In this paper, the nonlinear free vibration of fiber-reinforced lamina micro-switches is investigated, and a sensitivity analysis (SA) is given. The switches are modeled as solid rectangular beams consisting of an isotropic matrix with transversely and longitudinally isotropic reinforcements, incorporating a higher order Hamiltonian approach. An SA of the proposed micro-switch is presented by c...

Sensitivity analysis aims at quantifying influence of input parameters dispersion on the output dispersion of a numerical model. When the model evaluation is time consuming, the computation of Sobol' indices based on Monte Carlo method is not applicable and a surrogate model has to be used. Among all approximation methods, polynomial chaos expansion is one of the most efficient to calculate var...

Monte Carlo integration of multi-dimensional Gaussian functions is widely applicable in the statistical analysis of functions of many variables, and such analysis is encountered in many fields of science. In this write-up, we compare two Monte Carlo integration algorithms from the Cuba library, Vegas, and Suave, in terms of convergence time and accuracy of evaluation of a multi-dimensional Gaus...

This paper compares different types of simulated draws over a range of number of draws in generating Bayesian efficient designs for stated choice studies. The paper examines how closely pseudo Monte Carlo, quasi Monte Carlo and polynomial cubature methods are able to replicate the true levels of Bayesian efficiency for SC designs of various dimensions. The authors conclude that the predominantl...

We review and apply quasi-Monte Carlo (QMC) and global sensitivity analysis (GSA) techniques to pricing and risk management (Greeks) of representative financial instruments of increasing complexity. We compare QMC vs. standard Monte Carlo (MC) results in great detail, using high-dimensional Sobol’ low-discrepancy sequences, different discretization methods, and specific analyses of convergence,...

Quasi-Monte Carlo methods are based on the idea that random Monte Carlo techniques can often be improved by replacing the underlying source of random numbers with a more uniformly distributed deterministic sequence. Quasi-Monte Carlo methods often include standard approaches of variance reduction, although such techniques do not necessarily directly translate. In this paper we present a quasi-M...

The analysis of variance is now often applied to functions defined on the unit cube, where it serves as a tool for the exploratory analysis of functions. The mean dimension of a function, defined as a natural weighted combination of its ANOVA mean squares, provides one measure of how hard or easy the function is to integrate by quasi-Monte Carlo sampling. This paper presents some new identities...

An efficient method is proposed to perform global sensitivity analysis of a the computer model of a physical system whose input parameters are random. The so-called sensitivity indices are usually computed by Monte Carlo simulation, which reveals inappropriate for industrial applications due to an unaffordable computational cost. In the present paper, polynomial chaos (PC) expansions are introd...

Potential assessment has served various objectives in the development of renewable energies. However, the prospective nature of this type of assessment sometimes makes it difficult to evaluate and compare estimation results based on different data and modeling. To facilitate this comparison, uncertainty estimates need to be systematically provided. Since potential assessment sometimes relies on...