## 5 Conclusions  
In this study, we propose a lithium battery SOH estimation model based on WD-IWOA-DELM. The model is subjected to theoretical analysis and experimental validation, leading to the following conclusions:  
1. In this study, we use the capacity degradation sequences of lithium batteries as the health indicator. By employing WD, the data are divided into an overall degradation trend and a localized degradation trend, effectively reducing noise fluctuations and interference from capacity regeneration signals in the original data. A comparison with EEMD and CEEMDAN decomposition algorithm shows that the WD decomposition algorithm exhibits the lowest error, minimizing the impact of the decomposition process on the SOH prediction of lithium batteries.
2. By introducing adaptive weights and non-linear convergence behavior, the traditional WOA algorithm has been improved to prevent premature convergence caused by local optima, thereby enhancing both the accuracy of algorithmic optimization and the convergence speed. Utilizing this enhanced algorithm for parameter optimization of DELM has led to an improvement in predictive accuracy.
3. This approach underwent generalization validation on two sets of datasets. For the NASA dataset, the mean root mean square error across four lithium batteries was 0.67%. In the CALCE dataset, the mean \(RMSE\) across four lithium batteries was 0.72%. The fitting degree between predicted and actual values exceeded 98%. This demonstrates that the method possesses good accuracy and robustness.  
Limitations and Improvement: 1. The degradation of lithium batteries is influenced by multiple factors. This study only considers battery capacity as a health factor. In future research, a more comprehensive set of health factors, including resistance, voltage, current, and equalization charge and discharge time during battery cycling, will be taken into account. The selection of highly representative health factors that capture battery health status will be measured. 2. There exist differences between real-world and laboratory conditions for lithium-ion batteries. Achieving effective data transfer between these two scenarios and reducing the divergence between their data are directions for future research. 3. Enhancing data preprocessing and cleansing processes to ensure high-quality data for health state estimation. Integrating other neural network models to further optimize health state estimation algorithms, reducing time complexity, and achieving real-time and accurate estimation.  
Conceptualization, J.L.; methodology, J.L.; software, J.L.; validation, J.L. and G.Z.; formal analysis, J.L. and G.Z.; investigation, J.L.; resources, J.L.; data curation, J.L. and G.Z.; writing--original draft preparation, J.L.; writing--review and editing, H.W. and Y.L.; visualization, J.L. and Y.L.; supervision, H.W. and Y.L.; project administration, H.W.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Natural Science Foundation of China (61863016).  
Not applicable.  
The data used in this paper are openly available. [[https://calce.umd.edu/battery-data](https://calce.umd.edu/battery-data)]([https://calce.umd.edu/battery-data](https://calce.umd.edu/battery-data)) (accessed on 10 October 2022), [[https://www.nasa.gov/intelligent-systems-division](https://www.nasa.gov/intelligent-systems-division)]([https://www.nasa.gov/intelligent-systems-division](https://www.nasa.gov/intelligent-systems-division)) (accessed on 10 October 2022).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} SOH & State Of Health \\ WD & Wavelet Decomposition \\ WOA & While Optimization Algorithm \\ DELM & Deep Extreme Learning Machine \\ _RMSE_ & Root Mean Square Error \\ _MAPE_ & Mean Absolute Percentage Error \\ _RA_ & Relative Accuracy \\ _R\({}^{2}\)_ & R-squared \\ C/D & Charge/Discharge \\ \end{tabular}