# A New Fault Diagnosis Method for Unbalanced Data Based on 1 DCNN and L2-SVM
## 4 Experimental Verification
### Case Study 1: Application in CWRU Datasets
#### 4.1.4 Comparison Experiments  
In this section, the goal of experimental verification of the proposed method is the more effective identification of unbalanced datasets. Six fault identification algorithms are used for comparison experiments. (1) Compared with BPNN and SVM, which require manual feature extraction. The data in Table 2 are first extracted with 10 time-domain features shown in Tables 3 and 4 frequency-domain features shown in Table 5, and then the extracted 15 feature samples are input to BPNN and SVM for fault identification. Among them, the kernel function of SVM uses a Gaussian radial basis function (RBF) with C = 10; the hidden layer structure of BPNN is (32,16), and the activation function is ReLU. (2) the CNN using the ReLU function (R-CNN) and the CNN using the SELU function (S-CNN) are used for classification. (3) Compared with commonly used unbalanced data fault identification methods, CNN (CSCNN) and SMOTE-CNN are more cost-sensitive. The network structure and parameters of CSCNN are consistent with the proposed method, and the cost matrix is determined by the sample proportion. After SMOTE sampling, unbalanced training samples become balanced samples, and then fault identification is carried out through CNN. The data in Table 3 are used to conduct experiments. Note that each experiment is conducted 20 times to eliminate the impact of stochastic values. The  
Figure 7: Visualization of features learned in different layers. experimental results are shown in Figure 8. We use accuracy as the evaluation metric, which is a commonly used index to measure the performance of classification problems. Its formula is  
\[accuracy=\frac{TP+TN}{G} \tag{16}\]  
where \(TP\) (true positive) is correctly classified as a positive sample, \(TN\) (true negative) is correctly classified as a negative sample, and \(G\) is the total number of samples. \begin{table}
\begin{tabular}{c c c c} \hline Absolute mean & \(\frac{1}{n}\sum\limits_{i=1}^{n}|\mathrm{x_{i}}|\) & Crest factor & \(\frac{\max(|\mathrm{x_{i}}|)}{\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\mathrm{x_{ i}^{2}}}}\) \\ \hline Variance & \(\frac{1}{n}\sum\limits_{i=1}^{n}(\mathrm{x_{i}}-\overline{\mathrm{x_{i}}})^{2}\) & Root mean square & \(\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\mathrm{x_{i}^{2}}}\) \\ \hline Crest & \(\max\lvert\mathrm{x_{i}}\rvert\) & Pulse factor & \(\frac{\max(|\mathrm{x_{i}}|)}{\frac{1}{n}\sum\limits_{i=1}^{n}\lvert\mathrm{x_{ i}}\rvert}\) \\ \hline Clearance factor & \(\frac{\max\lvert\mathrm{x_{i}}\rvert}{\left(\frac{1}{n}\sum\limits_{i=1}^{n} \sqrt{\mathrm{x}}\right)^{2}}\) & Skewness & \(\frac{1}{n}\sum\limits_{i=1}^{n}\mathrm{x_{i}^{3}}\) \\ \hline Kurtosis & \(\frac{1}{n}\sum\limits_{i=1}^{n}\mathrm{x_{i}^{4}}\) & Shape factor & \(\frac{\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\mathrm{x_{i}^{2}}}}{\frac{1}{n} \sum\limits_{i=1}^{n}\lvert\mathrm{x_{i}}\rvert}\) \\ \hline \end{tabular} Note: n symbol is the volume of the sampling points, while \(\mathrm{x_{i}}\) is the signal amplitude at a single point.  
\end{table} 
Table 3: Features selected in the time domain. Figure 8: Identification accuracies on three datasets by seven methods. Since Dataset A is a balanced dataset, all seven methods obtained high accuracy. In the unbalanced Dataset B, the minority class samples used to train these methods become fewer in number; therefore, the accuracy of all seven methods decreased. Among them, the accuracy of BPNN and SVM decreased to 90.2% and 89.8%, respectively. This is because BPNN and SVM need manual feature extraction before training. However, the manually extracted features are not comprehensive and the key features may be missed, resulting in a rapid decline in accuracy. In addition, the accuracy of R-CNN is 93.4%, S-CNN is 92.4%, SMOTE-CNN is 94.1%, CSCNN is 97.5%, and 1 DCNN-L2 SVM is 98.5%. Obviously, 1 DCNN-L2 SVM obtains the highest accuracy because it uses dynamic adjustment parameters and modulation factors to deal with unbalanced data. The samples in Dataset C are more unbalanced than those in dataset B.