Entropy-based Regularized Regression for Advanced Distribution of Relaxation Times Deconvolution

Electrochemical impedance spectroscopy (EIS) coupled with distribution of relaxation times (DRT) analysis is a robust framework for characterizing electrochemical systems. However, DRT deconvolution is often plagued by spurious peaks, hindering accurate process identification and quantitative parameter estimation. To overcome this critical limitation, we rigorously evaluate entropy-based regularization within the standard regularized regression framework for DRT deconvolution. Building upon initial investigations, this study provides a detailed and quantitative evaluation of entropy-regularized DRT using a comprehensive suite of simulated impedance spectra, encompassing various impedance models and noise levels, and experimental data from lithium-ion batteries, fuel cells, and solar cells. Our results demonstrate that entropy regularization consistently outperforms conventional ridge regression, achieving significantly improved accuracy in DRT recovery and effectively eliminating spurious peaks. Furthermore, we demonstrate the novel capabilities of the entropy method for Bayesian DRT uncertainty quantification through sampling and for the simultaneous analysis of multiple impedance spectra. These findings establish entropy-based deconvolution as a superior and versatile technique for robust and insightful electrochemical system characterization, advancing the reliability of DRT analysis in electrochemistry.