Fitting Prony-Series Viscoelastic Models with Power-Law Presmoothing

An efficient method of fitting Prony-series models to viscoelastic experimental data with power-law presmoothing is presented. A direct fitting of a Prony-series function to experimental data without appropriate presmoothing is difficult when the data have significant variance. A power-law series comprising multiple power-law terms is found capable of portraying a globally smooth, broadband viscoelastic behavior with minimal impact from local variance in the data. However, from a computational point of view, a Prony series representation is preferred to a power-law series representation because of the computational efficiency associated with the exponential basis functions of a Prony series. In this paper, a procedure involving presmoothing of experimental data via power-law-series representation followed by fitting of a Prony-series model to the presmoothed data is discussed and illustrated. Discussion focuses on how experimental data with significant variance can be effectively presmoothed through power-law series representation and how presmoothing improves the quality of the subsequent Prony series fit. The feasibility and effectiveness of the approach are demonstrated through numerical examples in which Prony-series representations of the creep compliance and relaxation modulus of asphalt concrete are determined from available experimental data.