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

Content Provider	Springer Nature Link
Author	Yoo, David Lee, Ikjin Cho, Hyunkyoo
Copyright Year	2014
Abstract	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 non-central 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.
Starting Page	787
Ending Page	797
Page Count	11
File Format	PDF
ISSN	1615147X
Journal	Structural and Multidisciplinary Optimization
Volume Number	50
Issue Number	5
e-ISSN	16151488
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-10-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Sensitivity analysis Most probable point (MPP) Novel second-order reliability method (SORM) General chi-squared distribution Theoretical and Applied Mechanics Computational Mathematics and Numerical Analysis Engineering Design
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Computer Graphics and Computer-Aided Design Control and Systems Engineering Computer Science Applications Software

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