Surrogate modeling for transient electrochemical potential analysis for SOFC using proper orthogonal decomposition

This study presents a procedure for creating a surrogate model for the transient electrochemical potential analysis of solid oxide fuel cells (SOFCs) by applying proper orthogonal decomposition (POD), which takes into account the characteristics of the spatial distribution of oxygen potential. In the proposed procedure, the time-variation of oxygen potential distributions in an SOFC are determined by numerical simulations under various analytical conditions with different explanatory variables or, equivalently, input parameters, and the results are stored in a separate data matrix for each component in accordance with certain rules. Then, POD is applied to each data matrix to create an individual surrogate model for the corresponding component using the dominant modes on the basis of contribution rates and/or mean square errors. The created models are used separately to obtain the oxygen potential distribution in the entire domain of the SOFC for an arbitrary set of input parameters at a low computational cost. A notable aspect of the proposed approach is that the positions and values of oxygen potential in two electrodes and interconnectors are data points and responses, respectively, but play opposite roles in the electrolyte region where the oxygen potential changes abruptly. Therefore, before combining the responses from the individual surrogate models, the oxygen potential values must be calculated backward from the coordinate values in the electrolyte. Representative numerical examples are presented to validate the appropriateness of the analysis procedure by applying the surrogate models with input parameters other than those used in the training process in comparison with the results obtained using the transient electrochemical potential.