Sensitivity Analysis of a One-Dimensional SOFC Contaminant Degradation Model Using Dual Numbers Automatic Differentiation

Sensitivity analysis of a computational model with respect to a parameter is the derivative of the model outcome with respect to same parameter. In experimental studies, sensitivity of the experiment to the parameter is very crucial for the accuracy of the results. In this study, a one-dimensional contaminant performance degradation computational model for solid oxide fuel cells (SOFC) is utilized to study its sensitivity to changes in model parameters. Both finite difference (FD) method and dual numbers automatic differentiation (DNAD) are used to evaluate derivatives and compared to each other. The DNAD method uses dual number arithmetic to calculate the derivative of any mathematical functions or any numerical model with respect to a given parameter. Dual number arithmetic is a well-known strategy for automatic differentiation of computer codes which gives exact derivatives, to the machine accuracy, of the computed quantities with respect to any of the involved variables. The sensitivity to a model parameter calculated by DNAD is then verified and compared with finite differences.  This technique can be used to evaluate the sensitivity of simulation results on changes in the critical parameters involved in the mathematical model. It is those parameters which have to be carefully calibrated and validated against experiments to confidence on predictions.