Project

qGP-DRT: The quasi-Gaussian Process Distribution of Relaxation Times

This repository contains some of the source code used for the paper titled Probabilistic deconvolution of the distribution of relaxation times from multiple electrochemical impedance spectra. Journal of Power Sources, 621, 235236. https://doi.org/10.1016/j.jpowsour.2024.235236. The article is available online at Link and in the docs folder.

Introduction

Electrochemical impedance spectroscopy (EIS) is a widely used technique for investigating the properties of electrochemical materials and systems, but analyzing EIS data can be quite difficult [1]. The distribution of relaxation times (DRT) has emerged as promising non-parametric method [1,2]. Among DRT inversion techniques [3-5], those based on Gaussian processes (GP) are particularly advantageous because they offer uncertainty estimates for both EIS and DRT [6,7]. However, existing GP-based DRT methods are limited to analyzing one spectrum at a time [6,7]. This study introduces a new approach, the quasi-Gaussian process distribution of relaxation times, which enables the simultaneous analysis of multiple impedance spectra across different experimental conditions [8].

Dependencies

numpy

scipy

matplotlib

pandas

Tutorials

1. ex1_1xZARC Model.ipynb: This notebook demonstrates how to deconvolve DRTs from multiple EIS spectra (from 1xZARC model) over a frequency range of 1E-2 to 1E6 Hz with 10 points per decade.
2. ex2_2xZARC Model.ipynb: This notebook shows how the qGP-DRT method captures distant timescales using 2xZARC models in series, over the same frequency range as in ex1_1xZARC Model.ipynb.
3. ex3_LFP.ipynb: This notebook examines a lithium-ion battery with an LiFePO4 (LFP) cathode, lithium-metal anode, and 1M LiPF6 in ethylene carbonate: a 1:1 v/v diethyl carbonate as an electrolyte. EIS data were collected from 0.1 Hz to 7 MHz at a 5C rate for cycles 30, 60, 90, and 120.

Citation

@article{maradesa2024probabilistic,
  title={Probabilistic deconvolution of the distribution of relaxation times from multiple electrochemical impedance spectra},
  author={Maradesa, Adeleke and Py, Baptiste and Ciucci, Francesco},
  journal={Journal of Power Sources},
  volume={621},
  pages={235236},
  year={2024},
  publisher={Elsevier}
}

References

[1] Ciucci, F. (2018). Modeling electrochemical impedance spectroscopy. Current Opinion in Electrochemistry.132-139. https://doi.org/10.1016/j.coelec.2018.12.003.

[2] Wan, T. H., Saccoccio, M., Chen, C., & Ciucci, F. (2015). Influence of the discretization methods on the distribution of relaxation times deconvolution: implementing radial basis functions with DRTtools. Electrochimica Acta, 184, 483-499. https://doi.org/10.1016/j.electacta.2015.09.097.

[3] Saccoccio, M., Wan, T. H., Chen, C., & Ciucci, F. (2014). Optimal regularization in distribution of relaxation times applied to electrochemical impedance spectroscopy: ridge and lasso regression methods-a theoretical and experimental study. Electrochimica Acta, 147, 470-482. https://doi.org/10.1016/j.electacta.2014.09.058.

[4] Ciucci, F., & Chen, C. (2015). Analysis of electrochemical impedance spectroscopy data using the distribution of relaxation times: A Bayesian and hierarchical Bayesian approach. Electrochimica Acta, 167, 439-454. https://doi.org/10.1016/j.electacta.2015.03.123.

[5] Effat, M. B., & Ciucci, F. (2017). Bayesian and hierarchical Bayesian based regularization for deconvolving the distribution of relaxation times from electrochemical impedance spectroscopy data. Electrochimica Acta, 247, 1117-1129. https://doi.org/10.1016/j.electacta.2017.07.050.

[6] Liu, J., & Ciucci, F. (2020). The Gaussian process distribution of relaxation times: A machine learning tool for the analysis and prediction of electrochemical impedance spectroscopy data. Electrochimica Acta, 135316. https://doi.org/10.1016/j.electacta.2019.135316.

[7] Maradesa, A., Py, B., Quattrocchi, E., & Ciucci, F. (2022). The probabilistic deconvolution of the distribution of relaxation times with finite Gaussian processes. Electrochimica Acta, 413, 140119. https://doi.org/10.1016/j.electacta.2022.140119.

[8] Maradesa, A., Py, B., & Ciucci, F. (2024). Probabilistic deconvolution of the distribution of relaxation times from multiple electrochemical impedance spectra. Journal of Power Sources621, 235236, . https://doi.org/10.1016/j.jpowsour.2024.235236