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2DC, title[*]contributor[author]contributor[advisor]keywords[*]date[issued] publisher citationsidentifier[uri]identifier[doi]abstractrelation[journal]relation[volume]relation[no]relation[page]lЬE TШxD tǩ\ |)͕͜ X\ °ĳ 0 \$Ĭ;
Reliability-Based Design Optimization Using Kriging Metamodel with Latin Hypercube Sampling;\ܭ \ٳ2008-02\ՑYPxhttps://repository.hanyang.ac.kr/handle/20.500.11754/147963;
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X̹, |8 HXՔ RBDO 0 ( 0x \pt Ĭ (Constraint Boundary Sampling)D tǩX \ĬtD UXՌ XՔ Kriging TШxD (<\ 1X 4U`D !XՔ RA 0D \. 0| FORMtǘ SORMt ɔ 8D tհX ҈, MPP t DՔX䲔 D . H 0@ Kriging TШxD 0<\ |)͕͜(LHS)| X t \0 4U`п̹ DȲ| ĳ | X0 L8 00 0 \T LବD RBDO ȩ` . tٳ\͌ǹ(Moving Least Squares)D tǩX ĬX Ȅh(CDF)| ōx h\ \. \, ȹ 0 D\1T $Ĭ(Smart Initial Inactive Design)| tǩX RBDOX 4ĳ| ¨. L<\ Yx @ lp< $Ĭ 8| t H 0X (1D X. ȹɹ<\ H 0X U1D X0 t Lt|\ ¬tXD t RBDOt U` lptD ̹qXՔ X.; In a deterministic design optimization, the optimal designs are usually pushed to the limit of the constraints boundaries, leaving little or no margin for uncertainty. Consequently, the resulting deterministic optimum is obtained without considering influence of uncertainties inherently present during the mathematical modeling and manufacturing or operating process and need to be accounted for in the design process. To address this problem, Reliability-Based Design Optimization (RBDO) method is necessitated to be a sufficiently reliable engineering system design and assess uncertainties such as material properties, loads, etc. In a RBDO formulation, the critical deterministic constraints are replaced with probability constraints corresponding to probability of failure. Probability failure (or reliability) of a structure (or mechanical system) in the form of a limit state function can be calculated in four different ways: 1) sampling method; 2) expansion method; 3) the Most Probable failure Point (MPP)-based method; and 4) approximate integration method. The sampling method is most comprehensive but very expensive to use as an uncertainty assessment tool. The expansion methods have been traditionally employed to predict statistical moments of system responses with a small perturbation. The major limitation of these methods is that they require expensive calculation of higher-order partial derivatives. The MPP-based method, such as First Order Reliability Method (FORM) and Second Order Reliability Method (SORM), has been a most commonly used approach to compute the failure probability. But it may lead to large error and become expensive if the multiple MPPs exist. The approximate integration method which estimate the PDF or statistical moments by using numerical integration calculate the probability of failure using Pearson system and the only first four statistical moments. Although the approximate integration method gives accurate probabilistic quantities, it may provide a relatively large error of highly nonlinear response.
In all kinds of reliability analysis techniques based on MPP concept like <M
a reliability index to obtain the probability of failure, the original random variables is transformed to a standard normal independent random variables by a one-to-one transformation. However, if he Rosenblatt transformation, widely used to map non-normal random variables into standard normal space, yields a highly nonlinear limit state function and give rise to large errors.
However, the proposed RBDO methodology based on a simulation method with the Kriging metamodel and Constraint Boundary Sampling (CBS), which is sequential sampling for creating Kriging metamodel, is proposed to estimate efficiently the failure of probability. This reliability analysis method does not exhibit the limitations of MPP-based methods, such as FORM/SORM. The major advantage of developed method is that a MPP search is not required and it provides more computationally efficient than the Direct Monte Carlo Simulation (MCS). The Latin Hypercube Sampling (LHS) applied to the Kriging metamodel is used in this work to assess the uncertainty in a design can be incorporated with a gradient based optimizer for RBDO. Because the proposed method can make use of analytic sensitivities and smoothness of probability of failure estimate using the cumulative distribution function (CDF), which is constructed by moving least squares (MLS) method. RBDO starts at a smart initial inactive design (SIID) point to have a high-speed convergence. Several numerical examples involving mathematical functions and structural design problem are used to demonstrate the effectiveness of the proposed method. Finally, the reliability is evaluated using the Monte Carlo Simulation to evaluate the accuracy of the proposed method.&HQsj&)KLng
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