In this study, we deal with the problem of structural optimization under uncertainty. In previous studies, either of three philosophies were adopted: (a) probabilistic methodology, (b) fuzzy-sets-based design, or (c) nonprobabilistic approach in the form of given bounds of variation of uncertain quantities. In these works, authors are postulating knowledge of either involved probability densities, membership functions, or bounds in the form of boxes or ellipsoids, where the uncertainty is assumed to vary. Here, we consider the problem in its apparently pristine setting, when the initial raw data are available and the uncertainty model in the form of bounds must be constructed. We treat the often-encountered case when scarce data are available and the unknown-but-bounded uncertainty is dealt with. We show that the probability concepts ought to be invoked for predicting the worst- and best-possible designs. The Chebyshev inequality, applied to the raw data, is superimposed with the study of the robustness of the associated deterministic optimal design. We demonstrate that there is an intricate relationship between robustness and probability.
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September 2015
Research Papers
Intricate Interrelation Between Robustness and Probability in the Context of Structural Optimization
Oded Amir
,
Oded Amir
Faculty of Civil and Environmental Engineering,
Technion—Israel Institute of Technology
, Haifa 3200003
, Israel
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Isaac Elishakoff
Isaac Elishakoff
Department of Ocean and Mechanical Engineering,
Florida Atlantic University
, Boca Raton, FL 33431
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Oded Amir
Faculty of Civil and Environmental Engineering,
Technion—Israel Institute of Technology
, Haifa 3200003
, Israel
Isaac Elishakoff
Department of Ocean and Mechanical Engineering,
Florida Atlantic University
, Boca Raton, FL 33431
Manuscript received September 23, 2014; final manuscript received January 21, 2015; published online July 1, 2015. Assoc. Editor: Alba Sofi.
ASME J. Risk Uncertainty Part B. Sep 2015, 1(3): 031003 (7 pages)
Published Online: July 1, 2015
Article history
Received:
September 23, 2014
Revision Received:
January 21, 2015
Accepted:
April 27, 2015
Online:
July 1, 2015
Citation
Amir, O., and Elishakoff, I. (July 1, 2015). "Intricate Interrelation Between Robustness and Probability in the Context of Structural Optimization." ASME. ASME J. Risk Uncertainty Part B. September 2015; 1(3): 031003. https://doi.org/10.1115/1.4030456
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