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Electrochemical impedance spectroscopy (EIS) is a tool widely used to study the properties of electrochemical systems. The distribution of relaxation times (DRT) has emerged as one of the main methods for the analysis of EIS spectra. Gaussian processes can be used to regress EIS data, quantify uncertainty, and deconvolve the DRT, but current implementations do not constrain the DRT to be positive and can only use the imaginary part of EIS spectra. Herein, we overcome both issues by using a finite Gaussian process approximation to develop a new framework called the finite Gaussian process distribution of relaxation times (fGP-DRT). The analysis on artificial EIS data shows that the fGP-DRT method consistently recovers exact DRT from noise-corrupted EIS spectra while accurately regressing experimental data. Furthermore, the fGP-DRT framework is used as a machine learning tool to provide probabilistic estimates of the impedance at unmeasured frequencies. The method is further validated against experimental data from fuel cells and batteries. In short, this work develops a novel probabilistic approach for the analysis of EIS data based on Gaussian process, opening a new stream of research for the deconvolution of DRT.

Electrochemical impedance spectroscopy (EIS) is an experimental technique ubiquitously used to study electrochemical systems. However, conventional EIS data interpretation through physical and equivalent circuit models is challenging because physical models are problem-specific, and equivalent circuits are often just lumped-element analogs lacking physical meaning. The distribution of relaxation times (DRT) has emerged as a complementary approach to resolve these issues. One drawback of conventional DRT deconvolution is that the EIS data is understood to be (only) a function of frequency (i.e. 1D data) and deconvolved accordingly. This work proposes a novel deconvolution method based on deep neural networks (DNNs), allowing the analysis of multidimensional EIS spectra to bridge data dependency on both frequencies and experimental conditions. Two particularly appealing traits of the deep-DRT method developed in this article are that neither regularization nor specific spacing on the state variables defining the experiment are required. Leveraging DNN to examine complex EIS spectra and their dependence on experimental conditions, this work opens a new research direction in the area of EIS analysis and DRT deconvolution.

Electrochemical impedance spectroscopy (EIS) is a technique widely used to characterize electrochemical systems. While EIS is powerful and simple to use, interpreting EIS experiments is not a straightforward task. Equivalent circuits are by far the most commonly used EIS models. However, these circuits models are not unique. To overcome this issue, the research community has shown increasing interest in distributional methods such as the distribution of relaxation times (DRT), and the recently developed distribution of diffusion times (DDT). The DDT method captures the diffusional timescales of electrode particles, and for this reason, is particularly well suited for the study of the EIS response of batteries and supercapacitors. One major assumption of the DDT method is that the electrodes of these devices are thin. This article generalizes the DDT to electrodes of finite thickness, and this analytical model is termed the non-linear distribution of diffusion times (NL-DDT). The NL-DDT is studied using synthetic data and applying it to actual experiments. The study shows that the NL-DDT can recover the diffusional characteristics as well as the physical properties of the electrodes, including the chemical diffusion coefficient and ionic conductivities.