Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems

Lee, Ikjin; Choi, Kyung K.; Du, Lei; Gorsich, David

doi:10.1016/j.cma.2008.03.004

Cited by 163 publications

(90 citation statements)

References 20 publications

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“…Owing to the non-linearity of the input fatigue random parameters, the optimum results of FORM and MPP-based DRM are different. This is quite different from the previous work in Reference [11]. As the previous work does not consider the input correlation and assumes very small COV for the fatigue material properties, the problem is very mildly non-linear where the difference between FORM and MPP-based DRM almost disappears.…”

Section: M1a1 Abrams Tank Roadarmmentioning

confidence: 63%

“…The roadarm of the M1A1 tank [11] is used to show how the derived sensitivities work for the design optimization. The roadarm is modeled using 1572 eight-node isoparametric finite elements (SOLID45) and four beam elements (BEAM44) of ANSYS [31], as shown in Figure 2, and is made of S4340 steel with Young's modulus E = 3.0×10 7 psi and the Poisson's ratio = 0.3.…”

Section: M1a1 Abrams Tank Roadarmmentioning

confidence: 99%

“…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%

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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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Section: M1a1 Abrams Tank Roadarmmentioning

confidence: 63%

Section: M1a1 Abrams Tank Roadarmmentioning

confidence: 99%

“…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%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…MPP-based secondorder reliability method (SORM) (Breitung 1984;Hohenbichler and Rackwitz 1988;Adhikari 2004;Zhang and Du 2010) improves FORM in terms of accuracy; however it is computationally expensive compared to FORM since it requires the computation of the Hessian matrix. MPP-based dimension reduction method (DRM) (Rahman and Wei 2006;Lee et al 2008;Xiong et al 2009) can be also used for D. Yoo Department of Mechanical Engineering, University of Connecticut, Storrs, CT 06269-3139, USA e-mail: david.yoo@engr.uconn.edu approximately assessing the reliability of a system which is used as a probabilistic constraint in RBDO. Conventional SORM that improves accuracy of FORM still contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at the MPP in standard normal U-space, (2) error due to approximating the quadratic function in U-space by a parabolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. On the other hand, the recently proposed novel SORM contains only type (1) error, which leads to more accurate reliability analysis (Lee et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Probabilistic sensitivity analysis for novel second-order reliability method (SORM) using generalized chi-squared distribution

Yoo

Lee

Cho

2014

Struct Multidisc Optim

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Reliability-based design optimization (RBDO) requires evaluation of sensitivities of probabilistic constraints. To develop RBDO utilizing the recently proposed novel second-order reliability method (SORM) that improves conventional SORM approaches in terms of accuracy, the sensitivities of the probabilistic constraints at the most probable point (MPP) are required. Thus, this study presents sensitivity analysis of the novel SORM at MPP for more accurate RBDO. During analytic derivation in this study, it is assumed that the Hessian matrix does not change due to the small change of design variables. The calculation of the sensitivity based on the analytic derivation requires evaluation of probability density function (PDF) of a linear combination of noncentral chi-square variables, which is obtained by utilizing general chi-squared distribution. In terms of accuracy, the proposed probabilistic sensitivity analysis is compared with the finite difference method (FDM) using the Monte Carlo simulation (MCS) through numerical examples. The numerical examples demonstrate that the analytic sensitivity of the novel SORM agrees very well with the sensitivity obtained by FDM using MCS when a performance function is quadratic in U-space and input variables are normally distributed. It is further shown that the proposed sensitivity is accurate enough compared with FDM results even for a higher order performance function.

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Geotechnical reliability‐based design optimization updating under changing design scenarios

Wang,

2024

Num Anal Meth Geomechanics

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In the context of geotechnical uncertainty characterization, the reliability‐based design optimization (RBDO) provides an effective means to achieve the most balanced design outcome between the targeted safety and the risk‐based cost planning. As a common practice, the geotechnical RBDO is conducted on the premise of prescribed statistical information of those uncertain parameters. Nevertheless, the uncertain geotechnical parameters are usually subject to amendment resulting from further site investigation. In other words, changing design scenarios must be properly handled in advanced geotechnical RBDO. Thus, in this study, a novel reliability updating method using a sample reweighting technique that requires only a single simulation run is developed for RBDO. Simultaneously, the RBDO is readily extendable to RBDO updating under changing design scenarios while avoiding any further re‐evaluation of the performance functions. The proposed RBDO updating method allows for the consideration of a continuous design space encompassing an infinite number of feasible designs, whereas the existing simulation‐based method can only consider a finite number of feasible designs in a discrete design space. Moreover, the efficiency and flexibility of the proposed RBDO updating method are illustrated through a standard RBDO test problem and a practical rock slope design example, where the changing design scenarios of different means, standard deviations, correlation coefficient, and distributions are respectively studied.

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Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems

Cited by 163 publications

References 20 publications

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

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

Probabilistic sensitivity analysis for novel second-order reliability method (SORM) using generalized chi-squared distribution

Geotechnical reliability‐based design optimization updating under changing design scenarios

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