A univariate approximation at most probable point for higher-order reliability analysis

Rahman, Sharif; Wei, Dong

doi:10.1016/j.ijsolstr.2005.05.053

Cited by 113 publications

(90 citation statements)

References 13 publications

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“…Interested readers may refer to details in the literature [14][15][16]. Experience has shown that FORM/SORM are sufficiently accurate for engineering purposes, provided that (1) the MPP is accurately identified, (2) the limit state curve/surface at the MPP is close to being linear or quadratic and (3) no multiple MPPs exist [16].…”

Section: First-and Second-order Reliability Methodsmentioning

confidence: 99%

Structural Reliability Analysis of Wind Turbines: A Review

Jiang

Dong

et al. 2017

Energies

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Abstract:The paper presents a detailed review of the state-of-the-art research activities on structural reliability analysis of wind turbines between the 1990s and 2017. We describe the reliability methods including the first-and second-order reliability methods and the simulation reliability methods and show the procedure for and application areas of structural reliability analysis of wind turbines. Further, we critically review the various structural reliability studies on rotor blades, bottom-fixed support structures, floating systems and mechanical and electrical components. Finally, future applications of structural reliability methods to wind turbine designs are discussed.

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Section: First-and Second-order Reliability Methodsmentioning

confidence: 99%

Structural Reliability Analysis of Wind Turbines: A Review

Jiang

Dong

et al. 2017

Energies

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“…The estimation results are reported in Table 11. Table 11 lists the predicted failure probability of tenbar truss and the associated computational effort using FORM, several SORM, three variants of MPP-UDR, crude MCS (10 6 samples), and proposed hybrid reliability method Rahman and Wei (2006) combined with ordinary MLS and DWMLS. From Table 10, both versions of MLS predict the failure probability more accurately than FORM and all three variants of SORM.…”

Section: Example 3: a Cantilever Beammentioning

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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“…Using the univariate DRM, an N -dimensional performance function G(X) can be additively decomposed into the sum of one-dimensional functions at the MPP as [7,8,11]…”

Section: Drm-based Inverse Reliability Analysismentioning

confidence: 99%

“…Although the reliability analysis using SORM may be accurate, it is not easy to use as SORM requires the second-order derivatives, which are very difficult and expensive to obtain in practical engineering applications. To overcome these drawbacks and to maintain the efficiency of FORM and the accuracy of SORM, the MPP-based dimension reduction method (DRM) has been recently proposed [7][8][9][10][11]. DRM was originally proposed to approximate a multi-dimensional function using the sum of lower-dimensional functions for statistical moment estimation [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analyses of FORM‐based and DRM‐based performance measure approach (PMA) for reliability‐based design optimization (RBDO)

Lee

Choi

Gorsich

2009

Numerical Meth Engineering

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SUMMARYIn gradient-based design optimization, the sensitivities of the constraint with respect to the design variables are required. In reliability-based design optimization (RBDO), the probabilistic constraint is evaluated at the most probable point (MPP), and thus the sensitivities of the probabilistic constraints at MPP are required. This paper presents the rigorous analytic derivation of the sensitivities of the probabilistic constraint at MPP for both first-order reliability method (FORM)-based performance measure approach (PMA) and dimension reduction method (DRM)-based PMA. Numerical examples are used to demonstrate that the analytic sensitivities agree very well with the sensitivities obtained from the finite difference method (FDM). However, as the sensitivity calculation at the true DRM-based MPP requires the second-order derivatives and additional MPP search, the sensitivity derivation at the approximated DRM-based MPP, which does not require the second-order derivatives and additional MPP search to find the DRM-based MPP, is proposed in this paper. A convergence study illustrates that the sensitivity at the approximated DRM-based MPP converges to the sensitivity at the true DRM-based MPP as the design approaches the optimum design. Hence, the sensitivity at the approximated DRM-based MPP is proposed to be used for the DRM-based RBDO to enhance the efficiency of the optimization.

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A univariate approximation at most probable point for higher-order reliability analysis

Cited by 113 publications

References 13 publications

Structural Reliability Analysis of Wind Turbines: A Review

Structural Reliability Analysis of Wind Turbines: A Review

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

Sensitivity analyses of FORM‐based and DRM‐based performance measure approach (PMA) for reliability‐based design optimization (RBDO)

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