Finite element and reliability: a method for compound variables—application on a cracked heating system

2019

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 10n+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.

Section: Structural Reliability Modelmentioning

confidence: 99%

“…In this section, we describe the problem of reliability assessment . Let us denote by S ( θ )= Q ( u h ( x , θ )) the computational output of interest and R ( θ ) the threshold associated to this computational output.…”

Section: Problem Formulationmentioning

confidence: 99%

Adaptive reduced basis strategy for rare‐event simulations

2019

“…In this section, we describe the problem of reliability assessment . Let us denote by S ( θ )= Q ( u h ( θ ); θ ) the computational output of interest and R ( θ ) the threshold associated with this computational output.…”

Section: The Problem To Be Solvedmentioning

confidence: 99%

Towards error bounds of the failure probability of elastic structures using reduced basis models

Florentin

Ryckelynck

2017

International audienceStructural reliability methods aim at computing the probability of failure of systems with respect to prescribed limit state functions. A common practice to evaluate these limit state functions is using Monte Carlo simulations. The main drawback of this approach is the computational cost, because it requires computing a large number of deterministic finite element solutions. Surrogate models, which are built from a limited number of runs of the original model, have been developed, as substitute of the original model, to reduce the computational cost. However, these surrogate models, while decreasing drastically the computational cost, may fail in computing an accurate failure probability. In this paper, we focus on the control of the error introduced by a reduced basis surrogate model on the computation of the failure probability obtained by a Monte Carlo simulation. We propose a technique to determine bounds of this failure probability, as well as a strategy of enrichment of the reduced basis, based on limiting the bounds of the error of the failure probability for a multi-material elastic structur

“…In this section, we describe the problem of reliability assessment, and we introduce the reliability index . Structural reliability aims at computing the probability of failure of a mechanical system by accounting for uncertainties arising in a model description (geometry, material properties) or in the environmental data (prescribed displacement and external forces).…”

Section: Principle Of Reliability Analysismentioning

confidence: 99%

Coupling finite element and reliability analysis through proper generalized decomposition model reduction

Vidal

Polit

2013

SUMMARYThe FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi-material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi-material model. This parametrized solution is used in conjunction with a first-order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two-dimensional plane elasticity are presented.