## 4 Kernel Extreme Learning Machine Method for PQDs Classification
### Comparison of Algorithm Classification Results  
The optimal feature vector set with a dimension of 150 \(\times\) 10 is used as the input of the classifier, and the overall structure of the classification is shown in Figure 5. In this paper, the first 100 \(\times\) 10 data set of the optimal feature vector set of each PQD is used as the training sample set of ELM and KELM, respectively, and the last 50 \(\times\) 10 data set is used as the test sample set. The ELM selects the sigmoid function as the activation function, and the KELM selects the gaussian kernel function. The classification results of fourteen kinds of PQD by KELM in Matlab2020 environment are shown in Figure 6. From the diagram it can be seen that KELM has a high degree of discrimination for 14 PQDS, and a small number of samples for C8, C9, and C13 are not enough, but the discrimination is still considered to fully meet the expectations. Figure 5: The structure diagram of KELM to identify PQDs. The combination of KF, UKF, ELM, and KELM is used to detect and classify the data of fourteen kinds of PQDs test samples, and the corresponding success rate is calculated quantitatively. The results are shown in Table 4. The table records the success rate of KF-ELM, KF-KELM, UKF-ELM, and UKF-KELM in various cases from C1 to C14. Finally, it is concluded that the highest success rate is UKF-KELM. KELM replaces the randomly initialized weight matrix in ELM with an orthogonal matrix, which can better maintain the information of input data and improve the accuracy of classification. Table 4 shows that the success rate of the UKF-KELM detection-classification method is higher than that of other combination methods, and the average success rate of classification is 98.14%. In order to further verify the anti-noise performance of the combined detection classification method, the detection and recognition results of voltage swell disturbance in different signal-to-noise ratio environments are shown in Figure 7. It can be seen from the figure that as the signal-to-noise ratio gradually increases, the signal interference and instability become lower, and the overall success rate of voltage swell disturbance identification becomes higher. At the same time, the four combined detection and identification methods \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Label**} & \multicolumn{4}{c}{**Success Rate of Different Methods**} \\ \cline{2-5}  & **KF-ELM** & **KF-KELM** & **UFK-ELM** & **UKF-KELM** \\ \hline C1 & 97 & 95 & 96 & 95 \\ C2 & 95 & 96 & 94 & 98 \\ C3 & 96 & 99 & 100 & 100 \\ C4 & 98 & 97 & 99 & 96 \\ C5 & 100 & 98 & 96 & 98 \\ C6 & 95 & 100 & 100 & 100 \\ C7 & 98 & 100 & 98 & 100 \\ C8 & 100 & 99 & 96 & 99 \\ C9 & 95 & 98 & 100 & 98 \\ C10 & 97 & 100 & 97 & 96 \\ C11 & 98 & 97 & 96 & 98 \\ C12 & 100 & 96 & 100 & 100 \\ C13 & 99 & 98 & 96 & 97 \\ C14 & 97 & 100 & 100 & 99 \\ Average rate & 97.5 & 98.07 & 97.71 & 98.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average success rate of combined detection-classification methods. Figure 6: The classification results of fourteen kinds of PQDs by KELM. are higher in different noise environments. The recognition success rate and anti-noise performance of UKF-KELM are better. The comparison of training and testing times between UKF-ELM and UKF-KELM for recognition and classification is shown in Table 5. As indicated by the table, although the UKF-KELM achieves superior accuracy and performance, its training and testing times remain similar to those of the UKF-ELM, without any significant increase. UKF-KELM enhances nonlinear modeling capability by incorporating kernel techniques, but its computational complexity does not differ significantly from UKF-ELM, as both models' computational bottleneck mainly lies in the Kalman filter process. Nonetheless, UKF-KELM performs better in handling complex power quality disturbances, offering higher classification accuracy.