On Uncertainty Quantification in the Parametrization of Newman-type Models of Lithium-ion Batteries

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 quantity 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 parameter 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 but at the same time the fits to the voltage curves becomes less accurate. These observations highlight the ill-posedness of the inverse problem of parameter reconstruction in models of Li-ion battery operation.In practice, using simplified model appears to be a viable and useful strategy provided that the assumptions facilitating the model simplification are truly valid for the battery operating regimes in which the data was collected.