Fault Diagnosis of Planetary Gear Train Crack Based on DC-DRSN

Abstract

To solve the problem that the existing planetary gear train fault diagnosis methods have, namely their low diagnostic accuracy under low signal-to-noise ratio (SNR), a fault diagnosis method based on a double channel-deep residual shrinkage network (DC-DRSN) is proposed. The short-time Fourier transform (STFT) is used to convert the original vibration signal into a two-dimensional time-frequency graph, which effectively enhances the ability to express information. A DC-DRSN model is constructed, and the optimal number of residual shrinkage modules is determined by combining the diagnostic characteristics with different noises, which effectively improves the accuracy and anti-noise ability of fault diagnosis. The results of bearing and planetary gear train crack fault diagnosis show that the diagnosis method based on DC-DRSN has higher diagnostic accuracy while realizing fault diagnosis, which is better than other deep learning diagnosis methods. At the same time, the method can adapt to fault diagnosis in different noise environments, and has good expression ability and generalization ability.

1. Introduction

The safe development of nuclear power is important. As one of the key components of a nuclear power unit, the main role of the planetary gearbox is to transmit the rotational power of the motor to the impeller of the pump. The gears in the nuclear power planetary gearbox are prone to cracks, pitting corrosion, and other faults [1]. Moreover, current research on the fault diagnosis and health monitoring of the planetary gearbox is relatively weak. Therefore, it is of great significance to establish a fault diagnosis method for the planetary gear train of the nuclear power planetary gearbox.

The fault diagnosis methods are divided into three types [2]. (1) The mechanistic model-based approach. This method provides an in-depth system understanding with good epitaxy and reliability, but the mechanistic model needs sufficient knowledge and data support. With the increasing complexity of the system structure, some mechanism knowledge is difficult to obtain. Even if the mechanistic model is constructed, it is not possible to obtain all the information of the physical system. Especially when the system is highly coupled and has complex nonlinearities, the accuracy of the obtained mechanistic model is limited, which limits the application of this method. (2) The knowledge-based approach. This method is based on the integration of expert experience and prior knowledge, to explore the relationship between system faults, phenomena as well as causes, and to build a system diagnosis model according to certain rules. It does not require precise mathematical expressions and is suitable for many complex systems that are difficult to model. However, this method is poorly adaptable. An important prerequisite for obtaining accurate results is to have a knowledge base with a large amount of rich empirical knowledge. For unknown faults without any prior knowledge, not only there will be misdiagnoses, but also it is impossible to give accurate diagnostic information in the event of a fault. (3) The data-driven approach. This method aims to model and predict the physical system by processing and analyzing the input and output data of the physical system, mining the hidden rules and patterns in the data. The main advantage of this method is that it does not require any knowledge of the internal mechanism, and it can use a large amount of actual data to improve the accuracy and generalization ability of the model, which is outstanding in the absence of accurate mathematical/physical models. The vibration signal contains the essential information about the operating status of the monitored object. Therefore, it is a commonly used signal in data-driven diagnostic methods. The empirical mode decomposition [3] and wavelet transform [4] have been proven to be effective diagnostic methods. Shi [5] proposed an adaptive optimization algorithm for VMD parameters based on a differential search, combined with the relevant kurtosis index, to achieve the adaptive extraction of bearing fault features. The effectiveness of the method was verified by experiments. Chen et al. [6] proposed a fault diagnosis method for rolling bearings based on singular spectrum decomposition and independent component analysis, which solved the problem that the early failure of bearings was overwhelmed by noise due to low energy. Mauricio et al. [7] proposed a multi-band envelope extraction method based on cyclic bivariate mapping, which solved the problem of the difficulty in detecting faulty bearing noise signals using single-pass filtering. Wang et al. [8] proposed a fault diagnosis method based on parameter optimization variational mode decomposition and multi-domain manifold learning to solve the problem of difficult feature extraction of planetary gearbox features, and verified that the multi-domain feature extraction method is superior to the single-domain feature extraction methods in the time domain and frequency domain. Xu et al. [9] proposed a mixed-domain fault diagnosis method for chaotic particle swarm with improved cross-mutation, which effectively improved the accuracy of bearing fault classification based on a mixed eigendomain. Wang et al. [10] proposed a fault diagnosis method based on the combination of integrated empirical mode decomposition and a support vector machine for diesel engine vibration signal analysis and feature extraction, and verified that the method can accurately and effectively identify multiple sources of fault information of a gearbox in different states through comparative experiments. However, traditional machine learning methods are limited to shallow feature representation and struggle to deal with complex nonlinear relationships, which leads to low accuracy in fault diagnosis. In recent years, with the development of artificial intelligence and big data technologies, the methods such as deep learning as well as transfer learning have become widely used in the field of fault diagnosis [11,12,13]. Chen et al. [14] proposed an adaptive neural network model based on instantaneous speed information to realize the fault detection of a planetary gearbox under different working conditions. Zhang et al. [15] proposed a diagnostic method of a parallel multi-scale pooled branch convolutional neural network, which solved the fault diagnosis problem of mechanical vibration signals under multiple working conditions with less computational cost. However, with the increase in network layers and training data, problems such as network degradation and overfitting have become increasingly prominent, which greatly affects the accuracy of fault diagnosis. Therefore, He et al. [16] proposed to use a “shortcut connection” deep residual network (ResNet) to solve the degradation phenomenon and training problem of the deep network, which optimized the convergence speed and achieved the improvement of accuracy by solving the degradation problem during deep network processing. Zhao et al. [17] proposed a deep residual shrinkage network (DRSN) based on the residual network, which was used to improve the feature learning ability of strong noise vibration signals. Zhang et al. [18] combined variational mode Gaussian distortion with DRSN to improve the fault diagnosis performance. Cao [19] proposed a state-of-health identification method for rotating machinery based on Gramian angle field (GAF) and DRSN, which was used to identify faults in rotating machinery under the condition of nonlinear transformation speed and load. Sun et al. [20] converted the one-dimensional logging parameters into two-dimensional images by using GAF, input them into a DRSN model, and experimentally proved that the diagnostic accuracy of the proposed method was better than that of the traditional DRSN and convolutional neural network (CNN). Pei et al. [21] proposed a DRSN method based on characteristic noise energy ratio (CNER), which showed that the average recognition rate could reach 98.70% in the environment with 10 dB SNR. Yu et al. [22] proposed the Pareto-optimal adaptive loss residual shrinkage network (PALRSN), which effectively solves the problem of mechanical fault diagnosis when the fault sample data are insufficient.

In summary, the existing fault diagnosis methods have achieved certain results in low-noise environments, and the diagnostic accuracy is high. However, in strong-noise environments, the diagnostic performance and accuracy of the models need to be improved. Considering that the gearbox of a nuclear power unit works in the environment of strong noise and low SNR, a fault diagnosis method based on DC-DRSN is proposed to improve the fault diagnosis performance of the model. The main contributions of this paper are as follows: (1) The structure of one-dimensional and two-dimensional parallel residual shrinkage networks is constructed to enhance the feature extraction capability. (2) According to the diagnostic performance under different noise levels, the number of optimal residual shrinkage modules is determined. (3) Combined with the public dataset and the experimental dataset, the effectiveness and robustness of the proposed method are verified.

2. Theory and Method

2.1. Image Conversion Method

The visual representation of the vibration signal helps identify the failure mode of the gear. Commonly used image conversion methods for vibration signals include short-time Fourier transform (STFT), wavelet transform (WT), Gramian angular summation field (GASF), generalized S-transform (GST), and so on.

STFT is a common method in time-domain and frequency-domain analysis. In this method, the signal is divided into short periods, and the Fourier transform is applied to each short period to obtain the spectral information of the signal at different times and frequencies. STFT is able to capture the instantaneous frequency change of the signal in time, and the instantaneous frequency change can reflect abnormal patterns in the frequency domain, which helps identify the fault state of the system. Assuming that the vibration signal is x($\tau$), the STFT is calculated as [23]:

$$STFT(t,\omega )={\displaystyle {\int }_{-\infty }^{\infty }x}(\tau )\cdot w(\tau -t)\cdot e^{-j\omega \mathrm{t}}d\tau$$

(1)

where $w(\tau -t)$ is the window function; $e^{-j\omega \tau }$ is the complex exponential term that describes the components of the frequency domain, $\omega$ is the frequency; $STFT(t,\omega )$ is the result of the short-time Fourier transform at moments and frequencies.

In this paper, to reduce spectrum leakage and maintain computational efficiency, a Hanning window with 256 length and 50% overlap is used.

WT provides a time-frequency representation of a signal by convoluting it with a set of translational and scaled wavelet functions. This method inherits the localization idea of STFT and overcomes the defect that the size of the time window is unchanged, which makes the wavelet transform more advantageous in capturing the local information of the signal. The principle formula of WT can be described as [24]:

$$w(a,b)={\displaystyle {\int }_{-\infty }^{\infty }f(t)\psi \ast [(t-b)/a]dt}$$

(2)

where $w(a,b)$, $f(t)$ and $\psi (t)$ denote the wavelet coefficient, original signal, and wavelet basis function, respectively; a and b represent the scale factor and the translation factor, respectively.

In this paper, to extract enough feature information from original the vibration signal and accurately distinguish the subtle changes of features, the Morlet wavelet (cmor3-3) is used as the mother wavelet function with a total scale of 256.

GASF is the mapping of time series data to a polar coordinate system and the construction of images by calculating cosine similarity between angles. By adjusting the size and resolution of the image, the features of the signal can be extracted at different scales, and the results are as follows [25]:

$${\tilde{x}}_i={\displaystyle \frac{(x_i-\max (X)+(x_i-\min (X))}{\max (X)-\min (X)}}$$

(3)

$${\varphi }_i=\arccos ({\tilde{x}}_i)$$

(4)

$$r(i)={\displaystyle \frac{x_i}{n}}$$

(5)

$$GASF=\left[\begin{array}{ccc}\cos ({\varphi }_1+{\varphi }_1)& \cdots & \cos ({\varphi }_1+{\varphi }_n)\\ ⋮& \ddots & ⋮\\ \cos ({\varphi }_n+{\varphi }_1)& \cdots & \cos ({\varphi }_n+{\varphi }_n)\end{array}\right]$$

(6)

where ${\tilde{x}}_i\in \tilde{X}$, then encode the ${\tilde{x}}_i$ value of $\tilde{X}$ as the angular cosine, time as the radius $r(i)$, and ${\varphi }_i$ as the angular cosine value in polar coordinates, and for the time series in the interval [−1, 1], the value range is limited to the interval [0, π] by using the inverse trigonometric function under the polar mapping. In a polar coordinate system, the cosine and angle values for each polar coordinate are calculated.

In this paper, the data length of the GASF transformation is 1024, and the window size is 256.

GST decomposes a signal into a series of rectangular boxes on the time-frequency plane, and the values in each rectangular box represent the energy of the signal at the corresponding time and frequency, which is suitable for processing nonstationary signals, providing higher resolution and flexibility in time and frequency. According to the standard deviation of the generalized Gaussian window function ${\sigma }_m(f)=1/\mid f{\mid }^m$, the width of the Gaussian window can be controlled by adjusting the parameters, so as to optimize the time-frequency resolution of GST. For an arbitrary squared integrable signal $x(t)$, GST is defined as [26]:

$$S(\tau ,f)={\displaystyle {\int }_{-\infty }^{\infty }x(t)\cdot w(t-\tau ,f)\cdot e^{-j2\pi ft}dt}$$

(7)

where τ is the time variable; f is the frequency variable; $w(t-\tau ,f)$ is the window function of GST, and $e^{-j2\pi ft}$ is the complex exponential function that converts the signal from the time domain to the frequency domain.

In this paper, to balance the time and frequency resolution, and ensure the integrity and smoothness of signal features, a Gaussian window function with 1 window width, 256 scale and 50% overlap is selected.

2.2. Neural Network Model

DRSN is essentially a network integrated by ResNet with an attention mechanism and a soft threshold function. The core of ResNet is the residual block unit (RBU), as shown in Figure 1, which uses multiple parametric layers to learn the residual representation between the input and output. The input feature x is first stored in the variable, and then the residual part F(x) is learned through a series of nonlinear layers, and finally the residual is calculated. Through cross-layer identity mapping, RBU transforms the learning objective from the mapping between input and output to learning residuals, which reduces the training difficulty and accelerates the network convergence speed. It is expressed by the formula [16]:

$$H(x)=F(x)+x$$

(8)

The residual shrinkage block unit (RSBU) is the core of the DRSN network, and the structure is shown in Figure 2, which introduces the attention mechanism and soft thresholding on the basis of RBU. The attention mechanism uses the squeeze-and-excitation network (SENet) proposed by HU [27], which learns the weights of each channel through the small network “global pooling → fully connected layer → ReLu activation function → fully connected layer → Sigmoid function”, and applies it to the original input feature map, and weights the eigenvalues of each channel through multiplication operations to adjust the feature size of each channel. In this way, the attention of the network to important features is enhanced so as to improve the expressiveness, generalization ability, and robustness of the model. In this paper, the soft thresholding of different thresholds of channels is adopted, which can automatically calculate different scales and thresholds for each channel, so that the features of different channels are subject to different constraints in the sparsity process, allowing the network to process the features more flexibly. If α_c is the threshold of the cth channel of the feature map, and $\underset{i,j}{average}|x_{i,j,c}|$ is the average value of the absolute value of each channel of the input feature x, the threshold is calculated as follows [17]:

$${\tau }_c={\alpha }_c\cdot \underset{i,j}{average}|x_{i,j,c}|$$

(9)

Soft thresholding is the core step of signal denoising, which is combined with deep learning to decompose the input signal through the convolutional layer, then filter all the signals after decomposition within the threshold, and then reconstruct the filtered signal to achieve the purpose of denoising. The soft threshold function is as follows. After deriving the soft threshold function, the gradient is only 0 or 1, which avoids gradient explosion and gradient disappearance.

$$y=\{\begin{array}{cc}x-\tau & x>\tau \\ 0& -\tau \le x\le \tau \\ x+\tau & x<-\tau \end{array}$$

(10)

where x, y, and τ are the input, output, and threshold values, respectively.

3. Fault Diagnosis Method Based on DC-DRSN and Verification

3.1. Fault Diagnosis Method Based on DC-DRSN

Although DRSN implements adaptive learning thresholds and achieves good results in fault diagnosis, it is often used to deal with the spatial features contained in two-dimensional images and it fails to fully explore the dynamic changes on one-dimensional time series. Therefore, a fault diagnosis method based on a double channel-deep residual shrinkage network (DC-DRSN) is proposed in this paper.

The fault diagnosis process based on DC-DRSN is shown in Figure 3.

Step 1: For the one-dimensional signal and two-dimensional time-frequency diagram with different levels of noise, the training samples, verification samples, and test samples are randomly selected.

Step 2: Construct the DC-DRSN model, initialize the network weights, and set parameters such as the number of iterations and the learning rate.

The network structure of DC-DRSN is shown in Figure 3, which is composed of a two-channel neural network. The upper channel uses a two-dimensional deep residual contraction network, and its input is a two-dimensional time-frequency graph after the transformation of the original vibration signal to reflect the weak local characteristics of the signal at different angles and improve the feature learning ability of the signal. The lower channel uses a one-dimensional residual contraction network, which takes the original vibration signal as the input, retains the timing and correlation of the signal, and concisely and effectively expresses the global dynamic time domain characteristics. On this basis, the upper and lower channels are fused in the fusion layer, and the extracted time-frequency features are classified and identified by the SoftMax activation function.

The DRSN hyperparameters are shown in

Table 1. DRSN hyperparameter settings.

No. of Layer	Layer	Hyper-Parameters
Conv1_1	Convolution layer1_1	32 convolution kernels with the size of [3,3]. Stride: [1,1]. Padding: same.
BN	Batch Normalization layer	The scale is 32.
Conv2_1	Convolution layer2_1	32 convolution kernels with the size of [3,3]. Stride: [1,1]. Padding: same.
BN	Batch Normalization layer	The scale is 32.
Average Pooling	Average Pooling layer	Pooling size: [1,1]. Stride: [2,2]. Padding: [0,0,0,0].

. They consist of a convolutional layer, a batch normalization layer, and a max pooling layer.

Step 3: The one-dimensional signal and the two-dimensional time-frequency graph training samples are input to the upper and lower channels for model training at the same time.

Step 4: The model parameters are continuously optimized through training samples and validation samples until the network accuracy is satisfied and the number of iterations is reached to obtain a trained diagnostic model.

Step 5: Input test samples to the model and obtain diagnostic results through confusion matrix and T-SNE visualization.

3.2. Method Validation

3.2.1. Introduction of Dataset

At present, there is no authoritative report on the public dataset of planetary gearboxes, so the bearing public dataset of Case Western Reserve University (CWRU) in the United States is used to verify the fault diagnosis method proposed in this paper.

The rolling bearing test bench of CWRU is shown in Figure 4, which is mainly composed of a motor, a torque sensor, a power tester, and an electronic controller. During the test, the motor speed is 1720 r/min~1797 r/min. The test bearings are 6205-2RS JEM SKF deep groove ball bearings with single-point damage machined by EDM, which is made in Sweden. The load of the bearings has 1 hp and 3 hp loads two types, and the sampling frequency of the acceleration sensor is 48 kHz. The bearing conditions involved in the dataset include four types: normal, inner ring damage, outer ring damage, and rolling element damage. Each type is available in 0.007” (0.1778 mm), and 0.021” (0.5334 mm) damage diameters.

Table 2. Bearing public datasets.

Fault Location	Fault Diameter /mm	Load /hp	Labels	Dataset (Training/ Validation/Test)
Normal	0	3	0	540/180/180
Inner Race	0.1778	1	1	540/180/180
	0.1778	3	2	540/180/180
Ball	0.1778	1	3	540/180/180
	0.1778	3	4	540/180/180
Outer race (Centered@6:00)	0.1778	1	5	540/180/180
	0.1778	3	6	540/180/180
Outer race (Orthogonal@3:00)	0.1778	1	7	540/180/180
	0.1778	3	8	540/180/180

shows the dataset used in this paper, which contains nine fault states. The number of samples in each category is 900, and the number of data points in a single sample is 1024, for a total of 8100 samples. The dataset is randomly divided into training sets, validation sets and test sets in the ratio of 3:1:1. Thus, there are 540 training sets, 180 validation sets and 180 test sets for each fault type. The Fourier time-frequency diagram of size 112 × 112 is input in the upper channel, so the structure of the training set, the verification set and the test set of each fault type are 540 × 112 × 112, 180 × 112 × 112 and 180 × 112 × 112, respectively. While the structure of the training set, the verification set and the test set of each fault type in the lower channel are 540 × 1024, 180 × 1024 and 180 × 1024, respectively. In order to accelerate the convergence of the model and improve the stability and robustness of the model, all samples are normalized and preprocessed.

In this paper, TensorFlow and Keras frameworks are used to build the DC-DRSN network, with a learning rate of 0.001, a batch size of 64, and a training times of 150, in which the convolutional layer adopts the normal distribution initialization method and L2 regularization proposed in Ref. [10].

Table 3. Images of vibration signal conversion of the bearing datasets.

Label	Vibration Signal	Image Conversion Method
		STFT	WT	GASF	GST
0
1
2
3
4
5
6
7
8

shows the images obtained by using STFT, WT, GASF, and GST to convert the vibration signals in the nine different states of the common dataset. It can be seen that the time-frequency diagram converted by GASF and GST cannot clearly show the characteristics of the signal. The time-frequency diagram of STFT is clearer than that of WT and can clearly separate and analyze different frequency components. Therefore, in this paper, STFT is selected for time-frequency analysis of the fault signal to be diagnosed.

3.2.2. Experimental Results and Discussion

(1)

Comparison of different numbers of residual shrinkage modules

The signal-to-noise ratio (SNR )is a measure of the comparison between the intensity of a signal and noise and is usually used to evaluate the relative strength of a signal and noise. The formula of SNR is expressed as [28]:

$$SNR=10\cdot {\log }_{10}\left({\displaystyle \frac{P_{signal}}{P_{noise}}}\right)\begin{array}{c}\end{array}(dB)$$

(11)

where P_signal is the original signal power and P_noise is the power that contains noise in the signal. The higher the SNR value is, the stronger the signal relative to the noise is, which is easier to identify and analyze.

In order to test the noise immunity of a different number of RSBUs, the number of RSBUs is adjusted without changing the preprocessing and other layer hyperparameters. Five different SNRs are added to the original vibration signal to compare the effect of the number of RSBUs on diagnostic performance. Figure 5 shows the average of the network after 150 iterations of training and five tests.

When the number of RSBUs is one or two, the network depth is insufficient, which limits the expression and learning ability of the model, resulting in the performance of the model not reaching the optimum. When the number of RSBUs is four, the number of model parameters is too large, resulting in network degradation and decreased diagnostic capabilities. When the number of RSBUs is three, the model has the highest diagnostic accuracy, and the accuracy of the test set reaches 99.56% when the signal-to-noise ratio is 4 dB. In order to better simulate the noise in actual operation, taking the signal-to-noise ratio equal to 4 dB as an example, the accuracy curve of the model is shown in Figure 6. The convergence curves of training and testing have achieved a good fitting effect, and the visual classification of the test set in the confusion matrix and T-SNE is shown in Figure 7 and Figure 8. It can be clearly found that the same type of fault has a good aggregation and different types of features can be effectively distinguished. The proposed method can be used to reshape and classify them in the high-dimensional space.

(2)

Comparison of different image conversion methods

STFT, WT, GASF and GST are used to convert the two-dimensional image of the vibration signal, and the converted image is used as the input of the upper channel of the DC-DRSN model. The accuracy of fault diagnosis when a 4 dB signal-to-noise ratio noise is added to the original signal is shown in

Table 4. The accuracy of the bearing test set under different image conversion methods.

Methods	Testing Accuracy
STFT-DCDRSN	99.56%
WT-DCDRSN	99.06%
GASF-DCDRSN	98.67%
GST-DCDRSN	98.31%

. It can be seen that the GST-DCDRSN method has the lowest fault diagnosis accuracy of 98.31%. This is due to the high-resolution characteristics of GST and data redundancy, which allows the model to process irrelevant details that distract from key features. The STFT transform can accurately locate the time point of fault occurrence and track the dynamic changes in the system, with a fault diagnosis accuracy of up to 99.56%, which is 1.25% higher than that of the GST transform. At the same time, it is also proved that the 2D graph transformed by STFT can be used as the input of the channel on the DC-DRSN, which achieves higher diagnostic accuracy.

(3)

Comparison of DC-DRSN with other deep learning models

The proposed method, DC-DRSN, is compared with DRSN, VGG-16, GoogleNet, and Alexnet-18, where 4 dB noise is added to the original vibration signal, and the time-frequency image is input into each model to test the fault diagnosis performance of each model. The results are shown in

Table 5. The accuracy of the bearing test set under different deep learning models.

Methods	Testing Accuracy
DC-DRSN	99.56%
DRSN	99.07%
VGG-16	98.88%
GoogleNet	98.94%
Alexnet-18	99.06%

. With the increase in model complexity, the diagnostic effect of DRSN is better than that of VGG-16, GoogleNet, and Alexnet-18. However, STFT-DCDRSN allows the network to process image and one-dimensional signal data separately, which allows each channel to focus on extracting its own features. So STFT-DCDRSN has the best diagnostic effect, with a diagnostic accuracy of 99.56%, which is 0.49% better than DRSN.

4. Fault Diagnosis of Planetary Gear Train Crack Based on DC-DRSN

4.1. Introduction of Test Bench

Combined with the actual structure size of the nuclear power planetary gearbox, a proportionally reduced nuclear power planetary gearbox test bench is designed, as shown in Figure 9. The test bench is mainly composed of the control system, transmission device, power system, loading system, and lubrication system. The transmission device transmits power from the vertical motor to the horizontal load motor and realizes the effective connection between them. The lubrication system lubricates the transmission and filters, as well as cools the oil. The control system is responsible for changing the input speed and load of the equipment. During the test, the BK sensor and its supporting Pulse system were used for data acquisition, and the acquisition card used BK’s Type3053-B-120 made in Denmark. Combined with the test requirements, the transmission route of the planetary gear train is analyzed [29], and in order to ensure the quality of vibration signal acquisition, the sensor is installed on the box wall closest to the planetary gear.

4.2. Crack Failure Test of Planetary Gear Train

In this study, the fault tests of planetary gear train cracks under different working conditions are carried out. During the test, the control system controls the input motor speed, when the input motor speed is 750 r/min, the voltage of the electronic control system is 380 V, and the frequency is 50 Hz. Under different loads, the operating state and vibration signal characteristics of the planetary gear train are different, and the vibration amplitude and frequency components of the gear train meshing under high loads are more complex. In order to avoid aliasing the characteristic signals under different loads and improve the applicability and robustness of the diagnostic system, two load conditions of 50% medium load and 100% heavy load are set by the load motor. A series of tests are carried out for normal, planetary gear cracks and sun gear cracks under each working condition, and the test environment is shown in Figure 10. The crack is located at the root of the gear, and the crack depth is about 1 mm, as shown in Figure 11. In the process of data acquisition, the sampling frequency is 25.6 kHz, and the continuous sampling time is 1 min each time. The vibration data samples in five states of the planetary gear train are finally obtained, which are labeled as 0, 1, 2, 3, and 4, respectively.

Figure 12 shows the original vibration signal of a planetary gear system randomly selected for five states and their image (112 × 112 pixels) after STFT.

Table 6. Types of nuclear gearbox failures.

Fault Location	Status	Speed (r/min)	Load	Labels	Dataset (Training/ Validation/Test)
Normal	Normal	750	100%	0	540/180/180
Planet gear	Cracks	750 750	50% 100%	1 2	540/180/180 540/180/180
Sun gear	Cracks	750 750	50% 100%	3 4	540/180/180 540/180/180

shows the composition of the planetary gear train crack fault dataset obtained in this paper. A sliding window containing 1024 data points is used to sample the vibration signals of the planetary gear train in five states, with a window step size of 300, and each state contains 900 samples. Similarly, the training, validation, and test sets are randomly divided in the ratio of 3:1:1, and the final dataset contains 2700 training set samples, 900 validation sets, and 900 test set samples each. The structure of the training set, validation set, and test set of the upper and lower channels, as well as the data preprocessing steps and hyperparameter settings, are consistent with the preceding ones, and will not be repeated here.

4.3. Test Results and Analysis

(1)

Accuracy at different levels of noise

In order to simulate various noise interferences in the actual operation of the nuclear power gearbox and test the diagnostic accuracy of the model under different levels of noise, five kinds of noise with different SNR are set, and the accuracy of the test set under different SNRs and different RSBUs is shown in Figure 13. When RSBUs is equal to three, the fault diagnosis accuracy is the highest, which is consistent with the previous results. Therefore, RSBUs equal to three is determined as the fixed parameter of DC-DRSN. It is not difficult to see that with the increase in the SNR, the accuracy of diagnosis also increases, and the diagnostic accuracy of the test set is still as high as 97.22% when the SNR is 4 dB. In view of the fact that the SNR in gearbox fault diagnosis studies is often between 0 and 10 dB to simulate the noise level in the actual industrial environment [30], and 4 dB is in the middle of this range, which is a reasonable and representative value, and is helpful to test the robustness and reliability of the fault diagnosis method, therefore, under the SNR 4 dB, DC-DRSN is used to train and classify the nuclear power planetary gearbox dataset, and the accuracy changes in the obtained training set and the validation set are shown in Figure 14. It can be seen that when the number of iterations is less than 50, the accuracy of the training set and the validation set increases but there is oscillation, and the diagnostic performance of the model is improving but the stability needs to be improved. When the number of iterations is more than 50, the training set gradually stabilizes, and the accuracy is close to 100%, and the oscillation of the validation set is greatly reduced compared with before, and the accuracy reaches 99%. After about 150 iterations, the model has good diagnostic performance and stable accuracy.

The confusion matrix and the T-SNE visualization representation of the classification results are shown in Figure 15 and Figure 16, respectively. It is not difficult to find that label 2 has the best sample classification effect, with an accuracy rate of 100%. Label 0 and label 4 have six samples misclassified with each other, five samples from label 3 are classified into label 1, and eight samples from label 1 are misclassified. The results show that the change of gear crack type and load has a great influence on the classification accuracy, and most of the samples are correctly classified. Although there are a few sample errors, the minimum accuracy is still 95.56%, which verifies the effectiveness of DC-DRSN classification for different working conditions. The T-SNE visualization also shows that the distribution interval of each type of fault is regular and orderly, and the spacing of similar faults is very small, which further verifies the superiority of the proposed method.

(2)

Comparison of different image conversion methods

The collected planetary gearbox vibration signals are converted into two-dimensional time-frequency maps of 112 × 112 pixels by STFT, WT, GASF, and GST, and then the time-frequency maps are input into the upper channel of the DC-DRSN model for diagnosis. When the SNR is equal to 4 dB, the fault diagnosis accuracy of each method is shown in

Table 7. The accuracy of the gear test set under different image conversion methods.

Methods	Testing Accuracy
STFT-DCDRSN	97.22%
WT-DCDRSN	96.87%
GASF-DCDRSN	96.46%
GST-DCDRSN	95.74%

. It can be seen that the GST image conversion method has the lowest diagnostic accuracy of 95.74%, while the STFT is as high as 97.22%. This further verifies that the STFT conversion image is used as the input of the DC-DRSN upper channel, and the time and frequency information of the signal are retained through local analysis of the signal in time and frequency. Therefore, the network can better capture the transient changes, periodicity, and frequency changes of the signal, so as to improve the accuracy of model diagnosis.

(3)

Comparison of DC-DRSN with other deep learning models

Similarly, the proposed method DC-DRSN is compared with DRSN, VGG-16, GoogleNet, and Alexnet-18. The time-frequency diagram after short-time Fourier conversion is input into each model, and the vibration signal is input into the lower channel of DC-DRSN, the number of iterations is set to 150, and the diagnostic accuracy of each model is shown in

Table 8. The accuracy of the gear test set under different deep learning models.

Models	Testing Accuracy
DC-DRSN DRSN	97.22% 96.67%
VGG-16	95.49%
GoogleNet Alexnet-18	96.10% 96.24%

when the SNR is 4 dB. It can be seen that VGG-16 has the lowest classification and recognition accuracy of the test set, which is only 95.49%. Comparing the two classical networks, GoogleNet and Alexnet-18, it can be seen that the complexity of the model increases, and the accuracy of the test set is also improved accordingly. In comparison, the recognition accuracy of DC-DRSN is as high as 97.22% under the same situation, which is at least 0.98% higher than that of other deep neural networks. This further verifies that DC-DRSN has effective noise cancellation ability and strong feature extraction ability, so it has a higher fault diagnosis accuracy.

5. Conclusions

In order to solve the problems of weak feature extraction ability and low fault diagnosis accuracy of existing planetary gearboxes in noisy environments, a fault diagnosis method based on DC-DRSN is proposed to realize the fault monitoring of planetary gear train gears. With the help of the bearing public dataset of CWRU, the proposed method is compared with the traditional DRSN, and the diagnostic accuracy of the proposed method is higher than that of the traditional DRSN. On this basis, the method is applied to the proportionally reduced planetary gear train crack fault test data of a nuclear power gearbox, and the planetary gear train crack fault diagnosis is realized, with an accuracy of 97.22%. The results of this paper are as follows:

(1)

A one-dimensional and two-dimensional parallel residual contraction network structure is constructed, which not only retains the temporal sequence and correlation of one-dimensional signals but also includes the information expression ability contained in two-dimensional images. In this way, more feature information is extracted, and the diagnostic performance of the model is improved.

(2)

Combined with the diagnostic characteristics under different noises, the number of residual shrinkage modules is reasonably determined. Thanks to the soft thresholding in the module, each sample has its own unique set of thresholds, which can be adapted to fault diagnosis in different noise environments.

(3)

The accuracy of the proposed method in diagnosing crack faults under different loads of planetary gear train gearboxes is tested. The results show that only a few samples are misclassified, which verifies that the proposed method has good expression and generalization ability.