Fault diagnosis method of wind turbine planetary gearbox based on improved CNN

Abstract

When wind turbines operate in complex environments, planetary gearboxes easily generate faults that will lead to increased wreck of the equipment or transmission failures. In this paper, a CNN model with adaptive parameters is proposed to realize the identification of planetary gearbox faults and improve the real-time performance and accuracy of fault diagnosis. Firstly, Ensemble Empirical Mode Decomposition (EEMD) is applied to scale the one-dimensional signal to solve the modal mixing problem of input data. Gramian Angular Difference Fields (GADF) is used to convert the processed data into images as the input of CNN model. Secondly, to capture more information and reduce the risk of overfitting, two convolutional neural networks incorporating different activation functions are connected in parallel to propose a multilayer CNN model structure. Additionally, Pied Kingfisher Optimization algorithm (PKO) is improved by integrating Tent chaotic mapping, second-order optimization and simulated annealing algorithm to optimize the multilayer CNN model automatically. Finally, the experimental results show that this improved model achieves real-time diagnosis due to the adaptive parameters, the diagnosis accuracy exceeds 95% under the same proportion of samples, and over 85% under the different proportions of samples. This approach significantly enhances planetary gearbox fault identification reliability.

Introduction

Due to the complexity of operation and the intensity of work, the gearbox in wind turbines is one of the components with the highest failure rate during operation. As service time increases, various types of damage or failures are inevitable. During the duty cycle of wind turbines, drivetrain problems often lead to long downtime. Inadequately repaired gearboxes will also affect the safety of wind turbines, so analyzing the condition of the gearboxes is critical to the operation of the overall system. Meanwhile, during the operation of wind turbines, due to the strong coupling relationship¹, the load on the gearbox will be increased, thereby raising the likelihood of failure. In this context, the wind turbine gearbox structure must be designed with enhanced stability.

At present, data-driven methods are widely used to deal with the problem of mechanical diagnostics². Yu et al.³ proposed a neural network diagnosis method based on EMD to extract different frequency band energies as features, which can accurately and efficiently identify rolling bearing failure modes. Tang et al.⁴ proposed a novel wind turbine gearbox fault diagnosis method based on flow learning and Shannon wavelet support vector machine, which has nonlinear dimensionality reduction capability. Tang et al.⁵ also proposed a fault diagnosis method for wind turbine gearbox based on undersampling, XGBoost feature selection and improved whale optimization random forest. This method has false negative rate (FNR) of with good diagnostic results. Fu et al.⁶ chose the XGBoost method to establish a fault early warning model, which can monitor the generator winding in real time. Ma et al.⁷ proposed a gearbox fault diagnosis model based on Enhanced Hierarchical Diversity Entropy (EHDE) optimized Support Vector Machine (SVM), which solves the defects of the existing methods that are sensitive to the data length. Abdul et al.⁸ proposed SVM model based on Mel frequency cepstrum coefficients (MFCC) and Gammatone cepstrum coefficients (GTCC) in order to improve the diagnostic accuracy. However, the above-mentioned intelligent fault diagnosis methods are all based on traditional machine learning models⁹, which require a series of manual feature extraction as inputs. Due to its complex structure, long drive chain and high background noise environment, planetary gearboxes are prone to aliasing between fault features. Using the above model for planetary gearbox fault diagnosis may exhibit low accuracy.

In order to avoid the problems caused by manual feature extraction, deep learning has gained increasing attention from researchers in various fields¹⁰. It uses a hierarchical structure of multiple neural layers to extract information from the input data layer by layer and learn useful features layer by layer. The advantage of this feature learning ability just meets the requirements of an adaptive feature extraction method in mechanical fault diagnosis. Xu et al.¹¹ proposed a one-dimensional fully decoupled network to diagnose planetary gearbox faults. But its hyperparameters can only be set manually, which can take a lot of time. Wang et al.¹² proposed a fault diagnosis method combining empirical wavelet transform and streamlined regularized limit learning machine. In order to obtain good gearbox fault diagnosis results. Luo et al.¹³ used a deep residual contraction network model for fault diagnosis, which can achieve a high accuracy rate. Yang et al.¹⁴ proposed a multilayer limit learning CNN model for feature recognition and classification, demonstrating the importance of augmenting data with 2D features. In order to suppress the external noise, Liu et al.¹⁵ proposed a fault diagnosis model with multidimensional fused residual attention network, which demonstrated robust noise immunity under different noise levels, with a diagnostic accuracy of up to 93.91%. However, because there are too many parameters that the model needs to optimize during the learning process and the internal structure of the planetary gearbox is complex. Its harsh operating environment may lead to strong non-stationarity of the acquired vibration signals, making faults difficult to identify. Therefore, using raw vibration signals or time-frequency representations as inputs to the model may not be good enough for accurate diagnosis of nonlinear and unstable signals.

In order to solve the above problems, an improved convolutional neural network (CNN) + EEMD + GADF method is proposed in this paper. Firstly, the mathematical model of the planetary gearbox fault vibration signal is introduced to provide a theoretical basis for the fault signal generation mechanism. Secondly, the basic principles of CNN and its applicability in fault diagnosis are described. Then to overcome the nonlinear and non-stationary features in the vibration signals, EEMD is used to decompose the non-stationary vibration signals. GADF method is utilized to convert the processed new fault signal into a two-dimensional image to weaken nonlinearity of the signal. In Sect. 5, a multiple convolutional neural network model (PCNN) is built to explore the internal features of the faulty planetary gearbox using the above image data as input to the model. Finally, the improved Pied Kingfisher optimization (SPKO) algorithm is used to optimize the model parameters, so as to improve the diagnostic accuracy. The research results verify the effectiveness of the method in the fault diagnosis of planetary gearbox.

Mathematical model of planetary gearbox fault signal

A planetary gearbox¹⁶ typically consists of a sun gear, multiple planetary gears, an annular gear, a planetary carrier, and planetary bearings, as shown in Fig. 1. It rotates not only around its own axis, but also around the axis of the sun gear. Unlike fixed-shaft gearboxes¹⁷, the vibrations caused by the meshing of multiple pairs of planetary gearboxes are superimposed on each other. This makes the overall vibration response more complex. The gear failure rate is as high as 60%. It is the core research object of planetary gearbox inspection.

Fig. 1.

Planetary gear set structure diagram.

In order to make planetary gearbox faults easier to analyze and diagnose, it is necessary to establish a mathematical model of the fault vibration signal¹⁸. Firstly, the meshing point is analyzed, and a theoretical mathematical model of the vibration signal is established, as shown in Eq. (2.1).

2.1

where: is a fault amplitude modulation signal;is a fault frequency modulation signal; k is the order of the fault; is the meshing frequency; is the initial phase.

To simplify the analysis, the frequency doubling component in Eq. (2.1) is not considered, and the simplified signal model is shown in Eq. (2.2).

2.2

where: is the characteristic frequency of the local fault; , are the initial phase; A is the amplitude modulation coefficient of the planetary wheel; B is the frequency modulation coefficient of the planetary wheel. When a local failure occurs in the planetary gearbox, the planetary wheel engages simultaneously with both the sun wheel and the internal gear ring, rotating around the center of the sun wheel and the internal gear ring. The planetary frame will have a periodic amplitude modulation effect on the vibration signal because of the change in the position of the sensor during rotation. Consider the amplitude modulation effect in the signal model of formula (2.2), can establish a simplified model of the vibration signal of the planetary wheel local failure as

2.3

where: is the rotation frequency of the planetary carrier; is the characteristic frequency of the local fault of the planetary wheel, as shown in Eq. (2.4).

2.4

where: is the number of teeth of the planetary wheel. Based on the above theoretical basis, the planetary gearbox vibration signals were acquired by the experimental setup.

Convolutional neural network structure

Convolutional Neural Networks¹⁹ is one of the most widely used deep learning models for machine health monitoring because of its ability to discover patterns hidden in the input data. It is a feedforward neural network that includes convolutional computation and has a deep structure. Convolutional neural networks use convolutional kernels to scan input data and identify features based on specific rules. One of the distinguishing features is weight sharing, where the same convolutional kernel is reused on different input samples, reducing the number of parameters that need to be trained. In the process of information extraction, the layer-by-layer transmission between networks forms a multi-level feature map. This characterizes the representative high and low frequency features. As the number of network layers increases, deeper, more detailed, and more complete features will be efficiently extracted. These features are often difficult to capture with simple linear analysis.

As shown in Fig. 2, the structure of a CNN model generally includes an input layer, a convolutional layer, an activation function, a pooling layer, a fully connected layer, and an output layer. Due to the high nonlinearity and non-stationarity of the vibration signal data, there is a lot of redundant information. In order to capture richer data information and at the same time reduce the model runtime, the input data are processed using EEMD and GADF method, respectively.

Fig. 2.

Convolutional neural network model structure.

Data processing based on EEMD and GADF

Unstable signal processing based on EEMD

For planetary gearbox vibration signals with unstable characteristics, EEMD has good adaptability and decomposition accuracy. EEMD is to inject random noise of different intensities into the original signal to address the modal interference encountered during signal separation. Subsequently, the stable Intrinsic Mode Function (IMF) is extracted by iterating the decomposition process and averaging the results to more accurately capture key features of the signal. This provides effective solution for unstable signal processing. The decomposition steps of the EEMD method are as follows.

Step1: Set the number of decomposition M.

Step2: White noise with a standard normal distribution is added to the original signal to produce a new signal as in Eq. (4.1).

4.1

Step3: The EMD decomposition of the signal containing noise is performed to obtain the respective IMF and residual.

Step4: Repeat step2 and step3 M times, adding random white noise signals to each decomposition to obtain M sets of IMFs.

Step5: Based on the principle that the statistical mean of uncorrelated sequences is zero, the corresponding IMFs described above are subjected to an ensemble averaging operation to obtain the final IMF of the EEMD decomposition. As in Eq. (4.2).

4.2

Nonlinear signal processing based on GADF

In order to weaken the nonlinearity of the data, reduce the noise and improve classification accuracy, GADF method is used to generate an image of the processed new fault signal as an input to the CNN. Gramian Angular Field (GAF)^20,21 considers each data point in 1D time series data as a point in a vector space. By calculating the cosine value of the angle between these points, which is then mapped onto the pixels of a 2D image. Thus, images that reflect the dynamic and periodic characteristics of the time series are generated. This approach allows time series data, which would otherwise be difficult to use directly for image processing, to be transformed into a form suitable for image analysis.

For a time series , GAF diagram can be obtained by the following steps. First, using the min-max calibrator, the original time series data are scaled to [−1,1] as shown in Eq. (4.3):

4.3

The data obtained above are then transformed in polar coordinate system to obtain the radius and angle corresponding to each data point as shown in Eq. (4.4).

4.4

In particular, GADF is used to extract the temporal correlation in different time intervals by calculating the angular difference between each point after transforming a one-dimensional time series to a polar coordinate system²⁶. GADF is defined as shown in Eq. (4.5):

4.5

Where: I is the unit row phase [1, 1, …,1]; and is the row vector of the sequence before and after scaling; {i = 1, 2, …, n}is the angle between the two phases. Strongly nonlinear data is encoded with GADF to form images with great sparsity. This eliminates multimodal redundant information. Therefore, using GADF images as input to the CNN improves planetary gearbox fault diagnosis accuracy.

PCNN structure based on improved SPKO algorithm

Multilayer convolutional neural network architecture

Multi-layer convolutional neural network is a combination of multiple convolutional neural networks, which are generally connected in series or parallel, or in series and parallel. A convolutional neural network that combines these connections can integrate the unique features of each to obtain the relationship between samples and pixel points in the original data.

In order to reduce the risk of overfitting, this paper connects two convolutional neural networks in parallel. The two networks respectively add the Relu activation function and Leaky Relu activation function²² with different parameter settings. Among them, Relu activation function and Leaky Relu activation function can solve the problem of gradient disappearance to a certain extent and accelerate the convergence speed of the network. By using different activation functions, the two branches extract features in slightly different ways²³. Allowing the model to understand the data from multiple perspectives and learn more diverse feature representations. PCNN can capture richer information than a single-channel CNN, thus improving the model performance and recognition accuracy. In this paper, the vibration signals under five states of health, broken tooth, wear gear, crack and missing tooth are used as inputs to the PCNN model, and the categories are used as outputs to identify the planetary gearbox faults. The structure of applying EEMD and GADF data processing methods to the multilayer convolutional neural network model is shown in Fig. 3.

Fig. 3.

PCNN model based on EEMD and GADF.

Improved pied kingfisher optimization algorithm

PKO is a novel population-based meta-heuristic algorithm proposed by Abdelazim et al. in 2024²⁴. It draws inspiration from the unique hunting behaviors and symbiotic relationships of pied kingfishers observed in nature. The PKO algorithm is built around three distinct phases: perching/hovering prey, diving prey, and fostering symbiotic relationships. These behavioral aspects are translated into mathematical models that can efficiently solve various optimization challenges in various search spaces.

To improve the algorithm’s local optimization ability and accelerate the convergence speed of the algorithm, tent chaotic mapping²⁵ and second-order optimization methods are used to perform mutation operations on the current optimal solution to improve the global optimization ability of the algorithm. To prevent the algorithm from becoming trapped in a local optimum, the idea of probabilistic glitching in the simulated annealing algorithm²⁶ is introduced.

The improved PKO algorithm has accelerated convergence speed and significantly improved global optimization seeking ability. SPKO algorithm can meet the requirements of CNN parameter optimization. The specific steps of the improved SPKO algorithm can be described as follows.

Step1: Initialize the algorithm parameters, the size of the pied kingfisher population, the dimensionality of the search space, the upper and lower bounds of the space, the maximum number of iterations, and the jump factor.

Step2: Tent chaotic mapping is used to initialize the population, to enhance and improve the quality of the distribution of the initial population over the search space.

Step3: Calculate the fitness value for each pied kingfisher and sort the resulting fitness values to find the current optimal solution.

Step4: For each individual in the population, based on its fitness value and perched hovering behavior to update its location.

Step5: The current global optimal individual is selected as the initial point of Broyden-Fletcher-Goldfarb-Shanno (BFGS)²⁷. Use the BFGS method in second order optimization to optimize the problem . is the global optimal individual at the iteration t. Local optimization of from is performed using BFGS. The better solution is obtained for updating the position and fitness values.

Step6: Incorporate the idea of probabilistic jumps in simulated annealing algorithms to prevent the pied kingfisher population from falling into a local optimum.

Step7: Check if the termination condition is met. If not, return to Step3 to continue the iterative search, if satisfied, stop iterating and output the current optimal solution.

To verify the effectiveness of the SPKO, we conduct simulation experiments using four standard benchmark functions, as shown in Table 1. It is also compared with the Pied Kingfisher optimization algorithm, the commonly used Grey Wolf Optimizer (GWO)²⁸ and the new 2023 algorithm, Rime optimization algorithm (RIME)²⁹.

Table 1.

Benchmark function.

Test function	dim	Search scope	Optimum value
	30	[−30,30]	0
	30	[−100,100]	0
	30	[−50,50]	0
	4	[−5,5]	0.1484

Set the initial parameters of the algorithm with an overall size of 50 and a maximum number of loop iterations of 1000. All the test functions are run independently under the same conditions for 30 times, and then the experimental results are summarized in Table 2. Among them, the average and variance represent the convergence accuracy and stability of different algorithms, respectively.

Table 2.

Comparison of benchmark test results.

function	dim	algorithm	optimum value	minimum value	average	variance
f1	30	GWO	1.15e + 08	2.80e + 08	5.46e + 07	9.46e-01
		RIME	2.90e + 01	2.11e + 05	8.32e + 03	4.11e + 06
		PKO	2.71e + 01	1.88e + 08	4.11e + 06	6.30e + 04
		SPKO	2.34e + 01	1.92e + 04	1.24e + 02	7.06e-01
f2	30	GWO	2.61e + 04	6.35e + 05	5.81e + 05	8.68e + 02
		RIME	7.50e + 00	5.35e + 05	1.10e + 04	1.35e-01
		PKO	6.95e-05	−0.55e-01	−4.30e-02	2.30e-06
		SPKO	2.33e-05	−0.50e-01	−5.08e-02	7.29e-07
f3	30	GWO	3.13e + 08	1.11e + 09	1.57e + 09	2.94e + 02
		RIME	1.67e-00	3.30e + 00	1.30e + 01	6.67e-06
		PKO	1.10e-09	−1.00e-00	−2.04e-00	4.98e-09
		SPKO	4.45e-10	−1.00e-00	−1.00e-00	2.05e-09
f4	4	GWO	2.04e-02	−5.00e-00	2.42e-01	1.29e + 01
		RIME	9.88e-02	−4.71e-00	2.14e-01	1.02e + 01
		PKO	1.20e-03	−2.71e-00	−3.58e-01	1.86e-00
		SPKO	3.08e-04	1.93e-01	1.61e-01	9.92e-04

From Table 2, it can be concluded that compared with other algorithms, SPKO algorithm has better convergence accuracy and stability on the test functions f1, f2, f3 and f4. The goal of using the SPKO algorithm is to reduce the classification error by optimizing the parameters, learning rate, batch size, and L2 regularization coefficient of the CNN model.

Case analysis

In this paper, we use the publicly available planetary gearbox dataset as the source data³⁰. A faulty planetary wheel is used to replace the original normal planetary wheel in the simulation experiment. Vibration data is collected by a Sinocera CA-YD-1181 accelerometer. The sample rate for all channels is set to 48 kHz. The detailed parameters of the planetary gearbox and the relationship between the two critical fault-related frequencies and the input shaft frequency are listed in Table 3.

Table 3.

Planetary gearbox parameters.

Sun gear	Ring gear	Planet gear (number)	Meshing frequency	Fault frequency of sun gear
28	100	36(4)	(175/8)	(25/8)

In this study, only the first channel of the planetary gearbox vibration signal is used to test the performance of the proposed method to PCNN + EEMD + GADF + SPKO. The vibration signals in five states, such as health, broken tooth, wear gear, crack and missing tooth as inputs to this model and the classification as outputs. The diagnostic process of planetary gearbox fault signal is shown in Fig. 4.

Fig. 4.

Planetary gearbox fault signal diagnosis.

CNN input processing based on EEMD and GADF

The dataset contains five types of vibration signals: health, broken tooth, wear gear, crack and missing tooth. The EEMD method is used for signal decomposition. Broken tooth fault and cracked fault are taken as case studies and the results of decomposition of these two fault types using EEMD technique are shown in Fig. 5.

Fig. 5.

EEMD decomposition results of broken tooth fault (a) and cracked fault (b).

As can be seen in Figs. 5 and 10 IMFs³¹ with different periods are generated. The majority of the IMF components turned out to be stationary signals, oscillating around a zero mean. The EEMD efficiently converts the nonlinear series into multiple steady-state time series. Converting the above processed fault signals into GADF images as input to the CNN retains all fault information and preserves connections between signals at different time intervals. Therefore, GADF is suitable for processing planetary gearbox fault vibration signals with time-varying characteristics. To ensure that all the vibration samples collected by the vibration sensor contain at least one complete fault cycle, 2000 sampling points are taken as one sample. After GADF processing, the fault signals obtained in five states: health, broken tooth, wear gear, crack and missing tooth, as shown in Fig. 6. Each category has 3000 samples.

Fig. 6.

Category 5 fault signaling GADF diagram.

The vibration signals are processed using EEMD and GADF methods and then input into the CNN model for comparison of fault diagnosis accuracy. The comparison result is shown in Fig. 7.

Fig. 7.

Comparison of diagnostic accuracy with and without data processing.

As can be seen in Fig. 7, the vibration signals are decomposed using the EEMD method and are converted to 2D images using the GADF method. The raw signals are processed so that there is an improvement in the accuracy of fault diagnosis, proving the effectiveness of the method proposed in Sect. 4.

Fault prediction results for multilayer CNN

Comparative experiments with the same proportion of samples

There are 3000 samples for each type of fault data, and 70% of the data segments are randomly selected as the training dataset, while the other 30% are used for testing. To ensure the accuracy of the experiments, each set of experiments is repeated for five rounds and the final results are averaged. The results are shown in Table 4, where the optimal results are marked in bold.

Table 4.

Comparison of diagnostic results for the same proportion of samples.

Methods	1	2	3	4	5	average
CNN Accuracy (%)	87.67	87.32	86.84	87.10	87.12	87.21
PCNN Accuracy (%)	91.80	90.64	90.80	91.67	90.21	90.88

From Table 4, it can be seen that the CNN model has low diagnostic performance with an accuracy of only 87.21%. The diagnostic result of PCNN is 90.88%, which is higher than the CNN model. It shows that the parallel structure improves the diagnostic accuracy. The test set confusion matrices of the CNN and the PCNN models with diagnostic accuracies are shown in Figs. 8 and 9.

Fig. 8.

CNN Model Test Set Confusion Matrix and Diagnostic Accuracy.

Fig. 9.

PCNN Model Test Set Confusion Matrix and Diagnostic Accuracy.

In order to observe whether the PCNN model is overfitting, the learning curve³² needs to be analyzed as in Fig. 10.

Fig. 10.

Loss and accuracy curve of PCNN Model.

As can be seen in Fig. 10, both the loss function and the accuracy curve converge in the region after 30 iterations. The loss function value is about 0.04. The accuracy is about 91%. There is no overfitting.

Comparative experiments with samples of different proportions

In order to test the universality of the method in this paper, experiments are carried out on different proportions of data samples. According to the frequency of occurrence of different types of faults in gearboxes, sampling with 4:2:2:1:1. The experimental data set is divided into 3,000 groups for the normal state, 1,500 groups for the broken tooth state, 1,500 groups for the wear state, 750 groups for the crack state, 750 groups for the missing tooth state. The training set and test set are randomly divided in the ratio of 7:3. In order to avoid experimental chance, each group repeats the experiment 5 times and then takes the average. The diagnostic results are shown in Table 5.

Table 5.

Comparison of diagnostic results for different proportions of samples.

Methods	1	2	3	4	5	average
CNN Accuracy (%)	80.20	81.64	82.76	81.11	82.41	81.42
PCNN Accuracy (%)	87.42	86.21	83.67	85.00	86.10	85.68

As seen in Table 5, the diagnostic accuracy of the PCNN model is 85.68%, which is an improvement of about 4% compared to the CNN. Under different sample ratios, the multilayer convolutional neural network still shows superior performance than the traditional convolutional neural network. The test set confusion matrix and diagnostic accuracy of CNN and PCNN models are shown in Figs. 11 and 12. In order to further improve the accuracy and robustness of planetary gearbox fault identification, the SPKO algorithm is used to improve and optimize the hyperparameters of the PCNN model.

Fig. 11.

CNN Model Test Set Confusion Matrix and Diagnostic Accuracy.

Fig. 12.

PCNN Model Test Set Confusion Matrix and Diagnostic Accuracy.

In order to observe whether the PCNN model under unbalanced data is overfitted or not, the learning curve needs to be analyzed, as shown in Fig. 13.

Fig. 13.

Loss and accuracy curve of PCNN Model.

As can be seen in Fig. 13, both the loss function and the accuracy curve converge in the region after 30 iterations. The loss function value is about 0.07. The accuracy is about 86%. There is no overfitting.

Model optimization based on SPKO algorithm

The initial parameters of the PKO and SPKO algorithm are set with an overall size of 3 and a maximum number of loop iterations of 5, which are used to optimize the hyperparameters, learning rate, batch size, and L2 regularization coefficient in the convolutional neural network model. Then experiments are conducted on the same proportion of 15,000 samples and different proportion of 7,500 samples, respectively. The training and test sets are randomly divided in the ratio of 7:3. In order to avoid experimental chance, each set is averaged after repeating the experiment five times. The final diagnostic results are obtained as shown in Table 6, where the optimal results are marked in bold.

Table 6.

Diagnostic results of PCNN model based on improved PKO algorithm.

	Methods	1	2	3	4	5	average
Same proportion of samples	PKO-PCNN Accuracy (%)	92.23	90.69	92.78	91.19	93.51	92.08
	SPKO-PCNN Accuracy (%)	96.10	96.00	95.40	96.21	95.98	95.94
Sample of different proportions	PKO-PCNN Accuracy (%)	84.56	84.30	85.63	88.21	86.70	85.88
	SPKO-PCNN Accuracy (%)	90.24	90.67	89.98	89.41	89.40	89.94

The diagnostic accuracy of the proposed method SPKO-PCNN with balanced samples is 95.94%, which is higher than that of PKO-PCNN model. SPKO-PCNN still has more than 85% diagnostic accuracy under different proportions of samples. It indicates that SPKO-PCNN is able to diagnose faults in the case of lack and imbalance of data samples for the reduction of data samples. At the same time, the SPKO algorithm is used to learn the model parameters, and the fluctuation of the fault recognition accuracy is relatively small due to the robustness of the SPKO algorithm itself. The SPKO-PCNN model is used for diagnosis with the same proportion of samples, and the results are compared with previous studies, as shown in Fig. 14.

Fig. 14.

Comparative results with other studies.

As can be seen in Fig. 14, the diagnostic accuracy of the SPKO-PCNN model is higher than the literature^33–36. The SPKO-PCNN method adopted in this paper can effectively improve the accuracy of planetary gearbox fault identification. It meets the requirements of fault diagnosis in practical applications.

Conclusions

For the complex working conditions and signal non-stationarity challenges faced by wind turbine planetary gearbox fault diagnosis. The traditional CNN is difficult to fully extract the deep features and the subjectivity of parameter selection, resulting in poor diagnostic accuracy. In order to solve the above problems, a comprehensive diagnosis method that integrates signal processing, deep learning model improvement and intelligent optimization algorithm is proposed in this paper. The key contributions of this paper are as follows: (1)To address the problem of modal aliasing in the original vibration signals, EEMD method is used to separate the scale of the signals. And the GADF method to transform the processed 1D time series into 2D image, which improves the interpretability of the data. (2)The PCNN model is designed, and the two branches introduce ReLU and Leaky ReLU activation functions respectively. In order to achieve differential modelling of the feature space with different characteristics, and enhance the generalization ability of the model. (3)The SPKO algorithm is proposed. It incorporates the randomness of Tent chaotic mapping, the fine-tuning ability of BFGS optimization method and the probabilistic glitching mechanism in simulated annealing algorithm. The efficient search and global optimization of the hyperparameters of the PCNN model are achieved. The results show that the diagnostic accuracy is continuously stabilized at a high level in the validation of the same proportion of samples and different proportions of samples, which meets the fault diagnosis needs of floating wind turbine planetary gearboxes in the ideal environment of actual operation.

Author contributions

Chenhua Xu: Writing–review, editing, Conceptualization, Funding acquisition. Dan Liu: Writing–original draft, Software, Methodology, Formal analysis, Conceptualization. Jian Cen: Data curation, Funding acquisition. Jianbin Xiong: Data curation, Resources. Na Wang and Xi Liu: Data curation, Supervision.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.