B. Sudret

B. Sudret
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Statistics - Computation (11)
 
Statistics - Methodology (10)
 
Statistics - Applications (6)
 
Statistics - Machine Learning (4)
 
Mathematics - Numerical Analysis (1)

Publications Authored By B. Sudret

Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to model highly complex models at relatively low computational costs. A least-square minimization technique may be used to determine the coefficients of the sparse PCE by relying on the so called experimental design (ED), i. Read More

Polynomial chaos expansions (PCE) have proven efficiency in a number of fields for propagating parametric uncertainties through computational models of complex systems, namely structural and fluid mechanics, chemical reactions and electromagnetism, etc. For problems involving oscillatory, time-dependent output quantities of interest, it is well-known that reasonable accuracy of PCE-based approaches is difficult to reach in the long term. In this paper, we propose a fully non-intrusive approach based on stochastic time warping to address this issue: each realization (trajectory) of the model response is first rescaled to its own time scale so as to put all sampled trajectories in phase in a common virtual time line. Read More

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making efficient quantification and propagation of uncertainties an important aspect. In this context, a typical workflow includes the characterization of the uncertainty in the input variables. Read More

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may become intractable in cases when a single simulation is time demanding. Particularly challenging is the reliability analysis of systems represented by computationally costly models, because of the large number of model evaluations that are typically required to estimate small probabilities of failure. Read More

Global sensitivity analysis is now established as a powerful approach for determining the key random input parameters that drive the uncertainty of model output predictions. Yet the classical computation of the so-called Sobol' indices is based on Monte Carlo simulation, which is not affordable when computationally expensive models are used, as it is the case in most applications in engineering and applied sciences. In this respect metamodels such as polynomial chaos expansions (PCE) and Gaussian processes (GP) have received tremendous attention in the last few years, as they allow one to replace the original, taxing model by a surrogate which is built from an experimental design of limited size. Read More

Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty quantification by crude Monte-Carlo simulation is not feasible. Read More

Uncertainties are inherent to real-world systems. Taking them into account is crucial in industrial design problems and this might be achieved through reliability-based design optimization (RBDO) techniques. In this paper, we propose a quantile-based approach to solve RBDO problems. Read More

In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by post-processing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. Read More

The application of polynomial chaos expansions (PCEs) to the propagation of uncertainties in stochastic dynamical models is well-known to face challenging issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a sufficient level of long term accuracy requires the use of high-order polynomials. Read More

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. Read More

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. Read More

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. Read More

Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate models (a.k. Read More

The study makes use of polynomial chaos expansions to compute Sobol' indices within the frame of a global sensitivity analysis of hydro-dispersive parameters in a simplified vertical cross-section of a segment of the subsurface of the Paris Basin. Applying conservative ranges, the uncertainty in 78 input variables is propagated upon the mean lifetime expectancy of water molecules departing from a specific location within a highly confining layer situated in the middle of the model domain. Lifetime expectancy is a hydrogeological performance measure pertinent to safety analysis with respect to subsurface contaminants, such as radionuclides. Read More

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. Read More

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. Read More

Fragility curves are commonly used in civil engineering to estimate the vulnerability of structures to earthquakes. The probability of failure associated with a failure criterion (e.g. Read More

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. Read More

The optimal and robust design of structures has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible probabilities of failure for a set of performance functions. In order to address real-world problems in which the performance is assessed through computational models (e. Read More

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. Read More

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. Read More

The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate. Starting with the premise that simulation-based approaches are not affordable for such problems, and that the most-probable-failure-point-based approaches do not permit to quantify the error on the estimation of the failure probability, an approach based on both metamodels and advanced simulation techniques is explored. The kriging metamodeling technique is chosen in order to surrogate the performance functions because it allows one to genuinely quantify the surrogate error. Read More

Reliability-based design optimization (RBDO) has gained much attention in the past fifteen years as a way of introducing robustness in the process of designing structures and systems in an optimal manner. Indeed classical optimization (e.g. Read More