## 5 Experimental Validations
### Fault Diagnosis Results  
Shown in Figure 8 is the remaining discharge capacity change curve, which depicts the remaining discharge capacity under different cycles from cell 1 to cell 7. Among them, cell 7 is a lower-capacity battery, and observing the change in the remaining discharge capacity of cell 6, it can be seen that there are fluctuations in the remaining discharge capacity of cell 6 in the first 6 cycles, and the remaining discharge capacity of cell 6 decreases significantly in the 7 th-9 th cycles, which is precisely due to the occurrence of an internal short circuit in cell 6. This corresponds to the parallel connection of the 3000 \(\Omega\), 1000 \(\Omega\) and 500 \(\Omega\) resistors on both ends of cell 6 in the static stage of the experiments of the 7 th-9 th cycles, respectively. Overall, 3000 \(\Omega\), 1000 \(\Omega\), and 500 \(\Omega\) resistors were connected in parallel at both ends of cell 6 during the resting phase of the 7 th-9 th cycle experiments to simulate the occurrence of an internal short circuit. The significant reduction in the remaining discharge capacity is consistent with the fact that the lower the parallel resistance of the battery, the more severe the occurrence of internal short circuits. After the 9 th cycle, the remaining discharge capacity of cell 6 is lower than that of cell 7 with lower capacity. This proves that the internal short-circuit fault of cell 6 is becoming more and more obvious. Therefore, in this paper, the remaining discharge capacity of the battery is used as the feature vector to do the fault diagnosis analysis of lithium-ion battery.  
This paper utilizes box plots to perform fault diagnosis on feature vectors, with the feature value being the remaining discharge capacity of the battery, as shown in Figure 9. For each cell, the remaining discharge capacity after 9 cycles is analyzed in combination with the box plot. The box plot principle divides the data into four parts, so this paper starts the analysis with the first four cycles and performs a box plot analysis for each additional cycle. From the fourth to the sixth cycle, no abnormalities were observed. However, starting from the seventh cycle, an abnormal value appeared in the box plot  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **RSME** & **MAE** \\ \hline SSA + EKF & 0.0049 & 0.0034 \\ GA + EKF & 0.0063 & 0.0051 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of SOC estimation accuracy between SSA and GA.  
Figure 7: EKF estimation results and errors.  
of cell 6, which was precisely the remaining discharge capacity of cell 6 (connected in parallel with a 3000 \(\Omega\) resistor) after the seventh cycle. Cell 6 also showed abnormal values after the eighth cycle (connected in parallel with a 1000 \(\Omega\) resistor) and the ninth cycle (with two abnormal values). The abnormal value from the eighth cycle was at the upper side, while the abnormal value from the ninth cycle was precisely the remaining discharge capacity of cell 6 (connected in parallel with a 500 \(\Omega\) resistor). Other cells, including cell 7 of low capacity, showed abnormal values.  
Graphical results demonstrate that all internal short-circuit abnormalities of the No. 6 monomer can be fully displayed in the box plot, indicating the effectiveness and accuracy of the box plot in detecting short circuit abnormalities. This proves the effectiveness of the fault  
Figure 8: Remaining Capacity Change.  
Figure 9: Fault diagnosis results.  
diagnosis of lithium-ion batteries based on the historical trajectory of residual discharge capacity proposed in this paper. The experiments verify that the proposed method in this paper can accurately locate the failed monomer in the battery pack containing low-capacity monomers and can detect the abnormal situation of the monomer battery in time when the monomer battery has a micro-short-circuit fault.