## 2 Network Models
### Generative Adversarial Network Model
The network updates weights and biases through backpropagation in order to learn the complex mapping relationship between input noise data and motor samples. The hyperparameters of the artificial neural network need to be set before training, mainly including the number of hidden layers, the number of nodes in each layer, connection mode, activation function, optimization algorithm, etc. The selection and setting of hyperparameters play a vital role in the quality of network learning. The original GAN has many shortcomings in generating motor samples [21]. During the process of model training, a phenomenon known as mode collapse arises, wherein the generator G can only learn from training concentrates that encompass a limited number of modes instead of multiple modes. Consequently, this hinders the acquisition of other modes, ultimately resulting in a lack of diversity within generated samples. In addition, the network training speed is slow, the quality of generated samples is poor, and the performance is poor in the case of limited samples. Currently, most mainstream research on GAN theory focuses on optimizing the above problems to study and improve the model. [PERSON] et al. [11] proposed a circular consistent confrontation network for image-to-image conversion, which can capture the unique features of one image set and learn how to transfer these features to another image set. Inspired by this idea, this paper reconstructs and improves Cycle GAN and solves the problem that it can only process two-dimensional images. The reconstructed Cycle GAN can process one-dimensional time sequence signals and realize the function of migrating the characteristics of fault motor samples to healthy motor samples. Furthermore, it solves the problem that the original GAN is prone to mode collapse by classifying and establishing samples with different degrees of PMSMs' IITs. The priority purpose of this network is domain adaptation. By taking healthy samples and IIF samples as examples, two datasets, \(X\) and \(Y\), are established to store the three-phase stator current of the former and the latter, respectively. We want to train a generator \(G\) to input a motor health sample \(x\) and then output a motor fault sample \(y^{\prime}\). We also want to train a generator \(F\) to input a motor fault sample \(y\) and output a motor health sample \(x^{\prime}\), which is  
\[G(x)=y^{\prime},x\in X \tag{4}\]  
\[F(y)=x^{\prime},y\in Y \tag{5}\]  
To achieve this goal, we also need to train two discriminators, \(D_{X}\) and \(D_{Y}\), to judge the quality of the sample generated by generators \(G\) and \(F\), respectively. Specifically, when the motor fault sample \(y^{\prime}\) generated by generator \(G\) is fed into the discriminator \(D_{Y}\), the discriminator \(D_{Y}\) should output a lower value (between 0 and 1) if the distribution of \(y^{\prime}\) does not follow the distribution of sample \(y\) in the dataset \(Y\). Conversely, the discriminator \(D_{Y}\) should output a higher value in such cases. Similarly, when sample \(y\) from dataset \(Y\) is provided as input to the discriminator \(D_{Y}\), the discriminator \(D_{Y}\) should always output higher values. The same is true for the discriminator \(D_{X}\). During the training process, the discriminator and generator are alternately trained. We not only hope that the motor sample \(y^{\prime}\) generated by the generator \(G\) obeys the distribution of sample \(y\) in dataset \(Y\), but we also hope that it retains the characteristics of input sample \(x\). In short, the sample \(y^{\prime}\) generated by the generator \(G\) adds fault characteristics of fault sample \(y\) to the input sample \(x\) rather than simply duplicating fault sample \(y\), which is the same as the generator \(F\). Otherwise, it cannot improve the performance of the classification network. In order to achieve the above purpose, a cycle consistency structure is set up in this network.