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We introduce a framework for analyzing and designing EIS inversionalgorithms. Our framework stems from the observation of four features common towell-defined EIS inversion algorithms, namely (1) the representation of unknowndistributions, (2) the minimization of a metric of error to estimate parametersarising from the chosen representation, subject to constraints on (3) thecomplexity control parameters, and (4) a means for choosing optimal controlparameter values. These features must be present to overcome the ill-posednature of EIS inversion problems. We review three established EIS inversionalgorithms to illustrate the pervasiveness of these features, and show theutility of the framework by resolving ambiguities concerning three morealgorithms. Our framework is then used to design the generalized EIS inversion(gEISi) algorithm, which uses Gaussian basis function representation, modalitycontrol parameter, and cross-validation for choosing the optimal controlparameter value. The gEISi algorithm is applicable to the generalized EISinversion problem, which allows for a wider range of underlying models. We alsoconsidered the construction of credible intervals for distributions arisingfrom the algorithm. The algorithm is able to accurately reproduce distributionswhich have been difficult to obtain using existing algorithms. It is providedgratis on the repository https://github.com/suryaeff/gEISi.git.

Analysis, Design, and Generalization of Electrochemical Impedance Spectroscopy (EIS) Inversion Algorithms