## 5 Conclusions  
To improve the accuracy of SOH prediction and achieve precise estimation for electric vehicle applications, this study presents an innovative SOH estimation approach that combines the PSO-GWO-LSSVM prediction model with multi-dimensional HFs extraction. Initially, eight HFs were extracted from battery charge segments to accurately capture the aging process. These features were categorized into four groups: time-based, energy-based, similarity-based, and second-order HFs. A subsequent correlation analysis identified six highly correlated HFs, optimizing the system's efficiency. The proposed methodology employs a PSO-GWO hybrid algorithm for precision tuning of LSSVM hyperparameters, where the grey wolf optimizer enhances the local search capability of particle swarm optimization during parameter identification. This approach leverages the strengths of both algorithms, improving the balance between global and local search functions and addressing challenges such as overfitting, underfitting, and local optima. The resulting PSO-GWO-LSSVM model, which is characterized by high prediction accuracy and low computational cost, was developed for SOH estimation, making it well-suited for practical applications in electric vehicles. The proposed method was validated using a publicly available dataset containing four battery samples from the CALCE Research Center at the University of Maryland dataset \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Battery** & **Training Data** & **MAE (\%)** & **MAPE (\%)** & **RMSE (\%)** \\ \hline \multirow{3}{*}{B0005} & 50\% & 0.2651 & 0.3817 & 0.4499 \\  & 60\% & 0.1950 & 0.2881 & 0.2479 \\  & 70\% & 0.1672 & 0.2512 & 0.2098 \\ \hline \multirow{3}{*}{B0006} & 50\% & 0.5628 & 0.8710 & 0.7389 \\  & 60\% & 0.3142 & 0.4919 & 0.4216 \\ \cline{1-1}  & 70\% & 0.2574 & 0.4127 & 0.3381 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: SOH estimation errors for different battery types in different proportions of the training dataset. Figure 13: Comparison of prediction results for different battery types. SOH prediction results of (a) B0005; (c) B0006; SOH prediction results error of (b) B0005; (d) B0006. (CS2_35, CS2_36, CS2_37, and CS2_38). Experimental results demonstrate that the method consistently achieves a prediction error margin of approximately 0.5%, with R\({}^{2}\) values for all four batteries exceeding 0.985, highlighting the model's high accuracy. The average SOH prediction errors--MAE, MAPE, and RMSE--are 0.3939%, 0.5148%, and 0.5057%, respectively, outperforming other models. Compared to the LSSVM model and three alternative approaches, the proposed method shows superior accuracy, with maximum SOH prediction errors around 0.5%. To verify the model's generalization capability, experiments using cycle data from two 18650-type lithium-ion cells (B0005 and B0006) from the NASA Ames Research Center were conducted. The prediction errors are all within 1%, which demonstrates the generalization capability of the proposed model. Future research will extend the application of this method to other battery types, such as lithium-ion and sodium-ion batteries, to further evaluate its effectiveness. Another focus will be on SOH estimation for battery packs, with a particular emphasis on real-world applications. The primary goal is to provide accurate SOH assessments for battery packs, addressing the growing demands of energy storage systems and the electric vehicle industry. This work aims to tackle the issue associated with achieving highly accurate SOH estimations with limited data, thereby contributing to ongoing advancements in performance and reliability in the fields of energy storage and electric vehicles. Conceptualization, L.W. and X.H. ; methodology, X.H. and J.Z. ; software, Z.W. ; validation, Z.W. and J.B.; formal analysis, J.Z. ; investigation, L.L. ; data curation, Z.W. ; writing--original draft preparation, X.H. ; writing--review and editing, J.B. and L.W. ; visualization, L.L. ; supervision, L.L. ; project administration, L.L. and L.W.