Using piecewise polynomials to model open-circuit potential data

doi:10.1149/1.2401035

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Using piecewise polynomials to model open-circuit potential data

2007-01-01

PRE

Andrew T. Stamps *

Shriram Santhanagopalan

Edward P. Gatzke

DOI：10.1149/1.2401035

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Abstract

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Curve fitting is commonly used to determine a mathematical expression for sets of experimental data. While there are many instances when theory dictates a linear, quadratic, or other simple mathematical form for a relationship, there are often times when the theoretical form is either unknown or too unwieldy to be used effectively. A common example is the open-circuit-potential relationship of a Li-ion battery. One may use empirical correlations such as high-order polynomials (HOP ) or various types of splines which are piecewise polynomials of low order. Despite their simplicity, HOPs are often undesirable given their numerical instability as well as their poor extrapolation performance. Certain splines generally produce acceptably smooth curves but use an unacceptably large number of fitting parameters. A method is presented for construction of continuous and smooth piecewise polynomials. Using significantly fewer polynomial segments than experimental data points, the number of parameters required to develop the calibration curves of a Li-ion battery is substantially reduced from that of splines while maintaining a similar level of fit quality. Mixed-integer programming techniques are employed to ensure that the knot ( transition point ) placement is optimal. (c) 2006 The Electrochemical Society.

Keywords:

SMOOTHING NOISY DATA

APPROXIMATION

SYSTEMS

SPLINES

LOGIC

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