## 6 Simulation Setup and Results
### Simulation Results
#### 6.2.2 Dual-IMM Results with B034 Dataset  
As in the previous section, cycle 21 was selected to show the estimation process of the proposed strategies at the early stages of degradation. Furthermore, cycle 445 was selected to demonstrate the behavior of the algorithms toward the end of battery life. Based on the B034 dataset, the measured battery capacity at this cycle was 1.46 Ah. Figure 14 shows the battery capacity estimates at cycle 21. Part (a) illustrates the results of the dual-KF and dual-SIF and part (b) depicts the results of the dual-KF-IMM and dual-SIF-IMM. Here, the algorithms were still transitioning to the correct measured values. The dual-IMM algorithms showed faster convergence to lower capacity values compared to the dual-only strategies. Furthermore, at this stage, both SIF algorithms slightly outperformed their KF counterparts. Figure 15 shows the SOC estimation results of all the proposed strategies. At this stage of the estimation process, the SOC curves did not depict a fully discharged battery, which is most likely due to incorrect battery capacity estimates. Figure 14: (**a**) Dual-KF and dual-SIF battery capacity estimates at cycle 21. (**b**) Dual-KF-IMM and dual-SIF-IMM battery capacity estimates at cycle 21. Figure 15: (**a**) dual-KF and dual-SIF SOC estimates at cycle 21. (**b**) Dual-KF-IMM and dual-SIF-IMM SOC estimates at cycle 21. At cycle 445, the measured battery capacity based on the B034 dataset was 1.28 Ah. Figure 16 depicts the battery capacity of the proposed strategies. Part (a) shows the estimation results of the dual-KF and dual-SIF and part (b) illustrates the results of the dual-KF-IMM and dual-SIF-IMM. Both dual strategies started to lag compared to the dual-IMM strategies. The dual-SIF showed a better estimate compared to the dual-KF algorithm. Even though the dual-IMM algorithms did not depict the correct battery capacity estimate, both algorithms performed better than their dual-only counterpart. The dual-KF-IMM showed the best estimate. Next, Figure 17 shows the SOC curves generated by the algorithms. Part (a) illustrates the results of the dual-KF and dual-SIF and part (b) shows the dual-KF-IMM and dual-SIF-IMM results. In part (a), both dual-only strategies were only able to discharge the battery to about 10% SOC, most likely due to their high battery capacity estimate. On the other hand, the dual-KF-IMM demonstrated a better SOC curve profile compared to the other strategies, where the battery was depleted at the end of the cycle. The dual-SIF-IMM showed similar results to the dual-SIF. Figure 16: (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 17: (a) Dual-KF and dual-SIF SOC estimates at cycle 445. (b) Dual-KF-IMM and dual-SIF-IMM SOC estimates at cycle 445. Finally, in terms of results across all cycles, Table 5 details the RMSE battery capacity estimation results. The dual-IMM algorithms showed better accuracy compared to their dual-only counterparts. The dual-KF-IMM showed the best accuracy compared to the other algorithms. Figure 18 illustrates the internal resistance estimations across all cycles. Part (a) shows the results from the dual-KF and dual-KF-IMM and part (b) depicts the results from the dual-SIF and dual-SIF-IMM. All algorithms show a downward trend, which could be reflective of new battery dynamics due to the higher discharging current to which this dataset is subjected. The dual-KF-IMM makes use of different operating conditions (models) which causes internal resistance to change significantly at early cycles when compared with the non-IMM methods. Figure 19 shows the battery capacity estimation results of all algorithms across all cycles. Part (a) illustrates the dual-KF and dual-KF-IMM results and part (b) depicts the dual-SIF and dual-SIF-IMM results. In part (a), the dual-KF-IMM shows a better adaptation to the new aging conditions compared to the dual-KF results.