*4.2. Cell Characterization Results*

The cell capacity was captured at the beginning of each testing cycle, and it best represents the cell degradation since capacity decreases with degradation [12]. The results are presented in Table 2. The OCV–SOC relationship was also established and a look-up table was built, which was needed to estimate the cell OCV for the RLS algorithm. The OCV–SOC curve was found to change minimally with cell degradation, hence only one curve was used for all cell capacities in the RLS algorithm. The results can be seen in Figure 5.


**Table 2.** Initial cell capacity for each test cycle.

**Figure 5.** Experimental result for OCV–SOC relationship.

### *4.3. E*ff*ect of Degradation on ECM Parameters*

The RLS estimation was used to estimate the ECM parameters for the UDDS driving cycle at different cell capacities. The selected value for λ is 0.9999, as it gives optimal estimation accuracy for the LFP cell tested. Figure 6 shows how degradation affects these parameters. The effect of degradation on R0 does not show any clear trend. However, it can be clearly seen that R1 increases, while *C*1 decreases, with degradation. This makes sense as the RC pair represents the charge-transfer phenomenon, and degradation can affect the amount of available charge in the battery, which is simply capacity. The changes in these parameters are not significant over a short amount of time, i.e., a few drive cycles, but can be very prominent over the lifetime of the battery. These results confirm that the assumption about the parameters being constant in existing state observer FDI methods, is not valid. Therefore, a reliable FDI scheme should take into consideration the changes in the ECM parameters due to cell degradation.

**Figure 6.** Estimated ECM parameters at various cell capacities. (**a**) *R*0 estimation at different cell capacities; (**b**) *R*1 estimation at different cell capacities; (**c**) *C*1 estimation at different cell capacities.

### *4.4. E*ff*ect of Faults on ECM Parameters*

Bias and gain faults were injected into the UDDS driving cycles at various cell capacities, times, and sizes. The effects of the faults were found to be similar across fault types, regardless of the injection time and fault size. The changes in the parameters when the fault is injected can be seen to be more significant, than changes with SOC and temperature [25]. An example is shown in Figure 7, where a voltage gain fault of +10% was injected at the time 30,000 s. When this fault occurs, as shown in Figure 7b,d,f, the parameters diverge away from their original trends. It can also be seen from Figure 7a,c,e that the unfiltered values follow the WMA-filtered line closely during normal operation, while Figure 7b,d,f show that the two lines deviate significantly at the time the fault occurs. This confirms the workability of the proposed change-point detection method using WMA and CUSUM. It is noted that the ECM parameters estimated by RLS require some time to converge. This can be seen at the beginning of Figure 7a–f. Therefore, the proposed FDI scheme would not be able to detect sensor faults for the first hour of battery operation. Considering the long lifespan of Li-ion batteries and the unlikelihood of sensor faults happening within the first hour of operation, it is reasonable to assume there is no fault during the converging period of the RLS algorithm.

**Figure 7.** Unfiltered and WMA-filtered ECM parameters during normal operation versus when a fault occurs. (**a**) *R*0 during normal operation; (**b**) *R*0 when a fault occurs at time 30,000 s; (**c**) *R*1 during normal operation; (**d**) *R*1 when a fault occurs at time 30,000 s; (**e**) *C*1 during normal operation; (**f**) *C*1 when a fault occurs at time 30,000 s.
