Metamodel-based importance sampling for structural reliability analysis

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate computational model (e.g. a finite element model). In this respect simulation methods, which may require $10^{3-6}$ runs cannot be used directly. Surrogate models such as quadratic response surfaces, polynomial chaos expansions or kriging (which are built from a limited number of runs of the original model) are then introduced as a substitute of the original model to cope with the computational cost. In practice it is almost impossible to quantify the error made by this substitution though. In this paper we propose to use a kriging surrogate of the performance function as a means to build a quasi-optimal importance sampling density. The probability of failure is eventually obtained as the product of an augmented probability computed by substituting the meta-model for the original performance function and a correction term which ensures that there is no bias in the estimation even if the meta-model is not fully accurate. The approach is applied to analytical and finite element reliability problems and proves efficient up to 100 random variables.Comment: 20 pages, 7 figures, 2 tables. Preprint submitted to Probabilistic Engineering Mechanic

Metamodel-based importance sampling for the simulation of rare events

In the field of structural reliability, the Monte-Carlo estimator is considered as the reference probability estimator. However, it is still untractable for real engineering cases since it requires a high number of runs of the model. In order to reduce the number of computer experiments, many other approaches known as reliability methods have been proposed. A certain approach consists in replacing the original experiment by a surrogate which is much faster to evaluate. Nevertheless, it is often difficult (or even impossible) to quantify the error made by this substitution. In this paper an alternative approach is developed. It takes advantage of the kriging meta-modeling and importance sampling techniques. The proposed alternative estimator is finally applied to a finite element based structural reliability analysis.Comment: 8 pages, 3 figures, 1 table. Preprint submitted to ICASP11 Mini-symposia entitled "Meta-models/surrogate models for uncertainty propagation, sensitivity and reliability analysis

Meta-models for structural reliability and uncertainty quantification

A meta-model (or a surrogate model) is the modern name for what was traditionally called a response surface. It is intended to mimic the behaviour of a computational model M (e.g. a finite element model in mechanics) while being inexpensive to evaluate, in contrast to the original model which may take hours or even days of computer processing time. In this paper various types of meta-models that have been used in the last decade in the context of structural reliability are reviewed. More specifically classical polynomial response surfaces, polynomial chaos expansions and kriging are addressed. It is shown how the need for error estimates and adaptivity in their construction has brought this type of approaches to a high level of efficiency. A new technique that solves the problem of the potential biasedness in the estimation of a probability of failure through the use of meta-models is finally presented.Comment: Keynote lecture Fifth Asian-Pacific Symposium on Structural Reliability and its Applications (5th APSSRA) May 2012, Singapor

Reliability approach in spacecraft structures

This paper presents an application of the probabilistic approach with reliability assessment on a spacecraft structure. The adopted strategy uses meta-modeling with first and second order polynomial functions. This method aims at minimizing computational time while giving relevant results. The first part focuses on computational tools employed in the strategy development. The second part presents a spacecraft application. The purpose is to highlight benefits of the probabilistic approach compared with the current deterministic one. From examples of reliability assessment we show some advantages which could be found in industrial applications

Explicit Mapping of Acoustic Regimes For Wind Instruments

This paper proposes a methodology to map the various acoustic regimes of wind instruments. The maps can be generated in a multi-dimensional space consisting of design, control parameters, and initial conditions. The bound- aries of the maps are obtained explicitly in terms of the parameters using a support vector machine (SVM) classifier as well as a dedicated adaptive sam- pling scheme. The approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria. Examples of computation of the probability of occurrence of a specific acoustic regime are also provided. In addition, the approach is demonstrated on a design optimization example for optimal intonation

mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location

This paper develops mfEGRA, a multifidelity active learning method using data-driven adaptively refined surrogates for failure boundary location in reliability analysis. This work addresses the issue of prohibitive cost of reliability analysis using Monte Carlo sampling for expensive-to-evaluate high-fidelity models by using cheaper-to-evaluate approximations of the high-fidelity model. The method builds on the Efficient Global Reliability Analysis (EGRA) method, which is a surrogate-based method that uses adaptive sampling for refining Gaussian process surrogates for failure boundary location using a single-fidelity model. Our method introduces a two-stage adaptive sampling criterion that uses a multifidelity Gaussian process surrogate to leverage multiple information sources with different fidelities. The method combines expected feasibility criterion from EGRA with one-step lookahead information gain to refine the surrogate around the failure boundary. The computational savings from mfEGRA depends on the discrepancy between the different models, and the relative cost of evaluating the different models as compared to the high-fidelity model. We show that accurate estimation of reliability using mfEGRA leads to computational savings of $\sim$46% for an analytic multimodal test problem and 24% for a three-dimensional acoustic horn problem, when compared to single-fidelity EGRA. We also show the effect of using a priori drawn Monte Carlo samples in the implementation for the acoustic horn problem, where mfEGRA leads to computational savings of 45% for the three-dimensional case and 48% for a rarer event four-dimensional case as compared to single-fidelity EGRA