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

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

doi:10.1002/nme.2752

Cited by 61 publications

(32 citation statements)

References 28 publications

(35 reference statements)

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“…[13][14][15][16]22 This section is provided to give an overview of the fundamental concepts and terminology related to RBDO. In most conventional design optimisation algorithms, evaluations of the cost and objective functions in equations (1) and (2) are performed using 'true' evaluation of the functions.…”

Section: Overview Of Ddo and Rbdo Optimisation Methodsmentioning

confidence: 99%

Reliability based casting process design optimisation

Hardin

Choi

Gaul

et al. 2014

International Journal of Cast Metals Research

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Deterministic optimum designs are unreliable without consideration of the statistical and physical uncertainties in the casting process. In the present research, casting simulation is integrated with a general purpose reliability based design optimisation (RBDO) software tool that considers uncertainties in both the input variables as well as in the model itself. The output consists of an optimal design that meets a specified reliability. An example casting process design is presented where the shape of a riser is optimised while considering uncertainties in the fill level and riser diameter. It is shown that RBDO provides a much different optimum design than a traditional deterministic approach. The deterministic optimal solution offers a 12% increase in casting yield over typical safety margin design practice, but has an unacceptable 61% probability of failure. The RBDO design has a 7% increase in casting yield over the safety margin approach and a probability of failure of 4?6%.

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Section: Overview Of Ddo and Rbdo Optimisation Methodsmentioning

confidence: 99%

Reliability based casting process design optimisation

Hardin

Choi

Gaul

et al. 2014

International Journal of Cast Metals Research

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“…The sensitivity of the probabilistic constraint with respect to design variables is computed as

{(|, \frac{∂G}{\partial boldd})}_{boldx = {boldx}_{SORM}^{*}} = {(|, \frac{∂G}{\partial boldx})}_{boldx = {boldx}_{SORM}^{*}}

Equation is the assumed relation in SORM‐based PMA, while it is the exact relation in FORM‐based PMA as proved in Ref. .…”

Section: Rbdo Using the Proposed Sorm‐based Inverse Reliability Analysismentioning

confidence: 99%

Second-order reliability method-based inverse reliability analysis using Hessian update for accurate and efficient reliability-based design optimization

Lim

Lee

2014

Int. J. Numer. Meth. Engng

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SUMMARYFirst‐order reliability method (FORM) has been mostly utilized for solving reliability‐based design optimization (RBDO) problems efficiently. However, second‐order reliability method (SORM) is required in order to estimate a probability of failure accurately in highly nonlinear performance functions. Despite accuracy of SORM, its application to RBDO is quite challenging due to unaffordable numerical burden incurred by a Hessian calculation. For reducing the numerical efforts, a quasi‐Newton approach to approximate the Hessian is introduced in this study instead of calculating the true Hessian. The proposed SORM with the approximated Hessian requires computations only used in FORM, leading to very efficient and accurate reliability analysis. The proposed SORM also utilizes a generalized chi‐squared distribution in order to achieve better accuracy. Furthermore, SORM‐based inverse reliability method is proposed in this study. An accurate reliability index corresponding to a target probability of failure is updated using the proposed SORM. Two approaches in terms of finding an accurate most probable point using the updated reliability index are proposed. The proposed SORM‐based inverse analysis is then extended to RBDO in order to obtain a reliability‐based optimum design satisfying probabilistic constraints more accurately even for a highly nonlinear system. The numerical study results show that the proposed reliability analysis and RBDO achieve efficiency of FORM and accuracy of SORM at the same time. Copyright © 2014 John Wiley & Sons, Ltd.

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“…where du Ã dθ can be obtained by taking derivative of u * in (5) with respect to θ as (22) can be obtained as (Lee et al 2009)…”

Section: Sensitivity Analysis Using Novel Sormmentioning

confidence: 99%

“…Many works have been devoted to derive the sensitivity of the probabilistic constraint (Ditlevsen and Madsen 1996;Lee et al 2009;Lee et al 2011a;Lee et al 2011b;Hohenbichler and Rackwitz 1986;Rahman and Wei 2008;Madsen et al 1986). Thus, this study presents the sensitivity analysis of the novel SORM for more accurate RBDO.…”

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

Cited by 61 publications

References 28 publications

Reliability based casting process design optimisation

Reliability based casting process design optimisation

Second-order reliability method-based inverse reliability analysis using Hessian update for accurate and efficient reliability-based design optimization

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

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