Structural reliability analysis by univariate decomposition and numerical integration

Wei, Dong; Rahman, Sharif

doi:10.1016/j.probengmech.2006.05.004

Cited by 61 publications

(17 citation statements)

References 14 publications

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“…In recent past, several methods with the general objective of approximately developing multivariate expressions for response surface for mechanical engineering applications were proposed. One such method is the high-dimensional model representation (HDMR) (Alis and Rabitz 2001;Rao and Chowdhury 2009;Sobol 2003;Wei and Rahman 2007). It is also referred to as "decomposition method," "univariate approximation," "bivariate approximation," "Svariate approximation," etc.…”

Section: Seismic Reliability Evaluation For Large Structuresmentioning

confidence: 99%

Structural Reliability Estimation for Seismic Loading

Haldar¹

2015

Encyclopedia of Earthquake Engineering

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Section: Seismic Reliability Evaluation For Large Structuresmentioning

confidence: 99%

Structural Reliability Estimation for Seismic Loading

Haldar¹

2015

Encyclopedia of Earthquake Engineering

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“…8) is considered. The ten-bar truss structure is a classical structural analysis problem and widely studied (Wei and Rahman 2007;Kang et al 2010). The structure is simply supported at nodes 1 and 4, and is subjected to two concentrated loads P = 10 5 lb at nodes 2 and 3.…”

Section: Example 3: a Cantilever Beammentioning

confidence: 99%

“…Failure probability of ten bar truss *the results come from referenceWei and Rahman (2007) **the results come from reference…”

mentioning

confidence: 99%

Doubly weighted moving least squares and its application to structural reliability analysis

Wang

Kim

2011

Struct Multidisc Optim

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In this paper, we proposed a two-stage hybrid reliability analysis framework based on the surrogate model, which combines the first-order reliability method and Monte Carlo simulation with a doubly-weighted moving least squares (DWMLS) method. The first stage consists of constructing a surrogate model based on DWMLS. The weight system of DWMLS considers not only the normal weight factor of moving least squares, but also the distance from the most probable failure point (MPFP), which accounts for reliability problems. An adaptive experimental design scheme is proposed, during which the MPFP is progressively updated. The approximate values and sensitivity information of DWMLS are chosen to determine the number and location of the experimental design points in the next iteration, until a convergence criterion is satisfied. In the second stage, MCS on the surrogate model is then used to calculate the probability of failure. The proposed method is applied to five benchmark examples to validate its accuracy and efficiency. Results show that the proposed surrogate model with DWMLS can estimate the failure probability accurately, while requiring fewer original model simulations. KeywordsDoubly weighted moving least squares · Surrogate model · Two-stage hybrid method · Adaptive experimental design · Structural reliability analysis · Latin hypercube design Nomenclature n number of input random variables N number of experimental points x vector of input random variables β reliability index β H L reliability index by Hasofer-Lind algorithm μ mean σ standard deviation g(X) limit state function g(X) approximate limit state function/ response surface function X add new added experimental points in any iteration MLS moving least square DWMLS doubly weighted moving least square SVR support vector regression ANN artificial neural networks MPFP most probable failure point MCS Monte Carlo Simulation FORM first order reliability method SORM second order reliability method H-L Hasofer-Lind algorithm RSM response surface method LHD Latin hypercube design FEA finite element analysis CFD computational fluid dynamics COV coefficient of variation UDR Univariate Dimension-Reduction MPP-UDR Most probable point based UDR SGI Sparse Grid Interpolation 70 J. Li et al.

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“…For a brief list of the operative steps for these methods see Haldar and Mahadevan (2000). Several studies discuss the class of problems involving highly non-linear performance functions where linear (or quadratic) approximations may not be adequate (Wei and Rahman, 2007).…”

Section: Advanced Simplified Proceduresmentioning

confidence: 99%

Reliability analysis of wind-excited structures

Pagnini

2010

Journal of Wind Engineering and Industrial Aerodynamics

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Structural reliability analysis by univariate decomposition and numerical integration

Cited by 61 publications

References 14 publications

Structural Reliability Estimation for Seismic Loading

Structural Reliability Estimation for Seismic Loading

Doubly weighted moving least squares and its application to structural reliability analysis

Reliability analysis of wind-excited structures

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