Adaptive reduced basis strategy for rare‐event simulations. (25th June 2019)

• Record Type: Journal Article
• Authors: Gallimard, L.
• Is Part Of: International journal for numerical methods in engineering. Volume 120:Number 3(2019)
• Page Start: 283
• Page End: 302
• Publication Date: 2019-06-25
• Subjects: cross‐entropy -- error bounds -- failure probability -- finite element analysis -- model reduction -- rare‐event simulations -- reduced basis -- structural reliability; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6135
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: Monte Carlo methods are well suited to characterize events of which associated probabilities are not too low with respect to the simulation budget. For very seldom observed events, these approaches do not lead to accurate results. Indeed, the number of samples is often insufficient to estimate such low probabilities (at least 10 n +2 samples are needed to estimate a probability of 10 − n with 10 % relative deviation of the Monte Carlo estimator). Even within the framework of reduced order methods, such as a reduced basis approach, it seems difficult to predict accurately low‐probability events. In this paper, we propose to combine a cross‐entropy method with a reduced basis algorithm to compute rare‐event (failure) probabilities.