Failure prediction of steel components under the coupled effect of excessive plastic deformations and pitting corrosion

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Embedded multilevel monte carlo for uncertainty quantification in random domains

The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for uncertainty quantification (UQ) in partial differential equation (PDE) models. It combines approximations at different levels of accuracy using a hierarchy of meshes whose generation is only possible for simple geometries. On top of that, MLMC and Monte Carlo (MC) for random domains involve the generation of a mesh for every sample. Here we consider the use of embedded methods which make use of simple background meshes of an artificial domain (a bounding-box) for which it is easy to define a mesh hierarchy. We use the recent aggregated finite element method (AgFEM) method, which permits to avoid ill-conditioning due to small cuts, to design an embedded MLMC (EMLMC) framework for (geometrically and topologically) random domains implicitly defined through a random level-set function. Predictions from existing theory are verified in numerical experiments and the use of AgFEM is statistically demonstrated to be crucial for complex and uncertain geometries in terms of robustness and computational cost.Peer ReviewedPostprint (author's final draft

Embedded multilevel Monte Carlo for uncertainty quantification in random domains

The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of meshes in a similar way as multigrid. The generation of body-fitted mesh hierarchies is only possible for simple geometries. On top of that, MLMC for random domains involves the generation of a mesh for every sample. Instead, here we consider the use of embedded methods which make use of simple background meshes of an artificial domain (a bounding-box) for which it is easy to define a mesh hierarchy, thus eliminating the need of body-fitted unstructured meshes, but can produce ill-conditioned discrete problems. To avoid this complication, we consider the recent aggregated finite element method (AgFEM). In particular, we design an embedded MLMC framework for (geometrically and topologically) random domains implicitly defined through a random level-set function, which makes use of a set of hierarchical background meshes and the AgFEM. Performance predictions from existing theory are verified statistically in three numerical experiments, namely the solution of the Poisson equation on a circular domain of random radius, the solution of the Poisson equation on a topologically identical but more complex domain, and the solution of a heat-transfer problem in a domain that has geometric and topological uncertainties. Finally, the use of AgFE is statistically demonstrated to be crucial for complex and uncertain geometries in terms of robustness and computational cost. Date: November 28, 2019

Upscaling of a dual-permeability Monte Carlo simulation model for contaminant transport in fractured networks by genetic algorithm parameter identification

International audienceThe transport of radionuclides in fractured media plays a fundamental role in determining the level of risk offered by a radioactive waste repository in terms of expected doses. Discrete Fracture Networks (DFN) methods can provide detailed solutions to the problem of modeling the contaminant transport in fractured media. However, within the framework of the performance assessment (PA) of radioactive waste repositories, the computational efforts required are not compatible with the repeated calculations that need to be performed for the probabilistic uncertainty and sensitivity analyses of PA. In this paper, we present a novel upscaling approach, which consists in computing the detailed numerical fractured flow and transport solutions on a small scale and use the results to derive the equivalent continuum parameters of a lean, one-dimensional Dual-Permeability, Monte Carlo Simulation (DPMCS) model by means of a Genetic Algorithm search. The proposed upscaling procedure is illustrated with reference to a realistic case study of migration taken from literature

Research reports: 1991 NASA/ASEE Summer Faculty Fellowship Program

The basic objectives of the programs, which are in the 28th year of operation nationally, are: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate an exchange of ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participants' institutions; and (4) to contribute to the research objectives of the NASA Centers. The faculty fellows spent 10 weeks at MSFC engaged in a research project compatible with their interests and background and worked in collaboration with a NASA/MSFC colleague. This is a compilation of their research reports for summer 1991

Accelerated Fatigue Reliability Analysis of Stiffened Sections Using Deep Learning

Fatigue is one of the main failure mechanisms in structures subjected to fluctuating loads such as bridges and ships. If inadequately designed for such loads, fatigue can be detrimental to the safety of the structure. When fatigue cracks reach a certain size, sudden fracture failure or yielding of the reduced section can occur. Accordingly, quantifying the critical crack size is essential for determining the reliability of fatigue critical structures under growing cracks. Failure Assessment Diagrams (FADs) can be used to determine the critical crack size or whether the state of the crack is acceptable or not at a particular instant in time. Due to the presence of uncertainties in loads, material properties and crack growth behavior, probabilistic analysis is essential to understand the fatigue performance of the structure over its service life. A time dependent reliability profile for the structure can be established to help schedule maintenance and repair activities. However, probabilistic analysis of crack growth under complex geometrical and loading conditions can be very expensive computationally. Deep learning is a useful tool that is used in this study to curtail this lengthy process by establishing multi-variate non-linear approximations for complex fatigue crack growth profiles. This study proposes a framework for establishing the fatigue reliability profiles of stiffened panels under uncertainty. Monte Carlo simulation is used to draw samples from relevant probabilistic parameters and establish the time dependent reliability profile of the structure under propagating cracks. Deep learning is adopted to improve the computational efficiency of the probabilistic analysis in establishing the probabilistic crack growth profiles. The proposed framework is illustrated on a bridge with stiffened tub girders subjected to fatigue loading.Civil Engineerin

Reliability analysis of fatigue and fracture under random loading.

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