# Failure Warning at the End of Service-Life of Lead-Acid Batteries for Backup Applications
## 4 Conclusions  
The red line of the quantity of the remaining capacity is often different among batteries; the same red line ignores differentiation. The red line of the quality of the remaining capacity can be unified, such as by the saturation characteristic of the morphology correction factor. The saturation of the morphology correction factor at the end of service-life proposed in this paper is more suitable for battery failure decision, although the remaining useful capacity of an individual cell (E-11#) may above average alarm threshold. State-of-the-art approaches focus on factors that determine quantity of remaining useful capacity and determine remaining useful capacity before several years far away from battery failure to counter hysteresis of lead-acid battery. The proposed model in this paper focuses on  
Figure 12: Morphology correction factors (\(\xi\)) of parallel samples in 55 \({}^{\circ}\)C aging experiments. (**a**) E-14#; (**b**) E-48#; (**c**) E-23#; (**d**) E-26#.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cell** & **MBE** & **RMSE** \\ \hline E-14\# & 10.93 & 15.01 \\ E-48\# & 16.40 & 19.40 \\ E-23\# & 10.71 & 13.07 \\ E-26\# & 11.55 & 13.53 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Fitting errors of estimations of batteries capacity of proposed aging model.  
factors which determine quality of remaining useful capacity and model battery failure at the end of service-life to counter hysteresis of lead-acid battery.  
The linear-superposition-voltage-aging model proposed in this paper directly predicts internal resistances by contacting resistances from EIS. This method is particularly suitable for long-term floating service backup applications and for continuous prediction of remaining useful capacity between deep-discharging tests. While frequency of deep-discharging tests is increased, error of prediction is reduced. The linear-superposition-voltage-aging model can be extended to other batteries for prediction of remaining useful capacity.  
Interactive analysis of nonlinear element is an alternative to avoid limitations brought by numeric calculations. Advantages of equivalent circuit and mathematical models are combined by interactively analysis. Generally, equivalent circuit model is more intuitive to extract parameters by local linear superposition; and mathematical model is more flexible to extract parameters by global linear equations.  
Conceptualization, W.W., W.Y., W.C. and Z.L.; data curation, W.W., W.Y., W.C. and D.C.; formal analysis, W.W., W.Y., W.C., D.C. and Z.L.; funding acquisition, W.Y. and Z.L.; investigation, W.W., W.Y. and Z.L.; methodology, W.W., W.Y., W.C. and Z.L.; project administration, W.Y., W.C., D.C. and Z.L.; resources, W.Y., W.C., D.C. and Z.L.; software, W.W. and W.Y.; supervision, W.Y. and Z.L.; validation, W.W., W.C. and D.C.; visualization, W.W., W.C. and D.C.; writing-original draft, W.W., W.Y. and Z.L.; writing-review and editing, W.W., W.Y. and Z.L. All authors have read and agreed to the published version of the manuscript.  
The research presented within this study was supported by the National Natural Science Foundation of China under grants (51677168) and the National Major Science and Technology Projects of China under grants (2017 ZX06002009).  
Thanks to [PERSON], [PERSON] and [PERSON], from Zhejiang Narada Power Source Co., Ltd., for helpful discussions and experimental configuration.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript or in the decision to publish the results.