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Computation of tail probabilities for non-classical gasdynamic phenomena

Abstract : Calculation of tail probabilities remains very challenging even with the most recent and performing uncertainty quantification techniques. To tackle this problem, this work aims at proposing an efficient method basing on Monte Carlo method, importance sampling and interpolation methods making use of Adjoint states. Several approaches are proposed in literature for using adjoint evaluations for accelerating Monte Carlo convergence. Generally, they rely on the building of a linear approximation in order to compute the small probability that the objective function exceeds a certain critical value, usually representing the probability that a system fails or suffers catastrophic losses. The adjoint calculation is then used to calculate the sensitivity gradient, which can be used to approximate the objective function as a linear function of the random variables describing the sources of uncertainty. The information provided by this linear approximation permits to reduce the variance of the Monte Carlo method using control variate and importance sampling. The method proposed here is based on a continuous update of the interpolation function via the gradient computation, which is then used with the importance sampling technique. The advantages of such an approach is to improve and retain the good convergence properties of MC methods when treating a very high number of dimension, by further accelerating the convergence by using the interpolation on functional evaluations and gradients. The interest of this kind of approach for predicting non-classical gasdynamics phenomena is then demonstrated with several examples, such as the computation of a rarefaction shock wave (RSW) in a dense-gas shock tube. In this case, since a RSW is relatively weak and that the prediction of its occurrence and intensity are highly sensitive to uncertainties on the initial flow conditions and on the fluid thermodynamic model, the objective is to obtain a reliable estimate for the RSW probability of occurrence.
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Conference papers
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https://hal.inria.fr/hal-01378421
Contributor : Pietro Marco Congedo <>
Submitted on : Monday, October 10, 2016 - 10:57:26 AM
Last modification on : Thursday, January 11, 2018 - 6:27:21 AM

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  • HAL Id : hal-01378421, version 1

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Nassim Razaaly, Pietro Marco Congedo. Computation of tail probabilities for non-classical gasdynamic phenomena. NICFD Conference, Oct 2016, Varenna, Italy. ⟨hal-01378421⟩

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