## 3 Case Study  
### Measurements and Cells  
LIBs in the pouch format with nickel-manganese-cobalt (NMC) as the cathode and graphite as the anode material were analysed in this ageing study. Electrode manufacturing (Figure 5a) and cell assembling (Figure 5b) were done by the Battery LabFactory Braunschweig (BLB) (Braunschweig, Germany), ensuring full control of the battery components. A solvent mixture of ethylene carbonate (EC)/ diethyl carbonate (DEC) with a ratio of 3:7 with 1 M LiPF\({}_{6}\) as the conducting salt and Celgard 2320 as the separator were used. The inactive compounds included are polyvinylidene fluoride as the binder and carbon black as the conducting additive. Cycle ageing experiments at 25 \({}^{\circ}\)C were conducted by charging with 1 C constant current (CC)/constant voltage (CV) and discharging with 1 C CC in a potential window between 2.9 V and 4.2 V. NFRA was measured with a Zahner Electrochemical Workstation (Zennium) in the galvanostatic mode in a temperature chamber also at a constant environmental temperature of 25 \({}^{\circ}\)C prior to ageing and after each 50 th cycle. Detailed measurement settings are given in [24], and cell specifications are summarised in Table 1.  
Typically, the SoH of an LIB is estimated by dividing the actual maximum residual capacity \(C_{i}\) of the \(i\)-th cycles by the nominal capacity \(C_{0}\) as in:  
\[SoH_{i}=\frac{C_{i}}{C_{0}}. \tag{5}\]  
In the proposed case study, the SoH is calculated using highly informative NFR training data sets and is compared to the state-of-the art capacity based SoH estimation. This is motivated by the fact that we observed a monotonic correlation of NFR with capacity loss and increased resistance \(R\)[24]. Thus, this indicates to evaluate directly the SoH via NFRA. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameters** & **Symbol** & **Cell 1** & **Cell 2** \\ \hline Initial capacity & \(C_{0}\)/mAh & 32.8 & 33.6 \\ Initial resistance & \(R_{0}\)/\(\Omega\) & 0.21 & 0.29 \\ Anode thickness & \(\delta_{a}\)\(\upmu\)m & 44 & 45 \\ Cathode thickness & \(\delta_{c}\)\(\upmu\)m & 52 & 58 \\ Calendering degree anode & \(\Pi_{a}\)/\(\%\) & 10 & 10 \\ Calendering degree cathode & \(\Pi_{C}\)/\(\%\) & 10 & 0 \\ Mass fraction anode & \(\zeta_{a}\)/wt\(\%\) & 0.90 & 0.93 \\ Mass fraction cathode & \(\zeta_{c}\)/wt\(\%\) & 0.90 & 0.90 \\ Mass fraction inactive compounds anode & \(\zeta_{add,a}\)/wt\(\%\) & 0.10 & 0.07 \\ Mass fraction inactive compounds cathode & \(\zeta_{add,c}\)/wt\(\%\) & 0.10 & 0.10 \\ Porosity anode & \(\varepsilon_{a}\)/- & 0.60 & 0.59 \\ Porosity cathode & \(\varepsilon_{c}\)/- & 0.57 & 0.64 \\ Geometric surface area anode & \(A_{geo,a}\)/cm\({}^{2}\) & 30.25 & 30.25 \\ Geometric surface area cathode & \(A_{geo,c}\)/cm\({}^{2}\) & 30.25 & 30.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance and cell parameters of the investigated cells. Figure 5: Electrode manufacturing and cell assembling at the Battery LabFactory Braunschweig (BLB). (**a**) BLB-Electrode production; (**b**) BLB-Pouch cell. (Picture credits: [PERSON]/Battery LabFactory, TU Braunschweig). The extrapolated NFR at the \(y\)-axis intercept is evaluated by linear regression analysis for all cycles \(i\), \(NFR_{min,i}\) is used for this purpose and normalized with the extrapolated NFR at the \(y\)-axis intercept \(NFR_{min,0}\) prior to ageing. The \(SoH_{NFR}\) measure is defined as:  
\[SoH_{NFR,i}=\frac{NFR_{min,i}}{NFR_{min,0}}. \tag{6}\]  
Please note that with decreasing capacity \(C_{0}\) and increasing internal resistance \(R\), the sum of the higher harmonic amplitudes of the NFR increases for constant excitation amplitude \(I_{AC}\). Thereby, it can be deduced that an increase of NFR correlates to a decrease of the SoH. The initial NFR value, \(NFR_{min,0}\) corresponds to a new cell (SoH = 100%), and \(NFR_{min,i}\) correlates to a decreased SoH after \(i\) cycles.