# SOH Estimation of Lithium-Ion Battery Pack Based on Integrated State Information from Cells
## 4 Prediction Result Analysis
### Accuracy Analysis  
Based on the previous analysis result in Section 2.3, in order to clarify the evaluation of the effectiveness of the proposed method, the accuracies of multiple predictions are calculated in this section. Further, the differences were still concluded compared with the pack-prediction method. For the stability of the methods, box plots were adopted to assess the accuracy dispersion of many predictions. The box plots mainly focused on the highest and lowest data points, the median, and the first and third quartiles. These indicators are listed in Table 4 as follows. Figure 17: Correlation between the prediction degradation rate and the temperature fluctuation: (**a**) cells-prediction; (**b**) pack-prediction. In Table 4, the term IQR represents the interquartile deviation, which is the difference between the third quartile and first quartile. The error of different scale predictions is compared in Figure 18, and the data are explained in detail in Table 5. The compared scale was selected to be 20, 50, 100, and 400 prediction cycles for a fixed time series. It can be concluded from Figure 18 that there was an obvious disparity between the two prediction methods: \begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Definitions** \\ \hline The highest datum & The highest datum still within 1.5 IQR (interquartile range) of the upper quartile \\ \hline The lowest datum & The lowest datum still within 1.5 IQR of the lower quartile \\ \hline Median & The value separating the higher half from the lower half of a data sample \\ \hline The first quartile & The middle value between the smallest value and the median of the data set \\ \hline The third quartile & The middle value between the median and the highest value of the data set \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Indicators of the box plots. Figure 18: Stability comparison between prediction methods. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Methods** & **Cycles** & \begin{tabular}{c} **The Highest** \\ **Datum** \\ \end{tabular} & \begin{tabular}{c} **The Third** \\ **Quartile** \\ \end{tabular} & \begin{tabular}{c} **Median** \\ **Quartile** \\ \end{tabular} & \begin{tabular}{c} **The First** \\ **Quartile** \\ \end{tabular} & \
\begin{tabular}{c} **The Lowest** \\ **Datum** \\ \end{tabular} &
\begin{tabular}{c} **Outliers** \\ \end{tabular} \\ \hline \multirow{4}{*}{Cells-Prediction} & 20 & 0.002814 & 0.0024 & 0.001699 & 0.001274 & 0.000101 & 0\% \\ \cline{2-7}  & 50 & 0.004534 & 0.002395 & 0.002041 & 0.000443 & 0.000114 & 0\% \\ \cline{2-7}  & 100 & 0.002816 & 0.001903 & 0.001486 & 0.000746 & 0.0000524 & 0\% \\ \cline{2-7}  & 400 & 0004936 & 0.00261 & 0.001718 & 0.00091 & 0.0000406 & 4.08\% \\ \hline \multirow{4}{*}{Pack-Prediction} & 20 & 0.008563 & 0.008064 & 0.007585 & 0.006075 & 0.0030915 & 15\% \\ \cline{2-7}  & 50 & 0.007093 & 0.006376 & 0.005555 & 0.00439 & 0.00385 & 0\% \\ \cline{1-1} \cline{2-7}  & 100 & 0.005085 & 0.003641 & 0.003066 & 0.002615 & 0.001921 & 0\% \\ \cline{1-1} \cline{2-7}  & 400 & 0.00791 & 0.003753 & 0.001886 & 0.000919 & 0.0000073 & 6.56\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean error of different cycle predictions. * The accuracy of the SOH prediction with fused information from the cells was more stable when accompanied by the increase of the prediction cycles. In the pack-prediction method, the accuracy fluctuated too severely to be determined the best prediction scale. * With the premise that the cells provided sufficient deterioration information, there was less abnormal data for the prediction result. However, with limited input variances in the pack-prediction method, a large number of outliers occurred in the results (as seen in 400 cycles). * With the increase of the prediction scale, the mean and minimum of the relative errors in the pack-prediction method became better and better. However, in the repeated prediction process, the error fluctuation and abnormal data made it harder to optimize the parameters of the model.