## 3 Results and Discussion  
Calculation of experimental SoH was performed using the Qm value obtained from the ECBE model for each cell tested for a different number of cycles, and the results are shown in Table 2. The SoH drops as the cycle number increases as expected. Two decimals point were used inconsistently with  
Figure 2: Flowchart for difference estimation between experimental and estimated SoH. the accuracy of the SoH values obtained using the ECBE model as verified in our previous work (its accuracy is better than 99.6%) [9]. An interesting observation from our experiments is that batteries tested for a similar number of cycles under the same stress conditions show a difference in SoH drop, which signifies variation among the batteries. This could be due to the different imbalance in the internal state for an individual battery [25]. This renders it difficult to estimate single battery life, but users need to know the degradation of each of their batteries, instead of the entire population of batteries. Furthermore, a large number of battery samples is needed to estimate the population of the batteries, and this can be costly. Furthermore, one would expect a large standard deviation of the batteries degradation rate as electrochemistry degradation cannot be tuned as precisely as electronic components, in general. The computed SoH values were used to obtain the k1, k2, and k3 values using the above-mentioned semi-empirical capacity fading model with three different cycle numbers. We arbitrarily chose data of the 40\({}^{th}\), 150\({}^{th}\), and 250\({}^{th}\) cycle for all the batteries which are marked by a green circle in Figure 3. The computed values are shown in Table 3, and again, it is observed that the k values vary among the batteries from the same set tested under the same conditions for an equal number of cycles. This is in correlation with the SoH results which could be due to the difference in capacity degradation [26; 27]. In other words, assessing the SoH of batteries tested from the same batch under the same working conditions for companies' quality and reliability check can be difficult. It is also interesting to note that a few of the parameters have negative values. The negative k1 and k2 values were observed for the batteries with higher SoH which shows that there is an improvement in battery health. Some of the defects arising during the battery lifetime can enhance the battery lifetime due to improvement in the overall speed at which Li ion travels as published by [PERSON] et. al. [28]. Researchers believe that an electrode's lithium transport properties are fundamentally changed due to particle defects and this can enable lithium ions to penetrate inside the cathode in multiple directions. The reactive surface area increases in this process and more efficient exchange of Li ions is possible between the two electrodes [29]. However, more negative values were observed for k3 but the values are very close to 0 and thus can be ignored. These negative values could also be a result of a measurement error, thus we used two batteries at varying discharged cycle numbers and found that the negative values arise only for two batteries except for parameter k3. This shows the efficiency of the model used in this work. We use the computed k values for each cell to determine the SoH of the cell over the number of tested cycles, as shown in Figure 3, where Cell A2 is used for demonstration. Green circles indicate the points (the range of the half-cycle period) which were used to find the k values in the last step. The values of k1 and k2 were severely affected by the ambient temperature, while k3 was affected by the discharge current. The operating conditions of this experiment were room temperature and 1 C-rate discharge current, so we can observe that the difference between k-values of all cells is not large, but there is still a gap between individual samples.