Over the last few years there have been dramatic advances in the area of uncertainty quantification. In particular, we have seen a surge of interest in developing efficient, scalable, stable, and convergent computational methods for solving differential equations with random inputs. Stochastic collocation (SC) methods, which inherit both the ease of implementation of sampling methods like Monte...

Optimization and design in the presence of uncertain operating conditions, material properties and manufacturing tolerances poses a tremendous challenge to the scientific computing community. In many industry-relevant situations the performance metrics depend in a complex, non-linear fashion on those factors and the construction of an accurate representation of this relationship is difficult. I...

Stochastic reservoir models must honor as much input data as possible to be reliable numerical models of the reservoir under study. Traditional simulation algorithms are unable to honor either complex geological/morphological patterns or engineering data from well tests. The technique developed in this dissertation may be used to incorporate such information into stochastic reservoir models. Th...

1 Prliminaries 2 1.1 Basic Probability concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Stochastic Differential Equations (SDE’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Langevin equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Ito integral and basics of Ito calculus . . . . . . . . . . . . . . ....

Design and fabrication uncertainties have become an important issue in nano-scale integrated circuit design. Such uncertainties are typically randomly distributed, as described by probability density functions extracted from measurements. Such device-level uncertainties can propagate to the upper circuit level, leading to significant variations in circuit performances (such as power dissipation...

The increased complexity of the transmission grid can endanger operational security grid. Operational risk assessment, a stochastic tool, helps to enhance security. Contingency analysis and its impact quantification are main constituents assessment. In this study, different graphical methods proposed visualize contingency-based detailed results: heat-map risk-based contingency chart. Through he...

In the present work, an innovative method for solving stochastic partial differential equations is presented. A multiresolution method permitting to compute statistics of the quantity of interest for a whatever form of the probability density function is extended to permit an adaptation in both physical and stochastic spaces. The efficiency of this strategy, in terms of refinement/derefinement ...

— Models in electromagnetism are more and more accurate. In some applications, the gap between the experience and the model comes from the deviation on input data of the model which are not perfectly known. The stochastic approach can be used to quantify the effect of these input data uncertainties on the outputs of the model. In this article, the application of such approach in computational e...

In Operational Modal Analysis, the modal parameters (natural frequencies, damping ratios and mode shapes) obtained from Stochastic Subspace Identification (SSI) of a structure, are afflicted with statistical uncertainty. For evaluating the quality of the obtained results it is essential to know the appropriate confidence intervals of these figures. In this paper we present algorithms that autom...

We consider flows in fractured media, described by Discrete Fracture Network (DFN) models. We perform an Uncertainty Quantification analysis, assuming the fractures’ transmissivity coefficients to be random variables. Two probability distributions (log-uniform and log-normal) are used within different laws that express the coefficients in terms of a family of independent stochastic variables; t...