Maximum Entropy Multivariate Analysis of Uncertain Dynamical Systems Based on the Wiener–Askey Polynomial Chaos

Author

D´Antona, Gabriele ; Monti, Antonello ; Ponci, Ferdinanda ; Rocca, Luca

Author_Institution

Dipt. di Elettrotecnica, Politecnico di Milano

Volume

56

Issue

3

fYear

2007

fDate

6/1/2007 12:00:00 AM

Firstpage

689

Lastpage

695

Abstract

Many measurement models are formalized in terms of a stochastic ordinary differential equation that relates its solution to some given observables. The expression of the measurement uncertainty for the solution that is evaluated at some time instants requires the determination of its (joint) probability density function. Recently, the polynomial chaos theory (PCT) has been widely recognized as a promising technique in order to address the problem. The uncertainty estimation via PCT requires the use of a Monte Carlo integration sampling strategy. In this paper, a novel approach will be presented in order to achieve PCT uncertainty estimation on the basis of an analytical methodology, requiring only optimization calculus

Keywords

Monte Carlo methods; chaos; measurement uncertainty; polynomials; probability; Monte Carlo integration sampling; Wiener-Askey polynomial chaos; analytical methodology; maximum entropy multivariate analysis; measurement models; measurement uncertainty; optimization calculus; polynomial chaos theory; probability density function; stochastic ordinary differential equation; uncertain dynamical systems; uncertain systems; uncertainty estimation; Chaos; Differential equations; Entropy; Measurement uncertainty; Monte Carlo methods; Optimization methods; Polynomials; Probability density function; Sampling methods; Stochastic processes; Density function; maximum entropy (ME); measurement uncertainty; stochastic circuits; uncertain systems;

fLanguage

English

Journal_Title

Instrumentation and Measurement, IEEE Transactions on

Publisher

ieee

ISSN

0018-9456

Type

jour

DOI

10.1109/TIM.2007.894920

Filename

4200986