## 4 Experimental Results and Analysis
### The Comparison of SOH Prediction Results Using Different Prediction Models
In contrast, LSSVM, which optimizes the objective function through the least squares method, significantly improves computational efficiency, particularly excelling in small-sample data scenarios [45]. LSSVM exhibits not only high generalization capability and robustness, effectively handling noise and uncertainties in battery data but also offers strong interpretability due to its simple model structure, facilitating intuitive analysis of feature weights [46]. In this study, we employed bidirectional LSTM (Bi-LSTM) and bidirectional GRU (Bi-GRU) models for battery SOH prediction, using 60% of each battery's data for training and 40% for testing. The prediction results are shown in Figure 10, and the prediction error results are presented in Table 3. The prediction curve of LSSVM is shown in Figure 11, and the prediction error results are presented in Table 4 From the prediction results, the Bi-LSTM model outperformed the LSSVM and Bi-GRU models. However, LSSVM has a simpler structure with fewer parameters and lower computational complexity, especially when dealing with short sequence data, where it demonstrates higher computational efficiency and significantly reduces the time cost for training and prediction. Additionally, LSSVM can effectively handle nonlinear relationships through kernel functions and maintains good generalization ability even with small sample datasets. It also exhibits strong robustness against noise, and its prediction accuracy can be further enhanced by combining appropriate preprocessing methods and optimization algorithms. In contrast, although Bi-LSTM and Bi-GRU models perform well in processing \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Method** & **CS2\_35** & **CS2\_36** & **CS2\_37** & **CS2\_38** & **Mean Value** \\ \hline \multicolumn{5}{c}{MAE (\%)} \\ M1 & 1.8135 & 1.8533 & 2.4597 & 0.3447 & 1.6178 \\ M2 & 1.6059 & 1.8032 & 1.2836 & 0.3347 & 1.2569 \\ M3 & 0.6733 & 0.9779 & 0.9154 & 0.3208 & 0.7219 \\ MD & 0.3430 & 0.4675 & 0.4066 & 0.3584 & 0.3939 \\ \hline \multicolumn{5}{c}{MAPE (\%)} \\ M1 & 2.7036 & 2.5551 & 3.3765 & 0.4336 & 2.2672 \\ M2 & 2.3773 & 2.4907 & 1.7553 & 0.4164 & 1.7599 \\ M3 & 0.9467 & 1.3251 & 1.2402 & 0.3993 & 0.9778 \\ MD & 0.4597 & 0.6153 & 0.5331 & 0.4512 & 0.5148 \\ \hline \multicolumn{5}{c}{RMSE (\%)} \\ M1 & 2.7351 & 2.3641 & 3.3294 & 0.4567 & 2.2213 \\ M2 & 2.6235 & 2.3379 & 1.7205 & 0.4263 & 1.7771 \\ M3 & 0.9218 & 1.1777 & 1.1673 & 0.4117 & 0.9196 \\ MD & 0.4603 & 0.5725 & 0.5151 & 0.4747 & 0.5057 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SOH prediction errors resulting from different methods under 60% training dataset. Figure 11: Comparison of prediction results for different batteries using four methods. SOH prediction results of (**a**) CS2_35; (**b**) CS2_36; (**c**) CS2_37; (**d**) CS2_38. long sequence data, their complex network structures lead to high computational resource consumption and increased sensitivity to noise. Considering factors such as computational complexity, hyperparameter design, and training cost, the LSSVM model, with its simple structure, fewer parameters, and low computational complexity, especially its superior computational efficiency for short sequence data and the significant reduction in training and prediction time cost, was selected as the basic model after a comprehensive evaluation. To validate the effectiveness of the proposed model, we compare its SOH predictions with those from LSSVM, PSO-LSSVM, and GWO-LSSVM, using 60% of each battery's data for training and 40% for testing. The kernel parameter and regularization parameter are key hyperparameters in LSSVM that play a decisive role in the overall performance of the model. The PSO-GWO algorithm optimizes these critical hyperparameters to obtain their optimal values, thereby enhancing the model's prediction accuracy for battery SOH. For example, the CS2_38 battery's particle dimension for PSO, GWO, and PSO-GWO was set to 2, with a population size of 20 and 50 iterations.