322 research outputs found
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
Hierarchical adaptive polynomial chaos expansions
Polynomial chaos expansions (PCE) are widely used in the framework of
uncertainty quantification. However, when dealing with high dimensional complex
problems, challenging issues need to be faced. For instance, high-order
polynomials may be required, which leads to a large polynomial basis whereas
usually only a few of the basis functions are in fact significant. Taking into
account the sparse structure of the model, advanced techniques such as sparse
PCE (SPCE), have been recently proposed to alleviate the computational issue.
In this paper, we propose a novel approach to SPCE, which allows one to exploit
the model's hierarchical structure. The proposed approach is based on the
adaptive enrichment of the polynomial basis using the so-called principle of
heredity. As a result, one can reduce the computational burden related to a
large pre-defined candidate set while obtaining higher accuracy with the same
computational budget
Surrogate-assisted reliability-based design optimization: a survey and a new general framework
International audienc
Characterization of random stress fields obtained from polycrystalline aggregate calculations using multi-scale stochastic finite elements
The spatial variability of stress fields resulting from polycrystalline
aggregate calculations involving random grain geometry and crystal orientations
is investigated. A periodogram-based method is proposed to identify the
properties of homogeneous Gaussian random fields (power spectral density and
related covariance structure). Based on a set of finite element polycrystalline
aggregate calculations the properties of the maximal principal stress field are
identified. Two cases are considered, using either a fixed or random grain
geometry. The stability of the method w.r.t the number of samples and the load
level (up to 3.5 % macroscopic deformation) is investigated
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