Influence of the Discretization Methods on the Distribution of Relaxation Times Deconvolution: Implementing Radial Basis Functions with DRTtools

•Novel regularization method based on radial basis function discretization for calculating the DRT.•Improved estimation of DRT only when data collection range is truncated.•MATLAB GUI for computing the DRT. The distribution of relaxation times (DRT) is an approach that can extract time characteristi...

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Bibliographic Details
Published in:Electrochimica acta Vol. 184; pp. 483 - 499
Main Authors: Wan, Ting Hei, Saccoccio, Mattia, Chen, Chi, Ciucci, Francesco
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.12.2015
Subjects:
distribution of relaxation times
impedance spectroscopy
lithium-ion batteries
radial basis functions
regularization
impedance spectroscopy
radial basis functions
lithium-ion batteries
distribution of relaxation times
regularization
ISSN:0013-4686, 1873-3859
Online Access:Get full text
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Summary:•Novel regularization method based on radial basis function discretization for calculating the DRT.•Improved estimation of DRT only when data collection range is truncated.•MATLAB GUI for computing the DRT. The distribution of relaxation times (DRT) is an approach that can extract time characteristics of an electrochemical system from electrochemical impedance spectroscopy (EIS) measurements. Computing the DRT is difficult because it is an intrinsically ill-posed problem often requiring regularization. In order to improve the estimation of the DRT and to better control its error, a suitable discretization basis for the regularized regression needs to be chosen. However, this aspect has been invariably overlooked in the specialized literature. Pseudo-spectral methods using radial basis functions (RBFs) are, in principle, a better choice in comparison to other discretization basis, such as piecewise linear (PWL) functions, because they may achieve fast convergence. Furthermore, they can yield improved estimation by extending the estimated DRT to the entire frequency spectrum, if the underlying DRT decays to zero sufficiently fast outside the measured frequency range. Additionally, their implementation is relatively easier than other types of pseudo-spectral methods since they do not require ad hoc collocation point distributions. The as-developed novel RBF-based DRT framework was tested against controlled synthetic EIS spectra and real experimental data. Our results indicate that the RBF discretization performance is comparable with that of the PWL discretization at normal data collection range, and with improvement when the EIS acquisition is incomplete. In addition, we also show that applying RBF discretization for deconvolving the DRT problem can lead to faster numerical convergence rate as compared with that of PWL discretization only at error free situation. As a companion to this work we have developed a MATLAB GUI toolbox, which can be used to solve DRT regularization problems.
ISSN:0013-4686
1873-3859
DOI:10.1016/j.electacta.2015.09.097