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A systematic study of efficient sampling methods to quantify uncertainty in crack propagation and the Burgers equation

Author

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  • Jimenez Edwin

    (Florida State University, Tallahassee, Florida 32306-4120, United States of America. E-mail: ejimenez@fsu.edu)

  • Lay Nathan

    (Florida State University, Tallahassee, Florida 32306-4120, United States of America. E-mail: nlay@fsu.edu)

  • Hussaini M. Yousuff

    (Florida State University, Tallahassee, Florida 32306-4120, United States of America. E-mail: myh@scs.fsu.edu)

Abstract

We present a systematic study of efficient sampling methods to quantify parametric uncertainty in stage II crack propagation and in a Burgers equation with random viscosity. The samplingmethods employed are Monte Carlo and quasi-Monte Carlo methods enhanced through variance reduction techniques including stratified sampling. We also present a recent variance reduction technique called sensitivity derivative enhanced sampling that utilizes sensitivity derivatives to make more efficient use of random samples. The crack propagation problem is a benchmark problem proposed by the Society of Automotive Engineers (SAE); this problem was selected because its large variance can hinder the already slow convergence of typical Monte Carlo methods and thus provides an ideal test for efficient sampling methods. We also examine a steady-state Burgers equation, a model equation of perennial interest for its connections with the equations of fluid mechanics, with uncertain viscosity.

Suggested Citation

  • Jimenez Edwin & Lay Nathan & Hussaini M. Yousuff, 2010. "A systematic study of efficient sampling methods to quantify uncertainty in crack propagation and the Burgers equation," Monte Carlo Methods and Applications, De Gruyter, vol. 16(1), pages 69-93, January.
    • Handle: RePEc:bpj:mcmeap:v:16:y:2010:i:1:p:69-93:n:2
    DOI: 10.1515/mcma.2010.002
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    References listed on IDEAS

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    1. Ngnepieba Pierre & Hussaini M. Y. & Debreu Laurent, 2006. "Optimal Control and Stochastic Parameter Estimation," Monte Carlo Methods and Applications, De Gruyter, vol. 12(5), pages 461-476, November.
    2. A. M. Croicu & M. Y. Hussaini, 2008. "Multiobjective Stochastic Control in Fluid Dynamics via Game Theory Approach: Application to the Periodic Burgers Equation," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 501-514, December.
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