@article{783e21b7401f4b39b6865cddab5998b3,
title = "On fitting data for parameter estimates: residual weighting and data representation",
abstract = "We describe a fundamental problem in fitting rheological data to infer parameters and thus structural information about a material. The results may depend greatly on subjective choices in the fitting method making such inferences non-unique and therefore highly uncertain or wrong. We study experimental data and demonstrate that the most commonly used fitting scheme for oscillatory linear viscoelastic data is deceptively wrong for the purpose of inference, i.e., viscoelastic moduli (G′,G″) weighted by the experimental data. Our results establish best practices for fitting rheological data, linear viscoelastic or otherwise, with strong implications for inverse problems of structural inference.",
keywords = "Error propagation, Fitting, Inference, Linear viscoelasticity, Polyisoprene, Polymer, Small amplitude oscillatory shear, Uncertainty",
author = "Singh, {Piyush K.} and Soulages, {Johannes M.} and Ewoldt, {Randy H.}",
note = "Funding Information: The authors are grateful to Dr. Luca Martinetti of the University of Illinois at Urbana-Champaign for the helpful discussions. We thank Professor Jonathan B. Freund of the University of Illinois at Urbana-Champaign for insightful conversations on uncertainty quantification. The authors also thank Professor Emeritus Steven M. Errede of the University of Illinois at Urbana-Champaign for insightful discussions on the analysis of experimental measurements from a statistical perspective. The authors are also grateful to Professor Daniel J Read of the University of Leeds for prompting us to include covariances in calculations using Eq. 4, whenever it was applicable. This work was supported by the ExxonMobil Research and Engineering Company. Funding Information: The authors thank Ms. Tiffany R. Price for collecting the strain amplitude sweep data of Fig. S1, supplementary material and also for collecting a huge dataset of repeat SAOS measurements for various material systems, which although not included in this work, was instrumental in generating confidence in the experimental trend of uncertainties shown here. The authors are grateful to Dr. Luca Martinetti of the University of Illinois at Urbana-Champaign for the helpful discussions. We thank Professor Jonathan B. Freund of the University of Illinois at Urbana-Champaign for insightful conversations on uncertainty quantification. The authors also thank Professor Emeritus Steven M. Errede of the University of Illinois at Urbana-Champaign for insightful discussions on the analysis of experimental measurements from a statistical perspective. The authors are also grateful to Professor Daniel J Read of the University of Leeds for prompting us to include covariances in calculations using Eq. 4, whenever it was applicable. This work was supported by the ExxonMobil Research and Engineering Company. Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2019",
month = jul,
day = "1",
doi = "10.1007/s00397-019-01135-1",
language = "English (US)",
volume = "58",
pages = "341--359",
journal = "Rheologica Acta",
issn = "0035-4511",
publisher = "Springer",
number = "6-7",
}