On Uncertainty Quantification in the Parametrization of Newman-Type Models of Lithium-Ion Batteries
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abstract
We consider the problem of parameterizing Newman-type models of Li-ion batteries focusing on quantifying the inherent uncertainty of this process and its dependence on the discharge rate. In order to rule out genuine experimental error and instead isolate the intrinsic uncertainty of model fitting, we concentrate on an idealized setting where “synthetic” measurements in the form of voltage curves are manufactured using the full, and most accurate, Newman model with parameter values considered “true”, whereas parameterization is performed using simplified versions of the model, namely, the single-particle model and its recently proposed corrected version. By framing the problem in this way, we are able to eliminate aspects which affect uncertainty, but are hard to quantify such as, e.g., experimental errors. The parameterization is performed by formulating an inverse problem which is solved using a state-of-the-art Bayesian approach in which the parameters to be inferred are represented in terms of suitable probability distributions; this allows us to assess the uncertainty of their reconstruction. The key finding is that while at slow discharge rates the voltage curves can be reconstructed quite accurately, this can be achieved with some parameters varying by 300% or more, thus providing evidence for very high uncertainty of the parameter inference process. As the discharge rate increases, the reconstruction uncertainty is reduced. However, the fits to the voltage curves become less accurate and the reconstructed parameter values begin to deviate from the “true” ones. The decrease in the accuracy of fits is concomitant with the simplified models losing validity; at C-rates of 2C and above the single-particle model does not accurately capture the physics of (dis)charge. This reveals a pitfall that one needs to be mindful of, namely, that an accurate fit does not necessarily mean that the fitted model accurately describes the physics. We conclude that inverse modelling using simplified models appears to be a viable and useful strategy for parameterizing Newman-type models because they allow fitting to be carried out in a reduced parameter space, however, we should be careful to verify that the reduced models are valid before trusting the results.
