## 4 Random Forests Theory
### Improved Random Forest Algorithm
In order not to lose generality, the data are simulated in this paper, and DC voltage, output voltage and output current assignment are considered. The fault characteristics will be different under different operating conditions. Therefore, in order to contain more fault information in the fault database, we simulate various converter operation conditions. The data acquisition process is shown in Table 2, and the three-phase PWM converter simulation parameters are shown in Table 3. The simulation obtains a total of 88,000 sets of data as the model training database, \(DT\). Due to the risk of damage from real system open failure, only a few test databases, \(DP\) (2200 sets), are obtained through two real three-phase converter systems with different model parameters, as shown in Table 4. Of which, the parameters of the real system 1 are consistent with those of simulation as shown in Table 3.

The training dataset, \(T\), is extracted from \(DT\) according to coefficient \(X_{OS}\). Extract the test dataset \(P\) from the \(DP\) according to coefficient \(X_{OS}\). The out-of-bag data in the \(DP\) is used to calculate the evaluation index Equations (15)-(17). ### Simulation and Comparison Results

In order to verify and analyze the performance of the fault diagnosis model, the dataset \(T\) is used to train the proposed fault diagnosis model. In addition, Bayesian network (BN) fault diagnosis model, support vector machine (SVM) fault diagnosis model, RFs fault \begin{table}
\begin{tabular}{c c} \hline \hline
**Contents** & **Values** \\ \hline DC-link voltage \(U_{dc}\) & 400 V \\ Rated output voltage & 110 V (RMS) \\ Rated output current & 100 A (RMS) \\ Rated voltage frequency & 400 HZ \\ Switching frequency & 5 kHz \\ Filter inductance & 0.82 mL \\ Capacitance & 480 uF \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of real system 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Data Acquisition Condition** & \\ \hline DC Voltage & 400:700/20 V \\ Output voltage (RMS) & 100:300/10 V \\ Output voltage frequency & 30:130/10 Hz \\ Output current (RMS) & 10:100/10 A \\ Open-circuit fault type & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Database acquisition process. \begin{table}
\begin{tabular}{c c} \hline \hline
**Contents** & **Values** \\ \hline DC Voltage \(U_{dc}\). & 700 V \\ Rated output voltage & 220 V (RMS) \\ Rated output current & 40 A (RMS) \\ Rated voltage frequency & 50 HZ \\ Switching frequency & 12.8 kHzZ \\ Filter inductance & 1.2 mL \\ Capacitance & 480 uF \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters and real system 1 parameters of three-phase PWM converter. diagnosis model, ensemble extreme learning machine (ELM) fault diagnosis model and the proposed fault diagnosis model, are compared through the same training dataset, \(T\), and validation dataset, \(Vd\), which is the part of the database \(DP\) that excludes dataset \(P\). All algorithms adopt the same general fault diagnosis framework as shown in Figures 1 and 2. In order to search for the optimal fault diagnosis performance, the hyperparameters of all algorithms are optimized including architecture, learning rate, kernel function, the number of decision tree, etc. The optimization results and some decision tree weights of the proposed method are shown in Table 5.

In order to verify the training performance of the fault diagnosis algorithms, we conducted 10-fold cross-validation on the above model in 88,000 training datasets. The results are as shown in Table 6. After the hyperparameter optimization, all the fault diagnosis algorithms have a good fault diagnosis performance index (above 99.5%) in the training datasets. However, integrated fault diagnosis algorithms including RFS, ensemble ELM, and the proposed method have an excellent fault diagnosis performance index of nearly 100% in the OOB of training datasets. In order to verify the generalization performance of the fault diagnosis model, we performed performance verification on real system 1 and real system 2.