Sequential design of computer experiments for the estimation of a probability of failure

By Julien Bect, David Ginsbourger, Ling Li, Victor Picheny, Emmanuel Vazquez. 2010

386 citations recorded by the source corpus.

This paper deals with the problem of estimating the volume of the excursion set of a function f:ℝd→ℝ above a given threshold, under a probability measure on ℝd that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of f and aim at performing evaluations of f as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability, Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. François Deheeger
2. Bruno Sudret
3. Fabrice Gamboa
4. V. Dubourg
5. A. Arnaud
6. Nicolas Bousquet
7. Bertrand Iooss
8. E. Sergienko

In Management Science and Operations Research

1. Fabrice Gamboa
2. Bruno Sudret
3. Bertrand Iooss
4. V. Dubourg
5. François Deheeger
6. Paul Lemaître

In Statistics and Probability

1. Bruno Sudret
2. V. Dubourg
3. Bertrand Iooss
4. François Deheeger
5. Fabrice Gamboa
6. A. Arnaud
7. Nicolas Bousquet
8. E. Sergienko

In Probabilistic & Bayesian Methods

1. Bruno Sudret
2. V. Dubourg

Citations in the corpus

• Polynomial-Chaos-based Kriging (2015, neutral): “Practical applications can be found in many fields, such as structural reliability analysis Kaymaz (2005); Bect et al. (2012); Echard et al. (2011); Bichon et al. (2008); Dubourg et al. (2013); Dubourg and Sudret (2014) and design optimization Jones et al. (1998); Dubourg et al. (2011); Dubourg…”
• LIF: A new Kriging based learning function and its application to structural reliability analysis (2017, neutral): “Various kinds of sequential DoE based on the Kriging model have been proposed to improve the accuracy of structural reliability analysis and reduce the number of calls to the real performance function [8,29,32,38,41,42].”
• Metamodel-based importance sampling for structural reliability analysis (2011, background): “The interested reader may find the expressions for all these criteria together with a discussed comparison on two analytical examples in a recent paper by Bect et al. (2011).”
• Density modification-based reliability sensitivity analysis (2012, methodology): “The use of sequential methods [17] may also be tested.”
• Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes (2016, neutral): “This result is used in the R CRAN package “sensitivity” to perform sequential design for sensitivity analysis using a Stepwise Uncertainty Reduction (SUR) strategy [5].”