This article presents a unifying framework to uncertainty quantification for systems subject to several design requirements that depend polynomially on both aleatory and epistemic uncertainties. This methodology, which is based on the Bernstein expansions of polynomials, enables calculating bounding intervals for the range of means, variances and failure probabilities of response metrics corres...

Neural field models have been used for many years to model a variety of macroscopic spatiotemporal patterns in the cortex. Most authors have considered homogeneous domains, resulting in equations that are translationally invariant. However, there is an obvious need to better understand the dynamics of such neural field models on heterogeneous domains. One way to include heterogeneity is through...

The authors present a detailed analysis of the asymptotic frequentist properties of credible sets derived from posteriors with normal-linear measurement models and horseshoe priors. Although we disagree with the claim that “In Bayesian practice credible balls are nevertheless used as if they were confidence sets”, the results in the paper are important for identifying where the horseshoe priors...

Stability and performance of a system can be inferred from the evolution of statistical characteristic (i.e. mean, variance...) of system states. The polynomial chaos of Wiener provides a computationally effective framework for uncertainty quantification of stochastic dynamics in terms of statistical characteristic. In this work, polynomial chaos is used for uncertainty quantification of fracti...

Kinetic equations contain uncertainties in their collision kernels or scattering coefficients, initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic models have important engineering and industrial applications. In this article we survey recent efforts in the study of kinetic equations with random inputs, including their mathematical properties such as...

Article history: Received 27 October 2009 Received in revised form 12 April 2010 Accepted 25 May 2010 Available online 2 June 2010

The influence of dynamic eccentricity on the harmonic spectrum of the torque of a permanent magnet synchronous machine is studied. The spectrum is calculated by an energy balance method. Uncertainty quantification is applied by using generalized Polynomial Chaos and Monte Carlo. It is found that the displacement of the rotor impacts the spectrum of the torque the most.

Adaptive Sparse Grid Approaches to Polynomial Chaos Expansions for Uncertainty Quantification by Justin Gregory Winokur Department of Mechanical Engineering & Materials Science Duke University Date: Approved: Omar M. Knio, Supervisor

— 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...