This study presents a methodology for computing stochastic sensitivities with respect to the design variables, which are the mean values of the input correlated random variables. Assuming that an accurate surrogate model is available, the proposed method calculates the component reliability, system reliability, or statistical moments and their sensitivities by applying Monte Carlo simulation to the accurate surrogate model. Since the surrogate model is used, the computational cost for the stochastic sensitivity analysis is affordable compared with the use of actual models. The copula is used to model the joint distribution of the correlated input random variables, and the score function is used to derive the stochastic sensitivities of reliability or statistical moments for the correlated random variables. An important merit of the proposed method is that it does not require the gradients of performance functions, which are known to be erroneous when obtained from the surrogate model, or the transformation from X-space to U-space for reliability analysis. Since no transformation is required and the reliability or statistical moment is calculated in X-space, there is no approximation or restriction in calculating the sensitivities of the reliability or statistical moment. Numerical results indicate that the proposed method can estimate the sensitivities of the reliability or statistical moments very accurately, even when the input random variables are correlated.
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e-mail: ilee@engineering.uiowa.edu
e-mail: kkchoi@engineering.uiowa.edu
e-mail: noh@engineering.uiowa.edu
e-mail: liazhao@engineering.uiowa.edu
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February 2011
Research Papers
Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems With Correlated Random Variables
Ikjin Lee,
Ikjin Lee
Postdoctoral Research Scholar
Department of Mechanical and Industrial Engineering, College of Engineering,
e-mail: ilee@engineering.uiowa.edu
University of Iowa
, Iowa City, IA 52242
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K. K. Choi,
K. K. Choi
Roy J. Carver Professor
Department of Mechanical and Industrial Engineering, College of Engineering,
e-mail: kkchoi@engineering.uiowa.edu
University of Iowa
, Iowa City, IA 52242
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Yoojeong Noh,
Yoojeong Noh
Graduate Research Assistant
Department of Mechanical and Industrial Engineering, College of Engineering,
e-mail: noh@engineering.uiowa.edu
University of Iowa
, Iowa City, IA 52242
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Liang Zhao,
Liang Zhao
Graduate Research Assistant
Department of Mechanical and Industrial Engineering, College of Engineering,
e-mail: liazhao@engineering.uiowa.edu
University of Iowa
, Iowa City, IA 52242
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David Gorsich
David Gorsich
Chief Scientist
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Ikjin Lee
Postdoctoral Research Scholar
Department of Mechanical and Industrial Engineering, College of Engineering,
University of Iowa
, Iowa City, IA 52242e-mail: ilee@engineering.uiowa.edu
K. K. Choi
Roy J. Carver Professor
Department of Mechanical and Industrial Engineering, College of Engineering,
University of Iowa
, Iowa City, IA 52242e-mail: kkchoi@engineering.uiowa.edu
Yoojeong Noh
Graduate Research Assistant
Department of Mechanical and Industrial Engineering, College of Engineering,
University of Iowa
, Iowa City, IA 52242e-mail: noh@engineering.uiowa.edu
Liang Zhao
Graduate Research Assistant
Department of Mechanical and Industrial Engineering, College of Engineering,
University of Iowa
, Iowa City, IA 52242e-mail: liazhao@engineering.uiowa.edu
David Gorsich
Chief Scientist
J. Mech. Des. Feb 2011, 133(2): 021003 (10 pages)
Published Online: January 24, 2011
Article history
Received:
April 8, 2010
Revised:
November 20, 2010
Online:
January 24, 2011
Published:
January 24, 2011
Citation
Lee, I., Choi, K. K., Noh, Y., Zhao, L., and Gorsich, D. (January 24, 2011). "Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems With Correlated Random Variables." ASME. J. Mech. Des. February 2011; 133(2): 021003. https://doi.org/10.1115/1.4003186
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