## 3 Results and Discussion
### Model Validation and ANOVA Results
At \(-10\)\({}^{\circ}\)C, the sharp voltage drops at this temperature, especially during discharge pulses, are directly tied to a possible increase in internal resistance. These voltage fluctuations demonstrate the difficulty the battery faces in maintaining stable power output under cold conditions, which also increases the RMSE in the SOC estimation. At 40 \({}^{\circ}\)C, the electrochemical reactions occur more rapidly, and due to a possible increase in the internal resistance beng lower, the battery is prone to thermal degradation. The results show a smoother voltage curve compared to \(-10\)\({}^{\circ}\)C, but over time, high temperatures can lead to faster capacity fading and side reactions within the battery. These thermal effects increase the stress on the system, affecting long-term performance and the accuracy of SOC estimation models. While discussing the impact of pulse time gap and discharge pulse time, both pulse time gap and discharge pulse time significantly influence the battery's behaviour across different temperatures. A longer pulse time gap allows the battery to rest and recover, enabling thermal dissipation and charge redistribution within the cells. At low temperatures  
Figure 6: Current and voltage results for different cases at ambient temperature of 40 \({}^{\circ}\)C.  
like \(-10\)\({}^{\circ}\)C, this recovery period is crucial as it helps mitigate the effects of high internal resistance, leading to more stable voltage profiles and reduced errors in the SOC estimation. Conversely, at higher temperatures, a longer pulse time gap also helps manage thermal runaway by allowing the battery to cool down between pulses. At low temperatures, shorter discharge pulses are preferable because longer pulses exacerbate voltage drops due to increased internal resistance. Also, at low temperatures, extended discharge pulses lead to larger deviations in the voltage curve, highlighting the physical strain on the battery's electrochemical system. At 40 \({}^{\circ}\)C, longer discharge pulses also increase the risk of overheating, as shown by the gradual voltage degradation over time in the charts. The effect of input parameters (pulse time gap, discharge pulse time, discharge pulse C-rate, and rest time) on RMSE values for different ambient temperatures is evaluated in Figure 7. This figure shows the main effect plot for signal-to-noise (S/N) ratios, using the \"Smaller is better\" criterion. At the ambient temperature of \(-10\)\({}^{\circ}\)C (Figure 7a), the S/N ratio decreases slightly as the pulse time gap increases from 50 to 200 s, indicating that a larger pulse time gap may not significantly enhance the signal-to-noise performance of the system. However, the decrease is relatively small, suggesting that the influence of pulse time gap on battery parameter identification is minor. The S/N ratio fluctuates in relation to discharge pulse time, initially decreasing from 50 to 125 s but then increasing slightly. This suggests that an optimal discharge pulse time exists, likely between 100 and 150 s. Beyond this range, the performance degrades, possibly due to thermal or internal resistance effects in the battery. While evaluating the discharge pulse C-rate, a decreasing trend is shown from a C-rate of 2.9 to 8.7. This means that higher C-rates negatively affect the signal-to-noise ratio. A lower C-rate is preferable for minimizing parameter variance during identification, likely because high C-rates introduce larger thermal effects and voltage drops, which reduce the precision of parameter estimates. The most significant variation in S/N ratios is observed in the rest time. The ratio drops to its lowest at 120 s and then dramatically increases at 180 s. This indicates that inadequate rest time can degrade the performance of the parameter identification, but beyond a critical rest period, the signal-to-noise ratio improves significantly. A rest time around 180 s appears to provide the best conditions for battery relaxation and more accurate parameter extraction.