EIS fit

Fit a negative-electrode exchange-current density from electrochemical impedance spectroscopy (EIS) data with EIS and DataFit.

from ionworks import Ionworks
import ionworks_schema as iws
import matplotlib.pyplot as plt
import pandas as pd
import pybamm

# Synthetic example spectrum: Frequency [Hz], Z_Re [Ohm], Z_Im [Ohm]. Swap
# in your own export, or read a measurement with `client.cell_measurement`.
data = pd.read_csv(iws.example_data("eis_synthetic"))

# The Arrhenius form below needs an activation energy, which Chen2020
# does not define; zero gives j0 no temperature dependence.
baseline = pybamm.ParameterValues("Chen2020")
baseline["Negative electrode reaction activation energy [J.mol-1]"] = 0.0
known = iws.direct_entries.DirectEntry(parameters=baseline)

# j0 = j0_ref (c_e/c_e0)^0.5 (c_s/c_smax)^0.5 (1 - c_s/c_smax)^0.5
#      exp(E_r/R (1/T_ref - 1/T)), replacing Chen2020's own j0 function.
j0_function = iws.direct_entries.arrhenius_butler_volmer_exchange_current_density(
    electrode="negative"
)

# We fit j0_ref.
parameters = {
    "Negative electrode reference exchange-current density [A.m-2]": iws.Parameter(
        "Negative electrode reference exchange-current density [A.m-2]",
        initial_value=1.0,
        bounds=(0.1, 10.0),
    ),
}

objectives = {
    "impedance": iws.objectives.EIS(
        data=data,
        options=iws.objectives.EISOptions(
            model=pybamm.lithium_ion.DFN(options={"surface form": "differential"})
        ),
    )
}
fit = iws.DataFit(
    objectives=objectives,
    parameters=parameters,
    cost=iws.costs.RMSE(),
    # Capped to keep the example quick; a harder fit needs more.
    optimizer=iws.optimizers.ScipyMinimize(method="Nelder-Mead", max_iterations=20),
)

client = Ionworks()
submission = client.pipeline.create(
    iws.Pipeline({"known": known, "j0_function": j0_function, "eis": fit})
)
client.pipeline.wait_for_completion(submission.id)
result = client.pipeline.result(submission.id)
fit_result = result.element("eis")
figs = fit_result.plot_fit_results()
plt.show()