## 3 Simulation Results  
To identify faulty power transistors, fault states were divided into nine categories in this study: Failure of \(\text{S}_{41}{}^{+}\); \(\text{S}_{42}{}^{-}\); \(\text{S}_{b1}{}^{+}\); \(\text{S}_{b2}{}^{-}\); \(\text{S}_{c1}{}^{+}\); \(\text{S}_{c2}{}^{-}\); (\(\text{S}_{a1}{}^{-}\) or \(\text{S}_{a2}{}^{+}\)); (\(\text{S}_{b1}{}^{+}\) or \(\text{S}_{b2}{}^{+}\)); and (\(\text{S}_{c1}{}^{+}\) or \(\text{S}_{c2}{}^{+}\)). The principles underlying the categorization are described as follows. When \(\text{S}_{a1}{}^{-}\) or \(\text{S}_{a2}{}^{+}\) is faulty, the current path and voltage waveform are considered to be the same; thus, \(\text{S}_{a1}{}^{-}\) and \(\text{S}_{a2}{}^{+}\) are categorized under the same category. The same principle applies to the categories \(\text{S}_{b1}{}^{+}\) or \(\text{S}_{b2}{}^{+}\) and \(\text{S}_{c1}{}^{+}\) or \(\text{S}_{c2}{}^{+}\). Table 1 lists the fault categories. Figure 8: Schematic of the elementary correlation function. Table 2 presents the feature values of the chaos eyes for each phase under the switch failure state at an operating frequency of 60 Hz. The data in Table 2 were used as inputs in the established fault diagnosis system to execute fault detection. Tables 3-5 present the fault detection results, indicating that all faults could be correctly detected by the system. Consider, for example, the category F\({}_{2}\) (Table 2): The output weight determined for F\({}_{2}\) was the highest weight value (0.861617) (Table 3); thus, the fault was correctly identified to belong to F\({}_{2}\). To demonstrate the robustness of the proposed diagnostic system against interference, erroneous (\(\pm\)5%) test samples were considered at an operating frequency of 60 Hz, and the corresponding fault detection results are presented in Tables 6-8. The results indicated that after the consideration of errors, the proposed system could still correctly detect the fault category. Therefore, regardless of whether accurate or erroneous test data are used, the proposed system can correctly detect the fault category. \begin{table}
\begin{tabular}{c c} \hline
**Fault State** & **Category** \\ \hline Switch S\({}_{11}\)\({}^{+}\) fails & F\({}_{1}\) \\ Switch S\({}_{11}\)\({}^{-}\) or S\({}_{2}\)\({}^{+}\) fails & F\({}_{2}\) \\ Switch S\({}_{2}\)\({}^{-}\) fails & F\({}_{3}\) \\ Switch S\({}_{11}\)\({}^{+}\) fails & F\({}_{4}\) \\ Switch S\({}_{11}\)\({}^{-}\) or S\({}_{2}\)\({}^{+}\) fails & F\({}_{5}\) \\ Switch S\({}_{92}\)\({}^{-}\) fails & F\({}_{6}\) \\ Switch S\({}_{11}\)\({}^{+}\) fails & F\({}_{7}\) \\ Switch S\({}_{11}\)\({}^{-}\) or S\({}_{62}\)\({}^{+}\) fails & F\({}_{8}\) \\ Switch S\({}_{52}\)\({}^{-}\) fails & F\({}_{9}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Power transistor fault categories. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Phase** & **Fault Category** & \(\boldsymbol{C_{1}}\)**\(\boldsymbol{X}\) axis** & \(\boldsymbol{C_{1}}\)**\(\boldsymbol{Y}\) axis** & \(\boldsymbol{C_{2}}\)**\(\boldsymbol{X}\) axis** & \(\boldsymbol{C_{2}}\)**\(\boldsymbol{Y}\) axis** \\ \hline \multirow{8}{*}{_a_-phase chaos eye feature value} & F\({}_{1}\) & \(-\)0.049 & \(-\)39.988 & 0.046 & \(-\)42.584 \\  & F\({}_{2}\) & \(-\)0.046 & 32.789 & 0.049 & 30.448 \\  & F\({}_{3}\) & \(-\)0.068 & \(-\)1.429 & 0.075 & 17.557 \\  & F\({}_{4}\) & \(-\)0.074 & \(-\)36.222 & 0.067 & \(-\)11.218 \\  & F\({}_{5}\) & \(-\)0.079 & 15.843 & 0.069 & 13.017 \\  & F\({}_{6}\) & \(-\)0.07 & \(-\)24.913 & 0.08 & \(-\)31.164 \\  & F\({}_{7}\) & \(-\)0.06 & \(-\)8.153 & 0.057 & \(-\)4.901 \\  & F\({}_{8}\) & \(-\)0.08 & 15.631 & 0.07 & 13.255 \\  & F\({}_{9}\) & \(-\)0.05