## 5 Experimental Validation
### Result and Discussion
Besides, as shown in Table 4, the correlation coefficient of our presented approach is greater than those in four similar approaches, which indicates that our presented approach is equipped with a lesser reconstruction error and a better decomposition performance compared with some typical techniques mentioned in the study. To compare the decomposability of different methods more intuitively and quantify the time/memory costs of different methods more precisely, we add the percentage differences of the IAVMD method with respect to the others (OVMD, LMD, EMD, and WT). Tables 5 and 6 list the percentage differences between the IAVMD and other approaches in the simulation and experiment signal, respectively. It can be seen from Tables 5 and 6 that the index value (energy error \(\theta\) and orthogonal index \(OI\)) of the IAVMD method is reduced compared with the other approaches (OVMD, LMD, EMD, and WT). The smallest percentage difference of IAVMD is about 0.1%, but the largest percentage difference can reach 9%. This indicates that the proposed IAVMD method has a certain degree of advantage in signal decomposition. However, at present, the significance of quantification of this small degree is still undetermined, which is the focus of our future research. Table 7 lists the memory cost and average time of different methods. Note that the memory cost of different methods is measured based on the memory usage of the MATLAB file of different methods. As shown in Table 7, the memory cost of IAVMD is the highest (above 8 Kbyte), the second biggest memory cost is the OVMD method, and WT has the smallest memory cost (i.e., the average cost is 1.39 Kbyte). In addition, the average time costs of our method and OVMD are high (above 25 s), whereas the other three methods (LMD, EMD, and WT)) have low time costs which are under 4 s. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{4}{c}{**Energy Error \(\theta\)**} & \multicolumn{4}{c}{**Orthogonal Index \(OI\)**} \\ \cline{2-7}  & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** \\ \hline IAVMD vs. OVMD & 0.29\% \(\downarrow\) & 0.47\% \(\downarrow\) & 0.95\% \(\downarrow\) & 1.79\% \(\downarrow\) & 0.73\% \(\downarrow\) & 1.74\% \(\downarrow\) \\ IAVMD vs. LMD & 0.64\% \(\downarrow\) & 0.24\% \(\downarrow\) & 0.11\% \(\downarrow\) & 6.38\% \(\downarrow\) & 1.35\% \(\downarrow\) & 1.47\% \(\downarrow\) \\ IAVMD vs. EMD & 1.10\% \(\downarrow\) & 1.21\% \(\downarrow\) & 5.45\% \(\downarrow\) & 9.14\% \(\downarrow\) & 5.42\% \(\downarrow\) & 3.76\% \(\downarrow\) \\ IAVMD vs. WT & 3.54\% \(\downarrow\) & 5.28\% \(\downarrow\) & 5.23\% \(\downarrow\) & 4.79\% \(\downarrow\) & 2.43\% \(\downarrow\) & 3.94\% \(\downarrow\) \\ \hline \hline \end{tabular} Where \(\downarrow\) denotes the symbol of the reduced percentage.  
\end{table} 
Table 6: The percentage differences of the IAVMD with respect to other approaches in the experiment signal. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{3}{c}{**Energy Error \(\theta\)**} & \multicolumn{3}{c}{**Orthogonal Index \(OI\)**} & \multicolumn{3}{c}{**Computing Time (s)**} \\ \cline{2-7}  & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** \\ \hline IAVMD & 0.0209 & 0.0174 & 0.0158 & 0.0034 & 0.0060 & 0.0054 & 32.0132 & 27.0215 & 24.9027 \\ OVMD & 0.0238 & 0.0221 & 0.0253 & 0.0213 & 0.0133 & 0.0228 & 20.1082 & 16.8875 & 15.5641 \\ LMD & 0.0273 & 0.0198 & 0.0169 & 0.0672 & 0.0195 & 0.0201 & 1.9617 & 2.8573 & 2.9322 \\ EMD & 0.0319 & 0.0295 & 0.0703 & 0.0948 & 0.0602 & 0.0430 & 1.7810 & 2.6301 & 2.7835 \\ WT & 0.0563 & 0.0702 & 0.0681 & 0.0513 & 0.0303 & 0.0448 & 1.3016 & 1.5158 & 1.6914 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The quantitative comparisons among different approaches in the experiment signal.