## 4 Engineering Applications
### Sample Balanced by RTAE  
Due to different units, the attribute ranges vary significantly. Normalization is used to scale the range of each attribute to [0, 1]. The normalization method is presented below:  
\[\overset{\sim}{A}=\frac{A-A_{min}}{A_{max}-A_{min}} \tag{18}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Dataset** & **\# Normal** & **\# Cracking** & **Imbalance Ratio** \\ \hline
1 & Wind\_5 & 2000 & 100 & 20:1 \\
2 & Wind\_10 & 2000 & 200 & 10:1 \\
3 & Wind\_15 & 2000 & 300 & 6.67:1 \\
4 & Wind\_20 & 2000 & 400 & 5:1 \\
5 & Wind\_25 & 2000 & 500 & 4:1 \\
6 & Wind\_30 & 2000 & 600 & 3.33:1 \\
7 & Wind\_35 & 2000 & 700 & 2.86:1 \\
8 & Wind\_40 & 2000 & 800 & 2.5:1 \\
9 & Wind\_45 & 2000 & 900 & 2.22:1 \\
10 & Wind\_50 & 2000 & 1000 & 2:1 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Details of 10 datasets.  
Figure 4: Normal sample (**first row**) and cracking sample (**second row**).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Attribute** & **No.** & **Attribute** & **No.** & **Attribute** \\ \hline
19 & Inverter power grid side voltage & 44 & Hub temperature & 69 & Blake 3 Super-capacitor voltage \\
20 & Active power of inverter power & 45 & Hub control cabinet temperature & 70 & Drive 1 Thyristor temperature \\
21 & Inverter grid side reactive power & 46 & Cabin temperature & 71 & Drive 2 Thyristor temperature \\
22 & Inverter generator side power & 47 & Control cabinet temperature & 72 & Drive 3 Thyristor temperature \\
23 & Generator operating frequency & 48 & Inverter INU temperature & 73 & Drive 1 Output torque \\
24 & Generator current & 49 & Inverter ISU temperature & 74 & Drive 2 Output torque \\
25 & Generator torque & 50 & Inverter INU RMIO temperature & 75 & Drive 3 Output torque \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._where \(\widetilde{A}\) is the normalized attribute value; \(A_{min}\) and \(A_{max}\) are, respectively, the minimum and maximum values among all the samples.  
Auto-encoder is adopted to extract intrinsic features and reduce the dimension. Wind_50 dataset is used to train an AE model, with its structure [75; 20; 10]. The encoder include two hidden layers, with twenty units for the first layer and ten units for the second layer. Sigmoid is taken as the activation function. For the decoder, it has the inverse structure, namely, as shown in [10; 20; 75]. Figure 5 shows four samples and their reconstructed results. Obviously, the reconstructed data approximate original samples, implying the intrinsic feature can adequately represent the key information.  
Roundtrip is employed to generate virtual cracking samples. Table 5 lists detailed hyper-parameter settings. These parameters are determined by trial and error. To observe the results of roundtrip, loss values during 5000 iterations are shown in Figure 6. L\({}_{1}\) and L\({}_{2}\) in Equation (8) are relevant to the generator, thus they are added together. Both the losses of the generator and discriminator go down very fast and converge after 2000 iterations. In the last 100 iterations (see the inset window), both of them fluctuate to a small extent. When the red line goes down, blue line will go up, implying adversarial learning. To observe generated data, TSNE [22] is adopted to map the intrinsic features into two-dimension space. The results are shown in Figure 7. The generated data well fit the original data distribution and many samples lie on the border, which is helpful for improving classification accuracy.