3.1

Optimized generative countermeasure network

The richness of data sets is very important for the training of deep learning. This paper proposes an optimized GAN model. As shown in Figure 2, the trained AE is used as the generation model G of GAN, discriminant model D is usually a multilayer perceptron, the input of G in GAN is the data of normal motor operation, and the input of D is the data generated by G and the real fault data. D and G compete with each other. Finally, G depicts the distribution of fault samples by learning the characteristics of fault samples, and then generates pseudo data similar to it, achieve the purpose of data expansion. Define data parameters such as equation:

Figure 2.

Optimized generative countermeasure network.

where a^(t) and c^(t) are the t-th fault sample and the t-th normal sample respectively, m^(t) belongs to [1,0], which means that the profile that judges the sample data as true is 1, and the profile that judges the generated data as true is 0. T represents the total number of samples). Relationship between G and D such as equation:

In which means generate data. By fixing G, The loss function corresponding to D can be obtained, such as equation:

In the above formula, θ^D represents the parameters to be optimized in the discrimination model. a ~ p(a) represents the motor sample distribution. represents the distribution of generated data). The design requirements of D are: the likelihood of evaluating the created data to be fake is higher than the likelihood of judging the real defect sample to be true. The following are the design requirements for G : When D is fixed, the distribution features of the generated data shall, to the greatest extent possible, agree with the real fault samples., and the maximization objective function as equation:

θ^G represents the parameters to be optimized in the generated model. Combining the loss functions of equations (4) and (5), the final objective function of GAN is obtained, as shown in equation:

The parameters θ^G and θ^D of G and D are optimized by gradient descent to shorten the difference between created and actual data. When D(G(c)) = 1, the optimal state is reached between created and actual data.

3.2

SSAE neural network

SAE uses regularization strategy to restrict the network on the basis of ordinary AE, so as to improve the generalization ability of the network. The learning ability of the model is limited by adding norm penalty R(θ) to the objective function. At this time, the SAE optimization objective function as equation:

In the above formula, θ represents the network parameter set{W,b}, W represents the parameter weight, b represents the offset vector, M represents the total number of motor samples. x^(m) represents the m-th motor sample. x^(m) is the prediction of input sample x^(m). R(θ) is a regular term. δ is a super parameter that weighs the relative contribution between R(θ) and J(θ).

The schematic diagram of network structure is shown in Figure 3. In the coding stage, the important features of the input data are extracted, the sparse regular term is introduced, and the L₁ constraint is used to punish the output of the hidden layer nodes. In the decoding stage, the extracted features are recovered and the prediction results are output. The reliability of diagnosis results and actual results is compared by objective function. L₁ norm has the advantages of small amount of calculation and convenient operation. Therefore, the optimization objective function of sparse self-coding network based on L₁ norm as equation:

Figure 3.

Sparse self-coding network structure.

The objective function J_sparse(θ) is minimized through the back-propagation algorithm, and the gradient descent method is used to optimize the parameter weight W and offset b in the process of continuous iteration.

SAE consists of a three-tier network. Only one hidden layer limits the ability of feature extraction. In order to better learn the features with strong representation ability, SAE stack is formed into SSAE, and then a classification layer is added to construct SSAE neural network. The specific scheme is: when multiple SAE are superimposed, the hidden layer of the previous SAE is used as the input layer of the next SAE. Set the network coding phase parameter corresponding to layer l as and the decoding phase parameter as . For N -layer stack networks, the coding sequence is from front to back. The corresponding coding process of each layer as equation:

(e^(l) refers to the output of layer l, f (*) is the activation function. y(l) and y(l + 1) are the input of layer l and layer l + 1 respectively). if the multi-layer SAE behind the stack performs decoding from back to front, the decoding steps corresponding to each layer as equation:

(e^(N+l)is the output of the deepest hidden unit, g(*) is the activation function). The last hidden layer of SSAE can only reconstruct the original data and has no classification ability. Therefore, in order to realize the classification and diagnosis function of inter turn short circuit fault, a classification layer is added after the last hidden layer. The network model is shown in Figure 4. The number of neurons in the classification layer is the number of inter turn short circuit faults with different degrees.

Figure 4.

Deep sparse self coding neural network structure.

SSAE neural network includes two training steps: forward network pre training (unsupervised mode) and reverse fine tuning (supervised mode). It is pre trained by layer-by-layer greedy training method. The steps are as follows:

After pre training SAE of each layer through the above steps, establish SSAE network. Monitor and fine tune the network through labeled samples. All layers of SSAE are regarded as a model, and the parameters of SSAE are adjusted by back propagation algorithm. After several iterations, the parameter weight W and deviation b of each layer are optimized. The output of the last hidden layer and the category label are used as the input of the classification layer. The objective function of overall optimization as equation:

h⁽ⁱ⁾ is the fault type label. SSAE organically combines unsupervised self-learning with supervised fine-tuning, which can better extract the deep features of input data. By outputting the probability of fault type in the classification layer, the classification of PMSM inter turn short circuit fault is realized.

4.1

The proposed method

Figure 5 illustrates the deep learning-based fault diagnostic approach used in this study for turn-to-turn short circuits in permanent magnet synchronous motors.

Figure 5.

Overall flow diagram of PMSM turn to turn short circuit fault diagnosis.

4.2

Experimental description

A permanent magnet synchronous motor experimental test platform is constructed, as illustrated in Figure 6, to confirm the efficacy of this approach. One serves as the load motor, while the other serves as the experimental motor in the utilization of two permanent magnet synchronous motors. We decided to conduct the test when the motor operates at low speed, and the test parameters are stated in Table 1, in order to prevent the motor from suffering long-term damage as a result of high short-circuit current during the test.

Figure 6.

PMSM inverter open circuit experiment platform.

Table 1.

PMSM parameters.

We use current sensor to collect PMSM three-phase stator current signal and zero sequence voltage signal. Collect the data of 4000 groups of motors in normal operation and 1000 groups of motors in 5%, 10% and 15% fault operation. After preprocessing the collected data, the real data sets of PMSM with different degrees of inter turn short circuit fault are constructed.

4.3

The validity analysis of our method

In order to verify the efficiency of the optimized GAN extended fault sample data proposed in this paper, we use the general GAN and the optimized GAN to extend the real fault samples we collected respectively. The data volume and training batch (training time) required for the training of the two models are shown in Table 2.

Table 2.

A slightly more complex table with a narrow caption.

As can be seen from Table 2, even when the real data is a small sample, the optimized GAN can complete the training of the network model. However, for general GAN training, the amount of data in the training set should be much larger than the number of parameters in the generator. The training batch of optimized GAN is also less than that of ordinary GAN, indicating that its training time is shorter. The superiority of the optimized GAN proposed in this paper is verified.

We created a 3:1 split between the training and test sets from the real data set, and a fault type label is added to one quarter of the data in the divided training set. Firstly, the training set without label is used for unsupervised pre training of SSAE, and then the training set with label is used for supervised fine-tuning of SSAE. The last hidden layer of SSAE connects the classification layer and outputs the probability value of fault type. The test set verifies the diagnosis efficiency and generalization ability of the network. Considering the influence of the number of SSAE network layers on the diagnosis results, we construct a multilayer SSAE network, where N = 1,2,3,4,5. The recognition accuracy of N -layer network is shown in Table 3.

Table 3.

Curacy corresponding to n-layer network.

The same data is input into SSAE neural network with different network layers, the diagnosis results are obviously different. When the number of network layers is two, the diagnosis accuracy reaches the maximum. From the second layer, with the increase of the number of layers, not only the training time becomes longer, but also the diagnostic accuracy decreases. Therefore, we choose to use two-layer SSAE neural network.

In order to verify the effectiveness of data expansion, the optimized GAN is used to expand three different degrees of inter turn short circuit fault samples, and 1000 groups of pseudo samples are generated respectively. The real data set and pseudo samples are mixed to form an extended data set, with a total of 10000 groups of data. According to the division proportion of the above real data set, the same processing is performed on the extended data set. Based on the same SSAE neural network, the fault diagnosis results under the real data set and the extended data set are compared experimentally, as shown in Figure 7.

Figure 7.

Comparison of diagnostic accuracy under different training sets.

As shown in Figure 7, two groups of experiments were carried out. These two groups of experiments used SSAE neural network with the same parameters and the same number of network layers. Experiment 1 used real data sets as network input. Obviously, the insufficient number of samples directly affects the diagnostic efficiency. The accuracy of fault diagnosis tends to decline as sample size increases, and the final diagnosis accuracy is 97.4%. In Experiment 2, the extended data set was used as the network input because the pseudo samples in the extended data set contained irrelevant noise elements. Such samples can improve the generalization ability of the network. It can be seen from the figure that under the same number of samples, the diagnostic accuracy of the extended data set will be slightly higher than that of the actual data set. Too few samples will make the network unable to reach the optimal state. The additional sample set’s diagnosis results show that as sample size is increased, the accuracy rate of fault diagnosis begins to stabilize and eventually reaches 99.4%. Therefore, the pseudo data generated by GAN can not only make up for the shortage of network training samples, but also enhance the data set.

We compare this method with conventional ones to show how effective it is. Table 4 displays the comparison’s results.

Table 4.

Diagnostic results of different training methods.

In the above table 4, the training results of other traditional methods except the method in this paper are from the same real data sets. The combination of EMD and SVM is used for PMSM fault diagnosis. Compared with deep neural network, it has simple structure and convenient calculation, but its efficiency is not as good as other methods. SAE is connected through KL divergence coefficient, and the network generalization ability can be significantly improved and the diagnostic accuracy is satisfactory. But SAE is a shallow network, which still has some room to improve the accuracy of fault diagnosis. One-dimensional convolutional neural network (1D-CNN) is a kind of deep feedforward neural network with local connections and shared weights. It is also a common method in the field of PMSM fault diagnosis. The diagnostic accuracy is also optimistic. BP neural network is a commonly used classification and regression network. The diagnosis results are satisfactory, but the overall efficiency needs to be greatly improved. The combination of optimized GAN and SSAE neural network for fault diagnosis proposed in this paper has the advantage that it not only increases the amount of data, but also enhances the data set by generating noise data in pseudo samples. More robust features are extracted through SSAE neural network, and unsupervised and supervised organic sets are used to improve the generalization ability of the network, prevent the network from over fitting, and finally get more accurate diagnosis results.