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The Single-Particle Model (SPM) of Li ion cell \cite{Santhanagopalan06,Guo2011} is a computationally efficient and fairly accurate model forsimulating Li ion cell cycling behavior at weak to moderate currents. The modeldepends on a large number of parameters describing the geometry and materialproperties of a cell components. In order to use the SPM for simulation of a18650 LP battery cycling behavior, we fitted the values of the model parametersto a cycling data. We found that the distribution of parametric values forwhich the SPM fits the data accurately is strongly delocalized in the(nondimensionalized) parametric space, with variances in certain directionslarger by many orders of magnitude than in other directions.  This property of the SPM is known to be shared by a multitude of theso-called "sloppy models" \cite{Brown2003, Waterfall2006}, characterized by afew stiff directions in the parametric space, in which the predicted behaviorvaries significantly, and a number of sloppy directions in which the behaviordoesn't change appreciably. As a consequence, only stiff parameters of the SPMcan be inferred with a fair degree of certainty and these are the parameterswhich determine the cycling behavior of the battery. Based on geometricalinsights from the Sloppy Models theory, we derive an hierarchy of reducedmodels for the SPM. The fully reduced model depends on only three stiffeffective parameters which can be used for the battery state of healthcharacterization.

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