Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/13864
Title: Simulation of stochastic processes using Karhunen-Loeve expansion
Authors: HUANG HONGWEI
Keywords: Simulation, Stochastic processes, Karhunen-Loeve expansion,
Issue Date: 14-Apr-2004
Source: HUANG HONGWEI (2004-04-14). Simulation of stochastic processes using Karhunen-Loeve expansion. ScholarBank@NUS Repository.
Abstract: This study focuses on extending the unified framework which has been established by Huang (2001) for the simulation of stationary and non-stationary, Gaussian and non-Gaussian processes using Karhunen-Loeve (K-L) expansion. The key steps involve solving for the eigensolutions from the homogeneous Fredholm integral equation based on the target covariance function and selecting uncorrelated standardized K-L random variables such that the expansion produces the desired marginal distribution. To improve the efficiency of obtaining eigensolutions, the wavelet-Galerkin approach is adopted to solve the Fredholm integral equation. The applicability of the K-L expansion as a simulation tool for Gaussian stochastic processes is examined numerically and compared with that of the wavelet expansion. The simulation methodology is extended to non-Gaussian processes with an iterative procedure that updates the appropriate K-L variables, which is originally proposed by Phoon et al (2000b). A modified version of the algorithm is developed in this study, where the simulated marginal distribution and covariance function can both match with the targets for strongly non-Gaussian processes. Finally, a new technique of generating non-Gaussian processes is discussed, which utilizes the fractile correlation instead of the usual product moment correlation.
URI: http://scholarbank.nus.edu.sg/handle/10635/13864
Appears in Collections:Master's Theses (Open)

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TABLE_OF_CONTENTS.pdf22.41 kBAdobe PDF

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SUMMARY.pdf55.45 kBAdobe PDF

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REFERENCES.pdf115.23 kBAdobe PDF

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