Implementation of Karhunen–Loeve expansion for simulation using a wavelet-Galerkin scheme

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

doi:10.1016/s0266-8920(02)00013-9

Cited by 222 publications

(70 citation statements)

References 16 publications

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“…Galerkin) usually lead to dense matrices that are very costly to compute and solve the corresponding equations. It is important to note that the accuracy in the computation of the eigenpairs of the autocovariance function strongly influences the efficiency of K-L series [ 88,140,164,174,176]. Enhanced methods for the solution of the Fredholm integral equation have been proposed in [140,58,164].…”

Section: The Spectral Representation Methodsmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

871

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: The Spectral Representation Methodsmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

871

407

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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%

Dynamical Behavior of Trains Excited by a Non-Gaussian Vector Valued Random Field

Perrin¹,

Soize²,

Duhamel³

et al. 2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…First, a spatial and statistical representation is achieved, which is based on a Karhunen-Loève (KL) expansion. This very efficient method, which has first been introduced by Pearson [8] in data analysis, has been applied in many works for the last decades (see, for instance [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]). It is indeed particularly interesting as it allows the uncorrelation of the projection coefficients of X on the KL vector basis, while optimally compacting the signal energy.…”

Section: Kl and Pce Expansionsmentioning

confidence: 99%

Track irregularities stochastic modeling

Perrin

Soize

Duhamel

et al. 2013

Probabilistic Engineering Mechanics

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High speed trains are currently meant to run faster and to carry heavier loads, while being less energy consuming and still respecting the security and comfort certification criteria. To face these challenges, a better understanding of the interaction between the dynamic train behavior and the track geometry is needed. As during its lifecycle, the train faces a great variability of track conditions, this dynamic behavior has indeed to be characterized on track portions sets that are representative of the whole railway network. This paper is thus devoted to the development of a stochastic modeling of the track geometry and its identification with experimental measurements. Based on a spatial and statistical decomposition, this model allows the spatial and statistical variability and dependency of the track geometry to be taken into account. Moreover, it allows the generation of realistic track geometries that are representative of a whole railway network. First, this paper describes a practical implementation of the proposed method and then applies this method to the modeling of a particular French high speed line, for which experimental data are available.

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Implementation of Karhunen–Loeve expansion for simulation using a wavelet-Galerkin scheme

Cited by 222 publications

References 16 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Dynamical Behavior of Trains Excited by a Non-Gaussian Vector Valued Random Field

Track irregularities stochastic modeling

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