Journal ArticleDOI
Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion
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TLDR
An effective solution to this tail mismatch problem using a modified orthogonalization technique that reduces the degree of shuffling within columns containing empirical realizations of the K–L random variables is proposed.About:
This article is published in Probabilistic Engineering Mechanics.The article was published on 2005-04-01. It has received 211 citations till now. The article focuses on the topics: Gaussian process & Covariance.read more
Citations
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The stochastic finite element method: Past, present and future
TL;DR: A state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future are provided.
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Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion
TL;DR: The FEM and the FCM are more efficient than the EOLE method in evaluating a realization of the random field and are suitable for problems in which the time spent in the evaluation of random field realizations has a major contribution to the overall runtime – e.g., in finite element reliability analysis.
On the accuracy of the polynomial chaos approximation for random variables and stationary stochastic processes.
Richard V. Field,Mircea Grigoriu +1 more
TL;DR: In this article, the authors explored features and limitations of polynomial chaos (PC) approximations for non-Gaussian random variables and stochastic processes and developed metrics to assess the accuracy of the PC approximation.
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Simulation of simply cross correlated random fields by series expansion methods
TL;DR: A practical framework for generating cross correlated fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented and it is shown that the errors happen especially in the cross correlation between distant points and that they are negligibly small in practical situations.
References
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Book
Introduction to matrix computations
TL;DR: Rounding-Error Analysis of Solution of Triangular Systems and of Gaussian Elimination.
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Simulation of Stochastic Processes by Spectral Representation
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Computer rendering of stochastic models
TL;DR: A new algorithm is introduced that computes a realistic, visually satisfactory approximation to fractional Brownian motion in faster time than with exact calculations, and allows complex motion to be created inexpensively.
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Simulation of random fields via local average subdivision
TL;DR: A fast and accurate method of generating realizations of a homogeneous Gaussian scalar random process in one, two, or three dimensions is presented, motivated first by the need to represent engineering properties as local averages and second to be able to condition the realization easily to incorporate known data or change resolution within sub‐regions.
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Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes
TL;DR: In this article, the convergence and accuracy of the K-L expansion are investigated by comparing the second-order statistics of the simulated random process with that of the target process, and it is shown that the factors affecting convergence are: (a) ratio of the length of the process over correlation parameter, (b) form of the covariance function, and (c) method of solving for the eigen-solutions of the function.