## 5 Conclusions  
This paper proposes a method that utilizes charging feature extraction and ridge regression to estimate SOH and predict RUL of lithium-ion batteries. By extracting three sets of health features that can reflect battery degradation from the charging voltage curve. These health features are used as input and SOH as output, leading to the development of a battery aging model based on ridge regression. On this basis, a multiscale prediction model is designed to predict the changing trend of health features. The results of the multiscale prediction model are integrated with the battery aging model to estimate SOH through multiple steps, thus achieving an accurate prediction of RUL. The accuracy and reliability of the proposed method are confirmed using two battery datasets under varied operating conditions to validate its performance. Experimental results show that the prediction curves can approximate reality closely, the MAE and RMSE calculations of SOH remain below 0.02, and the maximum AE of RUL is no more than two cycles. By combining the SOH and RUL estimation results, a comprehensive and accurate prediction of battery aging can be obtained. Therefore, the proposed SOH and RUL prediction methods offer high accuracy and adaptability, serving as valuable references for SOH and RUL prediction of existing lithium-ion batteries.  
However, the method has not yet been validated in other more complex working conditions, such as the impact of temperature factors on battery aging. Battery temperature changes can reduce the reliability of battery SOC estimation and can even pose a risk of thermal runaway; accurate battery SOC estimation in temperature-varying environments can avoid battery thermal runaway [39]. This may result in the inability to provide a more comprehensive reflection of the battery state. Therefore, in future work, the method needs to be further optimized to consider the temperature factor and perform joint estimation to adapt to more complex operating environments.  
Conceptualization, M.W. and C.Y.; methodology, C.Y. and F.Z.; software, C.Y.; validation, C.Y. and R.S.; formal analysis, J.T. and S.H.; investigation, N.Z. and J.W.; resources, M.W.; data curation, J.T. and S.H.; writing--original draft preparation, C.Y.; writing--review and editing, F.Z. and R.S.; project administration, N.Z. and J.W.; funding acquisition, M.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Science and Technology Project of Hubei Province (No. 2022 BEC017), Natural Science Foundation of Hubei Province (No. 2022 CEA007), and Science and Technology Project of Hubei Province (No. 2022 BEB016).  
Not applicable.  
The data presented in this study are openly available at: [[https://www.nasa.gov/intelligent-systems-division/discovery-and-systems-health/pcoe/pcoe-data-set-repository](https://www.nasa.gov/intelligent-systems-division/discovery-and-systems-health/pcoe/pcoe-data-set-repository)]([https://www.nasa.gov/intelligent-systems-division/discovery-and-systems-health/pcoe/pcoe-data-set-repository](https://www.nasa.gov/intelligent-systems-division/discovery-and-systems-health/pcoe/pcoe-data-set-repository)) (accessed on 2 February 2024) and [[https://ora.ox.ac.uk/objects/uuid:03](https://ora.ox.ac.uk/objects/uuid:03) ba4b01-cfed-46d3-9b1a-7d4]([https://ora.ox.ac.uk/objects/uuid:03](https://ora.ox.ac.uk/objects/uuid:03) ba4b01-cfed-46d3-9b1a-7d4) a7 bfdffac (accessed on 2 February 2024).  
The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Current Number** & **Real Capacity** & **Estimated** & **Estimation** & **Real RUL** & **Prediction of** & **Prediction** \\
**of Cycles** & **(Ah)** & **Capacity (Ah)** & **Error (Ah)** & **RUL** & **Error** \\ \hline
111 & 1.4387 & 1.4382 & 0.0005 & 14 & 14 & 0 \\
121 & 1.4383 & 1.4336 & 0.0047 & 4 & 4 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Results of the joint SOH and RUL evaluation.