Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion

Phoon, Kok‐Kwang; Huang, Hongwei; Quek, Ser Tong

doi:10.1016/j.probengmech.2005.05.007

Cited by 220 publications

(100 citation statements)

References 21 publications

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“…Since all the joint multidimensional density functions are needed to fully characterize a non-Gaussian stochastic field, a number of studies have been focused on producing a more realistic definition of a non-Gaussian sample function from a simple transformation of some underlying Gaussian field with known second-order statistics e.g. [16,21,34,80,100,110,141,142,147].…”

Section: Simulation Methods For Non-gaussian Stochastic Processes Andmentioning

confidence: 99%

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The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

862

407

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a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing 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.

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Section: Simulation Methods For Non-gaussian Stochastic Processes Andmentioning

confidence: 99%

“…The method offers a unified framework for the simulation of homogeneous and nonhomogeneous stochastic fields and has been further improved in order to cover the case of highly skewed distributions [142].…”

Section: Methods Extending the Translation Field Conceptmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

862

407

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“…In case of non-Gaussian processes, the probability distribution of the KLE coefficients can be obtained by projecting an available set of realisations of the fields onto the KLE basis [40] or by an iterative procedure [41,42].…”

Section: Standard 1d Karhunen-loève Expansionmentioning

confidence: 99%

Large scale random fields generation using localized Karhunen–Loève expansion

Panunzio

Cottereau

Puel

2018

Adv. Model. and Simul. in Eng. Sci.

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In this paper the generation of random fields when the domain is much larger than the characteristic correlation length is made using an adaptation of the Karhunen-Loève expansion (KLE). The KLE requires the computation of the eigen-functions and the eigen-values of the covariance operator for its modal representation. This step can be very expensive if the domain is much larger than the correlation length. To deal with this issue, the domain is split in sub-domains where this modal decomposition can be comfortably computed. The random coefficients of the KLE are conditioned in order to guarantee the continuity of the field and a proper representation of the covariance function on the whole domain. This technique can also be parallelized and applied for non-stationary random fields. Some numerical studies, with different correlation functions and lengths, are presented.

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“…This modeling is based on a two steps decomposition. First, a Karhunen-Loève (KL) expansion is performed (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] for further details):…”

Section: Definition Of the Local Modelmentioning

confidence: 99%