Towards robust comparison of distributions of relaxation times

Distribution of relaxation times is a widely used method for the deconvolution of electrochemical impedance spectroscopy data. While proving to be a remarkable lens through which characterization can be done, it is in practice somewhat impaired by seemingly arbitrary choice for removing ill-posedness of the method. This, together with the rising use of distribution of relaxation times in condition monitoring raises the question of how to fairly compare the distributions. We introduce two complementary methods for comparing distributions of relaxation times: qualitatively via the cumulative distribution of relaxation times and quantitatively using the concept of unbalanced optimal transport. Both approaches relax the importance of regularisation, since they help to discern whether a perceived difference is significant or not. Additionally, the quantitative comparison offers information on the nature of the differences. Specifically, it can distinguish whether the difference can be attributed to a shift in distribution’s mass or not. The methodology is applied to experimental electrochemical impedance spectroscopy data from a solid-oxide fuel cell stack.