  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.
