## 3 Results
### Results Comparison for Different Algorithms  
To validate the effectiveness of the proposed method, ELM [26], GPR algorithm [28], and ANN [29] are introduced to compare the results of interval prediction with those of the proposed method. Figures 4-6 show the prediction results of applying the four methods in region 1, region 2, and region 3, respectively. In the figure, the black x mark represents the actual load, the red line is the upper limit of the predicted interval, the purple line is the lower limit of the predicted interval, and the red and purple lines form 96 little intervals, which are the results of the interval prediction. If the black x mark is between the red line and the purple line, the point prediction can be considered successful. If the black x mark is beyond the red line, then the measured value is considered beyond the upper limit of the prediction. If the black x mark is lower than the purple line, then the measured value is lower than the lower limit of the prediction. When the measured value exceeds the upper limit or lower limit, the point prediction is considered to be a failure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Point** & **PICP** & **PIAW** & \begin{tabular}{c} **Standardized** \\ **PICP** \\ \end{tabular} & \
\begin{tabular}{c} **Standardized** \\ **PIAW** \\ \end{tabular} &
\begin{tabular}{c} **Weight** \\ **Calculation** \\ \end{tabular} \\ \hline P8 (\(t=1\), \(K=377\)) & 0.844 & 222.148 & 0.480 & 0.985 & 0.734 \\ P9 (\(t=1\), \(K=394\)) & 0.813 & 221.481 & 0.377 & 0.990 & 0.686 \\ P10 (\(t=1\), \(K=418\)) & 0.760 & 221.149 & 0.200 & 0.993 & 0.599 \\ P11 (\(t=1\), \(K=456\)) & 0.740 & 220.967 & 0.133 & 0.994 & 0.567 \\ P12 (\(t=1\), \(K=544\)) & 0.700 & 220.171 & 0 & 1.000 & 0.500 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Point** & **PICP** & **PIAW** & \begin{tabular}{c} **Standardized** \\ **PICP** \\ \end{tabular} & \
\begin{tabular}{c} **Standardized** \\ **PIAW** \\ \end{tabular} &
\begin{tabular}{c} **Weight** \\ **Calculation** \\ \end{tabular} \\ \hline P1 (\(t=1\), \(K=48\)) & 1.000 & 377.187 & 1 & 0.000 & 0.500 \\ P2 (\(t=1\), \(K=69\)) & 0.990 & 298.588 & 0.967 & 0.609 & 0.788 \\ P3 (\(t=1\), \(K=119\)) & 0.979 & 288.157 & 0.930 & 0.690 & 0.810 \\ P4 (\(t=1\), \(K=134\)) & 0.969 & 251.691 & 0.897 & 0.972 & 0.935 \\ P5 (\(t=1\), \(K=245\)) & 0.958 & 251.563 & 0.861 & 0.973 & 0.917 \\ P6 (\(t=1\), \(K=287\)) & 0.948 & 250.422 & 0.828 & 0.982 & 0.905 \\ P7 (\(t=1\), \(K=348\)) & 0.938 & 250.154 & 0.795 & 0.984 & 0.889 \\ P8 (\(t=1\), \(K=395\)) & 0.844 & 249.565 & 0.483 & 0.989 & 0.736 \\ P9 (\(t=1\), \(K=457\)) & 0.813 & 249.194 & 0.381 & 0.991 & 0.686 \\ P10 (\(t=1\), \(K=478\)) & 0.760 & 248.568 & 0.205 & 0.996 & 0.601 \\ P11 (\(t=1\), \(K=515\)) & 0.740 & 248.421 & 0.139 & 0.997 & 0.568 \\ P12 (\(t=1\), \(K=556\)) & 0.700 & 248.084 & 0 & 1.000 & 0.500 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Weight calculation results of the points in the Pareto optimal solutions set in region 3. It can be observed from Figure 4a that the measured values of two points (34, 73) exceed the upper limit of the prediction, so they do not meet the prediction requirements. In Figure 4b, the measured values of three points (27, 34, 73) exceed the upper limit of the prediction, so they do not meet the prediction requirements. In Figure 4c, the measured values of four points (33, 34,37, 73) exceed the upper limit of the prediction, so they do not meet the prediction requirements. In Figure 4d, the measured values of five points (24, 33, 34, 37, 73) exceed the upper limit of the prediction, so they do not meet the prediction requirements. In Figure 4, we see that the load values of points 33-34 and 72-73 undergo a sudden change, but the four prediction methods cannot predict the dramatic change of this load in advance, so all the interval prediction upper bounds are a bit low, resulting in failed prediction with each method at points 34 and 73.