### Linear and Nonlinear Electrochemical Impedance Spectroscopy: A Data Science Perspective

#### Matthew D. Murbach and Daniel T. Schwartz

Electrochemical Materials and Interfaces Lab
Department of Chemical Engineering,
University of Washington, Seattle, WA

mmurbach@uw.edu

### Electrochemical Impedance Spectroscopy:

#### Linear + Nonlinear

Small perturbation =
Linear response

EIS provides a linearized method for separating physical processes via timescales.

M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy (2008)
E. Barsoukov and J. R. Macdonald, Impedance Spectroscopy (2005)

### Electrochemical Impedance Spectroscopy:

#### Linear + Nonlinear

Moderate perturbation =
Harmonic response

J. A. Medina and D. T. Schwartz, Journal of the Electrochemical Society, 144, 155–164 (1997).
J. R. Wilson, D. T. Schwartz, and S. B. Adler, Electrochimica Acta, 51, 1389–1402 (2006).

### Computing nonlinear impedance spectra using the pseudo 2-dimensional battery model

M. Doyle, T. F. Fuller, and J. Newman, Journal of the Electrochemical Society, 140, 1526–1533 (1993).
T. F. Fuller, M. Doyle, and J. Newman, Journal of the Electrochemical Society, 141, 1–10 (1994).
M. Doyle, J. Newman, A. S. Gozdz, C. N. Schmutz, and J.-M. Tarascon, Journal of the Electrochemical Society, 143, 1890–1903 (1996).

### A data driven approach

###### Method: Perform tens of thousands of simulations for each harmonic covering the 40-dimensional parameter space
• Explore interactions between parameters
• Analyze parameter sensitivities as a function of frequency
• Introduce supervised and unsupervised machine learning

### Computing spectra across the entire parameter space and frequency range

 The P2D model has dozens of parameters Sobol' sampling ensures efficient coverage of the parameter space

https://github.com/SALib
A. Saltelli et al., Computer Physics Communications, 181, 259–270 (2010)

### Computing spectra across the entire parameter space and frequency range

 The P2D model has dozens of parameters Sobol' sampling ensures efficient coverage of the parameter space

https://github.com/SALib
A. Saltelli et al., Computer Physics Communications, 181, 259–270 (2010)

### A data driven approach

###### Method: Perform tens of thousands of simulations for each harmonic covering the 40-dimensional parameter space
• Explore interactions between parameters
• Analyze parameter sensitivities as a function of frequency
• Introduce supervised and unsupervised machine learning

### Sensitivity Analysis

Traditional, one-factor at a time Varaiance-based
• Change one parameter at a time, calculate derivatives
• Limited to probing local sensitivity
• No sense of interactions between parameters
• Fast and easily interpreted
• Sample a distribution of parameters, calculate sensitivity indices
• Probes the global sensitivity
• Requires many more simulations

### Variance-based Sensitivity Analysis

 First Order Sensitivity $S_i = \frac{V_{X_i} \left(E_{X_{\sim i}} \left(Y | X_i \right)\right)}{V\left(Y\right)}$ How much the variance in the output would decrease if we knew $X_i$ Total Sensitivity $S_{Ti} = \frac{E_{X_{\sim i}} \left(V_{X_{i}} \left(Y | X_{\sim i} \right)\right)}{V\left(Y\right)} = 1 - \frac{V_{X_{\sim i}} \left(E_{X_{i}} \left(Y | X_{\sim i} \right)\right)}{V\left(Y\right)}$ How much variance that would be left if we could fix everything except $X_i$

A. Saltelli, Computer Physics Communications, 145, 280–297 (2002)
A. Saltelli et al., Computer Physics Communications, 181, 259–270 (2010)

### A data driven approach

###### Method: Perform tens of thousands of simulations for each harmonic covering the 40-dimensional parameter space
• Explore interactions between parameters
• Analyze parameter sensitivities as a function of frequency
• Introduce supervised and unsupervised machine learning

### Next steps: Extend insight from the model to the physical system

 Unsupervised Machine Learning Understand underlying structure of spectra Gain insight into clustering or classification of battery states Supervised Machine Learning Given an impedance spectra, predict parameters for the model Estimate internal state metrics (state of health + remaining usable lifetime)

### Summary

• Nonlinear electrochemical impedance spectroscopy (NLEIS) can provide additional information with the same effort and time as an EIS experiment.
• The harmonic spectra each provide different information about the physicochemical system
• Data science tools can provide insight into our electrochemical research -- we shouldn't just let them be used to sell advertisements...

### Acknowledgements

Prof. Dan Schwartz

Prof. Hanna Hajishirzi

 Dept. of Education GAANN NSF Data Science IGERT UW Clean Energy Institute

### Thank you!

#### Questions?

Presentatation can be found at:
http://projects.mattmurbach.com/ecs2016b/