Assessment of spectral representation and Karhunen-Loève expansion methods for the simulation of Gaussian stochastic fields

Stefanou, G; Papadrakakis, M

dc.contributor.author	Stefanou, G	en
dc.contributor.author	Papadrakakis, M	en
dc.date.accessioned	2014-03-01T01:25:57Z
dc.date.available	2014-03-01T01:25:57Z
dc.date.issued	2007	en
dc.identifier.issn	0045-7825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17840
dc.subject	Gaussian stochastic field	en
dc.subject	Karhunen-Loève expansion	en
dc.subject	Spectral representation	en
dc.subject	Wavelet-Galerkin scheme	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Galerkin methods	en
dc.subject.other	Integral equations	en
dc.subject.other	Mathematical models	en
dc.subject.other	Random processes	en
dc.subject.other	Statistical methods	en
dc.subject.other	Wavelet analysis	en
dc.subject.other	Gaussian stochastic field	en
dc.subject.other	Spectral representation	en
dc.subject.other	Wavelet-Galerkin scheme	en
dc.subject.other	Gaussian distribution	en
dc.subject.other	Galerkin methods	en
dc.subject.other	Gaussian distribution	en
dc.subject.other	Integral equations	en
dc.subject.other	Mathematical models	en
dc.subject.other	Random processes	en
dc.subject.other	Statistical methods	en
dc.subject.other	Wavelet analysis	en
dc.title	Assessment of spectral representation and Karhunen-Loève expansion methods for the simulation of Gaussian stochastic fields	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cma.2007.01.009	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cma.2007.01.009	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	From the wide variety of methods developed for the simulation of Gaussian stochastic processes and fields, two are most often used in applications: the spectral representation method and the Karhunen-Lo&ve (K-L) expansion. In this paper, an in-depth assessment on the capabilities of the two methods is presented. The spectral representation method expands the stochastic field as a sum of trigonometric functions with random phase angles and/or amplitudes. The version having only random phase angles is used in this work. A wavelet-Galerkin scheme is adopted for the efficient numerical solution of the Fredholm integral equation appearing in the K-L expansion. A one-dimensional homogeneous Gaussian random field with two types of autocovariance function, exponential and square exponential, is used as the benchmark test. The accuracy achieved and the computational effort required by the K-L expansion and the spectral representation for the simulation of the stochastic field are investigated. The accuracy obtained by the two approaches is examined by comparing their ability to produce sample functions that match the target correlation structure and the Gaussian probability distribution or, alternatively, its low order statistical moments (mean, variance and skewness). (c) 2007 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE SA	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.doi	10.1016/j.cma.2007.01.009	en
dc.identifier.isi	ISI:000246126700013	en
dc.identifier.volume	196	en
dc.identifier.issue	21-24	en
dc.identifier.spage	2465	en
dc.identifier.epage	2477	en