Efficient solution for Galerkin-based polynomial chaos expansion systems

Panayirci, H. Murat

doi:10.1016/j.advengsoft.2010.09.004

Cited by 18 publications

(6 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, the developed techniques are applied to a NASTRAN model of a satellite with 900 QUAD4 elements (∼ 5300 DOF) [18]. The model is available in the OpenCossan software [20].…”

Section: Problem Descriptionmentioning

confidence: 99%

Robust propagation of probability boxes by interval predictor models

2020

View full text Add to dashboard Cite

This paper proposes numerical strategies to robustly and efficiently propagate probability boxes through expensive black box models. An interval is obtained for the system failure probability, with a confidence level. The three proposed algorithms are sampling based, and so can be easily parallelised, and make no assumptions about the functional form of the model. In the first two algorithms, the performance function is modelled as a function with unknown noise structure in the aleatory space and supplemented by a modified performance function. In the third algorithm, an Interval Predictor Model is constructed and a re-weighting strategy used to find bounds on the probability of failure. Numerical examples are presented to show the applicability of the approach. The proposed method is flexible and can account for epistemic uncertainty contained inside the limit state function. This is a feature which, to the best of the authors' knowledge, no existing methods of this type can deal with.

show abstract

Section: Problem Descriptionmentioning

confidence: 99%

Robust propagation of probability boxes by interval predictor models

2020

View full text Add to dashboard Cite

show abstract

“…Therefore, novel strategies have been introduced, which determine adequate values for their input parameters, e.g. drop tolerance or convergence threshold (see [27] for details). It should be however noted that the proposed approaches do not remove the already existing drawbacks or limitations of the selected preconditioner, iterative solver or the P-C method itself.…”

Section: Efficient Implementations and Strategies For Stochastic Analmentioning

confidence: 99%

General purpose software for efficient uncertainty management of large finite element models

Patelli

Panayirci

Broggi

et al. 2012

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

The aim of this paper is to demonstrate that stochastic analyses can be performed on large and complex models within affordable costs. Stochastic analyses offer a much more realistic approach for analysis and design of components and systems although generally computationally demanding. Hence, resorting to efficient approaches and high performance computing is required in order to reduce the execution time.A general purpose software that provides an integration between deterministic solvers (i.e. finite element solvers), efficient algorithms for uncertainty management and high performance computing is presented. The software is intended for a wide range of applications, which includes optimization analysis, life-cycle management, reliability and risk analysis, fatigue and fractures simulation, robust design.The applicability of the proposed tools for practical applications is demonstrated by means of a number of case studies of industrial interest involving detailed models.

show abstract

“…In these cases, the sparsity of the corresponding deterministic matrix that has to be inverted is decreased, leading in a dramatic increase of the required computational effort. Stochastic adaptivity and model reduction techniques for the SSFEM have been proposed in in an effort to reduce the overall problem dimensionality and augment the sparsity of the deterministic matrix, in tandem with efficient preconditioning and domain decomposition‐based approaches which reduce the computational cost encountered in the inversion of coupled deterministic problems . Regarding the PDD method, an adaptive variant was recently introduced in where global sensitivity indices are used to truncate the PDD.…”

Section: Introductionmentioning

confidence: 99%

An adaptive spectral Galerkin stochastic finite element method using variability response functions

Giovanis

Papadopoulos

Stavroulakis

2015

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYA methodology is proposed in this paper to construct an adaptive sparse polynomial chaos (PC) expansion of the response of stochastic systems whose input parameters are independent random variables modeled as random fields. The proposed methodology utilizes the concept of variability response function in order to compute an a priori low-cost estimate of the spatial distribution of the second-order error of the response, as a function of the number of terms used in the truncated Karhunen-Loève (KL) expansion. This way the influence of the response variance to the spectral content (correlation structure) of the random input is taken into account through a spatial variation of the truncated KL terms. The criterion for selecting the number of KL terms at different parts of the structure is the uniformity of the spatial distribution of the second-order error. This way a significantly reduced number of PC coefficients, with respect to classical PC expansion, is required in order to reach a uniformly distributed target second-order error. This results in an increase of sparsity of the coefficient matrix of the corresponding linear system of equations leading to an enhancement of the computational efficiency of the spectral stochastic finite element method.

show abstract

Efficient solution for Galerkin-based polynomial chaos expansion systems

Cited by 18 publications

References 24 publications

Robust propagation of probability boxes by interval predictor models

Robust propagation of probability boxes by interval predictor models

General purpose software for efficient uncertainty management of large finite element models

An adaptive spectral Galerkin stochastic finite element method using variability response functions

Contact Info

Product

Resources

About