Selecting the Regularization Parameter in the Distribution of Relaxation Times

Electrochemical impedance spectroscopy (EIS) is used widely in electrochemistry. Obtaining EIS data is simple with modern electrochemical workstations. Yet, analyzing EIS spectra is still a considerable quandary. The distribution of relaxation times (DRT) has emerged as a solution to this challenge. However, DRT deconvolution underlies an ill-posed optimization problem, often solved by ridge regression, whose accuracy strongly depends on the regularization level lambda. This article studies the selection of lambda using several cross-validation (CV) methods and the L-curve approach. A hierarchical Bayesian DRT (hyper-lambda) deconvolution method is also analyzed, whereby lambda(0), a parameter analogous to lambda, is obtained through CV. The analysis of a synthetic dataset suggests that the values of lambda selected by generalized and modified generalized CV are the most accurate among those studied. Furthermore, the analysis of synthetic EIS spectra indicates that the hyper-lambda approach outperforms optimal ridge regression. Due to its broad scope, this research will foster additional research on the vital topics of hyperparameter selection for DRT deconvolution. This article also provides, through pyDRTtools, an implementation, which will serve as a starting point for future research.

Automated summary

Electrochemical impedance spectroscopy (EIS) is widely used in electrochemistry, and obtaining EIS data is easy with modern electrochemical workstations. However, analyzing EIS spectra remains a significant challenge. The distribution of relaxation times (DRT) has emerged as a solution, but DRT deconvolution is an ill-posed optimization problem. This article investigates the selection of regularization level lambda using cross-validation methods and the L-curve approach, as well as explores a hierarchical Bayesian DRT deconvolution method.