## 3 Case Study
### Results and Discussion
Thus, NFR data at high frequencies have minor ageing sensitivities and are therefore not applicable for SoH quantification and not considered for use as training data for the degradation model. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{\tau/s}\) & \(\mathbf{\omega}\)**-Range/Hz** & **Process** \\ \hline
50 to 1 & 0.02 to 1 & Solid diffusion \\
1 to 0.003 & 1 to 300 & Electrochemical reactions \\
0.003 to 0.0001 & 300 to 10,000 & Ionic transport processes at interfaces \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Typical time constants and frequency ranges of processes identified for analysed LIB in the NFR spectra. Figure 7: Correlation coefficient \(\rho_{S}\) for estimating the correlation degree of the variables NFR and cycle number. The ageing-sensitive data identified for frequencies less than 150 Hz are extracted and shown over frequency in Figure 8.  
For calculating the degradation model using SVR, the geometrical features, \(y\)-axis intercept of the extrapolated NFR and the slope of the NFR spectra, are extracted for each ageing cycle. In Figure 9, the cycle specific feature values of extrapolated NFR at the \(y\)-axis intercept and the slope are plotted over the frequency of each cycle step. Apparently, extrapolated NFR at the \(y\)-axis intercept is more sensitive to ageing than the slope of the NFR spectra. Extrapolated NFR increases monotonically with the cycle number. The slope, however, deviates at cycles 100 and 150. Therefore, extrapolated NFR at the \(y\)-axis intercept is used for the parametrisation and training of the SVR degradation model. In Figure 10, the correlation of the SoH with the extracted degradation feature is shown. In the inset of Figure 10, the values of the degradation features extracted from the data (blue) as well as the calculated values by the SVR model (red) are shown in terms of the cycle number to illustrate the high accuracy of the degradation model as the measured and calculated values match perfectly. In the next step, the performance of the degradation model is tested with validation data sets and additional cells, which are non-identical to the initial test cells. NFR data sets identical and not identical to the training cells were applied to the degradation model, and the SoH was identified. The results of this validation are shown in Table 4. Moreover, the algorithm predicts the SoH of an identical cell with a high accuracy of 3% and the SoH of a non-identical cell with a high accuracy of 4%. Thereby, it is shown that the NFR data recorded during cycle ageing are highly suitable for the quantification of the SoH of the cell for both identical and for non-identical cells. Please note that the battery cells used in the case study are manufactured by the Battery LabFactory Braunschweig and do not fulfill industrial standards, i.e., they may show substantial variations in their configurations that make a precise SoH identification difficult in general. The primary goal of this study was to provide the overall concepts and to demonstrate the proposed work-flow with first experimental results. Future work will focus on optimized and more sophisticated machine learning concepts with considerable higher accuracy, e.g., more informative features of NFRA data, empirical degradation models with memory (Bayesian concepts), and rigorous uncertainty analysis in SoH identification and SoH predictions. With NFRA, the measurement time  
Figure 8: Ageing-sensitive features in the NFR spectra extracted from high correlating training data sets. \begin{table}
\begin{tabular}{l c c} \hline \hline \(\mathbf{\omega_{Corr}}\)/Hz & **Correlation Coefficient** & **Process** \\ \hline A: \(<\)0.2 Hz & \(>\)0.95 & Solid diffusion \\ B: 0.2 to 150 & 1 & Electrochemical reactions \\ C: \(>\)150 & Random & Ionic transport \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation ranges \(\mathbf{\omega_{Corr}}\), correlation coefficients and underlying LIB processes.