Optimal Regularization for the Distribution of Relaxation Times via Frequency-Band Selection

Electrochemical impedance spectroscopy (EIS) is a powerful analytical technique for characterizing electrochemical energy storage and conversion systems. Among the methods for analyzing EIS data, the distribution of relaxation times (DRT) has emerged as a valuable tool for quantitative interpretation. DRT estimation typically relies on regularized least squares methods, where the selection of an appropriate regularization parameter remains a key challenge. This selection critically affects the balance between the smoothness of the estimated curves and the resolution of physically meaningful features in the DRT. We introduce a novel frequency-domain approach, specifically focused on ridge regression regularization, that provides objective criteria for regularization parameter selection. Our method employs specialized cost functions to analyze user-defined frequency components in the measurement data, complementing existing cross-validation approaches. Extensive Monte Carlo simulations demonstrate the method’s effectiveness in comparison to established techniques. The approach not only yields robust results but also provides intuitive visualizations to support parameter selection. Successful validation across multiple experimental datasets confirms its practical utility.