# A Sea Horse Optimization-Based Approach for PEM Fuel Cell Model Parameter Estimation
## 1 Introduction  
In recent years, fuel cells (FCs) have emerged as a key component in energy systems, owing to their high energy efficiency, low emission characteristics, and quiet operation. Among the various types, proton exchange membrane fuel cells (PEMFCs) attract significant attention due to their low operating temperature, compact structure, and rapid start-up capability. These features enable their use across a broad spectrum of applications, ranging from portable electronic devices to electric vehicles [1]. For the effective deployment of PEMFC systems, an accurate and reliable modeling approach is essential during the design and control stages. However, the modeling process is inherently complex and highly multi-variable, as these systems involve a range of interrelated physical phenomena, including electrochemical reactions, gas diffusion, humidity, and heat transfer, as well as fuel supply dynamics [2, 3]. These factors underline the needfor models that can accurately capture the physical behavior of fuel cells and highlight the critical balance between parametric accuracy and comprehensive system representation. The identification of accurate and reliable model design parameters plays a crucial role in both the performance prediction of PEMFCs and the overall system design process [4]. In the literature, a wide range of approaches have been developed for modeling PEMFCs. These models are generally categorized as mechanistic, empirical, semi-empirical, data-driven, and equivalent circuit models [3]. Mechanistic models represent the physical and chemical processes occurring within a fuel cell through detailed mathematical formulations. However, due to their complexity and the difficulty of obtaining precise parameter values, they are primarily used in theoretical studies. Experimental models provide straightforward estimations based on directly measured data but fail to reflect the internal dynamics of the system. Semi-empirical models combine both approaches, offering simplified yet practical solutions suitable for control-oriented applications. Data-driven models operate by learning from extensive experimental datasets; however, they are often costly and time-consuming to develop. For this reason, one of the most commonly adopted methods in engineering applications is the equivalent circuit model, which represents the electrical behavior of PEMFCs using conventional electronic components [3; 5]. However, the effectiveness of this model largely depends on the accurate estimation of its parameters, which is why optimization algorithms are frequently employed. One of the most critical challenges across all modeling approaches lies in the reliable identification of these parameters. Since the required parameters are often not provided by manufacturers and can be difficult to determine experimentally, the accuracy of the model may be compromised. As a result, the use of optimization techniques becomes essential to ensure model fidelity [6]. In recent years, metaheuristic algorithms--such as Genetic Algorithms (GAs) [7], Particle Swarm Optimization (PSO) [8; 9], Artificial Bee Colony (ABC) [10; 11], Gazelle Optimization Algorithm (GOA) [12] and Grey Wolf Optimizer (GWO) [13]--have been widely utilized in the parameter estimation processes of PEMFC models. However, these methods do not always yield sufficient accuracy due to issues such as premature convergence or entrapment in local minima. This has increased the demand for more flexible and innovative optimization strategies. In this context, the Sea Horse Optimization (SHO) algorithm has emerged as a promising alternative, offering fast convergence, the ability to avoid local optima, low computational cost, and a high level of accuracy--making it particularly well-suited for complex engineering applications [14].