## 4 Result Analysis and Discussion
### Feature Extraction Using Improved RBSWT  
In this subsection, the feature extraction process for various signal tests of a faulted power transformer is addressed, focusing on external fault with saturation, internal faults, inrush currents, and internal faults occurring simultaneously with CT saturation, as discussed in the previous subsection. Figures 7-10 depict these signals both with and without the inclusion of white noise. It should be noted that in the external fault scenario depicted in Figure 10, a three-phase short circuit to ground fault is used to ensure the absolute condition of saturation. As shown in Figure 7, inrush currents exhibit a rapid increase in magnitude at the onset of space gaps, transitioning either from zero to a significant value or from a specific value back to zero. This abrupt change in current results in smooth ripples along the signal's length as it swiftly shifts between different states. Upon inspecting the shape of the decomposition details depicted in Figures 11-14 both the origin and detail coefficients of each faulted signal reveal discernible features. These features are indicative of distinct characteristics within the signal, which can be effectively captured and utilized for further analysis and diagnosis. On the other hand, the wavelet decomposition of each faulted signal is shown in Figures 11-14. These wavelet decompositions can be used for extracting the component levels of the faulted signals. This process allows for a detailed analysis of the signal components, providing valuable insights into the nature and characteristics of each fault. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & **Power Source** & **Number of** & \multirow{2}{*}{**Fault Location**} & **Fault Ground** & **Transformer Load** \\ \cline{2-2}  & **Phase Angle** & & & & **Resistance** & **Transformer Load** \\ \hline \multirow{2}{*}{Inrush current} & (0–360\({}^{\circ}\)) & 500 & - & - & - \\ \cline{2-2}  & & 500 & HV and LV & & \\ \cline{2-2}  & & 500 & HV and LV & & (0.001, 0.01, 0.1, \(\ldots\), 75), & (5 MVA to 33 MVA) \\ \cline{2-2}  & & 250 & HV & & (0.001, 0.01, \(\ldots\), 75, & (5 MVA to 33 MVA) \\ \cline{2-2} saturation & & 250 & LV & & 125, 150), & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Various fault scenarios in the power transformer for training and testing the proposed framework. Figure 8: Differential current signal of the power transformer during an internal fault without CT saturation effect. Figure 7: Differential current signal of the power transformer during inrush current under CT saturation condition. Figure 10: Differential current signal of the power transformer during an external fault under CT saturation condition. Figure 9: Differential current signal of the power transformer during an internal fault under CT saturation condition. Figure 11: Various levels of detail coefficients for the differential current signal of a power transformer during inrush current under CT saturation condition. Figure 12: Various levels of detail coefficients for the differential current signal of a power transformer during an internal fault without CT saturation condition. Additionally, the analysis of these features provides valuable insights into the behavior of the power transformer under various fault conditions. By examining the detail coefficients, one can identify specific patterns and anomalies associated with each type of fault. This information is crucial for developing robust diagnostic tools and improving the reliability of fault detection methods. The detailed examination of inrush currents, external  
Figure 14: Various levels of detail coefficients for the differential current signal of a power transformer during an external fault under CT saturation condition. Figure 13: Various levels of detail coefficients for the differential current signal of a power transformer during an internal fault under CT saturation condition.