## 6 Simulation Setup and Results
### Simulation Results
#### 6.2.1 B036 Dataset Dual-IMM Results
Finally, the overall battery capacity estimation results of all algorithms were compared based on the results at the end of each cycle. Due to the nature of the battery capacity curves, the mean value was selected to represent the final battery capacity estimate at the end of the cycle. It is important to note that selecting the end value yields the same results as the mean but selecting the minimum value at each cycle generated a different curve. Table 4 depicts the RMSE values from each algorithm based on Figure 2. The RMSE values show good accuracy in estimating the battery capacity for all algorithms. The dual-KF-IMM had the greatest accuracy compared to the other algorithms. Figure 8: (a) Dual-KF and dual-SIF battery capacity estimates at cycle 445. (b) Dual-KF-IMM and dual-SIF-IMM battery capacity estimates at cycle 445. Figure 9: (a) Dual-KF and dual-SIF SOC estimates at cycle 445. (b) Dual-KF-IMM and dual-SIF-IMM SOC estimates at cycle 445. Based on the LiB literature, the internal resistance should increase as the battery ages. Figure 10 shows the internal resistance results of all algorithms across all cycles. Part (a) depicts the results from the dual-KF and dual-KF-IMM and part (b) illustrates the results of the dual-SIF and dual-SIF-IMM. In part (a), both dual-KF and dual-KF-IMM show this trend of increased internal resistance as the battery ages. However, the dual-SIF and dual-SIF-IMM illustrate a downward trend in internal resistance, which could be the main contributor to higher errors compared to the KF algorithms. Based on part (a), the dual-KF-IMM makes use of the _fast-aging_ process to show an accelerated aging compared to the dual-KF. The use of faster aging rates becomes more evident in Figure 11.  
Figure 11 depicts the battery capacity estimation results of all algorithms across all cycles. Part (a) shows the results of the dual-KF and dual-KF-IMM and part (b) illustrates the results of the dual-SIF and dual-SIF-IMM. As can be seen, all algorithms were initialized with the manufacturer's battery capacity (2 Ah) as opposed to the measured battery capacity of 1.8 Ah. Initializing the battery capacity at a different value tests the adaptability of the proposed strategies. Based on part (a), the dual-KF-IMM shows the fastest convergence to the measured values but then it slightly overestimates the battery capacity. The dual-KF on the other hand takes longer to converge to the measured values. Part (b) shows that the dual-SIF and dual-SIF-IMM take longer to converge to the measured values, which most likely is due to the internal resistance estimates. Figure 12 depicts all the battery capacity estimation results from all algorithms across all cycles in one plot for better visualization. Lastly, Figure 13 illustrates the mode probability results from the dual-IMM strategies. Part (a) depicts the dual-KF-IMM mode probability and part (b) shows the mode probability of the dual-SIF-IMM. Both algorithms set the _slow_ mode degradation rate higher than the _fast_ mode. The dual-KF-IMM mode probability remains about the same, with values of 0.68 for the _slow_ mode and 0.32 for the _fast_ mode, whereas the dual-SIF-IMM sets the _slow_ mode at 0.75 and higher past the 300 th cycle. Figure 12: Battery capacity estimation results of each algorithm. Figure 13: (**a**) Dual-KF-IMM mode probability. (**b**) Dual-SIF and dual-SIF-IMM mode probability.