Extraction of Distribution Function of Relaxation Times by using Levenberg-Marquardt Algorithm: A New Approach to Apply a Discretization Error Free Jacobian Matrix

Abstract

Nowadays, Electrochemical Impedance Spectroscopy is attracting more attention due to an increasing production of power sources. One of highly popular tools to diagnose diverse power sources is Distribution Function of Relaxation Times (DRT). Because of that, there are numerous approaches to extract DRT from impedance data. The majority of them are based on the numerical approximation of integral. However, herein we have applied an analytical approximation of the EIS integral. For the first time, we have employed Levenberg-Marquardt algorithm (LMA) to extract the applicable DRT from impedance data by using the Jacobian matrix that was obtained without any discretization errors. Although LMA was previously used to fit EIS data by DRT characteristics, the DRT profile was not applicable due to discretization errors. In this work, LMA was applied as it has an automatic update of the regularization (λ) parameter. The tests conducted in this work have shown that LMA is capable of extracting DRT from ZARC and FRAC synthetic data.