Multi-scale multi-objective optimization and uncertainty analysis of methane-fed solid oxide fuel cells using Monte Carlo simulations

In this work, a multi-objective optimization approach is adopted for methane fueled solid oxide fuel cells in both microstructural and operational points of view. The optimization procedure was performed at different stages where microstructural parameters were considered separately and also in combination with operational variables in 2-objective and 3-objective cases. Effective reaction area, total conductivity and average pore radius are taken as the micro-model objective functions while system efficiency and power density as the multi-scale objectives are to be maximized. Electronic phase volume fraction, porosity, fuel utilization and steam/methane ratio are some of the important design parameters. The results of multi-objective problem are presented in terms of Pareto fronts of non-dominated solutions in which the compromised designs depicted among them. By multi-objective optimization of the microstructure of a solid oxide fuel cell anode, optimal electronic and ionic particle size of 0.4 and 0.26 μm, electronic volume fraction of 59% and porosity of 48% are determined. In addition, an optimum trade-off solution with 52% efficiency and 0.699 W/cm2 power density is achieved by multi-scale multi-objective optimization of the system. Finally, an uncertainty analysis is implemented based on Monte Carlo simulations to show the statistical performance of system outputs as well as the probability of failure of system constraints.