Monte Carlo Variance Reduction Methods with Applications in Structural Reliability Analysis
Field | Value | Language |
dc.contributor.author | Song, Chenxiao | |
dc.date.accessioned | 2022-12-14T23:00:08Z | |
dc.date.available | 2022-12-14T23:00:08Z | |
dc.date.issued | 2022 | en_AU |
dc.identifier.uri | https://hdl.handle.net/2123/29801 | |
dc.description.abstract | Monte Carlo variance reduction methods have attracted significant interest due to the continuous demand for reducing computational costs in various fields of application. This thesis is based on the content of a collection of six papers contributing to the theory and application of Monte Carlo methods and variance reduction techniques. For theoretical developments, we establish a novel framework of Monte Carlo integration over simplices, throughout from sampling to variance reduction. We also investigate the effect of batching for adaptive variance reduction, which aims at running the Monte Carlo simulation simultaneously with the parameter search algorithm using a common sequence of random realizations. Such adaptive variance reduction is moreover employed by strata in a newly proposed stratified sampling framework with dynamic budget allocation. For application in estimating the probability of failure in the context of structural reliability analysis, we formulate adaptive frameworks of stratified sampling with variance reduction by strata as well as stratified directional importance sampling, and survey a variety of numerical approaches employing Monte Carlo methods. | en_AU |
dc.language.iso | en | en_AU |
dc.subject | Monte Carlo methods | en_AU |
dc.subject | variance reduction | en_AU |
dc.subject | importance sampling | en_AU |
dc.subject | stratified sampling | en_AU |
dc.subject | adaptive simulation | en_AU |
dc.subject | structural reliability analysis | en_AU |
dc.title | Monte Carlo Variance Reduction Methods with Applications in Structural Reliability Analysis | en_AU |
dc.type | Thesis | |
dc.type.thesis | Doctor of Philosophy | en_AU |
dc.rights.other | The author retains copyright of this thesis. It may only be used for the purposes of research and study. It must not be used for any other purposes and may not be transmitted or shared with others without prior permission. | en_AU |
usyd.faculty | SeS faculties schools::Faculty of Science::School of Mathematics and Statistics | en_AU |
usyd.degree | Doctor of Philosophy Ph.D. | en_AU |
usyd.awardinginst | The University of Sydney | en_AU |
usyd.advisor | Kawai, Reiichiro |
Associated file/s
Associated collections