## 5 Experiment Results and Discussion
### Identification Results by IHHT  
An original detected signal is analyzed here by the IHHT approach as referred to in Section 3. As the first step, the first run of EMD process is performed on such original discharge signal for the purpose of the removal of the trend curve embedded. In the course of the second run of the EMD process, the shifting number remains invariant and the process proceeds until a K-S test result matches the sorting result by signal energy ratio. Subsequently, all the illusive components are ruled out by a cumulative IMF with the highest probability in the proposed IHHT. In the end, time-frequency-energy 3D spectrums are made once again, as demonstrated in Figure 12. As presented in Figure 13, a feature distribution is plotted by way of features, namely fractal dimension and lacunarity, gained by use of an extension theory, and averaged discharged energy. It is seen that the feature distributions, evaluated by IHHT, for Types II, III and IV tend to stay apart from each other, that is, the identification ratio is promoted accordingly. In other words, little difference between similar features can be made more distinguishing through a fractal theory such as the case between Type III and IV. As tabulated in Table 2, the IHHT analysis is demonstrated able to provide an identification ratio up to 50% in the case of Type III. In comparison of 3D spectrums, there is a higher distinction between Types III and IV in Figure 12c,d, the result analyzed by IHHT, than that in Figure 10c,d. In a brief conclusion, the proposed IHHT is an approach able to promote defect mode identification ratios as intended. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ModelNoise** & **0\%** & **\(\pm\)10\%** & **\(\pm\)20\%** & **\(\pm\)30\%** \\ \hline Type I & 100 & 100 & 80 & 50 \\ Type II & 95 & 90 & 90 & 85 \\ Type III & 0 & 5 & 10 & 20 \\ Type IV & 80 & 70 & 65 & 60 \\ Type V & 100 & 95 & 95 & 85 \\ Type VI & 95 & 80 & 80 & 45 \\ Average & 78.3 & 73.3 & 70 & 57.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Identification results by HHT versus features fractal dimension (FD)- lacunarity (\(\Lambda\))-mean-discharged (M). Figure 11: Feature distributions for time–frequency–energy 3D spectrums by HHT. Even though the identification ratio and the ability against noise interference are improved as a consequence of the removal of illusive components and mode confusions, the identification ratio still remains relatively low between similar defect modes. For this sake, the energy level (E), denoted by \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ModelNoise** & **0\%** & **\(\pm\)10\%** & **\(\pm\)20\%** & **\(\pm\)30\%** \\ \hline Type I & 100 & 100 & 80 & 32 \\ Type II & 100 & 65 & 60 & 35 \\ Type III & 50 & 40 & 25 & 15 \\ Type IV & 80 & 80 & 65 & 45 \\ Type V & 100 & 95 & 85 & 80 \\ Type VI & 100 & 80 & 60 & 50 \\ Average & 88.3 & 76.6 & 62.5 & 42.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Identification results by IHHT versus features FD-\(\Lambda\)-M.  
Figure 12: Time–frequency–energy 3D spectrums by IHHT for (**a**) Type I (**b**) Type II (**c**) Type III (**d**) Type IV (**e**) Type V and (**f**) Type VI. Figure 13: Feature distributions for time–frequency–energy 3D spectrums by IHHT. the \(z\)-axis in the IHHT spectrum, is adopted as the fourth feature. The idea stems from the fact that distinct defect modes represent distinct discharge signals, i.e., various amount of energy is released through insulators. Hence, it is presumed that the adoption of the average energy level as a feature can render a higher identification result. Demonstrated in Figure 14 are the feature distributions of the fractal dimension, lacunarity and average energy, from which it is seen as expected that Type IV exhibits a smaller amount of discharged energy than Type III, simply for the reason that Type IV is designed as an unflawed case, a case supposed to release the minimal amount of discharge energy. As a result, a high distinction is reached in the discharge energy aspect.