Publication

MATHICSE Technical Report : Quantifying uncertain system outputs via the multilevel Monte Carlo method – Part I: Central moment estimation

Fabio Nobile
2017
Working Papers

Abstract

In this work we introduce and analyze a novel multilevel Monte Carlo (MLMC) estimator for the accurate approximation of central moments of system outputs affected by uncertainties. Central moments play a central role in many disciplines to characterize a random system output's distribution and are of primary importance in many prediction, optimization, and decision making processes under uncertainties. We detail how to effectively tune the MLMC algorithm for central moments of any order and present a complete practical algorithm that is implemented in our accompanying Python library cmlmc-py1. In fact, we validate the methodology on selected reference problems and apply it to an aerodynamic relevant test case, namely the transonic RAE 2822 airfoil affected by operating and geometric uncertain- ties.

Official source

https://infoscience.epfl.ch/entities/publication/97a59e33-abc5-4720-95be-83c9f0e9f470

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Fabio Nobile
2017
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/97a59e33-abc5-4720-95be-83c9f0e9f470

About this result

Related concepts (30)

Moment (mathematics)

In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis.

Method of moments (statistics)

In statistics, the method of moments is a method of estimation of population parameters. The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest. Those expressions are then set equal to the sample moments. The number of such equations is the same as the number of parameters to be estimated.

Monte Carlo method

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

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MATHICSE Technical Report : Quantifying uncertain system outputs via the multilevel Monte Carlo method – Part I: Central moment estimation

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