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

Abstract

Electrochemical impedance spectroscopy is attracting more attention due to an increasing production of power sources. One highly popular tool for diagnosing diverse power sources is distribution function of relaxation times (DRT), which has led to numerous approaches for extracting DRT from impedance data. The majority of these 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. Tests conducted in this work have shown that LMA is capable of extracting DRT from ZARC and FRAC synthetic data.

Extraction of Distribution Function of Relaxation Times by using DRT-RBLM Tools: A New Approach to Combine Levenberg-Marquardt Algorithm and Radial Basis Functions for Discretization Basis

“…Since the DRT deconvolution is an inverse ill-posed problem, it is advisable to apply different extraction approaches, e.g., 3,6,7 in order to conduct a model-free EIS study.…”

“…Methods to extract distribution function of relaxation times.-The available strategies for DRT extraction are based on regularization techniques, 2,3,[6][7][8][9]4 Fourier filtering, 10,11 evolutionary programming [12][13][14] grammatical evolution, 15 maximum entropy model, 16 Monte Carlo techniques, 17 deconvolution using deep neural networks 18 and Finite Gaussian Processes. 19,20 Interestingly enough, only a few of the listed aforementioned regularization approaches apply the Levenberg-Marquardt algorithm (LMA) to extract the applicable DRT profiles from EIS data.…”

“…19,20 Interestingly enough, only a few of the listed aforementioned regularization approaches apply the Levenberg-Marquardt algorithm (LMA) to extract the applicable DRT profiles from EIS data. 6,7,9 Herein, we are focused on both the LMA regularization and on the Jacobian matrix approximation; and thus, we have revisited several DRT strategies 3,6,7,9 that are of keen interest (Scheme 1).…”

“…This parameter can be manually given, 3,4 obtained by cross-validation 3 and self-consistent techniques, 5 and automatically tuned. 2,6 Also, the DRT extraction is an inverse ill-posed problem; and thus, DRT is prone to oscillations.…”

The Effect of Y3+ Addition on Morphology, Structure, and Electrical Properties of Yttria-Stabilized Tetragonal Zirconia Dental Materials

“…For example, by studying EEC parameter trend(s), it should be possible to gain a deeper insight related to the location of the Y 3+ ions within the material. However, one should be aware of the fact that nowadays, an EEC model-free approach to analyze IS data is gaining prominence [ 20 , 21 , 22 ]. Nevertheless, EEC analysis still offers a fair amount of data; thus, it should be used more frequently while investigating this sort of material (see, e.g., [ 8 ]).…”