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Title: Second-order statistical bootstrap for the uncertainty quantification of time-temperature-superposition analysis

Abstract

Time-temperature superposition (TTS), which for decades has been a powerful method for long-term prediction from accelerated aging data, involves rigid-shifting isotherms in logarithmic time to produce a single master prediction curve. For simple thermo-rheological properties that accurately follow the TTS principle, the shifts can be easily determined, even manually by the eye. However, for many properties of interest, where the principle is obeyed only approximately, or the data is noisy, it is imperative to develop objective shifting techniques along with reliable uncertainty bounds. This work analyzes in detail the method of arclength-minimization as an unsupervised algorithm to determining optimum shifts and demonstrates that the method is nearly unbiased for all practical datasets with a variety of noise distributions. Moreover, if averaged over with-replacement (bootstrap) resamples, the predicted shifts follow a normal distribution, a fact that can be used to construct confidence interval for the master curve through a second-order bootstrap procedure.

Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1560977
Report Number(s):
LLNL-JRNL-755393
Journal ID: ISSN 0035-4511; 941910
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Rheologica Acta
Additional Journal Information:
Journal Volume: 58; Journal Issue: 5; Journal ID: ISSN 0035-4511
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Maiti, Amitesh. Second-order statistical bootstrap for the uncertainty quantification of time-temperature-superposition analysis. United States: N. p., 2019. Web. doi:10.1007/s00397-019-01138-y.
Maiti, Amitesh. Second-order statistical bootstrap for the uncertainty quantification of time-temperature-superposition analysis. United States. doi:10.1007/s00397-019-01138-y.
Maiti, Amitesh. Thu . "Second-order statistical bootstrap for the uncertainty quantification of time-temperature-superposition analysis". United States. doi:10.1007/s00397-019-01138-y.
@article{osti_1560977,
title = {Second-order statistical bootstrap for the uncertainty quantification of time-temperature-superposition analysis},
author = {Maiti, Amitesh},
abstractNote = {Time-temperature superposition (TTS), which for decades has been a powerful method for long-term prediction from accelerated aging data, involves rigid-shifting isotherms in logarithmic time to produce a single master prediction curve. For simple thermo-rheological properties that accurately follow the TTS principle, the shifts can be easily determined, even manually by the eye. However, for many properties of interest, where the principle is obeyed only approximately, or the data is noisy, it is imperative to develop objective shifting techniques along with reliable uncertainty bounds. This work analyzes in detail the method of arclength-minimization as an unsupervised algorithm to determining optimum shifts and demonstrates that the method is nearly unbiased for all practical datasets with a variety of noise distributions. Moreover, if averaged over with-replacement (bootstrap) resamples, the predicted shifts follow a normal distribution, a fact that can be used to construct confidence interval for the master curve through a second-order bootstrap procedure.},
doi = {10.1007/s00397-019-01138-y},
journal = {Rheologica Acta},
number = 5,
volume = 58,
place = {United States},
year = {2019},
month = {3}
}

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Works referenced in this record:

Compression set in gas-blown condensation-cured polysiloxane elastomers
journal, December 2010


New method for estimating shift factors in time–temperature superposition models
journal, April 2013

  • Naya, Salvador; Meneses, Antonio; Tarrío-Saavedra, Javier
  • Journal of Thermal Analysis and Calorimetry, Vol. 113, Issue 2
  • DOI: 10.1007/s10973-013-3193-1

Structural analysis of viscoelastic materials
journal, May 1964


Empirical Model-Building and Response Surfaces.
journal, June 1988

  • Kshirsagar, Anant M.; Box, George E. P.; Draper, Norman R.
  • Journal of the American Statistical Association, Vol. 83, Issue 402
  • DOI: 10.2307/2288890

Measure of morphological and performance properties in polymeric silicone foams by X-ray tomography
journal, October 2012

  • Patterson, Brian M.; Henderson, Kevin; Smith, Zachary
  • Journal of Materials Science, Vol. 48, Issue 5
  • DOI: 10.1007/s10853-012-6965-2

X-ray CT microtomography and mechanical response of foamed polysiloxane elastomers
journal, February 2012


The sensitivity of the time-temperature shift process to thermal variations—A note
journal, April 2008


Thermal ageing studies on room-temperature vulcanised polysiloxane rubbers
journal, January 2001


Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy
journal, February 1986


Challenges in Multiscale Modeling of Polymer Dynamics
journal, June 2013


Origin of the Vogel–Fulcher–Tammann law in glass-forming materials: the α–β bifurcation
journal, July 2000


Molecular Origins of Macroscopic Mechanical Properties of Elastomeric Organosiloxane Foams
journal, July 2015


Application of geometric algorithm of time-temperature superposition to linear viscoelasticity of rubber compounds
journal, June 2011

  • Bae, Jung-Eun; Cho, Kwang Soo; Seo, Kwan Ho
  • Korea-Australia Rheology Journal, Vol. 23, Issue 2
  • DOI: 10.1007/s13367-011-0011-9

3D printed cellular solid outperforms traditional stochastic foam in long-term mechanical response
journal, April 2016

  • Maiti, A.; Small, W.; Lewicki, J. P.
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep24871

Time-Temperature Superposition to Determine the Stress-Rupture of Aramid Fibres
journal, June 2006


Automated Procedure for Generation of Creep Compliance Master Curve for Asphalt Mixtures
journal, January 1998

  • Buttlar, William G.; Roque, Reynaldo; Reid, Brian
  • Transportation Research Record: Journal of the Transportation Research Board, Vol. 1630, Issue 1
  • DOI: 10.3141/1630-04

Analytical-Numerical Procedure to Determine if a Set of Experimental Curves Can Be Superimposed to Form a Master Curve
journal, September 1994


A note on estimating mastercurves
journal, January 1993


Applicability of the time–temperature superposition principle in modeling dynamic response of a polyurea
journal, December 2007

  • Zhao, J.; Knauss, W. G.; Ravichandran, G.
  • Mechanics of Time-Dependent Materials, Vol. 11, Issue 3-4
  • DOI: 10.1007/s11043-008-9048-7

The closed form t-T-P shifting (CFS) algorithm
journal, January 2011

  • Gergesova, M.; Zupančič, B.; Saprunov, I.
  • Journal of Rheology, Vol. 55, Issue 1
  • DOI: 10.1122/1.3503529

The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids
journal, July 1955

  • Williams, Malcolm L.; Landel, Robert F.; Ferry, John D.
  • Journal of the American Chemical Society, Vol. 77, Issue 14
  • DOI: 10.1021/ja01619a008

A Bayesian analysis of the compression set and stress–strain behavior in a thermally aged silicone foam
journal, August 2006


Long-term Coarsening and Function-time Evolution of an Initiator Powder
journal, November 2017

  • Maiti, Amitesh; Olson, Tammy Y.; Han, T. Yong
  • Propellants, Explosives, Pyrotechnics, Vol. 42, Issue 12
  • DOI: 10.1002/prep.201700186

Equivalent Time Temperature Model for Physical Aging and Temperature Effects on Polymer Creep and Relaxation
journal, October 2004

  • Barbero, Ever J.; Ford, Kevin J.
  • Journal of Engineering Materials and Technology, Vol. 126, Issue 4
  • DOI: 10.1115/1.1789956

Sublimation Pressure and Vapor Molecular Weight of Pentaerythritol Tetranitrate
journal, May 2004

  • Lau, Kai H.; Hildenbrand, Donald L.; Crouch-Baker, Steven
  • Journal of Chemical & Engineering Data, Vol. 49, Issue 3
  • DOI: 10.1021/je0302203