Computational uncertainty quantification in a probabilistic setting is a special case of a parametric problem. Parameter dependent state vectors lead via association to a linear operator to analogues of covariance, its spectral decomposition, and the associated Karhunen-Loève expansion. From this one obtains a generalised tensor representation. The parameter in question may be a tuple of number...

The most convenient models of Solid Transportation (ST) problems have been justly considered a kind of uncertainty in their parameters such as fuzzy, grey, stochastic, etc. and usually, they suggest solving the main problems by solving some crisp equivalent model/models based on their proposed approach such as using ranking functions, embedding problems etc. Furthermore, there exist some shortc...

Matrix variate distributions are are used to quantify uncertainty in the mass, stiffness and damping matrices. The proposed approach is based on the so called Wishart random matrices. The probability density function of the system matrices are derived using the maximum entropy method. It is assumed that the mean of the system matrices are known. A new optimal Wishart distribution is proposed to...

We quantitatively examine the relative importance of uncertainty in emissions and physicochemical properties (including reaction rate constants) to Northern Hemisphere (NH) and Arctic polycyclic aromatic hydrocarbon (PAH) concentrations, using a computationally efficient numerical uncertainty technique applied to the global-scale chemical transport model GEOS-Chem. Using polynomial chaos (PC) m...

REPEATED PARAMETRIC UNCERTAINTIES K. B. Lim , D. P. Giesyy NASA Langley Research Center, MS 161, Hampton, Virginia, 23681-0001 Abstract A new methodology in which linear fractional transformation uncertainty bounds are directly constructed for use in robust control design and analysis is proposed. Existence conditions for model validating solutions with or without repeated scalar uncertainty ar...

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gauss...

The design of robust time-optimal controllers using the sensitivity concept is presented in this paper. A parameter optimization problem is solved using the Switch Time Optimization algorithm to determine a bang-bang control profile that minimizes the maneuver time subject to the constraint that the sensitivity of the final states with respect to system parameters are zero. The proposed approac...

The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg’s uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable qu...

Robust performance is said to be achieved if the performance specifications are met for all plants in a specified set. Classical loopshaping was developed decades ago to design for robust performance for single-loop systems with simple uncertainty and performance specifications. Specifications are often not so simple-multiple real parameter variations are not handled by classical loopshaping, f...

A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB) formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing t...