# A Sea Horse Optimization-Based Approach for PEM Fuel Cell Model Parameter Estimation
## 5 Discussion
The experimental results are compared with other studies in the literature in Table 10.  
The SSE metric used in this study is calculated using the polarization curve obtained under a constant temperature of 70 \({}^{\circ}\)C and pressure of 1 bar, conditions commonly adopted in the literature [9]. This approach, as in previous studies, is generally based on optimization only for a specific operating condition. The main reason for this is that the current-voltage characteristics of the PEMFC are highly sensitive to temperature and pressure changes. Since changes in these parameters significantly alter the current-voltage curve, direct comparison of SSE values calculated under different conditions is not meaningful in the evaluation of model performance [17]. Therefore, the vast majority of studies in the literature perform SSE calculations only using a standard polarization curve to make performance evaluations meaningful and comparable. Furthermore, even if the model is optimized for different conditions in some studies, the reported SSE values are calculated only using the polarization curve for a fixed reference condition (usually 70 \({}^{\circ}\)C and 1 bar) [21; 24]. The same method is adopted in this study. Although the evaluation in this study is conducted under fixed conditions (70 \({}^{\circ}\)C and 1 bar), which are widely adopted in the literature, PEMFC model parameters, such as membrane conductance, contact resistance, and exchange current density, are known to be sensitive to environmental variations. Such dynamic variations are a fundamental challenge inherent in PEMFC modeling. The direction-adaptive and balanced search structure of the SHO algorithm stands out for its flexibility in nonlinear and time-varying optimization problems, offering advantages over fixed-structure metaheuristic methods. This feature creates promising potential for future research under different operating conditions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Study** & **Best SSE** & \(\varepsilon_{1}\) & \(\varepsilon_{2}\) & \(\varepsilon_{3}\) & \(\varepsilon_{4}\) & \(\lambda\) & \(R_{c}\) & \(\beta\) \\ \hline
[15] & 0.2872 & \(-\)0.8775 & 0.0025 & 0.000064439 & \(-\)0.00012531 & 12.016 & 0.0006369 & 0.0198 \\
[16] & 0.8537 & \(-\)1.1978 & 0.0044183 & 0.000097214 & \(-\)0.00016273 & 23.0 & 0.0001002 & 0.0136 \\
[17] & 0.0023765 & \(-\)0.9728 & 0.0034480 & 0.000083832 & \(-\)0.00011328 & 21.6995 & 0.0008 & 0.0136 \\
[11] & 0.002067 & \(-\)1.1827 & 0.0037080 & 0.0000936 & \(-\)0.00011925 & 11.7603 & 0.00078773 & 0.0136 \\
[21] & 0.8710 & \(-\)0.8532 & 0.0034173 & 0.000098 & \(-\)0.00015955 & 22.8458 & 0.0001 & 0.0136 \\
[22] & 0.000017729 & \(-\)1.1942 & 0.001 & 0.000041234 & \(-\)0.00016807 & 15.3311 & 0.0002 & 0.2083 \\
[6] & 0.0000104 & \(-\)1.1993 & 0.00362 & 0.000036704 & \(-\)0.0001784 & 19.6862 & 0.0003039 & 0.0665 \\
[23] & 0.85361 & \(-\)0.97997 & 0.0036946 & 0.000090871 & \(-\)0.00016282 & 23.0 & 0.0001 & 0.0136 \\
[24] & 0.85361 & \(-\)1.192042 & 0.0036124 & 0.000040797 & \(-\)0.0001628 & 23 & 0.0001 & 0.0136 \\
**SHO** & **0.00001** & \(-\)**0.8532** & **0.003250** & **0.000036** & \(-\)**0.000095** & **12.0685** & **0.000293** & **0.0136** \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Unknown parameter and SSE comparison for Ballard Mark V PEMFC with other methods.