Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method

Abstract In this paper, the distribution of relaxation times (DRTs) functions are calculated numerically in Matlab for synthetic impedance data from single parallel $$RC$$ RC circuit and two parallel $$RC$$ RC circuits connected in series, experimental impedance data from supercapacitors and α-LiFeO...

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Autores principales:	T. Paul, P. W. Chi, Phillip M. Wu, M. K. Wu
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/c5d454f3928248feace72f2c52a728b0
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spelling	oai:doaj.org-article:c5d454f3928248feace72f2c52a728b02021-12-02T16:04:27ZComputation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method10.1038/s41598-021-91871-32045-2322https://doaj.org/article/c5d454f3928248feace72f2c52a728b02021-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-91871-3https://doaj.org/toc/2045-2322Abstract In this paper, the distribution of relaxation times (DRTs) functions are calculated numerically in Matlab for synthetic impedance data from single parallel $$RC$$ RC circuit and two parallel $$RC$$ RC circuits connected in series, experimental impedance data from supercapacitors and α-LiFeO2 anode based Li ion batteries. The quality of the impedance data is checked with the Kramers–Krönig (KK) relations. The DRTs are calculated within the KK compatible regime for all the systems using Tikhonov regularization (TR) method. Here we use a fast and simple L-curve method to estimate the TR parameter (λ) for regularization of the Fredholm integral equations of first kind in impedance. Estimation of the regularization parameters are performed effectively from the offset of the global corner of the L-curve rather than simply using the global corner. The physical significances of DRT peaks are also discussed by calculating the effective resistances and capacitances coupled with peak fitting program. For instance, two peaks in the DRTs justify the electrical double layer capacitance and ion diffusion phenomena for supercapacitors in low to intermediate frequencies respectively. Moreover, the surface film effect, Li/electrolyte and electrode/electrolyte charge transfer related processes are identified for α-LiFeO2 anode based Li-ion batteries. This estimation of the offset of the global corner extends the L-curve approach coupled with the Tikhonov regularization in the field of electrochemistry and can also be applied in similar process detection methods.T. PaulP. W. ChiPhillip M. WuM. K. WuNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q T. Paul P. W. Chi Phillip M. Wu M. K. Wu Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method
description	Abstract In this paper, the distribution of relaxation times (DRTs) functions are calculated numerically in Matlab for synthetic impedance data from single parallel $$RC$$ RC circuit and two parallel $$RC$$ RC circuits connected in series, experimental impedance data from supercapacitors and α-LiFeO2 anode based Li ion batteries. The quality of the impedance data is checked with the Kramers–Krönig (KK) relations. The DRTs are calculated within the KK compatible regime for all the systems using Tikhonov regularization (TR) method. Here we use a fast and simple L-curve method to estimate the TR parameter (λ) for regularization of the Fredholm integral equations of first kind in impedance. Estimation of the regularization parameters are performed effectively from the offset of the global corner of the L-curve rather than simply using the global corner. The physical significances of DRT peaks are also discussed by calculating the effective resistances and capacitances coupled with peak fitting program. For instance, two peaks in the DRTs justify the electrical double layer capacitance and ion diffusion phenomena for supercapacitors in low to intermediate frequencies respectively. Moreover, the surface film effect, Li/electrolyte and electrode/electrolyte charge transfer related processes are identified for α-LiFeO2 anode based Li-ion batteries. This estimation of the offset of the global corner extends the L-curve approach coupled with the Tikhonov regularization in the field of electrochemistry and can also be applied in similar process detection methods.
format	article
author	T. Paul P. W. Chi Phillip M. Wu M. K. Wu
author_facet	T. Paul P. W. Chi Phillip M. Wu M. K. Wu
author_sort	T. Paul
title	Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method
title_short	Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method
title_full	Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method
title_fullStr	Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method
title_full_unstemmed	Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method
title_sort	computation of distribution of relaxation times by tikhonov regularization for li ion batteries: usage of l-curve method
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/c5d454f3928248feace72f2c52a728b0
work_keys_str_mv	AT tpaul computationofdistributionofrelaxationtimesbytikhonovregularizationforliionbatteriesusageoflcurvemethod AT pwchi computationofdistributionofrelaxationtimesbytikhonovregularizationforliionbatteriesusageoflcurvemethod AT phillipmwu computationofdistributionofrelaxationtimesbytikhonovregularizationforliionbatteriesusageoflcurvemethod AT mkwu computationofdistributionofrelaxationtimesbytikhonovregularizationforliionbatteriesusageoflcurvemethod
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Computation of distribution of relaxation times by Tikhonov regularization for Li ion batteries: usage of L-curve method

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