Parameters inference and model reduction for the Single-Particle Model of Li ion cells

The Single-Particle Model (SPM) of Li ion cell \cite{Santhanagopalan06, Guo2011} is a computationally efficient and fairly accurate model for simulating Li ion cell cycling behavior at weak to moderate currents. The model depends on a large number of parameters describing the geometry and material properties of a cell components. In order to use the SPM for simulation of a 18650 LP battery cycling behavior, we fitted the values of the model parameters to a cycling data. We found that the distribution of parametric values for which the SPM fits the data accurately is strongly delocalized in the (nondimensionalized) parametric space, with variances in certain directions larger by many orders of magnitude than in other directions. This property of the SPM is known to be shared by a multitude of the so-called "sloppy models" \cite{Brown2003, Waterfall2006}, characterized by a few stiff directions in the parametric space, in which the predicted behavior varies significantly, and a number of sloppy directions in which the behavior doesn't change appreciably. As a consequence, only stiff parameters of the SPM can be inferred with a fair degree of certainty and these are the parameters which determine the cycling behavior of the battery. Based on geometrical insights from the Sloppy Models theory, we derive an hierarchy of reduced models for the SPM. The fully reduced model depends on only three stiff effective parameters which can be used for the battery state of health characterization.