## 3 Data Acquisition and Processing
### Data Processing  
To determine the input data of the neural network more scientifically and reasonably, we first drew the scatter figures between the 7 variables of the battery and the actual remaining capacity, and added a confidence ellipse to the scatter figure, where the confidence level of the ellipse was 95%, as shown in Figures 4-10. Then, the eight variables of the battery were analyzed for the Pearson and Spearman correlation analyses. The coefficient of Pearson assesses the linear correlation between two variables while the coefficient of Spearman assesses the monotonic relationship between two variables. Taking the two variables of \(X\) and \(Y\) as examples, the coefficient of Pearson could be obtained using Equation (14), and the coefficient of Spearman could be obtained using Equation (15), where \(d_{i}\) is the difference of the rank of the \(i\)-th data pair, and \(N\) is the number of samples. Table 3 shows the judgment criteria between the degree of correlation and the correlation coefficient. The results are shown in Table 4.  
Analyzing Figures 4-10 and Table 4, the coefficients of Spearman corresponding to \(T_{I}\), \(T_{total\_discharge}\), and \(\Delta Temp_{discharge}\) are all positive. This shows that the relationship between these three variables and the available remaining capacity monotonically increased. The coefficients of Spearman corresponding to \(T_{V}\), \(T_{total\_charge}\), \(\Delta V_{charge}\), and \(\Delta V_{discharge}\) are all negative, indicating that the relationship between these four variables and the available remaining capacity monotonically decreased. In Figure 4, the ratio of the long axis to the short axis of the confidence ellipse corresponding to \(T_{I}\) is the largest, and the coefficients of Pearson and Spearman are the largest. This indicates that the linear correlation between \(T_{I}\) and the actual remaining capacity is the largest, and the monotonic correlation is the strongest. The absolute value of the Pearson and Spearman coefficients of \(T_{total\_charge}\) is the smallest, and the ratio of the major axis to the minor axis of the confidence ellipse corresponding to \(T_{total\_charge}\) is the smallest, indicating that the correlation between \(T_{total\_charge}\) and the actual remaining capacity is the smallest. Figure 3: Relationship between the actual remaining capacity and cycles. Figure 4: Scatter figure of \(T_{I}\). Figure 5: Scatter figure of \(T_{V}\). Figure 6: Scatter figure of \(T_{total\_charge}\). Figure 8: Scatter figure of \(\Delta\)_Temp\({}_{discharge}\)._  
Figure 7: Scatter figure of \(T_{total\_discharge}\). Figure 9: Scatter figure of \(\Delta\)_V\({}_{charge}\)._  
\[\rho_{X,Y}=\frac{N\sum XY-\sum X\sum Y}{\sqrt{N\sum X^{2}-\left(\sum X\right)^{2} }\sqrt{N\sum Y^{2}-\left(\sum Y\right)^{2}}} \tag{14}\]  
\[\rho=1-\frac{6\sum d_{i}{}^{2}}{N(N^{2}-1)} \tag{15}\]  
According to the absolute value of [PERSON]'s correlation coefficient, the order of linear correlation can be expressed as follows:  
Figure 3:0  
According to the absolute value of [PERSON]'s correlation coefficient, the order of monotonic correlation is as follows:  
Figure 3:1  
Through a comparative analysis, the variable \(T_{total,charge}\) with the lowest correlation was eliminated. The constant current charging time \(T_{I}\), constant voltage charging time \(T_{V}\), battery voltage change at charging \(\Delta V_{charge}\), total discharge time \(T_{total,discharge}\), battery temperature change during discharge \(\Delta Temp_{discharge}\), and battery voltage change at discharge \(\Delta V_{discharge}\) were determined as the input variables of the model. The actual remaining capacity of the battery \(C_{agpt}\) was determined as the output variable. In this study, the values of the six input variables have different dimensional ranges. For example, the min value of \(\Delta V_{discharge}\) is 0.2; the max value of \(T_{V}\) is 9800; the difference between the two is 49,000 times. The large gap will oscillate the neural network model