An efficient response surface method using moving least squares approximation for structural reliability analysis

Kang, Sang-Wook; Koh, Hyun‐Moo; Choo, Jinkyo F.

doi:10.1016/j.probengmech.2010.04.002

Cited by 176 publications

(67 citation statements)

References 22 publications

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“…In this work, we focus on the derivation and performance of the proposed second order RBDO approach and therefore only consider explicit analytical expressions on f and g. Surrogate model based RBDO can e.g. be found in (Gomes et al 2011;Duborg et al 2011;Qu et al 2003;Youn and Choi 2004a;Song and Lee 2011;Kang et al 2010;Zhu and Du 1403;Ju and Lee 2008). The QP-problem is solved in the standard normal space instead of the physical space.…”

Section: Pr[h(y ) < 0] ≈ (−β Hl )mentioning

confidence: 99%

Reliability-based design optimization using SORM and SQP

Strömberg

2017

Struct Multidisc Optim

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In this work a second order approach for reliabilitybased design optimization (RBDO) with mixtures of uncorrelated non-Gaussian variables is derived by applying second order reliability methods (SORM) and sequential quadratic programming (SQP). The derivation is performed by introducing intermediate variables defined by the incremental iso-probabilistic transformation at the most probable point (MPP). By using these variables in the Taylor expansions of the constraints, a corresponding general first order reliability method (FORM) based quadratic programming (QP) problem is formulated and solved in the standard normal space. The MPP is found in the physical space in the metric of Hasofer-Lind by using a Newton algorithm, where the efficiency of the Newton method is obtained by introducing an inexact Jacobian and a line-search of Armijo type. The FORM-based SQP approach is then corrected by applying four SORM approaches: Breitung, Hohenbichler, Tvedt and a recent suggested formula. The proposed SORMbased SQP approach for RBDO is accurate, efficient and robust. This is demonstrated by solving several established benchmarks, with values on the target of reliability that are considerable higher than what is commonly used, for mixtures of five different distributions (normal, lognormal, Gumbel, gamma and Weibull). Established benchmarks are also generalized in order to study problems with large number of variables and several constraints. shown that the proposed approach efficiently solves a problem with 300 variables and 240 constraints within less than 20 CPU minutes on a laptop. Finally, a most well-know deterministic benchmark of a welded beam is treated as a RBDO problem using the proposed SORM-based SQP approach.

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Section: Pr[h(y ) < 0] ≈ (−β Hl )mentioning

confidence: 99%

Reliability-based design optimization using SORM and SQP

Strömberg

2017

Struct Multidisc Optim

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“…In determining the initial distribution of fault type, fault parameters required to estimate the probability density function. Simply least squares method is one of useful parameter estimation method [9], the basic idea is assumed that there are n observations {xi, y} i (i = 1,2, …, n), if there is a linear relationship between x and y, then it can be used to fit a straight line relationship between the change in x, y between the formula (3) below. ˆŷ…”

Section: Parameter Estimationmentioning

confidence: 99%

“…The formula (8) on both sides of the two logarithmic, if Weibull distribution is a linear relationship can be determined by least square method estimates the Weibull distribution parameters, such as the formula (9). ˆe…”

Section: Parameter Estimationmentioning

confidence: 99%

Methods based on CNC grinding fault Distribution Parameter Estimation for Reliability Assessment

Fan¹,

Ji²,

Wang³

et al. 2016

Proceedings of the 2016 4th International Conference on Machinery, Materials and Information Technology Applications

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“…However, due to the rotation of the coordinate system in each computation step, the total computational time apparently has been increased when there are many random variables. Another improved RSM for reliability analysis of structures has also been proposed by Kang et al (2010). Although the precision efficiency of the proposed improved RSM method is higher, its weight function has to be determined in structural reliability estimation.…”

Section: Introductionmentioning

confidence: 99%

Structural reliability analysis using response surface method with improved genetic algorithm

Fang¹,

Tee²

2017

Structural Engineering and Mechanics

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Abstract. For the conventional computational methods for structural reliability analysis, the common limitations are long computational time, large number of iteration and low accuracy. Thus, a new novel method for structural reliability analysis has been proposed in this paper based on response surface method incorporated with an improved genetic algorithm. The genetic algorithm is first improved from the conventional genetic algorithm. Then, it is used to produce the response surface and the structural reliability is finally computed using the proposed method. The proposed method can be used to compute structural reliability easily whether the limit state function is explicit or implicit. It has been verified by two practical engineering cases that the algorithm is simple, robust, high accuracy and fast computation.

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An efficient response surface method using moving least squares approximation for structural reliability analysis

Cited by 176 publications

References 22 publications

Reliability-based design optimization using SORM and SQP

Reliability-based design optimization using SORM and SQP

Methods based on CNC grinding fault Distribution Parameter Estimation for Reliability Assessment

Structural reliability analysis using response surface method with improved genetic algorithm

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