Electrochemical impedance spectroscopy (EIS) is a versatile characterization technique used extensively in electrochemistry, biology, medicine and beyond. However, EIS data analysis remains challenging. Both equivalent circuit and physical models used for EIS data analysis have limitations, such as non-unique solutions and system-specific challenges, respectively. The distribution of relaxation times (DRT) has emerged as a promising non-parametric method for EIS data analysis. However, DRT deconvolution involves solving an ill-posed inverse problem requiring advanced mathematical and programming skills.

To deconvolve DRT from EIS data, ridge regression (RR) can be used, with its success depending on optimal regularization level A selection. This work first focuses on A selection using...[ Read more ]

Electrochemical impedance spectroscopy (EIS) is a versatile characterization technique used extensively in electrochemistry, biology, medicine and beyond. However, EIS data analysis remains challenging. Both equivalent circuit and physical models used for EIS data analysis have limitations, such as non-unique solutions and system-specific challenges, respectively. The distribution of relaxation times (DRT) has emerged as a promising non-parametric method for EIS data analysis. However, DRT deconvolution involves solving an ill-posed inverse problem requiring advanced mathematical and programming skills.

To deconvolve DRT from EIS data, ridge regression (RR) can be used, with its success depending on optimal regularization level A selection. This work first focuses on A selection using cross-validation (CV) and the L-curve method. A hierarchical Bayesian DRT framework, utilizing CV to select an optimal parameter A₀(analogous to A), outperformed RR in synthetic EIS data analysis. These findings underscore the importance of A in RR-based DRT inversion, leading to updates in pyDRTtools for seamless A selection. While useful, RR as a point estimator cannot quantify the uncertainty of the deconvolved DRT, limiting the assessment of its credibility. To address this, a probabilistic approach using finite Gaussian process (fGP) was developed, improving on the previous GP-DRT model by utilizing the complete impedance spectrum and ensuring non-negative DRT values. Another challenge lies in simultaneously analyzing multiple EIS spectra. The recently developed quasi-GP (qGP) DRT framework addresses this issue. Validation with both synthetic and real data shows that, like fGP-DRT, qGP-DRT is noise-robust and effectively deconvolves DRTs from noisy spectra. Moreover, it outperforms fGP-DRT by enabling simultaneous multi-spectra processing and multidimensional DRT fitting.

To advance the DRT field, this work conducted the first-ever statistical survey, highlighting current usage and future potential. The survey underscores the need for community-based collaboration to develop a large impedance database for software validation and user-friendly automated DRT analysis tools. Overall, this work advances EIS data analysis, optimizing electrochemical energy storage systems (batteries, fuel cells) and enabling deeper insights into electrochemical processes occurring in electrochemical systems for efficient system design and operation.