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esf — empirical stress factor degradation model

esf models Li-ion battery capacity loss as a product of empirical stress factors (temperature, state of charge, depth of discharge, time) scaling a nonlinear SEI-driven fade. It is based on Xu et al., "Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment" (IEEE Trans. Smart Grid, 2018), adapted at IFE.

It does three things:

  • Fit

    Extract model parameters from calendar-aging and cycle-life data (staged SEI → rates → stress-factor fits).

    Fitting

  • Simulate

    Predict capacity loss for a drive cycle — rainflow cycle counting → stress factors → loss — given a set of parameters.

    Predicting degradation

  • Quantify uncertainty

    Propagate the fit covariance through the simulation as quantile bands.

    Uncertainty

The model in one paragraph

Capacity loss L = 1 − SoH follows a nonlinear "SEI" envelope wrapped around a linear degradation rate f:

\[ L(x) = 1 - \alpha\,e^{-x\,\beta f} - (1-\alpha)\,e^{-x f} \]

where x is time (calendar) or cycle number (cycling). Everything condition-dependent lives in f, as a product of independent stress factors:

\[ \text{calendar: } f = S_t(t)\,S_\sigma(\text{SoC})\,S_T(T) \qquad \text{cycling: } f = S_\delta(\text{DoD})\,S_\sigma(\text{SoC})\,S_T(T) \]

This structure dictates a staged fitting procedure — you cannot fit everything from one data set. See the fitting architecture for the full picture.

Where to go next

Early release

This is a first public version. Expect bugs, incomplete features, and possible API changes. Please open an issue if something looks wrong.

Status

All fitting stages (calendar SEI, rates, SoC/temperature/time/DoD stress factors) are implemented and numerically pinned by tests, along with uncertainty propagation and an end-to-end reproduction of the paper's DST degradation curves. See the project README and CHANGELOG.md for the current release.

Contributors

Jonathan Fagerström Jonathan Fagerström Jinsong Hua Jinsong Hua Julia Wind Julia Wind Jan Petter Mæhlen Jan Petter Mæhlen

Acknowledgments

This work was supported by Jernbanedirektoratet (the Norwegian Railway Directorate) through the Europe's Rail project FP4-Rail4EARTH. The work within the Europe's Rail project FP4-Rail4EARTH is supported by the Europe's Rail Joint Undertaking and its members. The project is funded by the European Union. Views and opinion expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the Europe's Rail Joint Undertaking. Neither the European Union nor the granting authority can be held responsible for them.