Publications

The need for accurate simulations and reliability estimates of predictions has led to a variety of techniques to mathematically model and quantify uncertainty and variability. Depending on the problem characteristics, techniques based on probability theory or non-probabilistic techniques, for example based on fuzzy theory, are used. In the first category, the stochastic finite element method has received a lot of attention in recent years. This ...

The stochastic finite element method is a recent technique for solving partial differential equations (PDE) that contain stochastic coefficients. It can result in high-order accurate stochastic solutions while avoiding the computation of numerous Monte Carlo simulations. Two prominent variants are the stochastic collocation and stochastic Galerkin technique. The former samples a stochastic PDE in a set of well-chosen collocation points and ...

In this paper a framework is introduced for robust structural topology optimization for 2D and 3D continuum and truss problems. Spectral stochastic nite element method is used, with a polynomial chaos expansion to propagate uncertainties on the material characteristics to the response quantities. The uncertain parameters are modelled using a spatially correlated random eld which is discretized using the Karhunen-Loeve expansion. Special ...

This paper presents an overview and comparison of iterative solvers for linear stochastic partial differential equations (PDEs). A stochastic Galerkin finite element discretization is applied to transform the PDE into a coupled set of deterministic PDEs . Specialized solvers are required to solve the very high-dimensional systems that result after a finite e lement discretization of the resulting set. This paper discusses one-level iterative ...

When considering a wall in between two rooms, in an important part of the audio frequency range the local response of the rooms may be highly sensitive to uncertainty in spatial variations in geometry, material properties, boundary conditions, etc, while the local response of the wall is rather insensitive to such uncertainty. For this mid-frequency problem, a hybrid strategy is adopted that accounts for the uncertainty in the local room ...

© 2014 Elsevier Ltd. When considering the sound transmission through a wall in between two rooms, in an important part of the audio frequency range, the local response of the rooms is highly sensitive to uncertainty in spatial variations in geometry, material properties and boundary conditions, which have a wave scattering effect, while the local response of the wall is rather insensitive to such uncertainty. For this mid-frequency range, a ...

The dependence of the eigenfrequencies of a superconductive cavity on its geometry are represented by a stochastic response surface model. The model is constructed on the basis of both information on the eigenfrequencies as on their sensitivities with respect to the geometry. The eigenmodes are calculated using the 2D or 3D finite element method or finite integration technique. The stochastic representation does not only model uncertainties on ...

In this paper, we present a framework to deal with uncertainty quantification in case where the ranges of variability of the random parameters are ill-known. Namely the physical properties of the corrosion product (magnetite) which frequently clogs the tube support plate of steam generator, which is inaccessible in nuclear power plants. The methodology is based on Polynomial Chaos (PC) direct approaches and on Bayesian inference for inverse ...

In this paper a framework is introduced for robust structural topology optimization for 2D and 3D continuum and truss problems. The uncertain material parameters are modelled using a spatially correlated random field which is discretized using the Karhunen-Loève expansion. Spectral stochastic finite element method is used, with a polynomial chaos expansion to propagate uncertainties on the material characteristics to the response quantities. In ...

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals ...