## 6 Conclusions  
This paper proposes an analytical model-based fault diagnosis method for T\({}^{2}\)3L inverters, achieving diagnosis of single- and double-switch OC faults within the same phase. First, an improved adaptive sliding mode observer is designed by integrating the hyperbolic tangent function with an adaptive term, which effectively mitigates chattering and improves the precision of phase currents estimation. Then, an adaptive threshold-based fault detection method is proposed to enhance detection robustness and accuracy. Furthermore, fault location variables generated from observed and actual currents enable the precise location of single-switch faults and partial same-phase double-switch faults. The proposed method requires neither additional hardware circuits nor extensive data. Simulation results validate the method's capability to diagnose single-switch and simultaneous same-phase double-switch faults under complex operating conditions. Building on this, future research could consider more double-switch fault scenarios and design more comprehensive fault diagnosis strategies.  
Methodology and idea proposal, X.Z. and S.G.; simulation and validation, X.Z. and Z.S.; writing--original draft preparation, Z.S.; results analysis, Z.S.; manuscript polishing, C.C.; writing--review and editing, K.W. and S.Z.; All authors have read and agreed to the published version of the manuscript.  
This research was funded by Young Talent Nurturing Program of Shaanxi Provincial Science and Technology Association (Grant No. 20240109), ShenZhen Undertakes Industrialization Application Projects of Major National Science and Technology project (Grant No. CJGZD2020517141401003), Technology and Industry Basic Scientific Research Project of National Defense (Grant No. G20230823), National Natural Science Foundation of China (Grant No. 6230367), Scientific research project of Shaanxi Provincial Educational Committee (Grant No. 23 JK0486), Key Research and Development Program of Shaanxi (Grant No. 2024 GX-YBXM-050) and The Youth Innovation Team of Shaanxi Universities (Grant No. 2023997).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Research Plant** & \
\begin{tabular}{c} **Single/** \\ **Multiple Fault** \\ \end{tabular} & **Diagnosis Variable** &
\begin{tabular}{c} **Hardware/** \\ **Calculation Cost** \\ \end{tabular} & **Robustness** \\ \hline
[15] & T\({}^{2}\)3L inverter & Multiple & \(u_{c1},u_{c2},i_{x}\) & No/High & High \\
[33] & T\({}^{2}\)3L inverter & Multiple & \(u_{x0},i_{x}\), switching state & Yes/Low & Low \\
[23] & T\({}^{2}\)3L inverter & Single & \(i_{x}\), \(u_{c1},u_{c2},l_{x}\) and etc. & Yes/Low & High \\
[19] & T\({}^{2}\)3L inverter & Single & \(i_{x},l_{x}\) and etc. & No/Low & Low \\
[18] & T\({}^{2}\)3L inverter & Single & \(u_{x0}\) & Yes/Low & low \\
[32] & SPTL inverter & Single & \(i_{x},u_{x}\) & No/Low & High \\
[31] & NPC inverter & Single & \(i_{x}\) & No/Low & High \\ The proposed method & T\({}^{2}\)3L inverter & Multiple & \(i_{x}\) & No/Low & High \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison with previous fault diagnosis methods.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors claim no conflicts of interests.