# Fault Diagnosis of Universal Circuit Breakers Based on Variational Mode Decomposition and WOA-DBN
## 4 Results and Discussion  
The proposed approach is compared with the current mainstream machine learning algorithms such as SVM, Backpropagation Neural Network (BPNN), Long Short-Term Memory Network (LSTM), Stacked Self-Encoder (SDAE), and DBN. The parameters of the comparison models are set as follows:  
Figure 10: Fault diagnosis flowchart. SVM  
The kernel function selects the RBF (Radial Basis Function) function based on the time and frequency domain features of the multiple modal components of the VMD decomposition. Based on the grid optimization findings, the penalty coefficient C was adjusted to 9, and the gamma function's radius was adjusted to g = 0.008. The precision of the stopping training error was set to \(1\times 10^{-3}\). 2 BPNN  
Multiple modal components' time and frequency domain features after VMD decomposition were used as data inputs, the three-layer network structure 216-100-10 with WOA optimization was used, and the network learning rate was set as \(\eta\) = 0.001. 3 LSTM  
Multiple modal components' time and frequency domain features after VMD decomposition were used as data inputs, the network structure was 216-100-50-6, and the network learning rate was set as \(\eta\) = 0.001. 4 SDAE  
Multiple modal components' time and frequency domain features after VMD decomposition were used as data inputs, the network structure was 216-100-50-6, and the network learning rate was set as \(\eta\) = 0.001. 5 DBN  
A stepwise decreasing neuron selection approach used time and frequency domain feature data input. The network structure was determined as 216-200-100-50-6, and the network learning rate was set as \(\eta\) = 0.001. 6 WOA-DBN  
Network layer structure 216-471-668-456-6, \(\eta\) = 9.06878 \(\times\) 10\({}^{-4}\). Overall, 10 iterations of the experiments were conducted in this paper, with each experimental model using identical training and test sets. The results of the 10 experiments are displayed in Figure 11. Figure 11 illustrates how the accuracy of SVM, BPNN, and LSTM models was low, and the average accuracy was 0.7253, 0.7938, and 0.7929, respectively. This is because SVM relies heavily on expert experience and requires much experience and multiple attempts to select better features for a particular task, resulting in lower model accuracy. In short sample datasets, the BPNN model was ineffective since it settles into the local optimum throughout the training phase and needs plenty of data. The SDAE model had an accuracy of 0.8403. The total accuracy was poor because of the SDAE model's restricted feature processing capability. The DBN model had an accuracy rate of 0.8631, which is why DBN relies heavily on selecting hyperparameters and using appropriate hyperparameters will significantly raise the DBN model's accuracy rate. Figure 12 shows the box plots and scatter plots for 10 training runs. The box plot of the WOA-DBN approach adopted in this paper has the highest height and the narrowest width, which can help determine the high-precision diagnosis of the universal circuit breaker. In addition, the scatter plot shows that the WOA-DBN model had the most negligible dispersion and the best stability, indicating that it is more robust. In this experiment, the recognition rate of each fault was tracked through various models to understand better the model's recognition rate for each fault category and to rule out extreme cases of recognition rates for specific types of faults. Figure 13 illustrates the confusion radar chart of the fault diagnosis results of various diagnosis approaches and the diagnosis results of various faults. Every axis denotes a fault condition of a universal circuit breaker, and the length of the axis indicates how accurately that fault may be identified using different techniques. The analysis findings demonstrate how well the approach described in this work can identify different kinds of faults. The diagnostic accuracy of every state is the highest.