Adaptive Distribution of Relaxation Time Analysis Using Bayesian Mixtures

Interpreting electrochemical impedance spectroscopy data through the lens of the distribution of relaxation times (DRT) faces significant challenges due to the ill-posed nature of its deconvolution, which can generate ambiguous spurious peaks. Current methods struggle with regularization parameter selection and often require manual intervention to achieve meaningful results. Herein, we present a fully automated Bayesian nonparametric framework using a Bayesian mixture model that overcomes these limitations. Our approach automatically determines a finite number of relaxation processes and their parameters directly from experimental data, yielding parsimonious representations that naturally suppress artifacts. The method performs unsupervised deconvolution while providing rigorous uncertainty quantification for the DRT itself and its underlying parameters through Markov Chain Monte Carlo sampling. We demonstrate the framework's effectiveness on synthetic benchmarks and experimental systems. Results show superior performance in separating overlapping spectral features, revealing hidden electrochemical dynamics, and accurately characterizing complex impedance behavior compared to conventional approaches. The methodology's automated model selection and comprehensive uncertainty quantification provide researchers with a robust, interpretable tool for advancing understanding of electrochemical mechanisms, transport phenomena, and degradation processes.