Parameters extraction of PEMFC's model using manta rays foraging optimizer

Abstract

Summary In this article, a recently developed bio‐inspired based manta rays foraging optimizer (MRFO) is attempted for reliable and accurate extraction of the model uncertain parameters of proton exchange membrane fuel cells (PEMFCs). The parameter estimation is formulated as a non‐linear optimization problem subject to set of restrictions. The great development and tremendous revolution of computation heuristic‐based algorithms are the impetus of the authors to apply the MRFO to solve this constrained optimization problem resulting in a precise PEMFC model. Three case studies of typical field PEMFC stacks namely Ballard type Mark V, NedStack type PS6, and Horizon type H‐12. Various I to V datasets are demonstrated to appraise the performance of MRFO among other recent optimizers available in the literature. To be objective and for sake of quantifications, the best scores of minimum fitness values are 0.8533, 2.1360, and 0.0966 for the later said PEMFC stacks, correspondingly. At a later stage, production of various characteristics under varying operating conditions such as changeable cell temperature and regulating pressures are established using the generated best values of PEMFCs model. Further calculations of statistical indices are performed to validate the robustness of obtained results by the MRFO. Through comprehensive performance assessments, it can be confirmed that MRFO is very promising tool for the effective extraction of PEMFCs' model and suggested to be applied for solving other engineering problems.

Fuel Cell Characteristic Curve Approximation Using the Bézier Curve Technique

“…The datasheet specifications of these four commercial PEMFCs stacks are concluded from [14,25,49,50], and represented in Table 1, respectively. The measured experimental data characteristic curves of these four FCs are accessible online and reproducible in the literature in terms of parameter and curves estimation by several researchers [14,19,38,46]. The efficiency of the proposed effective computer graphic technique used to approximate the FC characteristics curve is compared with various algorithms to validate the performance of each algorithm.…”

“…The second case study is about the approximation of the characteristic curves of Horizon H-12 12 W. The primary information and characteristics datasheet of this fuel cell are reported in Table 2. The primary objective of this test case study was to validate the implementation of Bézier curve method compared to WOA [14], GA [38], and MRFO [38] for the effective determination of voltage, current and power of Horizon H-12 PEMFC stack. The measured pairs current and experimental voltage data of PEMFC stack are collected from [14,38], in which the fuel cell is operated at a normal atmospheric pressure of 0.5 bar and the ambient temperature of 29 • C. The main configuration for this fuel cell illustrated in Table 2.…”

“…The fuel cell is with 225 A maximum cell current, and operating partial pressures lie between 1 and 5 bar. Table 4 present the approximated values obtained by Bézier curve method compared with the algorithms MRFO [38], FOA [25], ICA [25], SFLA [25], SMSA [26] and SSO [32]. Figure 13a,b show the reconstructed V-I and P-I curves of NedStackPS6 PEMFC stack using the approximated value using Bézier curve method compared to experimental data and MRFO and FOA algorithms.…”

“…On the other hand, the meta-heuristic algorithms have prospered over the last few years, and have been effectively used to overcome several challenging optimization difficulties in specific various fields. In the literature, numerous meta-heuristic optimization techniques have been proposed to approximate the FC characteristic curves, including Shuffled Frog-Leaping Algorithm (SFLA), Firefly Optimization Algorithm (FOA), Imperialist Competitive Algorithm (ICA) [25], Shuffled Multi-Simplexes Search Algorithm (SMSA) [26], Hybrid Grey Wolf Optimization (HGWO) [27], Hybrid Vortex Search Algorithm and Differential Evolution [28], Eagle Strategy [8], Cuckoo Search Algorithm with Explosion Operator (CAEO) [29], Neural Network Optimizer (NNO) [30], Shark Smell Optimizer (SSO) [31], Slap Swarm Optimizer (SSO) [32], Grasshopper Optimization (GO) [33], Grey Wolf Optimizer (GWO) [34], Hybrid Teaching Learning Based Optimization-Differential Evolution [35], Hybrid Adaptive Differential Evolution Algorithm [36], Evolutionary Strategy [37], Genetic Algorithm (GA) and Manta Rays Foraging Optimizer (MRFO) [38], Transferred Adaptive Differential Evolution (TADE) [39], Adaptive Differential Evolution Algorithm (ADEA) [40], and Harmony Search Algorithm (HSA) [41]. In particular, these nature-inspired or artificial swarm intelligence have their own benefits and drawbacks, in which someone can overcome an unsolvable problem and not solve another one.…”

“…To check the efficiency of the used technique and the performance of the obtained results, a statistical analysis is conducted to assess the precision and accuracy of the approximated V-I and P-I curves. The results obtained are compared to latest methods, such as the Whale Optimization Algorithm (WOA) [14], GRG-1 [22], GRG-2 [22], FOA [25], ICA [25], SFLA [25], SMSA [26], SSO [32], Modified Artificial Ecosystem Optimizatio (MAEO) [49], GA [38], MRFO [38], Grouping-based Global Harmony Search GGHS [50], Improved Harmouny Search (HIS) [50], Particle Swarm Optimization with adaptive inertia Weight (PSO-w) [50], and Chaotic Harris Hawks Optimization (CHHO) [51]. To evaluate the performance of the proposed method, various error parameters are computed, examined, and compared, such as Individual Absolute Error (IAE), Relative Error (RE), Root Mean Square Error (RMSE), Mean Bias Error (MBE), and Autocorrelation Function (ACF).…”