hybrid-drt

hybrid-drt is a Python package for probabilistic analysis of electrochemical impedance data using the distribution of relaxation times (DRT) and distribution of phasances (DOP). The key features of hybrid-drt are:

1. DRT estimation using a robust, self-tuning hierarchical Bayesian approach (no manual tuning needed)
2. Introduction of the DOP for handling constant-phase features like (pseudo)-inductance, (pseudo)-capacitance, or Warburg-like diffusion
3. DRT/DOP estimation from accelerated joint time/frequency-domain impedance measurements
4. Probabilistic DRT analysis methods (distinguishing pseudo-peaks from true peaks)
5. Automatic creation of equivalent circuit analogs from the DRT
6. Multi-dimensional DRT fitting and analysis

For methodology details, see this work on probabilistic DRT analysis and this work on joint-domain impedance measurements and DOP transformation.

Disclaimer: hybrid-drt is experimental and under active development. The code is provided to demonstrate several conceptual approaches to electrochemical analysis, but the details of the implementation may change in the future.

Probabilistic DRT analysis and interpretation

The philosophy underpinning the probabilistic methods in hybrid-drt is that distribution of relaxation times (DRT) analysis should fulfill two objectives: (1) determine the relaxation magnitude as a function of timescale and (2) identify the distinct processes that comprise the total distribution. The first objective is a regression task that is fulfilled by conventional DRT algorithms, while the second objective is a pseudo-classification task that is ignored by most DRT algorithms. hybrid-drt unites the regression and classification views of DRT inversion to clarify DRT interpretation and meaningfully express uncertainty, following the framework developed in this paper. The package currently provides several methods for analyzing electrochemical impedance spectroscopy (EIS) data:

• Conventional DRT estimation via a self-tuning hierarchical Bayesian model
• Probabilistic EIS deconvolution using the probability function of relaxation times (PFRT)
• A "dual inversion" algorithm for autonomous discrete model generation, comparison, and selection
• Methods for scoring the accuracy of DRT estimates using regression, classification, and hybrid metrics

Joint-domain impedance measurement and DRT transformation

Joint-domain ("hybrid") impedance measurements use time-domain chronopotentiometry measurements to quickly probe low-frequency processes ($\leq \sim 100$ Hz), while still accessing high frequencies ($\geq \sim 100$ Hz) with conventional frequency-domain impedance measurements. The two data components can then be joined with the DRT transform, thereby allowing recovery of the full impedance spectrum with high accuracy. This allows full-frequency-range impedance measurements to be completed more than 10x faster than with conventional impedance. For more details, see this paper.

Tutorials

You can find a variety of tutorials in the corresponding folder. There are not yet tutorials for multi-dimensional DRT analysis, as this is a more complex topic. Please feel free to reach out if you are interested.

Webinar

I gave a webinar providing a general introduction to the DRT, which may be helpful for understanding the DRT and this package. You can find the webinar recording and materials in the webinar folder. This uses hybrid-drt for a short software demonstration, which can be found in the same folder.

Requirements

hybrid-drt requires the mittag-leffler package. hybrid-drt also requires the following packages:

• numpy
• matplotlib
• scipy
• pandas
• cvxopt
• scikit-learn
• scikit-image

The galvani package can optionally be installed for direct reading of EC-Lab mpr files.

Installation

Install hybrid-drt from the repository files using either conda or pip. See installation.txt for step-by-step instructions.

Citing hybrid-drt

If you use hybrid-drt in published work, please consider citing the revelant work(s) linked above (bibliographic details below):

@article{huang2023reliable, title={How reliable is distribution of relaxation times (DRT) analysis? A dual regression-classification perspective on DRT estimation, interpretation, and accuracy}, author={Huang, Jake and Sullivan, Neal P and Zakutayev, Andriy and O’Hayre, Ryan}, journal={Electrochimica Acta}, volume={443}, pages={141879}, year={2023}, publisher={Elsevier} }

@article{huang2024rapid, title={Rapid mapping of electrochemical processes in energy-conversion devices}, author={Huang, Jake D and Meisel, Charlie and Sullivan, Neal P and Zakutayev, Andriy and O’Hayre, Ryan}, journal={Joule}, volume={8}, number={7}, pages={2049--2072}, year={2024}, publisher={Elsevier} }