Surrogate model based sequential sampling estimation of conformance probability for computationally expensive systems: application to fire safety science

Demeyer, Séverine; Fischer, Nicolas; Marquis, Damien

Journal de la société française de statistique, Tome 158 (2017) no. 1, pp. 111-138.

Le recours à la simulation numérique est devenue courant lorsque les expériences réelles sont impossibles ou réalisables qu’en très petit nombre. La modélisation statistique d’expériences numériques à partir de modèles de krigeage offre un cadre de décision probabiliste pour évaluer la probabilité de défaillance d’un système. La combinaison de simulations rapides de basse fidélité avec des simulations coûteuses de haute fidélité s’est avérée une méthode efficace pour diminuer le coût en simulations lors de la prévision de sorties d’un système. Par ailleurs, l’échantillonnage séquentiel est couramment utilisé pour estimer une probabilité de défaillance d’un système modélisé par krigeage. Dans cette étude, une méthodologie est exposée d’utilisation d’un plan séquentiel dans un cadre multi-fidélité pour prédire la probabilité de défaillance d’un système numérique coûteux et son incertitude. La méthodologie est appliquée à un cas d’étude en ingénierie de la sécurité incendie pour évaluer la probabilité de non-conformité d’un système d’évacuation de fumée à partir d’outils numériques complexes de simulation incendie.

The use of complex simulation systems has become common practice when physical experiments are not feasible or when too few are feasible. The statistical modelling of numerical experiments with kriging models yields a probabilistic decision framework to assess the probability of failure of the system. Combining fast low-fidelity simulations with costly high-fidelity simulations has proved an efficient method to decrease the burden of costly simulations when predicting the output of a system. In addition, sequential design is commonly used to estimate the probability of failure of a system modelled by kriging. In this work, a methodology is derived to benefit from sequential design in a multi-fidelity framework to predict the probability of failure of a computationally expensive system and its uncertainty. The methodology is applied to a fire safety engineering case study to assess the probability of non-conformity of a smoke control system from complex numerical fire tools.

Keywords: numerical experiments, Monte Carlo Method, co-kriging, sequential sampling, probability of exceeding a threshold, conformity assessment
Mot clés : expériences numériques, méthode Monte Carlo, co-krigeage, échantillonnage séquentiel, probabilité de dépassement de seuil, évaluation de conformité

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