 × 4	6 × 6	3 × 3	5 × 5
Pooling layer	average pooling 2 × 2
Output size	3 × 3	2 × 2	1 × 1	3 × 3	2 × 2	1 × 1	2 × 2	1 × 1
Result	93.80%	95.80%	95.20%	93.80%	94.20%	96.40%	95.80%	95.40%

. When the second layer’s convolutional kernel size was 3 × 3, and when comparing models 1, 9, and 15, which had first-layer convolutional kernel sizes of 5 × 5, 9 × 9, and 13 × 13, respectively, the diagnostic results were 90.30%, 93.80%, and 95.80%. These results indicate a positive trend as the convolutional kernel size increases. Additionally, when comparing models 3, 11, 5, and 12, as well as models 7 and 14, it can be observed that when the second convolutional kernel’s size remains constant, an increase in the first convolutional kernel’s size leads to an improvement in the model’s diagnostic accuracy.

When the second convolutional kernel size is 5 × 5, and when comparing models 2, 10, and 16, it is observed that as the first convolutional kernel size increases from 5 × 5 to 9 × 9, the diagnostic results improve. However, when the first convolutional kernel size is increased to 13 × 13, the diagnostic accuracy decreases by 0.40%. Similarly, when the second convolutional kernel size is 4 × 4, upon comparing models 6 and 13, it is found that as the first convolutional kernel size increases from 7 × 7 to 11 × 11, the diagnostic results decrease by 1.20%.

When the size of the first convolutional kernel remains constant, and when comparing models 1 and 4, it is observed that as the size of the second convolutional kernel increases, the diagnostic result improves from 90.30% to 94.20%. However, further increases to 7 × 7 and 9 × 9 result in a decrease in the diagnostic accuracy. Similarly, when the first convolutional kernel size is 7 × 7, upon comparing models 5 and 8, it is found that as the second convolutional kernel size increases from 2 × 2 to 8 × 8, the diagnostic results show an initial improvement, followed by a decrease and then another improvement. On the other hand, comparing models 12, 13, and 14, when the first convolutional kernel size is 11 × 11, the accuracy increases with the size of the second convolutional kernel, reaching the maximum fault recognition accuracy of 96.40%. Lastly, when the first convolutional kernel size is 13 × 13, changes in the size of the second convolutional kernel do not significantly improve the diagnostic results.

The results of this comprehensive comparison of the models indicate that, while increasing the size of the convolutional kernel can expand the convolutional receptive field, which aids in feature learning and extraction, this relationship is not linear. In fact, blindly increasing the size of the convolutional kernel may result in a decrease in diagnostic accuracy, producing the opposite effect. Therefore, it is crucial to choose the network structure parameters carefully. Upon comparing the models, it is found that the recognition accuracy is optimal when the first convolutional kernel size is 11 × 11 and the second convolutional kernel size is 6 × 6.

3.3. RVDCNN Model Structure

The proposed two-dimensional deep convolutional neural network’s structure is shown in Figure 3. The network consists of two convolutional layers, two pooling layers, and one fully connected layer. The input layer is a 24 × 24 numerical matrix of the original vibration signals, and the first convolutional layer consists of eight large-sized 11 × 11 convolutional kernels. The pooling layer uses average pooling to maintain feature homogenization. The second convolutional layer consists of 24 small-sized 6 × 6 convolutional kernels. The first convolutional layer uses large-sized convolutional kernels, while the second convolutional layer has three times the number of kernels as the first layer. These configurations are beneficial in extracting features that reflect the different health conditions of rotating machinery. After the pooling layer, the number of neurons in the fully connected layer depends on the fault label of the diagnostic object. As an adaptive parameter, in this section, the number of neurons in the fully connected layer is 4~10, and the results of the fault types are classified.

The model adopts the cross-entropy loss function and mini-batch gradient descent optimization algorithm. The signal data used as input for the model are time-domain vibration acceleration data collected on the surface of the gearbox or gearbox housing. Each sample undergoes an initial layer of large-scale convolution and average pooling to generate eight 7 × 7 abstract numerical feature matrices. Then, after the second layer of deep convolution and average pooling, 24 abstract numerical features are generated. Finally, a one-dimensional feature matrix consisting of 4~10 values is generated through a fully connected layer.

4. Experimental Verification of Bearing Fault Diagnosis

4.1. Experimental Verification of CWRU Bearing Dataset

In this set of experiments, the ability to perform feature extraction from raw time-domain numerical matrices is tested. Ten datasets are applied to diagnose and analyze the fault bearings using the proposed model. A comprehensive description of the dataset is given in

Table 5. Description of dataset.

Fault Location	None	Inner Race			Ball			Outer Race
Fault diameter (mm)	0	0.18	0.36	0.53	0.18	0.36	0.53	0.18	0.36	0.53
Label	NO	IR7	IR14	IR21	B7	B14	B21	OR7	OR14	OR21
1797 r/min, 0 hp Dataset AA	200	200	200	200	200	200	200	200	200	200
1772 r/min, 1 hp Dataset BB	200	200	200	200	200	200	200	200	200	200
1750 r/min, 2 hp Dataset CC	200	200	200	200	200	200	200	200	200	200
1730 r/min, 3 hp Dataset DD	200	200	200	200	200	200	200	200	200	200

. There are ten fault types in each working condition, which are labeled as NO, IR7, IR14, IR21, B7, B14, B21, OR7, OR14, and OR21. Each dataset comprises a total of 2000 samples, with 80% allocated for model training and the remaining 20% for testing. The model undergoes 80 iterations, and the batch size is configured to 10.

The diagnosis results obtained with the four datasets for ten repeated trials are shown in Figure 4.

Table 6. Average accuracy and standard deviation of four datasets.

Dataset	Average Accuracy (%)	Standard Deviation
AA	99.05	0.39
BB	98.83	0.93
CC	99.03	0.48
DD	99.78	0.21

presents the average accuracy and standard deviation for the four datasets. The best average classification result among the four datasets appears in dataset DD. The average accuracy for dataset DD is 99.78%, with a standard deviation of 0.30. As shown in Table 6, datasets AA, BB, and CC perform well with raw time-domain signals too, with the average accuracy being around 99.05%, 98.83%, and 99.03%, respectively.

To illustrate the diagnostic ability of the RVDCNN model proposed in this paper with raw signal numerical matrices, the results are compared with those of an image CNN [29], frequency-domain DNN [30], and time–frequency-domain CNN [31], as presented in

Table 7. Diagnostic results for CWRU bearing datasets.

Dataset	RVDCNN	Image CNN [29]	Frequency DNN [30]	CSCoh-CNN [31]
DD	99.78 ± 0.21	99.79 ± 0.08	99.74 ± 0.16	97.68 ± 0.98
Data points (million)	1.152	39.3216	4.8	14.4

. The average accuracies and the standard deviations for ten trials and the number of input data points for each dataset are shown in Table 7.

A fault diagnosis method based on a data-driven approach was proposed by Wen et al. [29], which converts signals into images with a size of 64 × 64. Dataset DD is selected as the CNN input data and contains 2400 samples. There are 39.3216 million data points used for training and testing, which is 34.13 times greater than in the proposed method. The method of Wen et al. [29] performed well, but the amount of input data was large, leading to a time-consuming process.

Jia et al. [30] put forward an intelligent fault diagnosis DNN model based on frequency-domain signals. There were 200 samples for each health type, where 1200 Fourier coefficients were included in each sample. Meanwhile, in the present research, each sample included 576 data points, which reduced the amount of data by 76.02%, and it did not require the Fourier transform method. The diagnostic results were 0.04% higher than those of the DNN, and it had a greater advantage regarding the size of the dataset.

Chen et al. [31] used a two-dimensional map to represent cyclic spectral coherence (CSCoh) features. The 2D CSCoh maps of 10 bearing health conditions were obtained using the cyclic spectral analysis method, and discriminative patterns for specific types of bearing faults were provided. Then, they used a CNN model to learn the features and achieve fault classification. The results of the four datasets are shown in Table 6. The accuracy of the CSCoh-CNN was 2.10% lower than that of the proposed RVDCNN for dataset DD. Regarding the data points, the requirement of RVDCNN is 8% of that of the CSCoh-CNN method, providing it with a great advantage in terms of the computing time.

Table 7 shows that RVDCNN, with the capacity for intelligent feature learning, achieves similar diagnostic accuracies with the smallest number of data points compared with other feature extraction methods for bearing data. The proposed method does not require advanced artificial feature extraction methods and can mitigate the influence of the feature extraction method on fault diagnosis. It achieves satisfactory performance when directly using raw time-domain signals, with the advantage of a simple structure and fewer calculations.

4.2. Experimental Verification on Two-Speed Mechanical Automatic Transmission Bearing Fault Diagnosis

4.2.1. Two-Speed Mechanical Automatic Transmission

The faulty bearing is intended for use in a two-speed automatic transmission system for purely electric vehicles, as illustrated in Figure 5. The two-speed mechanical automatic transmission system consists of an input shaft system, an intermediate shaft system, a differential, front housing, rear housing, a shifting mechanism, and a parking mechanism. The input shaft system comprises an input gear shaft and supporting bearings, incorporating the first and second drive gears directly into the shaft. The intermediate shaft system, on the other hand, consists of the first and second driven gear, the main reduction gear, a synchronizer system, and supporting bearings. The red bearing on the right side of the middle shaft system is the faulty bearing in this experiment, and the outer race is installed on the rear housing for the easy arrangement of vibration acceleration sensors.

The maximum working conditions and gear ratio parameters of the transmission system are shown in

Table 8. Structural parameters of two-speed mechanical automatic transmission system.

Parameter Name	Value
Maximum speed (r/min)	12,000
Maximum torque (Nm)	250
1st gear ratio	3.000
2nd gear ratio	1.194
Final drive ratio	3.905

. The maximum input speed is 12,000 r/min and the maximum input torque is 250 Nm when implemented in a purely electric passenger car. The bearings inside the transmission mainly include two types, deep groove ball bearings and needle roller bearings, with a total of eight bearing supports. The faulty bearing model is 6307.

4.2.2. Three-Motor Powertrain Comprehensive Performance Test Bench

To collect bearing vibration acceleration data under the working conditions of two-speed mechanical automatic transmission in electric vehicles, a comprehensive performance test bench for a three-motor powertrain is built. The test bench is shown in Figure 6 and consists of a drive motor, a loading motor, a gearbox, a torque sensor, a cooling system, a temperature control system, a drive unit, and a loading unit. The two-speed mechanical automatic transmission system is fixed to the flange fixture plate of the experimental platform by bolts, and two half-shafts are connected to two loading motors to simulate the working conditions of the transmission system and conduct bearing vibration acceleration experiments under different health states.

4.2.3. Rolling Bearing Dataset

The experimental bearing is a deep groove ball bearing located on the right side of the intermediate transmission shaft of the automatic transmission, with a brand and model number of SKF 6307, and the parameters are shown in

Table 9. Deep groove ball bearing data.

Parameter Name	Value
Inside diameter (mm)	35
Outside diameter (mm)	80
Width (mm)	21
Number of rollers	8

. For convenience in disassembling and assembling the bearings, pitting damage faults were created on the inner race, outer race, and roller. The bearing model was replaced with the 6307-2RZ, and the cage was an integrated structure composed of nylon material.

To construct a database of multiple types of bearing faults, including single and composite faults, six types of faulty bearings were produced using laser processing technology, as shown in

Table 10. Fault types of deep groove ball bearings in two-speed automatic mechanical transmission.

Location of Pitting Fault	Fault Size (mm)
Inner race	0.53
Roller	0.53
Outer race	0.53
Inner and outer race	0.18
Inner race and rolling	0.18
Outer race and rolling	0.18

. Circular pitting faults were machined on the inner and outer raceway and roller surfaces. This included single faults in the inner race, outer race, and roller positions, as well as composite faults in the inner and outer race, inner roller, and outer roller. The pitting diameter of a single fault was 0.53 mm, and the pitting diameter of a composite fault was 0.18 mm. The damage diameter of the fault was derived from the CWRU dataset, with values of 0.18 mm and 0.53 mm, respectively. The damage diameter of the composite fault was 0.18 mm, and the fault depth was 0.15 mm. Figure 7 shows the disassembly and labeling of the six types of faulty bearings in Table 10. The location and diameter of the fault were marked on the outer race surface through laser engraving.

Based on the Chinese automotive driving condition CLTC-P, and according to the comprehensive shifting rules of two-speed automatic transmission, the working range for the second speed was 5000~9000 r/min [32]. Then, the experimental conditions for the faulty bearing of the transmission were formulated, with input speeds of 5000 r/min, 6000 r/min, and 7000 r/min and torque of 32 Nm. Three directional vibration acceleration sensors were arranged at the bearing supports of the input shaft, intermediate shaft, and differential shaft ends of the transmission housing, as shown in Figure 8.

The data acquisition system was a 24-channel LMS Test Lab, and the experimental bench control system and data acquisition system worked together to conduct transmission vibration signal acquisition experiments on 7 types of bearings, including single-point corrosion with a diameter of 0.53 mm on the inner race, outer race, and roller, normal bearings, and three composite fault types, under three working conditions.

The vibration signal acquisition time for each type of bearing was 30 s, and the sampling frequency was 16,384 Hz. We selected the Z channel of the sensor located at the end of the intermediate shaft when analyzing and processing the vibration signals. Taking the working conditions of 5000 r/min and 32 Nm as an example, 7 types of bearing vibration acceleration signals were extracted, as shown in Figure 9.

The dataset for the end-to-end intelligent fault diagnosis of rolling bearings in a two-speed mechanical automatic transmission system for purely electric vehicles is shown in

Table 11. Transmission bearing raw signal dataset.

Label	Location of Pitting Fault	Fault Size (mm)	Working Conditions (r/min, Nm)
N	None		① 5000, 32 ② 6000, 32 ③ 7000, 32
IP	Inner race	0.53
BP	Roller	0.53
OP	Outer race	0.53
IOP	Inner and outer race	0.18
IBP	Inner race and rolling	0.18
OBP	Outer race and rolling	0.18

. We use the labels N, IP, BP, OP, IOP, IBP, and OBP to represent normal, inner race pitting, roller pitting, outer race pitting, inner race and outer race composite pitting, inner race and roller composite pitting, and outer race and roller composite pitting fault samples. Under the three different speed conditions, the total sample for each label was composed of data with ratios of 30%, 30%, and 40%, respectively. The original time-domain vibration signal data length for each label was 115,200 data points, which were segmented and reorganized into 200 sample matrices with a size of 24 × 24.

4.2.4. Experimental Results

Based on the proposed RVDCNN model, feature adaptive learning and diagnostic recognition were performed on the vibration signals of seven types of deep groove ball bearings applied in the two-speed mechanical automatic transmission of an electric vehicle. Under the conditions of a batch processing volume of 10 and an iteration count of 80, fault diagnosis was performed 10 times, and the results are shown in Figure 10.

As shown in Figure 10a, the highest diagnostic accuracy was 54.64%, and the lowest was 26.43%. The diagnostic results were not ideal. Considering the small batch size and large number of training samples, the method required 112 training iterations to complete one iteration in the forward and backward propagation processes, which could easily lead to overfitting. Therefore, the loss function value during the first training process was extracted, as shown in Figure 10b. In the first 20 iterations, the loss value oscillated and then stabilized at around 1.25, without reaching convergence.

We increased the batch sample size to 20, 28, and 40 for the comparison of the bearing fault diagnoses. The relationship between the loss value and iterations is shown in Figure 11. When the batch training sample size was 20, the loss value decreased the fastest in the first 20 iterations, indicating an advantage in terms of the convergence speed and computational time. However, as the number of iterations increased to 30, the loss values of the three tended to be relatively stable, and the difference was not significant. After zooming in on the local image, it could be observed that when the batch training sample size was 40, the loss value tended to converge smoothly. When the batch processing sample sizes for training were 20 and 28, there was slight oscillation and convergence.

Therefore, for the fault diagnosis experiment on deep groove ball bearings in transmission, a batch training sample size of 40 was adopted and 10 diagnostic experiments were conducted on the faulty bearings of the two-speed mechanical automatic transmission, as shown in

Table 12. Results of 10 fault diagnosis tests.

Serial Number	1	2	3	4	5	6	7	8	9	10
Accuracy (%)	99.64	99.29	100	99.29	98.93	99.29	99.29	99.29	98.21	97.86

. The average accuracy in the 10 experiments reached 99.11%, with a standard deviation of 0.20. The model showed excellent performance in terms of feature extraction, feature recognition, classification, and diagnosis and also had good stability.

To reveal the training, recognition, and diagnostic processes of the RVDCNN model for seven types of bearings, taking the second diagnostic experiment as an example, we analyze the visualization results of the classification of bearings with different health types during the iteration process and obtain the confusion matrix of the final diagnostic results. The classification results for different types of bearings under different iteration times are visualized using the t-Stochastic Neighbor Embedding (t-SNE) dimensionality reduction method, as shown in Figure 12. Each color represents a corresponding bearing type, and the horizontal and vertical axes denote dimensionless values.

When the number of iterations is five, the seven types of bearings in different states are mixed, which creates confusion. When the number of iterations is 20, as shown in Figure 12, the model’s loss value drops rapidly, resulting in a notable improvement in its fault recognition capabilities. Although a preliminary classification of the seven bearing types emerges, there are still numerous classification errors. However, as the number of iterations reaches 30, the overall diagnosis and classification of most fault types is essentially achieved, and a small number of bearings with outer race and roller composite faults are incorrectly identified as single roller fault types. There is a slight conflict and an unclear boundary in the classification of a single fault in the inner race and a composite fault in the inner and outer race. As the number of iterations continues to increase, the recognition and classification boundaries of the seven types of bearings become clearer, and the recognition accuracy is further improved.

Regarding the second diagnostic experiment, the specific sample sizes of seven healthy bearings among 280 test samples are shown in

Table 13. Second diagnostic test samples.

Label	N	IP	OP	BP	IOP	IBP	OBP
Number of actual samples	46	34	36	35	52	36	41
Number of predicted samples	46	34	38	35	52	34	41

. There are feature recognition errors for the labels OP and IBP, i.e., there is a classification diagnosis error between the outer race pitting fault sample and the inner race and roller composite fault sample.

The diagnostic results are represented by a confusion matrix in Figure 13. While the composite fault diagnosis accuracy reaches 94.00% for the inner race and roller, the recognition accuracy for the other six types of bearing faults reaches 100.00%. Moreover, 6% of the samples with inner race and roller composite faults were mistakenly identified as outer race faults, as shown in Table 13. Two samples with the label IBP were assigned the label OP.

The t-SNE visualization and representation of the confusion matrix is shown in Figure 14. Because the diagnosis result was 99.29%, the overall clustering of the seven different types of bearings is obvious and the boundaries are clear. Purple circles represent IBP samples, and black plus signs represent OP samples. In the magnified images of the OP and IBP samples, it can be observed that there are two sample points with the label OP in the purple group of samples labeled IBP.

5. Conclusions

A two-dimensional deep convolutional neural network intelligent fault diagnosis model (RVDCNN) is proposed for the original time-domain vibration signals of bearings. It addresses the difficulties in establishing personalized diagnosis models for automotive transmission systems, the strong dependence on expert experience, and the insensitivity to the fault characteristics. Using the two-dimensional numerical matrix of the original time-domain vibration signals of the bearings in electric vehicle transmission as input data, the end-to-end intelligent fault identification and diagnosis of rotating components in automatic transmission was achieved. The conclusions are as follows.

(1)

An experimental comparison using the CWRU rolling bearing dataset was conducted to analyze how the number and size of the convolutional kernels in each layer of the CNN affect the accuracy of bearing fault diagnosis. The findings indicate that the model achieves the highest fault diagnosis accuracy when the first convolutional layer has eight kernels with a size of 11 × 11 and the second convolutional layer has 24 kernels with a size of 6 × 6.

(2)

Compared with feature extraction methods, the proposed end-to-end fault diagnosis model uses raw vibration signals as CNN training samples, requires the smallest amount of data, and achieves higher accuracy than other models.

(3)

A comprehensive performance test bench for a three-motor powertrain was built, and vibration experiments were conducted on deep groove ball bearings in a two-speed mechanical automatic transmission system for purely electric vehicles under service conditions. Accuracy of 99.11% was achieved in the 2AMT deep groove ball bearing dataset.

In the future, high-precision intelligent fault diagnosis research will be carried out to address the scarcity and imbalance of fault samples from transmission bearings or gears.