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

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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.

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Acknowledgments

The author would like to thank colleagues at LLNL for sharing experimental data and for useful discussions, particularly Ward Small, Jim Lewicki, Sarah Chinn, Tom Wilson, Andrew Saab, Chris Grant, Richard Gee, and Bob Maxwell. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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  1. Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA

    Amitesh Maiti

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Maiti, A. Second-order statistical bootstrap for the uncertainty quantification of time-temperature-superposition analysis. Rheol Acta 58, 261–271 (2019). https://doi.org/10.1007/s00397-019-01138-y

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