Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms

Puig, Bénédicte; Poirion, Fabrice; Soize, Christian

doi:10.1016/s0266-8920(02)00010-3

Cited by 106 publications

(51 citation statements)

References 12 publications

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“…The method leads in most cases to good approximations of the target non-Gaussian distribution. Puig et al [149,150] examined the convergence behaviour of PC expansion and proposed an optimization technique for the determination of the underlying Gaussian autocorrelation function. Some limitations of PC approximations have been recently pointed out by Field and Grigoriu [55,83].…”

Section: Methods Based On Polynomial Chaos (Pc) Expansionmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

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: Methods Based On Polynomial Chaos (Pc) Expansionmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

869

407

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“…Other modeling and simulation techniques for nonGaussian Fields with targeted marginal distribution, moments and correlation functions have been proposed based on Polynomial Chaos decomposition [119,120] or more recently on the information theory [121].…”

Section: Stochastic Model For the Incident Fieldmentioning

confidence: 99%

Dynamics of structures coupled with elastic media—A review of numerical models and methods

Clouteau

Cottereau

Lombaert

2013

Journal of Sound and Vibration

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This paper reviews issues and developments in the field of structure-environment interaction problems, in which the environment is an elastic body, possibly unbounded. It covers in particular the fields of soil-structure interaction, ground-borne noise and vibration emitted by transportation systems and wave diffraction by obstacles in an elastic medium. The general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled, and the domain decomposition technique classically used for its description is put up. Extensions for the cases of non-linear structure and uncertain environment are then discussed. Finally, the ongoing research in the fields of unbounded interface, moving interface, and multiple interfaces are reviewed and summarized.

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“…The use of PC approximations is widespread. Applications include structural fatigue [95], structural reliability [100], structural mechanics [41,43], linear structural dynamics [82], nonlinear random vibration [42], solution of stochastic differential equations [6], soil mechanics [40], soil-structure interaction [72], and simulation of non-Gaussian random fields [39,77,78,86]. Generally, the PC approximations used in applications have ten or fewer terms [39,41,42,86].…”

Section: Chapter 4 the Polynomial Chaos Approximationmentioning

confidence: 99%

Methods for model selection in applied science and engineering.

Field¹

2004

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Mathematical models are developed and used to study the properties of complex systems and/or modify these systems to satisfy some performance requirements in just about every area of applied science and engineering. A particular reason for developing a model, e.g., performance assessment or design, is referred to as the model use. Our objective is the development of a methodology for selecting a model that is sufficiently accurate for an intended use.Information on the system being modeled is, in general, incomplete, so that there may be two or more models consistent with the available information. The collection of these models is called the class of candidate models. Methods are developed for selecting the optimal member from a class of candidate models for the system. The optimal model depends on the available information, the selected class of candidate models, and the model use.Classical methods for model selection, including the method of maximum likelihood and Bayesian methods, as well as a method employing a decisiontheoretic approach, are formulated to select the optimal model for numerous applications. There is no requirement that the candidate models be random. Classical methods for model selection ignore model use and require data to be available. Examples are used to show that these methods can be unreliable when data is limited. The decision-theoretic approach to model selection does not have these limitations, and model use is included through an appropriate utility function. This is especially important when modeling high risk systems, where the consequences of using an inappropriate model for the system can be disastrous. 3The decision-theoretic method for model selection is developed and applied for a series of complex and diverse applications. These include the selection of the: (1) optimal order of the polynomial chaos approximation for non-Gaussian random variables and stationary stochastic processes, (2) optimal pressure load model to be applied to a spacecraft during atmospheric re-entry, and (3) optimal design of a distributed sensor network for the purpose of vehicle tracking and identification.4

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Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms

Cited by 106 publications

References 12 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Dynamics of structures coupled with elastic media—A review of numerical models and methods

Methods for model selection in applied science and engineering.

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