Diesel engine small-sample transfer learning fault diagnosis algorithm based on STFT time–frequency image and hyperparameter autonomous optimization deep convolutional network improved by PSO–GWO–BPNN surrogate model

2.1 Time–frequency image generation

In the fault diagnosis process, the original equipment generally collects 1D signals, but the input type of the deep network model is generally a 2D matrix or a 3D red green blue (RGB) picture sample. The two types of convolutional networks in this article both take pictures as input, so it is necessary to convert 1D vibration signals into 3D image data. One conversion method is to directly intercept the vibration signal at equal intervals and reorganize it into a 2D matrix, which is then saved as a three-dimensional image; however, this method cannot reflect the frequency domain characteristics of the signal; another method is based on the time–frequency domain transform, which mainly includes STFT, continuous wavelet transforms, and Hilbert–Huang transform. Ahmad Taghizadeh-Alisaraei and Mahdavian [35] comparatively analyzed the effectiveness of four time–frequency representation methods, Welch test, STFT, WVD, and Choi–Williams distribution, in diesel injector fault detection. It has been verified by experiments that in the real-time performance monitoring of the engine, the STFT technology is more effective for the fault diagnosis and knock detection of fuel nozzles. In the process of studying the combustion characteristics of diesel engines for biodiesel fuel, Siavash et al. [36] found that STFT can effectively analyze the time–frequency information of noise other than effective acoustic signals such as piston flapping and outlet valve closing during diesel combustion.

Therefore, the STFT that is more suitable for analyzing the time–frequency characteristics of diesel engine fault signals is selected to generate time–frequency image samples. The basic idea of STFT is to localize the integration interval of the FT of the time-domain signal of the device. Suppose there is a continuous signal y(t), which can be expanded in the complete quadrature signal space as [37],

Eq. (1) is the definition of FT, which is used to convert the signal from the time domain to the frequency domain. ω represents frequency, t represents time, and e^−jwt is a complex function. The sufficient condition for the establishment of the formula is: in the infinite interval, y(t) is integrable, which is

For the nonstationary vibration signal of the diesel engine cylinder head, it is necessary to use a window function to intercept the signal to limit the time domain range of the transformation so that the intercepted samples are within a certain frequency range. Then, the FT operation is performed on the signal after the windowing, and finally, the signal after the operation is superimposed, that is, the STFT is performed on the signal. The definition formula of STFT is as follows:

where f(t − τ) is the window function and τ is the center of the window function. The frequency obtained after STFT can be regarded as the instantaneous frequency at that point [38].

In MATLAB, after the signal is subjected to STFT operation, the result is directly saved as a three-channel color time–frequency diagram of RGB. In this way, time–frequency picture samples of the vibration signal of the cylinder head at different faults of the diesel engine can be obtained.

2.2 Transfer learning

In recent years, transfer learning has been widely used as a frontier field of deep learning. The main idea is to use existing (source domain) knowledge to solve problems in different but related domains (target domain). Therefore, it relaxes the stringent requirements of traditional machine learning that require a large amount of data as training samples [39,40].

Transfer learning is defined as follows: given a source domain D s = { X s , P ( X s ) } and a learning task T s { Y s , f s ( ⋅ ) } , a target domain D t = { X t , P ( X t ) } and a learning task T t { Y t , f t ( ⋅ ) } . Its purpose is to acquire knowledge in the source domain D s and learning task T s to help improve the learning of the prediction function in the target domain, where D s ≠ D t and T s ≠ T t [41]. Figure 1 shows the schematic of transfer learning.

Figure 1

Schematic diagram of transfer learning.

In terms of technical means, transfer learning can be divided into instance-based transfer learning, feature-based transfer learning, association rule-based transfer learning, and parameter-based transfer learning. Instance-based transfer learning improves the effect and robustness of transfer learning by adjusting the weights of the parts in the source domain that are more similar to the target domain; feature-based transfer learning attempts to construct a feature subspace, which integrates the shared latent feature factors of the source domain and the target domain, which can reduce the feature difference between the two and enhance the transferability of knowledge; The purpose of transfer learning based on association rules is to find potential connections between the source domain and the target domain, focusing on the study of transferability; Parameter-based transfer learning reduces the differences between domains. The idea is to use a large amount of source domain data to train a model and then use a small amount of target domain data to fine-tune the deep parameters of the model under the transfer learning strategy of shallow parameter freezing and deep parameter learning. Make the parameters of the deep network layer more in line with the classification characteristics of the target domain data [42].

This article adopts a parameter-based transfer learning method. The source domain knowledge is a sufficient number of ImageNet datasets, and the target domain is the time–frequency image samples of diesel engine cylinder head vibration signals. The network models are the AlexNet convolutional network and the ResNet-18 convolutional network. The migration strategy uses the freezing of the shallow network layer and the fine-tuning of the deep network layer. This approach eliminates the need for end-to-end training of the network model and the computation and reversed iteration of the difference metric between the source and target domain data at each iteration. Only a small number of samples are needed to fine-tune the deep classification parameters of the network so that the classification layer has the edge distribution characteristics of the target domain data. Then, use the deep feature extraction ability of the network to distinguish the subtle differences between the pictures to distinguish the subtle differences between the time–frequency images under different faults of the diesel engine and achieve the purpose of quickly classifying faults under the condition of small samples of equipment.

2.3 Network architecture

In recent years, high-quality deep network models such as AlexNet, Inception, GoogleNet, and ResNet have been proposed one after another, and their capabilities in image feature extraction and recognition have been effectively tested in the ImageNet image classification task competition [43,44]. Second, these network models have a certain parameter base after being trained on the ImageNet image dataset; this solves the model problem and the need for massive knowledge in the source domain for transfer learning. However, a network model with too many network layers and too large a parameter space will experience slow training speed and overfitting of training results when learning from small sample data [45]. Therefore, this article chooses to adopt a transfer learning strategy that avoids network overfitting and implements parameter-based transfer learning fault diagnosis between ImageNet image datasets and diesel engine fault data on AlexNet and ResNet-18 network models with fewer network layers.

The AlexNet network consists of five convolutional layers (Conv), three max-pooling layers, and three fully connected layers (dense), and convolutional layers and max-pooling layers are alternately arranged [46]. Figure 2(a) depicts the structure diagram of the AlexNet network, with only the convolutional layer and fully connected layer with parameter space listed, and the relevant pooling and activation layers omitted. The highlight of the AlexNet network is that it uses dual graphics processing unit (GPUs) for network acceleration training; compared with single GPU training and learning, the learning speed is greatly improved. The activation function used by the AlexNet network is the ReLU function instead of the traditional Sigmoid function, which also speeds up the learning and solves the gradient dispersion problem well. The local response normalization of local response normalization is to establish a competition mechanism for local neurons after ReLU, so that the value with a larger response becomes relatively larger, suppressing the neuron with a smaller response and strengthening the generalization ability of the network [47]. In terms of network structure, the last two layers of the AlexNet model are changed to a fully connected layer and a Softmax classification layer corresponding to the number of diesel engine failure modes.

Figure 2

Network architecture diagram of (a) AlexNet and (b) ResNet-18.

ResNet-18 network, as one of the typical deep residual networks, uses skipping connections by constructing residual blocks. Let the input X of the network be directly connected to the output Y of the parameterized layer through an identity map I : X → X , so that the parameterized network layer learns a residual map f : X → Y − X . Literature research shows that compared with convolution learning, the introduction of residual mapping can effectively reduce the learning difficulty of the network and speed up the convergence speed of the model [48]. The structure of the ResNet-18 model is mainly composed of a convolutional layer (Conv), four basic residual layers (basic layers), an average pooling layer, and a fully connected layer (dense); each residual block is, in turn, skipping connected by two convolutional layers. Different from the AlexNet model, the ResNet-18 model is a directed acyclic graph network [49]. After changing the end network layer, the global average pooling layer needs to be connected to the fully connected layer to ensure smooth network transmission. The network structure of the ResNet-18 model is shown in Figure 2(b), with only the convolutional layers and fully connected layers with parameter space listed, and the related pooling layers and activation layers omitted.

The image input dimension of the AlexNet model is 227 × 227 × 3 , and the input dimension of the ResNet-18 model is 224 × 224 × 3 . This means that the feature map needs to be adjusted to the size corresponding to the input dimension of the model before being input to the network for training; this operation is implemented in MATLAB through the augmentedImageDatastore function.

2.4 Surrogate model

In the optimization of network hyperparameters, three key hyperparameters, namely initial learning rate, batch size, and the maximum number of training rounds, are optimized. For supervised learning, an appropriate initial learning rate can make the objective function converge to a local minimum within the verification time; an appropriate batch size can increase the accuracy of gradient descent so that the amplitude of fluctuations during training is reduced. It is closely related to memory utilization and training speed during training; the maximum number of training rounds determines the degree of convergence of the network. Too small training rounds will cause the network to converge in advance, and too large rounds will waste time [50,51].

The surrogate model mainly includes two parts: the group optimization algorithm and the calculation of the fitness function value. The swarm optimization algorithm adopts the GWO optimized by the PSO algorithm, which improves the convergence speed and global optimization ability of the gray wolf optimization algorithm and helps optimize the hyperparameters of the network model efficiently. In terms of solving the fitness function value, first, use different hyperparameter samples to train the network to obtain the corresponding training accuracy. Then, the trained BPNN model is embedded into the solution of the fitness function to realize the efficient and autonomous optimization of the hyperparameters of the convolution network.

2.4.1 GWO

Inspired by the way wolves hunt, in the gray wolf optimization algorithm, the variants are divided into four different groups according to the rank of wolves in nature, namely α , β , δ , and γ . Under the leadership of a wolf, the wolves continuously perform behaviors such as hunting, encircling, and attacking to realize the optimization process. The optimization diagram is shown in Figure 3 [52].

Figure 3

Schematic diagram of the GWO algorithm.

In the search process, use ∣ A ∣ > 1 to force the gray wolf to separate from its prey to determine the optimal attack target. After determining the attack target, the surrounding behavior of wolves can be expressed as follows:

(4) D → = ∣ C → ⋅ X → P ( t ) − X → ( t ) ∣ , X → ( t + 1 ) = X → P ( t ) − A → ⋅ D → , A → = 2 a → ⋅ r 1 → − a → , A → = 2 ⋅ r 2 → ,

where D → is the Euclidean distance between the gray wolf and its prey; X → ( t ) and X → P ( t ) are the position vectors of the gray wolf and the prey after moving t times, respectively; during the encirclement process, the convergence factor a → decreases linearly from 2 to 0 according to the encirclement behavior of the gray wolf; the value range of the modulo of the r 1 → and r 2 → is [0,1], which represents a random change parameter with direction. After encircling the prey, consider α , β , and δ to be three potential solutions, and their positions change with the movement of the prey, such a chasing behavior can be expressed as follows:

(5) D j → = ∣ C → ⋅ X → j − X → ∣ , X → n = X → j − A n → ⋅ D j → , X → p ( t + 1 ) = ∑ n X → n 3 ,

where j = α , β , and δ ; n = 1, 2, 3; D j → represents the Euclidean distance from α , β , and δ to γ ; X → n defines the step size and direction of γ moving toward α , β , and δ ; X → p ( t + 1 ) represents the final position of γ . When the prey stops moving and the gray wolf attacks the prey, the optimal value is determined. The value of a → decreases linearly from 2 to 0, which is the core of this stage, indicating that the value of the corresponding A → changes in the corresponding interval, and the next update position of the gray wolf will be closer to the prey position (optimal solution) [53,54].

2.4.2 GWO optimized by PSO (PSO–GWO)

Because the GWO algorithm does not consider the individual’s own experience in the optimization process and lacks communication between the individual position and the group position, it may lead to premature convergence of the algorithm, and it is easy to fall into the local optimum. The group optimization algorithm used needs to have strong global optimization ability. So, consider improving the deficiencies of the GWO algorithm.

The essence of the PSO algorithm is that the particles continue to make directional variable-speed movements in space and find the next position through their memory and group communication to find the optimal solution. Therefore, the position update method of the particle can be used to replace the position update of the individual gray wolf, so that the GWO has memory during optimization. The update formulas for the velocity and position of the PSO algorithm are [55] as follows:

(6) v i k + 1 = v i k + c 1 r 1 ( p best k − x i k ) + c 2 r 2 ( g best − x i k ) , x i k + 1 = x i k + v i k + 1 ,

where x represents the position of the particle; v represents the flight speed of the particle; c 1 and c 2 are acceleration constants, which control the speed of the particles, represent the individual historical best position, and represent the global best position. In addition, the adjustment inertia constant γ is introduced to enhance the global search ability and local development ability of GWO, and the variation range of γ is [0.5, 1]. Therefore, the updated formula of the speed and position of wolves in the PSO–GWO algorithm is expressed as follows:

(7) v i k + 1 = ω ⋅ [ v i k + c 1 r 1 ( x 1 − x i k ) + c 2 r 2 ( x 2 − x i k ) + c 3 r 3 ( x 3 − x i k ) ] , x i k + 1 = x i k + v i k + 1 .

The first formula in formula (5) becomes

(8) D j → = ∣ C n → ⋅ X → j − ω ⋅ X → ∣ .

To verify the improvement of the improved PSO–GWO algorithm in the optimization ability, six types of optimization algorithm performance test functions were selected to conduct simulation tests on GWO and PSO–GWO, respectively, and for each test, the number of populations and the maximum number of iterations of the algorithm were set to 30 and 500. The experimental results are shown in Figure 4. From the image of the performance test function, it can be concluded that in addition to the maximum value, the test function also has dense and continuous local minima and local maxima, which can greatly test the global optimization ability and optimization efficiency of the group optimization algorithm. From the simulation test results of the six types of test functions on the GWO and PSO–GWO algorithms, it can be concluded that the improved PSO–GWO algorithm has a better convergence effect and global optimization ability than the GWO algorithm.

2.4.3 BPNN

Use the network prediction process to replace the practical training process of convolutional networks, then the network should meet the following two requirements: (1) simple structure and fast training speed; (2) fast prediction speed and high accuracy. As a typical three-layer neural network, BPNN is composed of only input layers, hidden layers, and output layers, and the structure composition is relatively simple. In addition, BPNN is widely used in non-linear forecasts. Liang et al. [56] used BPNN to predict the deformation temperature of coal ash, which has higher predictive accuracy compared to traditional linear regression and Factsage calculation. Aiming at the nonstationarity and complexity of traffic flow, Peng and Xiang [57] established a prediction model through BPNN, optimized it through the GA, and finally realized an accurate prediction of traffic flow. Zhang and Lou [58] used BPNN and a deep learning fuzzy algorithm to predict stock prices and concluded that the trend prediction of stock prices by BPNN is better than that of the deep learning fuzzy algorithm. It can be seen that the BPNN has a strong predictive ability for nonlinear complex situations.

This article uses the 3-layer BPNN as a prediction model. Assuming the input super-added combination vector is x = ( x 1 , x 2 , x 3 ) , the output of the hidden layer can be represented as follows:

(9) y i = f ∑ j w i j x j − θ j ,

where y i is the output of the ith neuron in the hidden layer; x j is the jth feature; w i j is the weight value from the jth neuron in the input layer to the ith neuron in the hidden layer; θ j is the threshold of the jth neurons in the hidden layer; and f ( ⋅ ) is the transfer function from the input layer to the hidden layer. The output of the output layer is similar to the output of the hidden layer and can be expressed as follows:

(10) z l = g ∑ i h l i y i − n l ,

where z l is the output of the lth neuron in the output layer; y i is the output of the ith neuron in the hidden layer; h l i is the weight value from the ith neuron to the lth neuron in the hidden layer; n l is the threshold of the lth neuron in the output layer; and g ( ⋅ ) is the transfer function from the hidden layer to the output layer [59,60].

The above process is the positive transmission process of the network. To optimize the weight and threshold of the network, the network still needs to be adjusted by feedback to minimize the error of the output layer. The schematic diagram of the BPNN algorithm is shown in Figure 5.

Figure 5

Schematic diagram of the BPNN.

To enable BPNN to have the ability to predict the training accuracy of convolutional networks, first, the actual training accuracy of corresponding convolutional networks under different hyperparameter combinations is counted, thus generating a certain number of sample pairs. Let BPNN train on these sample pairs, learn the nonlinear relationship between the values of hyperparameters and the network training results, and then use them as a prediction model to predict the fitness value of the optimization algorithm.

2.4.4 PSO–GWO–BP surrogate model

The design flow of the proposed surrogate model is shown in Figure 6. It should be noted that the inverse of the output result of BPNN is used as the fitness value of PSO–GWO, that is, if the output value of BPNN is ac, then the fitness value is 1/ac. After the PSO–GWO algorithm reaches the maximum number of iterations, the values of the convolutional network’s training accuracy and hyperparameter combination corresponding to the best fitness can be output.

Figure 6

Surrogate model hyperparameter optimization flowchart.

5.1 Transfer learning fault diagnosis based on AlexNet network model

First, the hyperparameters of the AlexNet network model are optimized. The empirical values of the initial learning rate, the batch size, and the maximum number of training epochs of the model, and the optimization range of the surrogate model are shown in Table 5 [63,64]. Taking the total number of samples as 440, as an example, 25 sets of different hyperparameter combinations are used to train the network. The hyperparameter values and training results are shown in Table 6. The values of the hyperparameters in the table are the initial learning rate, batch size, and the maximum number of training epochs. Use these results to train the BPNN, then use the PSO–BPNN, GWO–BPNN, and the PSO–GWO–BPNN surrogate models to optimize the network’s hyperparameters and finally use the optimized hyperparameter values to train the network to get the test results. In the same way, the optimization results and network training results under other sample sizes can be obtained. Table 7 and Figure 11 list the variation of the network training results with the sample size under different hyperparameter values. Figure 12 lists the confusion matrix of the network training results and the classification features calculated by the fully connected layer under different data amounts.

Figure 11

Comparison chart of different hyperparameter optimization methods for the AlexNet network model.

Figure 12

Confusion matrix of the AlexNet network training results and the classification features calculated by the fully connected layer underdifferent data amounts: (a) 440; (b) 360; (c) 280; (d) 200.

From the above experimental results, the following conclusions can be drawn:

1. From the training results in Table 7 and Figure 11, the PSO–GWO–BPNN surrogate model optimizes effective hyperparameters for the network. The network training results optimized by the PSO–GWO–BPNN surrogate model are better than the network optimized by the PSO–BPNN and GWO–BPNN surrogate models and the network under the empirical value; in addition, the optimization effect of the GWO–BPNN surrogate model is not obvious compared with the empirical value, which is even lower than the empirical value in some cases. This shows that the PSO–BPNN and GWO–BPNN surrogate models do not find the globally optimal hyperparameters, and it also proves the effectiveness of the PSO–GWO–BPNN surrogate model in autonomously optimizing network hyperparameters.

2. The proposed diagnostic algorithm can achieve excellent performance in fault diagnosis under small sample conditions. First, the diagnostic accuracy of the network does not fluctuate greatly with the decrease in the sample size and remains above 90%. When the sample size is 440, the highest accuracy rate can reach 98.58%.

3. It can be concluded from Figure 12 that the proposed diagnosis algorithm can discriminate most of the eight types of mixed faults with high precision. Only M1 (normal state) faults and M2 (one cylinder misfire) faults will cause misjudgments. The reason may be that the characteristics of M1-type faults and M2-type faults are similar. In addition, when the sample size drops to 200, the phenomenon of misjudgment will be more serious, and there is a misjudgment of M4 (insufficient oil supply) faults. The reason may be that the sample size is insufficient and the data features that lead to M4-type failures are not sufficiently learned.

4. In terms of training time, the network can efficiently complete training and realize diesel engine fault diagnosis in a short time due to the strategy of freezing some parameter layers.

5.2 Transfer learning fault diagnosis based on ResNet-18 network model

The hyperparameters of the ResNet-18 network model are also optimized first. The empirical values of the initial learning rate of the model, the batch size, and the maximum number of training epochs, and the optimization range of the surrogate model are shown in Table 8 [65]. Taking the total number of samples as 440, as an example, 25 sets of different hyperparameter combinations are used to train the network. The hyperparameter values and training results are shown in Table 9. Table 10 and Figure 13 list the variation of the network training results with the sample size under different hyperparameter values. Figure 14 lists the confusion matrix of the network training results and the classification features calculated by the fully connected layer under different data amounts.

Figure 13

Comparison chart of different hyperparameter optimization methods for the ResNet-18 network model.

Figure 14

Confusion matrix of the ResNet-18 network training results and the classification features calculated by the fully connected layer under different data amounts: (a) 440; (b) 360; (c) 280; (d) 200.

From the above experimental results, the following conclusions can be drawn:

1. The same experimental results as the AlexNet network model can be obtained from Table 10 and Figure 13. After the optimization of the PSO–GWO–BPNN surrogate model, the ResNet-18 network is efficiently trained, and the test results are better than the PSO–BPNN and GWO–BPNN surrogate models and the empirical method. The ability of the PSO–GWO–BPNN surrogate model to well optimize the network hyperparameters is once again demonstrated.

2. The fault diagnosis algorithm based on the ResNet-18 network model can still achieve stable and excellent performance in the fault diagnosis under the conditions of small samples. The diagnostic accuracy of the network will not fluctuate greatly with the decrease in the sample size. Even when the sample size is 440, the accuracy rate can reach 96.31%; even when the sample size drops to 200, the accuracy rate can reach 86.25%. However, the overall diagnostic accuracy of the ResNet-18 network model is lower than that of the AlexNet network model, which means that the model training effect is not necessarily better with more network layers.

3. It can be concluded from Figure 14 that compared with the AlexNet network model, the ResNet-18 network model can also better identify most of the eight types of mixed faults. The misjudged fault types are also basically consistent with the AlexNet network model, including M1 (normal state) faults, M2 (first cylinder misfire), and M4 (insufficient fuel supply) faults. The difference is that when the number of samples is 360 and 200, the ResNet-18 network model has misjudged the M6 (the first- and second-cylinder misfire) faults and the M7 (the second-cylinder misfire and air filter blockage) faults. The possible reasons are that: the deep features extracted by the ResNet-18 network model and the AlexNet network model are different, and the decrease in the amount of data leads to the fact that the features of some faulty types of data are not completely learned.

4. In terms of training time, due to the introduction of residual connections in the ResNet-18 network model, it has a shorter training time cost and higher training efficiency than the AlexNet network model.

5.3 Validity analysis of surrogate model

To verify the prediction accuracy of the surrogate model, taking the sample size of 440 as an example, the trained BP network is used to predict the accuracy of the four hyperparameter combinations outside the optimization range of the AlexNet network and the ResNet-18 network. The comparison results with the actual training results are shown in Table 11 and Figure 15. It can be seen from the experimental results that the surrogate model can predict the actual training results of the network with high accuracy, and the error can be kept between 0.23% and 1.45%. This strongly demonstrates the effectiveness of the model. In the case of large errors, the reason may be that the number of training samples of BPNN is not enough, and the implicit relationship between the values of hyperparameters and the training results cannot be fully learned; but such errors are allowed.

Figure 15

The predicted results of the surrogate model and the actual training values of the network. (a) AlexNet; (b) ResNet-18.

In addition, based on ensuring the prediction accuracy, the role of the surrogate model is also reflected in the shortening of the time cost. Taking the training of the AlexNet network with a sample size of 440 as an example, the training time of the network is 24 s. If the traversal parameter adjustment method is used, the network needs to be trained at times. With the surrogate model, only 25 training sessions are required. The latter has a time cost of 701 × 24 s less than the former. Compared with such a large time gap, the iteration time of the PSO–GWO algorithm of the surrogate model is negligible. The efficiency of the PSO–GWO–BPNN surrogate model in network hyperparameter optimization time is thus demonstrated.

5.4 Performance comparison analysis

To further verify the comprehensive performance of the diagnostic algorithm proposed in this article, the time–frequency image samples of the diesel engine were input into the following models for training. These models include the AlexNet network model and the ResNet-18 network model without a freezing strategy, that is, the network layer parameters of the whole domain will be learned. These two methods are denoted by NF-AlexNet and NF-ResNet-18, respectively. Inception-v3 network with freezing strategy (F-Inception-v3) [66], VGG-16 network with freezing strategy (F-VGG-16) [67], support vector machine with PSO parameter optimization (PSO–SVM) [68], kernel learning machine with PSO (PSO–KLM) [69], and random forest with PSO (PSO–RF) [70]. The input of the SVM is the one-dimensional spectral distribution of the vibration signal after STFT calculation. The two convolutional models in this article are denoted by PSO–GWO–BPNN-AlexNet and PSO–GWO–BPNN-ResNet-18, respectively. It should also be noted that the network models used all have initial parameters, that is, they are pre-trained on the ImageNet image set. First, the sample size was set to 440, and the mean of the 10 experimental results for each model is shown in Table 12.

From the above experimental results, it can be concluded that the PSO–GWO–BPNN-AlexNet and PSO–GWO–BPNN-ResNet-18 methods proposed in this article can reach the highest 98.58% and 96.31%, respectively, surpassing other models; and the time cost is the least, which reduces the time by 40–100 s compared with other models. This fully proves that the diagnosis method in this article can complete the hybrid fault diagnosis of a diesel engine with high precision and efficiency.

In addition, to further verify the stable performance of the diagnostic algorithm under small sample conditions. Set the sample sizes to 440, 360, 280, and 200, respectively, and reenter the above model for training. The mean of 10 experimental results is shown in Figure 16. It can be seen from the experimental results that the PSO–GWO–BPNN-AlexNet and PSO–GWO–BPNN-ResNet-18 methods in this article perform very stable under the conditions of small samples and maintain high diagnostic accuracy. NF-AlexNet and NF-ResNet-18 perform parameter learning for all network layers, so the fault features of the data are relatively fully learned. Therefore, when the amount of data is reduced, the accuracy will not drop significantly. However, since the hyperparameters of the network cannot be optimized, the overall diagnostic accuracy is still lower than that of PSO–GWO–BPNN-AlexNet and PSO–GWO–BPNN-ResNet-18. NF-AlexNet and NF-ResNet-18 perform parameter learning for all network layers, so the fault features of the data are relatively fully learned. Therefore, when the amount of data is reduced, the accuracy will not drop significantly. However, since the hyperparameters of the network cannot be optimized, the overall diagnostic accuracy is still lower than that of PSO–GWO–BPNN-AlexNet and PSO–GWO–BPNN-ResNet-18. This shows that the deeper the number of network layers does not necessarily mean that the learning effect of the data is better, but the appropriate network model and diagnosis method need to be selected according to the data. Finally, the diagnostic effect of PSO–RF, PSO–KLM, and PSO–SVM is not very satisfactory, and the accuracy rate drops greatly when the sample size decreases. This is because traditional machine learning methods cannot learn classification features only from the spectral distribution of the data, and they do not have the powerful feature extraction ability of deep networks.

Figure 16

Model training results with different sample sizes.

To sum up, compared with the common deep models and machine learning diagnosis algorithms, the diagnosis method proposed in this article can not only realize the hybrid fault diagnosis of a diesel engine with high accuracy and efficiency but also has very stable and good performance under the condition of small samples.