Research on Fault Diagnosis of Wind Turbine Gearbox with Snowflake Graph and Deep Learning Algorithm

Abstract

Wind power generation is one of the important development projects for renewable energy worldwide. As wind turbines operate in harsh environments, failure of the wind turbines often occurs, thus leading to lower power generation efficiency and high maintenance cost. Earlier detection of the fault type can reduce the maintenance cost. This study proposed a hybrid recognition algorithm based on the symmetrized dot pattern (SDP) and convolutional neural network (CNN) for wind turbine gearbox fault diagnoses. In addition to a fault-free type, four fault types were discussed in this paper, including gear rustiness, broken tooth, wear, and aging. A vibration sensor was used for measurement. The original vibration signals of the gearbox were captured by a NI-9234 high-speed data acquisition card, filtered by a fast Fourier transform, and imported into the SDP to create the snowflake image features. Afterward, CNN diagnosed the gearbox fault type. There were 1500 test data in this study. A total of 200 data items for each fault type were used as training samples, and 100 data of each type were used as test samples. The test result shows that the training accuracy was 98.8%. The proposed method can diagnose the fault condition of the gearbox effectively and identify the fault type of the gearbox accurately. This is favorable for the quick maintenance of wind turbines.

1. Introduction

In recent years, under continuous technological developments worldwide, people’s demand for energy is also growing. The increasing environmental awareness of the public has made renewable energy one of the important development projects of power supply systems [1,2,3]. Wind power generation has rapidly developed in many countries with good wind fields. However, offshore or onshore wind turbines are exposed to the atmosphere for a long time, and the operational environment is quite harsh. The probability of parts deterioration and machine aging increases relatively as the system running time extends. There are many challenges to wind turbine system repair and fault diagnosis.

Presently, many studies concerning large wind turbine fault diagnosis aim at diagnosing faults in the gearbox and blades [4,5,6]. Gearbox damage has been a very important topic. The common faults of gearboxes include rust [7], stripping, wear, shaft misalignment, fracture, spalling, and aging [8,9]. Scholars have used different methods to discuss the gearbox fault diagnosis. Joel Igba et al. measured the vibration signals of faults in gears and bearings, calculated the RMS value and peak of vibration, and used the data to analyze fault features [10]. Yayu Peng et al. measured the phase current of the generator and the RMS value of vibration signals. They predicted the health index of the gearbox by a recurrent neural network (RNN) using the real-time recurrent learning (RTRL) algorithm. The predicted health index was compared with the threshold to evaluate the gearbox faults. The experimental results showed the effectiveness of the method [11]. Guolin He et al. proposed a new method for wind turbine gearbox vibration analysis based on discrete spectrum correction. They analyzed the vibration of the stationary and planetary gears in the gearbox [12]. Wei Guo et al. built a dynamic model for double planetary gear, applied a sun gear with cracks at its root, and analyzed the gear’s vibration signals. They compared the vibration signals induced by the cracks in different positions. Their method successfully identified the position of cracks [13]. Rusmir Bajric et al. processed the measured gearbox vibration signals by filtering and Wavelet Transform. They compared the vibration signals from normal and damaged gear. The results proved the effectiveness of their method in extracting the vibration characteristics of the faulty gearbox [14]. Cheng et al. calculated the amplitude of fault characteristic frequency from the power spectrum density (PSD) of resampling envelope signals as the feature of gear fault detection. The feature was imported into the support vector machine (SVM) based on stacked AE (SAE) to identify the types of gear faults, such as missing teeth, cracks, and breaking. The method proposed by Cheng et al. was compared to the traditional SVM and the deep belief network (DBN)–deep neural network (DNN). The results of Cheng et al.’s research show that the recognition rate of the SAE-based SVM was 89.3%, the highest among the three classifiers [15]. Li Lu et al. used a random Bernoulli matrix to compress the vibration signals of a high dimensional original planetary gearbox and a mixed chaotic quantum particle swarm optimization (CQPSO) algorithm with deep belief network (DBN) to extract deep fault features. The gear crack and wear were identified using the least-squares support vector machine (LSSVM) classifier; the accuracy was 98.54%. The advantage of this method is that noise pollution is eliminated from the compressed signals, and the overall amount of computation is reduced [16]. He et al. proposed a multiview sparse filtering (MVSF) method that can extract useful and complementary features in different views from the original current signals. These features and the features extracted from wavelet packet transform (WPT), empirical mode decomposition (EMD), stacked autoencoder, and DBN were imported into the SVM for fault recognition. The identification types included gear crack, wear, and plastic deformation. The subsequent results show that the features extracted by MVSF resulted in the highest recognition rate, 98.5% [5]. Xia et al. used ensemble empirical mode decomposition (EEMD) to denoise and reconstruct original vibration signals to extract significant fault features. They built an output–input–hidden feedback (OIHF) Elman neural network and used the AdaBoost-bagging double ensemble algorithm to optimize it. The method was used to identify the gearbox’s missing tooth and crack faults. The results show that the recognition accuracy of the method was 90.6%, higher than the other methods that used AdaBoost or bagging alone or did not use AdaBoost and bagging [17]. Zhong et al. proposed an improved Hilbert–Huang transformation (HHT) to extract fault features, and the method analyzed time-domain signals so that the features were more concise. The pairwise-coupled sparse Bayesian extreme learning machine (PC-SBELM) algorithm was used for recognition, and the missing tooth, crack and wear fault types were established. The method was compared with pairwise-coupled probabilistic neural networks (PC-PNN) and pairwise-coupled relevance vector machine (PC-RVM). The results of Zhong et al. show that the PC-SBELM had a shorter training time and higher recognition rate than PC-PNN and PC-RVM; the recognition rate was 93.92% [18]. Regarding fault diagnosis, Lu et al. proposed a classifier mixed with a genetic algorithm (GA) and SVM. The method was used to identify missing tooth and crack fault types and compare them with traditional SVM recognition rates. Their results show that the recognition rate of traditional SVM was 91.5%. Further, the recognition accuracy of the SVM optimized by GA was 98.7%. The advantage is that the GA-SVM had the SVM classifier of multi-class radial basis function (RBF) of the one-against-one (OAO) classification strategy, which could optimize the accuracy of classification to the maximum extent [19]. Mahmoud et al. developed an MGGASVM model based on GA optimization and a fuzzy logic (FL) model to identify the cracks, wear, surface fatigue, and plastic deformation of gears. The recognition rate of MGGASVM was 97%, and the recognition rate of the FL-based model was 96% [20]. The reference for gearbox fault models and recognition rates of the methods mentioned above are detailed in

Table 1. Literature review of gearbox fault detection methods and accuracy.

	Failure Types	Tooth- Missing	Gear Crack	Chipped	Wear	Surface Fatigue	Plastic Deformation	Accuracy Rate (%)
Methods
SAE-based SVM [15]		✔	✔	✔				89.3
DBN-DNN [15]		✔	✔	✔				85.3
CQPSO-DBN-LSSVM [16]			✔		✔		✔	98.54
MVSF+SVM [5]		✔			✔	✔		98.5
OIHF Elman AdaBoost-Bagging [17]		✔		✔				90.6
PC-SBELM [18]		✔		✔	✔			93.92
GA-SVM [19]		✔	✔					98.7
Fuzzy Logic [20]				✔	✔	✔	✔	96
MGGASVM [20]				✔	✔	✔	✔	97

.

Signals collected by vibration sensors during the operation of a wind turbine gearbox are susceptible to interference from other coupling units, e.g., blades, hubs, or generators. Noise signals generated by nearby components can often mix with the vibration signals of gearboxes so that the actual gearbox fault type cannot be identified. As a new signal analysis method, the SDP can fully describe the characteristics of signals so that subtle differences in input signals are more apparent. These subtle differences represent and allow for the detection of the essential features of any vibration signal, making input signals more favorable for analyses. When the amplitude of a characteristic signal is lower than the background noise, the SDP can extract the signal features effectively [21] and highlight them in a point symmetry graph. Referring to the above literature, most of the studies proposed their own feature extraction and recognition methods for wind turbine gearboxes. However, most of them identified data signals, and few studied image recognition. Furthermore, most of the said methods removed noise numerically before feature extraction. The SDP has good resistance to noise; the noise is eliminated while the data are made into an image, and the fault features can be extracted. CNN matches images and the topological structure of networks well, and the weight-sharing characteristic can reduce the complexity of network models. Therefore, this study used an accelerometer to measure the vibration signals to extract the gearbox fault features and proposed a hybrid algorithm of the SDP and CNN to identify the fault type of the gearbox. The gearbox fault types in this study included a normal gearbox (Type 1), a rusted gearbox (Type 2), a stripped gearbox gear (Type 3), a worn gearbox gear (Type 4), and an aged gearbox (Type 5). First, the accelerometer was installed on the gearbox to acquire a vibration signal. The captured signals were then filtered and imported into the SDP to draw a snowflake diagram [22,23,24]. Next, the snowflake diagram was led as a feature map in the CNN to identify the fault type of the signals. The SDP can visualize data and is highly sensitive. Even with a subtle change in data, the differences could be displayed in the exported image.

2. Research System Architecture

To measure the abnormal vibration signals induced by the failure of the gearbox, a small gearbox measuring table was designed referring to the large wind turbine architecture. The testing platform could test and analyze the vibration signals in the gearboxes with different faults. Figure 1 shows the research process for the overall system. First, the vibration signals of each faulty gearbox were measured. The signals were captured by a NI-9234 high-speed DAQ card. The captured vibration signals were filtered by fast Fourier transforms (FFTs) and imported into the SDP. The filtered fault vibration signal data were then plotted into a snowflake diagram. Finally, the fault type was identified by a CNN. The values were imported into SDP to transform the filtered vibration time-domain signal data into polar coordinates to draw a snowflake diagram. Next, the CNN model was built and trained. Finally, the gearbox fault type was identified by using the trained CNN model.

Fault Testing Platform

The gearbox fault testing platform constructed in this study is shown in Figure 2. A single-phase motor was used to drive the gearbox to simulate the blades driven by wind energy. The kinetic energy was transferred through the gearbox to the generator and exported by the generator as the load. Regarding the signal acquisition, the vibration signals of gearboxes were captured by vibration sensors.

To discuss the abnormal vibration when the wind turbine gearbox fails, five models were set up based on the gearbox fault testing platform in Figure 2, including a normal gearbox (Type 1) and four fault types of gearboxes (Type 2–Type 5). The vibrations induced by different faults in the gearbox were analyzed.

3. Gearbox Fault Design

3.1. Normal Gearbox (Type 1)

This study designed the gearbox referring to a large wind turbine structure, with the gear ratio of the gearbox being 1:12.25. HD 220 lubricating oil was used, and the entity and internal structure are shown in Figure 3. $Z_1, Z_2, Z_3, Z_4$ are the numbers of gear teeth of four gears. The rotation speed between the input and output shafts is expressed as Equation (1).

$$f_1=\frac{Z_2}{Z_1}{f}_2=\frac{Z_2}{Z_1}\frac{Z_4}{Z_3}{f}_3$$

(1)

3.2. Rusty Gearbox (Type 2)

When a wind turbine is operating for a long time in a harsh environment, particles and water intrude into the lubricating oil in the gearbox, thus deteriorating the lubricating oil and rusting the gears [7]. High moisture content can induce rupture of oil film, oil aging, corrosion, and rust. Therefore, gears in the gearbox were rusted in this study to simulate corrosion when the moisture content in the wind turbine gearbox lubricating oil is too high, as shown in Figure 4.

3.3. Stripping Gearbox (Type 3)

Due to the frequent occurrences of extreme wind speed, it is difficult to predict the wind speed variation in the wind field. An instantaneous extreme wind speed would result in complex dynamic responses inside the wind turbine, and a fast-changing wind speed would create instantaneous heavy torque on the gearbox, thus leading to stripping or fracture. Gear A and Gear D were damaged in this study to simulate the gearbox stripping induced by extreme wind speeds, as shown in Figure 5.

3.4. Gear Wear Gearbox (Type 4)

Lubricating oil was added to the inside of the gearboxes. However, the lubricant cannot completely separate the meshing teeth under the huge contact pressure as the metal surface of the gear directly rubs each other upon complete separation. Because the metal spalls under a heavy load would result in gear wear [25], the gears could not fully engage. Therefore, Gear A, Gear B, Gear C, and Gear D were burnished in this study to simulate the gear wear inside the gearbox, as shown in Figure 6.

3.5. Gear Aging Gearbox (Type 5)

Compared to other industrial gears, the wind turbine gearbox works in a small room at more than 60 m above the ground. Its volume and weight directly affect the installation and maintenance costs of wind turbines. It is difficult to repair wind turbine gearboxes, and the maintenance cost is high. As specified in CNS 15176-1, the design life of the gearbox of wind turbines should be at least 20 years. This study used a gearbox that has been used for more than 20 years as the aging model, as shown in Figure 7.

4. Research Methods

4.1. Gearbox Fault Vibration Signal Measurement

Five gearbox models with different faults were made in this study and tested on a 100 W wind power generation testing platform. The gearbox vibration was measured by the KS943B.100 vibration sensor. The measuring range was from −60 g to 60 g, and the sensitivity was 100 ± 5% mV/g. The vibration signals were captured by a NI-9234 high-speed capture card, and the maximum sampling frequency reached 51.2 kHz. There was a 32-bit resolution, and the vibration signals of this gearbox could be measured accurately.

4.2. Signal Processing

The wind turbine is a large and complex device and is easily disturbed by the ambient environment and electrical equipment while measuring vibration signals. Due to the difficulty in fault detection, the signals were filtered in this study using a bandpass filter after FFT. The power supply frequency interference below 60 Hz and the micro noise above 1.5 kHz were filtered out, and only the relatively apparent frequency signals between 60 Hz and 1.5 kHz were maintained, as shown in Figure 8.

The vibration signals of each gearbox were measured at a high speed of 300 rpm. The bandpass filter parameters used in this experiment are shown in

Table 2. Bandpass filter parameters.

Parameters Name	Parameters
low-pass cutoff frequency	15,175 Hz
High-pass cutoff frequency	63 Hz
center frequency	7619 Hz
bandwidth	15,112

.

4.3. Symmetrized Dot Pattern (SDP)

The SDP, as an algorithm, can map the time domain waveform to the symmetric space of points. The 2D scatter diagram is drawn in polar coordinates. The SDP can graphically describe the signal amplitude and frequency variation of time domain signals. The SDP calculates time domain signal data to find the positions of data in the polar coordinate space. The mirror symmetry image is drawn to display the variation between different vibration signals.

Even when there were subtle signal changes, there would be significant differences in the symmetric pattern of output. Figure 9 shows the image of normal gearbox vibration time-domain signals. The appearance has snowflake-like sextuple symmetry (also known as snowflake diagrams). The differences among different vibration signals can be visualized, and the SDP can process noise signals effectively. Figure 9 is the snowflake diagram of a normal gearbox.

The time-domain vibration signals of the gearbox were captured by the capturing system and transformed into a 2D feature image by SDP. Figure 10 shows the schematic diagram of SDP. The time-domain vibration signals of the gearbox were transformed in the polar coordinate space of point $P\left(\psi \left(i\right),\partial \left(i\right),\rho \left(i\right)\right)$, where $\psi \left(i\right)$ is the polar coordinate radius of the pattern; $\rho \left(i\right)$ is the initial angle line of clockwise rotation; and $\partial \left(i\right)$ is the initial counterclockwise rotation angle line, as expressed by Equations (2)–(4).

The gearbox time-domain vibration signal is $VI{B}_x=\left\{x_1,x_2,x_3,\dots ,x_i\right\}$, where $x_i$ is No. i sampling point in vibration time-domain signal $VI{B}_x$, and $x_{i+\Delta T}$ is No. $i+\Delta T$ sampling point of vibration time-domain signal after interval time $\Delta T$. The $x_i$ is substituted in Equation (2) to obtain the radius of $x_t$ from the image center in polar coordinates. The $x_{i+\Delta T}$ is substituted in Equations (3) and (4). $\partial \left(i\right)$ is the initial angle line of the clockwise rotation of $x_{i+\Delta T}$ in polar coordinates, and $\rho \left(i\right)$ is the initial counterclockwise rotation angle line of $x_{i+\Delta T}$ in polar coordinates.

$$\psi \left(i\right)=\frac{x_i-x_{min}}{x_{max}-x_{min}}$$

(2)

$$\partial \left(i\right)=\mathsf{\beta }-\frac{x_{i+\Delta T}-x_{min}}{x_{max}-x_{min}}J$$

(3)

$$\rho \left(i\right)=\mathsf{\beta }+\frac{x_{i+\Delta T}-x_{min}}{x_{max}-x_{min}}J$$

(4)

In the vibration time-domain signals of the wind turbine gearbox, if the vibration value at time $t$ is $x_t$, and the vibration value at time $t+\Delta T$ is $x_{t+\Delta T}$. $x_t$ and $x_{t+\Delta T}$ were substituted in Equations (2)–(4), respectively, and transformed into the points in the polar coordinate space. As a result, the snowflake feature map based on vibration signals can be generated by changing the rotation angle.

Wherein $x_{min}$ and $x_{max}$ are the minimum and maximum values of vibration signals, respectively. $\Delta T$ is the interval time, and the range is 1 to 10. $\mathsf{\beta }$ is the initial rotation angle. $J$ is the magnification of the rotation angle, generally smaller than the initial rotation angle $\mathsf{\beta }$. According to the test results, when $\mathsf{\beta }=60°, \Delta T=3, J=30$, the formed image was the optimal wind turbine gearbox vibration feature extraction map.

4.4. Convolutional Neural Network (CNN)

The vibration time-domain signals were transformed into a snowflake diagram by SDP, which was imported into the CNN as a feature map to identify the fault type. The CNN processed the data in the snowflake diagram to extract the features from the snowflake diagram for learning and training. CNN has been extensively used in image processing and classification for its good recognition accuracy.

The network model architecture of CNN varies with the eigenstructure of the image. The basic structure of CNN comprises multiple convolution layers, pooling layers, and fully connected layers. The picture features were extracted by loop computation of the convolution and pooling layers and classified by the fully connected layer. The classification result was exported. Figure 11 shows the network architecture of a CNN.

4.4.1. Convolution Layer

After importing the snowflake diagram into the CNN, the convolutional layer extracted the features. To extract the image’s feature map and enhance the features, the convolution layer used a filter or convolution kernels of different sizes for convolution operation, thereby achieving the effect of spatial filtering. The selection of the convolution kernel affects the feature extraction performance. For example, when a 3 × 3 convolution kernel is used for the convolution operation of a 6 × 6 image and each stride is 1, two corresponding grids are multiplied in each operation. The feature map is obtained after scanning and calculating all the pixels in the target image, as shown in Figure 12.

$$x_j^l=f({\displaystyle \sum }_{i\in M_j}{x}_j^{l-1}·W_{ij}^l+b_j^l)$$

(5)

$$f\left(x\right)=\max \left(0,x\right)$$

(6)

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

(7)

In Equation (5), $x_j^l$ is j elements of Layer 1; $x_j^{l-1}$ is an element of $M_j$; $M_j$ is the j-th convolution area of the $l-1$ layer feature map; $W_{ij}^l$ is the weighting matrix corresponding to the convolution kernel; $b_j^l$ is the deviation. Equation (5) is in the activation function. This study uses Rectified Linear Unit (ReLU) as an activation function to enhance the nonlinear characteristics of the network. Equations (6) and (7) are the operational mathematical expressions of ReLU, and Figure 13 is the curve of the ReLU function.

4.4.2. Pooling Layer

The function of the pooling layer is relatively simple as compared to the convolution layer. By compressing the image further, the dimension of each image could be reduced while maintaining important features. Thus, the overall system is more efficient and resistant to interference and can reduce over-fitting. After the CNN is provided with the pooling layer, the computation complexity of the whole network is reduced, and more attention is paid to the coincident features in the image. The general pooling methods are max pooling and average pooling. Like the convolution layer, the pooling layer uses the kernel to obtain the values of various image regions for operation, but it is free of the activation function. Figure 14 shows the max pooling operation process.

Max pooling was used as the pooling method in this study. The feature map from the convolution layer was filtered by n x n in the pooling layer and scanned in the stride of n. The maximum value was selected in each filter to the next layer, defined as Equation (8). In the rectangular region $R_{ij}, y_{kij}$ is the max pooling output of the k-th feature map, and $x_{kpq}$ is the element at (p,q) in $R_{ij}$.

$$y_{kij}=\underset{\left(p,q\right)\in R_{ij}}{\max }{x}_{kpq}$$

(8)

4.4.3. Fully Connected Layer

The fully connected layer is also known as the dense layer. The neural network is composed of flattened layers, hidden layers, and output layers. The output layer adjusts the weight and deviation to obtain the classification result. The fully connected layer has the most parameters due to the characteristics of a full connection. Like MLP, each neuron of the fully connected layer is connected to all the neurons of the previous layer so that the local information can be integrated with class discrimination in the convolution layer or pooling layer, as shown in Figure 15.

5. Experimental Results

There were five gearbox fault models in this study. With 300 vibration signals captured from each faulty gearbox, there were 1500 vibration signals in total. After SDP calculation, each fault model had 300 snowflake diagrams. There were 200 snowflake diagrams randomly selected from each fault model as training samples, and 100 diagrams were used as test samples. Therefore, the five fault types had 1000 training and 500 test samples imported into the CNN for fault recognition.

5.1. SDP

The measured fault model vibration signals of the wind turbine gearbox were imported into SDP for calculation. The snowflake images were drawn after the calculation of Equations (2)–(4). The snowflake diagrams of fault models are shown in Figure 16. The snowflake diagrams of different fault models show different appearances. Therefore, the snowflake diagrams of five fault types were imported into the CNN for training and recognition. The results were compared with other traditional algorithms to identify the performance.

5.2. CNN

The network model recognition of the CNN in this study is based on the snowflake diagram of the gearbox vibration signals. According to the actual test results, the network model had two convolution layers, two pooling layers, one fully connected layer, and a convolution kernel size of 1 × 1. ReLU activation function and max pooling as the filter of the pooling layer had the maximum recognition rate, as shown in Figure 17.

This study aimed to find a suitable CNN model for identifying the gearbox fault types, as shown in Figure 17. We selected different numbers of network layers, convolution kernel sizes, activation functions, and pooling methods to evaluate the optimal CNN model. The selection procedure is described below:

5.2.1. Network Layer Selection

First, this study used a 1 × 1 convolution kernel, activation function ReLU, and max pooling to evaluate the performance of different numbers of CNN layers. The snowflake diagrams drawn using SDP were identified from the network models with three layers (one convolution layer, one pooling layer, and one fully connected layer), five layers (two convolution layers, two pooling layers, and one fully connected layer), and to 17 layers (eight convolution layers, eight pooling layers, and one fully connected layer). The test results are shown in Figure 18. The results indicate that the training time increased with the number of network layers. The capability of CNNs for training data fitting was enhanced while the probability of over-fitting increased. Figure 18 indicates that the recognition performance was the best when there were five network layers. When the number of network layers was larger than five, the recognition rate decreased as the number of layers increased, and more training was required. Therefore, this study selected five CNN layers for the experiment.

5.2.2. Convolution Kernel Size Selection

The results in Figure 18 show how this study used five CNN layers, the activation function of ReLU, and max pooling to evaluate the performance of CNN models with different convolution kernel sizes. The convolution kernel sizes tested in this study were 1 × 1, 2 × 2, and 8 × 8. The test results are shown in Figure 19. The convolution kernel size significantly influenced the recognition capability of CNN models. A convolution kernel that was too small limited the ability of CNN models to search for picture features. If the convolution kernel were too large, there would be high computational costs. Figure 19 shows that the 1 × 1 convolution kernel resulted in the best accuracy and the least training time. As such, this study selected the 1 × 1 convolution kernel as the architecture for the CNN models.

5.2.3. Activation Function Selection

According to the above measurement results, the number of network layers of the CNN model was set as 5, the convolution kernel size was 1 × 1, and the pooling method was max pooling. Four activation functions, including tanh, Sigmoid, ReLU, and Swish, were used to evaluate the recognition performance of the CNN models. The test results are shown in Figure 20. The activation function could enhance the learning ability of CNNs. As shown in Figure 20, ReLU had the highest recognition rate and the least training time compared to the other three activation functions. Therefore, this study used ReLU as the activation function for the CNN models.

5.2.4. Activation Function Selection

According to the above measurement results, the number of network layers of the CNN model was set as 5, the convolution kernel size was 1 × 1, and the pooling method was max pooling. Four activation functions, including tanh, Sigmoid, ReLU, and Swish, were used to evaluate the recognition performance of the CNN models. The test results are shown in Figure 21. The activation function could enhance the learning ability of CNNs. As shown in Figure 21, ReLU had the highest recognition rate and the least training time compared to the other three activation functions. Therefore, this study used ReLU as the activation function for the CNN models.

This study’s CNN model for gearbox design used five network layers, a 1 × 1 convolution kernel, a ReLU activation function, and max pooling.

5.3. Result Comparison

The CNN network model recognition results of this study are presented in

Table 3. Test results of recognition methods.

Algorithm	Training Time (s)	Testing Time (s)	Epoch	Accuracy Rate (%)			Ranking
				0% Noise	10% Noise	20% Noise
SDP + CNN	46.52	0.0004	50	98.8	98.6	98.6	1
SDP + VGG16	353	0.0075	50	97.6	96.2	94	2
SDP + HOG + SVM	9.04	0.972	N/A	97.2	96.6	95.8	3
SDP + HOG + BPNN	174.11	0.359	10,000	96.8	93.6	89.6	4
SDP + HOG + ENN	2952	1.23	50	89	85.4	82.6	5
Chaos dynamic error scatter + CNN	49.2	0.0043	50	84	78.4	76.8	8
Chaos dynamic error scatter + VGG16	376	0.0057	50	84.4	83	78.2	7
Chaos dynamic error scatter + HOG + SVM	2.9787	0.0311	N/A	78.6	74.6	72.8	9
Chaos dynamic error scatter + HOG + BPNN	184.32	0.549	10,000	74.2	68.4	52.8	10
Chaos dynamic error scatter + HOG + ENN	3673	2.34	50	84.8	80.4	78.8	6

. This study’s proposed method was compared with the Lorenz e1e2 chaos dynamic error scatter diagram with four other algorithms: visual geometry group (VGG) 16, SVM [26], back propagation neural network (BPNN) [27], and edited nearest neighbor (ENN) [28]. The test data were mixed with 20% and 30% noises to conduct recognition tests.

From the feature extraction method perspective, in the case of the same recognition method, the SDP had a higher recognition rate than chaos dynamic error scatter diagrams. Regarding training time, the methods using SDP other than SVM had a shorter training time than chaos dynamic error scatter diagrams. The results indicate that the SDP could extract fault features effectively and increase recognition accuracy.

From the perspective of recognition methods, in the case of the same feature extraction method, CNN and VGG 16 had higher recognition rates than the other methods. The SDP with CNN had the highest recognition rate.

Typically, when the SDP or chaos dynamic error scatter diagram was used, the SVM needed the least training time. However, it had lower accuracy than CNN and VGG 16. The chaos dynamic error scatter diagram, combined with VGG 16, had a higher recognition rate than CNN. However, the recognition rate was lower than that of SDP with CNN. When the SDP or chaos dynamic error scatter diagram was used, the CNN had a shorter training time than VGG 16. Therefore, the method proposed in this study could extract fault features effectively, reduce the training cost and increase the recognition accuracy.

In this study, the training data of each model were increased to 300 and 400 for comparison. The test results are shown in Figure 22. The findings indicate that even if the total number of training data was increased to 2000, the recognition accuracy did not increase significantly. Figure 23 shows that the training curve of each model using 200 training data had converged before 50 iterations. The result indicates that 200 training data were enough for each model, and the benefit of increasing the training data was insignificant.

Figure 24 presents the recognition result of using 200 training data for training in the confusion matrix. The x-axis is the actual fault type, and the y-axis is the identified fault type. The red grids in the confusion matrix represent the number of misidentified types. The green grids represent the number of correctly identified types. Each fault type’s recognition accuracy and error rate were the green and red values in the x-axis light gray grids. The overall fault type recognition accuracy and error rate were the green and red values in the dark gray grids in the lowest right portion of Figure 24. The overall fault type recognition accuracy was calculated by dividing the total value of green grids by the total value of green and red grids. In Figure 24, 97 out of 100 test data of Type 2 were identified correctly; the recognition rate was 97%. Similarly, the recognition accuracy rates of Type 1, Type 3, Type 4, and Type 5 were 100%, 100%, 99%, and 98%, respectively. The calculated total recognition accuracy was 99.8%.

This study compared the Lorenz e1e2 chaos dynamic error scatter diagram and SDP feature extraction methods, where 10% and 20% noise were added to the test data, respectively. Figure 25 shows the recognition variation curves of the methods. The decreasing amplitude of the recognition rate was observed to be smaller after the noise was added when the SDP was used for feature extraction. The decreasing amplitude of the recognition rate was larger after the noise was added in when the Lorenz e1e2 chaos dynamic error scatter diagram was used as a feature map. The data comparison showed that the chaos dynamic error scatter diagram was likely to be influenced by noise, and the SDP had better resistance to noise.

6. Conclusions

This study proposed an SDP + CNN diagnostic method for wind turbine gearbox fault diagnosis. For five common fault types of gearboxes, the vibration signals were made into snowflake diagrams by SDP, which were used as training samples. Finally, they were imported into the CNN to analyze the gearbox state. Additionally, the recognition result of the CNN was compared with four algorithms, namely VGG16, SVM, BPNN, and ENN. According to the actual measurement result, the proposed method had the highest recognition accuracy of 98.8%. It was proven that the proposed method could extract the gearbox fault features effectively and increase the accuracy of gearbox fault diagnosis. The method can be used for diagnosing the faults in other components of wind turbines, such as generators, bearings, or power conversion systems, in the future.