Fast Electrochemical Impedance Characterization via Joint Time-Frequency Distribution of Relaxation Times Inversion

Conventional electrochemical impedance spectroscopy (EIS) can require hours for broadband frequency sweeps. Broadband time-domain excitations accelerate acquisition, but most workflows reconstruct frequency-domain spectra before applying the distribution of relaxation times (DRT) analysis, introducing spectral leakage and discretization artifacts. We present a convex framework that jointly estimates a shared DRT from impedance data and voltage transients within a single Bayesian formulation, incorporating non-negativity and smoothness priors. Regularization parameters are selected by minimizing a K-fold cross-validation objective with residual-based variance re-estimation, solved via Bayesian optimization. On synthetic circuits with up to two generalized constant-phase elements, the method achieves median DRT errors below 5% and impedance errors below 1%, reducing acquisition time by factors of 4–8 relative to stepped-sine protocols.