# State of Health Prediction for Lithium-Ion Batteries Using Transformer-LSTM Fusion Model
## 2 Extraction and Selection of Multidimensional Features
### Feature Selection  
In order to evaluate the correlation between the extracted features and the battery SOH, we used the Pearson correlation coefficient for analysis. The Pearson correlation coefficient is a statistical indicator that measures the strength of the linear relationship between two variables. Its value range is [\(-\)1, 1], where positive values indicate positive and negative values indicate negative correlations. The closer the absolute value is to 1, the stronger the correlation. We calculated Pearson correlation coefficients between 102 features and the battery SOH, and the results are shown in Figure 5. The analysis results show a significant correlation between most features and the battery SOH, and the absolute values of the correlation coefficients of these features are close to 1, which further verifies the representativeness and effectiveness of these features. It can be seen that the extracted features can not only reflect the health status of the battery but also provide reliable input for SOH prediction. The calculation method of the Pearson correlation coefficient is shown below:  
\[r=\frac{\sum_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{\sqrt{\sum_ {i=1}^{n}{(x_{i}-\overline{x})^{2}}.\overline{\sum_{i=1}^{n}{(y_{i}-\overline{ y})}^{2}}}} \tag{6}\]  
where \(x_{i}\) and \(y_{i}\) represent the \(i\)-th feature data point and the corresponding SOH data point, respectively, \(\overline{x}\) and \(\overline{y}\) are the means of the feature data and SOH data, respectively, and \(n\) is the number of feature data points.  
To reduce model complexity and improve prediction accuracy, we ranked feature correlation coefficients and selected the 10 most strongly correlated features with battery SOH to extract a representative feature set, as shown in Figure 6. As can be seen from the figure, the changing trends of the SOH curve and the characteristic curve are highly similar, indicating a close correlation between these features and SOH. Especially in the degradation process, the changing pattern of the green curve can better reflect the fluctuation in the SOH curve, proving the critical role of these features in SOH prediction. These features include the time from the start of charging to the cut-off voltage of 3.6 V, the constant-current charging time, the energy in the constant-current discharge stage, the energy in the equal discharge voltage interval, the average energy in the charging stage, the energy variance in the discharge stage, the standard deviation of the energy in the discharge stage, the integral of the energy curve in the charging stage, the root mean square value of the energy in the charging stage, and the root square amplitude of the energy in the charging stage. The energy-based features are most relevant to SOH because the battery's energy output directly reflects its storage and release capabilities, which gradually decrease as the battery ages. The energy attenuation of the battery is closely related to its internal chemical reactions and structural changes, so the energy features can effectively characterize the health of the battery. As the battery is used for a longer time, the energy loss of the battery increases.  
Figure 5: Pearson correlation coefficients between SOH and features.  
The energy features can capture this change earlier, thus becoming an indicator closely related to SOH.