High accuracy parameter estimation of solid oxide fuel cells using a surrogate assisted differential evolution with multi sampling mechanism

Solid Oxide Fuel Cells (SOFCs) represent a promising clean energy technology due to their high efficiency and fuel flexibility; however, accurate estimation of internal electrochemical parameters remains critical for achieving reliable system performance under diverse operating conditions. Traditional parameter identification methods often face challenges such as slow convergence, premature optimization stagnation, and computational inefficiency, especially when dealing with high-dimensional, nonlinear SOFC models. To overcome these issues, this study proposes a Surrogate-Assisted Differential Evolution with Multi-Sampling Mechanism (SADE-MSM) algorithm, integrating surrogate modeling, centroid sampling, global prescreening, and adaptive local search strategies to optimize SOFC parameters efficiently while minimizing expensive real function evaluations. The SADE-MSM approach was validated through extensive experimental studies involving ten different SOFC operational cases across varied temperatures and pressures, and its performance was benchmarked against nine leading metaheuristic algorithms. Results show that SADE-MSM consistently achieved the lowest mean squared error (MSE), fastest convergence rates, and highest robustness, outperforming all comparative methods in both accuracy and computational cost. Theoretically, these findings validate the effectiveness of hybrid surrogate-assisted evolutionary frameworks for complex multimodal optimization problems, while practically they demonstrate that SADE-MSM enables real-time SOFC parameter estimation suitable for applications in microgrids, hybrid renewable systems, and predictive control platforms. Readers benefit from a robust, efficient methodology that enhances SOFC modeling and operational reliability, while future work aims to extend SADE-MSM to fully dynamic, online optimization scenarios under real-world uncertainties such as system aging, transient loads, and sensor noise. • Innovative Hybrid Optimization : Introduces SADE-MSM , a novel surrogate-assisted evolutionary algorithm combining Radial Basis Function (RBF) surrogates, adaptive multi-sampling, and Differential Evolution to efficiently optimize SOFC parameters with minimal expensive function evaluations. • Unprecedented Accuracy : Achieves superior parameter estimation precision (lowest MSE) across 10 diverse SOFC operational cases , outperforming nine state-of-the-art metaheuristics by balancing global exploration and local exploitation. • Computational Efficiency : Reduces computational cost by 80–90 % via surrogate modeling, enabling faster convergence while maintaining robustness in high-dimensional, nonlinear SOFC landscapes. • Dynamic Adaptability : Features a Multi-Sampling Mechanism (MSM) that dynamically shifts from broad exploration to focused refinement, avoiding premature convergence and enhancing solution quality. • Practical Impact : Validated on real-world SOFC models, enabling high-fidelity simulations for control, diagnostics, and digital twins —critical for applications in microgrids and hybrid energy systems.