Influence of the Discretization Methods on the Distribution of Relaxation Times Deconvolution: Implementing Radial Basis Functions with DRTtools
Influence of the Discretization Methods on the Distribution of Relaxation Times Deconvolution: Implementing Radial Basis Functions with DRTtools
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DOI：
10.1016/j.electacta.2015.09.097
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发表时间：
2015-12-01
影响因子：
6.6
通讯作者：
Ciucci, Francesco
中科院分区：
文献类型：
--
作者：
Wan, Ting Hei;Saccoccio, Mattia;Ciucci, Francesco
弛豫时间分布 (DRT) 是一种可以从电化学阻抗谱 (EIS) 测量中提取电化学系统时间特征的方法。计算 DRT 很困难，因为它本质上是一个不适定问题，通常需要正则化。为了改进DRT的估计并更好地控制其误差，需要为正则回归选择合适的离散化基础。然而，这一方面在专业文献中总是被忽视。原则上，与分段线性 (PWL) 函数等其他离散化基相比，使用径向基函数 (RBF) 的伪谱方法是更好的选择，因为它们可以实现快速收敛。此外，如果基础 DRT 在测量的频率范围之外足够快地衰减到零，它们可以通过将估计的 DRT 扩展到整个频谱来产生改进的估计。此外，它们的实现比其他类型的伪谱方法相对容易，因为它们不需要特别的搭配点分布。根据受控合成 EIS 谱和真实实验数据对所开发的新型基于 RBF 的 DRT 框架进行了测试。我们的结果表明，在正常数据采集范围内，RBF 离散化性能与 PWL 离散化性能相当，并且当 EIS 采集不完整时，RBF 离散化性能有所改善。此外，我们还表明，仅在无误差情况下，与 PWL 离散化相比，应用 RBF 离散化对 DRT 问题进行反卷积可以带来更快的数值收敛速度。作为这项工作的配套，我们开发了一个 MATLAB GUI 工具箱，可用于解决 DRT 正则化问题。 (C) 2015 Elsevier Ltd. 保留所有权利。
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. (C) 2015 Elsevier Ltd. All rights reserved.