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Uncertainty quantification using high-dimensional numerical integration
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

We consider quantities that are uncertain because they depend on one

or many uncertain parameters. If the uncertain parameters are stochastic

the expected value of the quantity can be obtained by integrating the

quantity over all the possible values these parameters can take and dividing

the result by the volume of the parameter-space. Each additional

uncertain parameter has to be integrated over; if the parameters are many,

this give rise to high-dimensional integrals.

This report offers an overview of the theory underpinning four numerical

methods used to compute high-dimensional integrals: Newton-Cotes,

Monte Carlo, Quasi-Monte Carlo, and sparse grid. The theory is then applied

to the problem of computing the impact coordinates of a thrown ball

by introducing uncertain parameters such as wind velocities into Newton’s

equations of motion.

Place, publisher, year, edition, pages
2016. , 29 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-195701OAI: oai:DiVA.org:kth-195701DiVA: diva2:1045128
Available from: 2016-11-08 Created: 2016-11-08 Last updated: 2016-11-08Bibliographically approved

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