## 4 Simulation Results
### DBN Training and Test Results Analysis  
In this paper, the input of DBN under each open-circuit failure state is a 24 dimensions trend feature vectors \(I_{x}=\left[\begin{array}{cc}I_{x,1}&I_{x,2}&\cdots&I_{x,24}\end{array} \right]\), \(x=1,2,\cdots,22\),where \(x\) denotes the failure coding number. The DBN consists of double-layer RBM and Softmax classifier. In order to reduce the dimensions and retain the feature information of the trend feature vectors, the number of neurons in the first layer of RBM is set to 14, and the number of neurons in the second layer of RBM is set to 5. Then, the input of Softmax classifier is 5 dimensions. The output of Softmax classifier is a 22 dimensions probability vectors \(S=\left[\begin{array}{cc}S_{1}&S_{2}&\cdots&S_{22}\end{array}\right]\), where \(S_{j}(j=1,2,\cdots,22)\) denotes the probability of the \(j\)-th fault. Table 4 shows the probability output results of Softmax classifier and corresponding failure coding number.  
Table 4 shows that, for instance, put the No. 1 trend feature vectors into DBN model, the classification result is \(S=\) [0.999990, 0.000000,..., 0.000000], which means the probability of No. 1 trend feature vectors belonging to No. 1 state is 99.999%. Put the No. 22 trend feature vectors into DBN model, the classification result is \(S=\) [0.000000, 0.000001,..., 0.999997], which means the probability of No.  
To compare the performance of proposed method, the other 7 methods are involved to address the same samples and 1 classical method stated in [16] is utilized too. The total 9 methods are: 1, proposed method, VMD, trend feature and DBN (VMD-TFA-DBN); 2, the classical method, wavelet transform, feature analysis, judgment and BPNN (WT-FA-JD-BP); 3, VMD, trend feature analysis and BPNN (VMD-TFA-BP); 4, trend feature analysis and DBN (TFA-DBN); 5, trend feature analysis and BPNN (TFA-BP); 6, VMD and DBN (VMD-DBN); 7, VMD and BPNN (VMD-BP); 8, only DBN (DBN); 9, only BPNN (BP). To increase the credibility, every method trains the same training set and tests the same test set at 100 times. Table 5 shows the comparison results between 9 methods.  
The following conclusions can be analyzed and drawn from Table 5:  
1. The method of VMD-TFA-DBN, proposed in this paper, has generated the best classifying capability under the 22 circumstances that the accuracy is 100%, the error times is 0.
2. The method of only BP has produced the worst classifying performance, the accuracy is 3.75%, the error times is 423500.
3. When the accuracy of VMD-TFA-DBN is higher than VMD-TFA-BP, TFA-DBN is higher than TFA-BP, VMD-DBN is higher than VMD-BP, and DBN is higher than BP. All of these illustrate the classification accuracy of DBN in higher than BP in the models.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Coding Number** & **1** & **2** & **3** & **19** & **20** & **21** &  
The accuracy of each method used proposed TFA is higher than corresponding who does not use TFA, which verifies the great function of TFA for increasing classification accuracy.
5. The accuracy of each method used VMD is higher than corresponding who does not use VMD, which verifies the function of VMD in proposed method.
6. The classical method WT-FA-JD-BP has generated the second best performance that the accuracy is 99.99%, the error times is 3.