## 2 Materials and Methods
### Design of Experiments Using Taguchi Orthogonal Arrays and ANOVA Analysis  
An experimental design is typically employed to assess the impact of different parameters on the system's output. Taguchi orthogonal array (OA) is a DOE technique commonly used for robust experimental design. It employs an OA to systematically design and analyse experiments involving multiple factors and levels [25]. In Taguchi OA, different factors at various levels are given equal weight. This ensures that every level of each factor appears an equal number of times, and all possible combinations of different levels of any two factors occur equally often. This approach eliminates interference between factors, allowing the method to effectively assess the sensitivity of system output to different levels of various factors [14]. Taguchi OA is typically denoted as LA(BC), where L represents the orthogonal design, A indicates the number of experiments, B denotes the number of levels of each factor, and C refers to the number of factors [26]. The partial factorial design used in Taguchi OA necessitates significantly fewer experiments compared to the full factorial design. Despite the reduced number of experiments, the OA design yields results comparable to those of the full factorial design [27]. In the widely used standard HPPC test, that can be controlled in the HPPC profile include the discharge pulse C-rate, the charge pulse C-rate, the pulse time, and the rest time between charge and discharge pulses, and the values of these parameters are 1C, 0.75C, 10 s and 40 s, respectively [14]. In this study, for an accurate comparison with the standard test, HPPC profile parameters will be adjusted based on the standard parameters. In this context, two additional higher values for the discharge pulse C-rate (2C and 3C) are used to further investigate their effect on model performance. It has been stated in the literature that the discharge pulse duration should be limited to a maximum of 200 s since the HPPC test is to be performed in a range of 0 to 100% SOC [14]. This prevents the battery voltage from being outside the permissible operating voltage range for long periods of time. Therefore, in this study, the discharge pulse time values were selected as 50 s, 125 s, and 200 s, respectively. The pulse time gap, which is the interval between the discharge pulse and the sweep discharge pulse, significantly impacts battery performance. A longer pulse time gap may enhance energy efficiency by allowing the battery to stabilize between pulses, potentially reducing energy losses and extending battery life by minimizing thermal stress and material degradation. Conversely, shorter pulse time gaps can lead to increased power output but might cause performance instability and greater wear on the battery due to more frequent charge-discharge cycles. Additionally, adequate pulse time gaps contribute to effective thermal management by facilitating heat dissipation, influence charge redistribution within battery cells, and affect internal resistance and overall cycling performance. Thus, optimizing the pulse time gap is crucial for maintaining battery efficiency, longevity, and performance. Therefore, in this study, the pulse time gap values were selected as 50 s, 125 s, and 200 s, respectively. The performance of the ECM may also be influenced by the rest time. To evaluate this effect, the rest time was set to three levels: 60, 120, and 180 s. The Taguchi design is beneficial in this case because it allows for the determination of the effects of individual factor levels on model performance without needing to evaluate all possible combinations of factor levels. Given that there are four control factors, each at three levels, the Taguchi OA L9 (34) was selected, as detailed in Table 2.  
The impact of control factors on the quality function is referred to as factor effects.