Post optimization for accurate and efficient reliability‐based design optimization using second‐order reliability method based on importance sampling and its stochastic sensitivity analysis

Lim, Jang Keun; Lee, Byung-Chai; Lee, Ikjin

doi:10.1002/nme.5150

Cited by 43 publications

(7 citation statements)

References 46 publications

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“…Gu et al (2015) presented a practical approach for RBDO using SORM for vehicle occupant systems, which was further developed in Gu et al (2016). RBDO using Breitung's formula and non-Gaussian variables was demonstrated in Lim et al (2016). Mansour and Olsson (2016) demonstrated the importance of using SORM-based methods for non-linear problems by solving a problem with a quadratic objective and quadratic constraints taken from Lee et al (2015).…”

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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“…Traditional structural reliability analysis is based on probability theory, that is, the distribution of variables is precisely known. [1][2][3] There are several probability-based reliability analysis methods, such as the first-order reliability method (FORM), [4][5][6] the second-order reliability method (SORM), [7][8][9] and the Monte Carlo simulation (MCS). [10][11][12] However, determination of all variables precisely is impossible in practical engineering due to the limited information.…”

Section: Introductionmentioning

confidence: 99%

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Huang

et al. 2021

Numerical Meth Engineering

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Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this article, an efficient and robust hybrid reliability analysis method is proposed for structures with both random and interval variables. Firstly, a single-loop procedure is proposed by performing probabilistic analysis and interval analysis simultaneously in each most probable point search process. Then an improved conjugate sensitivity factor method based on hybrid conjugate gradient direction and adaptive finite step length is developed for probabilistic analysis. Meanwhile, the hybrid conjugate gradient direction together with active set is introduced into the projected gradient method for interval analysis. Finally, a comparison analysis with six numerical examples is provided to validate the performance of the proposed method. The results demonstrate that the proposed method is better than the existing methods in terms of efficiency and robustness for hybrid reliability analysis with random and interval variables.

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“…Some existing methods, namely, Monte Carlo simulation (MCS) [11][12][13], Taylor expansion-based method [14,15], reliability-based method [16][17][18], polynomial chaos expansion (PCE) [19][20][21] and numerical integration-based method [1,22,23] have already contributed to UP. The MCS method was first used in simulating a neutron chain reaction.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty propagation analysis by an extended sparse grid technique

Jia

Jiang

et al. 2018

Front. Mech. Eng.

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In this paper, an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle, aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function (PDF) of the system response. The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis. Moreover, assisted by the Rosenblatt transformation, the various types of extended integration points are transformed into the extended Gauss-Hermite integration points, which makes the method suitable for any type of continuous distribution. Subsequently, within the sparse grid numerical integration framework, the statistical moments of the system response are obtained based on the transformed points. Furthermore, based on the maximum entropy principle, the obtained first four-order statistical moments are used to fit the PDF of the system response. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed method, which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

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Post optimization for accurate and efficient reliability‐based design optimization using second‐order reliability method based on importance sampling and its stochastic sensitivity analysis

Cited by 43 publications

References 46 publications

Reliability-based design optimization using SORM and SQP

Reliability-based design optimization using SORM and SQP

An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Uncertainty propagation analysis by an extended sparse grid technique

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