Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times

Mark Žic, Sergiy Pereverzyev Jr., Vanja Subotić, Sergei Pereverzyev

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Determination of the distribution function of relaxation times (DFRT) is an approach that gives us more detailed insight into system processes, which are not observable by simple electrochemical impedance spectroscopy (EIS) measurements. DFRT maps EIS data into a function containing the timescale characteristics of the system under consideration. The extraction of such characteristics from noisy EIS measurements can be described by Fredholm integral equation of the first kind that is known to be ill-posed and can be treated only with regularization techniques. Moreover, since only a finite number of EIS data may actually be obtained, the above-mentioned equation appears as after application of a collocation method that needs to be combined with the regularization. In the present study, we discuss how a regularized collocation of DFRT problem can be implemented such that all appearing quantities allow symbolic computations as sums of table integrals. The proposed implementation of the regularized collocation is treated as a multi-parameter regularization. Another contribution of the present work is the adjustment of the previously proposed multiple parameter choice strategy to the context of DFRT problem. The resulting strategy is based on the aggregation of all computed regularized approximants, and can be in principle used in synergy with other methods for solving DFRT problem. We also report the results from the experiments that apply the synthetic data showing that the proposed technique successfully reproduced known exact DFRT. The data obtained by our techniques is also compared to data obtained by well-known DFRT software (DRTtools).
Original languageEnglish
Article number2
Number of pages23
JournalGEM - International Journal on Geomathematics
Volume11
Issue number1
DOIs
Publication statusE-pub ahead of print - 30 Dec 2019

Fingerprint

relaxation time
distribution functions
collocation
impedance
spectroscopy
integral equations
adjusting
computer programs

Cite this

Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times. / Žic, Mark; Pereverzyev Jr., Sergiy ; Subotić, Vanja; Pereverzyev, Sergei.

In: GEM - International Journal on Geomathematics, Vol. 11, No. 1, 2, 30.12.2019.

Research output: Contribution to journalArticleResearchpeer-review

@article{98b29dae9260476380419c39dfcc85cf,
title = "Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times",
abstract = "Determination of the distribution function of relaxation times (DFRT) is an approach that gives us more detailed insight into system processes, which are not observable by simple electrochemical impedance spectroscopy (EIS) measurements. DFRT maps EIS data into a function containing the timescale characteristics of the system under consideration. The extraction of such characteristics from noisy EIS measurements can be described by Fredholm integral equation of the first kind that is known to be ill-posed and can be treated only with regularization techniques. Moreover, since only a finite number of EIS data may actually be obtained, the above-mentioned equation appears as after application of a collocation method that needs to be combined with the regularization. In the present study, we discuss how a regularized collocation of DFRT problem can be implemented such that all appearing quantities allow symbolic computations as sums of table integrals. The proposed implementation of the regularized collocation is treated as a multi-parameter regularization. Another contribution of the present work is the adjustment of the previously proposed multiple parameter choice strategy to the context of DFRT problem. The resulting strategy is based on the aggregation of all computed regularized approximants, and can be in principle used in synergy with other methods for solving DFRT problem. We also report the results from the experiments that apply the synthetic data showing that the proposed technique successfully reproduced known exact DFRT. The data obtained by our techniques is also compared to data obtained by well-known DFRT software (DRTtools).",
author = "Mark Žic and {Pereverzyev Jr.}, Sergiy and Vanja Subotić and Sergei Pereverzyev",
year = "2019",
month = "12",
day = "30",
doi = "10.1007/s13137-019-0138-2",
language = "English",
volume = "11",
journal = "GEM - International Journal on Geomathematics",
issn = "1869-2672",
publisher = "Springer",
number = "1",

}

TY - JOUR

T1 - Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times

AU - Žic, Mark

AU - Pereverzyev Jr., Sergiy

AU - Subotić, Vanja

AU - Pereverzyev, Sergei

PY - 2019/12/30

Y1 - 2019/12/30

N2 - Determination of the distribution function of relaxation times (DFRT) is an approach that gives us more detailed insight into system processes, which are not observable by simple electrochemical impedance spectroscopy (EIS) measurements. DFRT maps EIS data into a function containing the timescale characteristics of the system under consideration. The extraction of such characteristics from noisy EIS measurements can be described by Fredholm integral equation of the first kind that is known to be ill-posed and can be treated only with regularization techniques. Moreover, since only a finite number of EIS data may actually be obtained, the above-mentioned equation appears as after application of a collocation method that needs to be combined with the regularization. In the present study, we discuss how a regularized collocation of DFRT problem can be implemented such that all appearing quantities allow symbolic computations as sums of table integrals. The proposed implementation of the regularized collocation is treated as a multi-parameter regularization. Another contribution of the present work is the adjustment of the previously proposed multiple parameter choice strategy to the context of DFRT problem. The resulting strategy is based on the aggregation of all computed regularized approximants, and can be in principle used in synergy with other methods for solving DFRT problem. We also report the results from the experiments that apply the synthetic data showing that the proposed technique successfully reproduced known exact DFRT. The data obtained by our techniques is also compared to data obtained by well-known DFRT software (DRTtools).

AB - Determination of the distribution function of relaxation times (DFRT) is an approach that gives us more detailed insight into system processes, which are not observable by simple electrochemical impedance spectroscopy (EIS) measurements. DFRT maps EIS data into a function containing the timescale characteristics of the system under consideration. The extraction of such characteristics from noisy EIS measurements can be described by Fredholm integral equation of the first kind that is known to be ill-posed and can be treated only with regularization techniques. Moreover, since only a finite number of EIS data may actually be obtained, the above-mentioned equation appears as after application of a collocation method that needs to be combined with the regularization. In the present study, we discuss how a regularized collocation of DFRT problem can be implemented such that all appearing quantities allow symbolic computations as sums of table integrals. The proposed implementation of the regularized collocation is treated as a multi-parameter regularization. Another contribution of the present work is the adjustment of the previously proposed multiple parameter choice strategy to the context of DFRT problem. The resulting strategy is based on the aggregation of all computed regularized approximants, and can be in principle used in synergy with other methods for solving DFRT problem. We also report the results from the experiments that apply the synthetic data showing that the proposed technique successfully reproduced known exact DFRT. The data obtained by our techniques is also compared to data obtained by well-known DFRT software (DRTtools).

U2 - 10.1007/s13137-019-0138-2

DO - 10.1007/s13137-019-0138-2

M3 - Article

VL - 11

JO - GEM - International Journal on Geomathematics

JF - GEM - International Journal on Geomathematics

SN - 1869-2672

IS - 1

M1 - 2

ER -