The macroscopic behavior of many materials is complex and the end result mechanisms that operate across a broad range disparate scales. An imperfect knowledge material scales source epistemic uncertainty overall behavior. However, assessing this difficult due to nature response prohibitive computational cost integral calculations. In paper, we exploit multiscale hierarchical develop an approach...

Numerical quantification of the results from a measurement uncertainty computation is considered in terms of the inputs to that computation. The primary output is often an approximation to the PDF (probability density function) for the univariate or multivariate measurand (the quantity intended to be measured). All results of interest can be derived from this PDF. We consider uncertainty elicit...

This paper presents an overview of various aspects of uncertainty quantification in prognostics and health management. Since prognostics deals with predicting the future behavior of engineering systems and it is almost practically impossible to precisely predict future events, it is necessary to account for the different sources of uncertainty that affect prognostics, and develop a systematic f...

Uncertainty quantification (UQ) for porous media flow is of great importance for many societal, environmental and industrial problems. An obstacle to the progress in solving such problems, as well as in solving other stochastic PDEs, SPDEs, is the extreme computational effort needed for solving realistic problems. It is expected that the computers will open the door for a significant progress i...

In this paper, a methodology for propagation of uncertainty in stochastic nonlinear dynamical systems is investigated. The process noise is approximated using KarhunenLoève (KL) expansion. Perron-Frobenius (PF) operator is used to predict the evolution of uncertainty. A multivariate Kolmogorov-Smirnov test is used to verify the proposed framework. The method is applied to predict uncertainty ev...

A spectral formalism has been developed for the “non-intrusive” analysis of parametric uncertainty in reacting-flow systems. In comparison to conventional Monte Carlo analysis, this method quantifies the extent, dependence, and propagation of uncertainty through the model system and allows the correlation of uncertainties in specific parameters to the resulting uncertainty in detailed flame str...

In this work we develop an adaptive and reduced computational framework based on dimension-adaptive hierarchical approximation and reduced basis method for solving high-dimensional uncertainty quantification (UQ) problems. In order to tackle the computational challenge of “curse-ofdimensionality” commonly faced by these problems, we employ a dimension-adaptive tensor-product algorithm [29] and ...