## 4 Gas Turbine Test Bench Experiment and Fault Diagnosis
### The Training of Improved DCGAN  
Because the labeling of fault samples requires a lot of experimental and expert experience, the fault samples are not enough. Therefore, in order to improve the accuracy of fault diagnosis, the proposed method is used to generate fault samples with very high similarity with the original samples to supplement all kinds of samples and make up for the imbalance of samples. Figure 12 is the flow chart of gas turbine fault data generation and fault diagnosis of gas turbine rotor systems. The original gas turbine sample is labeled and used as the training dataset; the length of each fault sample is 1024. Then, the labeled samples are taken as the input to Improved DCGAN to achieve the generated samples. The number of samples in the training dataset including generated samples is 1000 for each class. The number of samples in the original training dataset, the training dataset including the generated samples, and the testing dataset are shown in Table 3.  
Figure 11: Fatigue crack of blade.  
Figure 10: The fatigue damage of the shaft.  
Figure 9: Time–frequency analysis of gas turbine rotor faults. (**a**) Misalignment. (**b**) Unbalanced.  
The training parameters of the proposed Improved DCGAN network model are set as follows: the batch size is set as 11, the learning rate is 0.000001, the number of model training iterations is 80,000, the generator gradient penalty parameter \(\beta\) is 0.000001, and the discriminator gradient penalty parameter \(\lambda\) is 10. The optimization method of the generator and discriminator is the Adam optimization algorithm. In order to ensure that the generated signals and the real signals have a large degree of similarity and a small error, the MMD should be set as less than 0.125.  
In the adversarial training between the generator and discriminator, the generator tries to generate samples that could cheat the discriminator, and the discriminator learns to distinguish between the generated samples and the real signals with training.  
Figure 13 shows the loss function waveform of the generator and discriminator. In adversarial learning between the generator and discriminator, the generated samples increase with iteration, and the loss function gradually changes. At the beginning, the loss of generator is smooth, and then gradually increases and finally tends to be stable. The loss of the discriminator gradually decreases with the training time, and tends to be stable. After adversarial training, the generator generates higher-quality vibration signals.  
It can be seen from Figure 13 that compared with DCGAN, the newly added gradient penalty term in the proposed DCGAN made the overall training of the Deep Convolutional Generative Adversarial Network more stable, and the convergence speed faster.  
Figure 12: Fault data generation and classification of gas turbine rotor system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Class**} & **Number of Samples in Original Training** & **Number of Samples in Dataset Including Generated** & **Number of Samples in Testing Dataset** \\  & & **Dataset (Labeled)** & **Samples (Labeled)** & **(Unlabeled)** \\ \hline
1 & Normal & 600 & 1000 & 500 \\ \hline
2 & Airflow excitation & 500 & 1000 & 500 \\ \hline
3 & Unbalanced & 500 & 1000 & 500 \\ \hline
4 & Misalignment & 500 & 1000 & 500 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Number of training dataset and testing dataset samples.