Probability and convexity concepts are not antagonistic
This study is devoted to two objectives to illustrate that the probability and convexity concepts are not antagonistic and to introduce a new non-probabilistic convex model for structural reliability analysis. It is shown that the new measure of safety is easier to evaluate than the corresponding measure utilizing the interval analysis. Moreover, interrelation between the classical probabilistic method and convex modeling method is demonstrated. The purpose of this study is not to replace the probabilistic approach by the convex modeling method, but to illustrate that the probability and convexity concepts are compatible. Some numerical examples are presented to illustrate the feasibility of the proposed methodology.
KeywordsUncertain Parameter Interval Analysis Safe Region Uncertain Variable Limit State Function
Unable to display preview. Download preview PDF.
- 1.Wang G.Y.: On the development of uncertain structural mechanics (in Chinese). Adv. Appl. Mech. 32(2), 205–211 (2002)Google Scholar
- 5.Qiu Z.P., Wang X.J.: Set-Theoretical Convex Methods for Problems in Structural Mechanics with Uncertainties (in Chinese). Science Press, Beijing (2008)Google Scholar
- 8.Guo S.X., Lu Z.Z., Feng S.Y.: A non-probabilistic model of structural reliability based on interval analysis (in Chinese). Chin. J. Comput. Mech. 18(1), 56–60 (2001)Google Scholar
- 10.Guo X.S., Lu Z.Z.: Procedure for analyzing the fuzzy reliability of mechanical structures when parameters of probabilistic models are fuzzy (in Chinese). J. Mech. Strength 25(5), 527–529 (2003)Google Scholar
- 12.Qiu P.Z., Chen Q.S., Wang J.X.: Criterion of the non-probabilistic robust reliability for structures (in Chinese). Chin. J. Comput. Mech. 21(1), 1–6 (2004)Google Scholar
- 13.Wang X.J.: Robust reliability of structural vibration. J. Beijing Univ. Aeronaut. Astronaut. 29(11), 1006–1010 (2003) (in Chinese)Google Scholar
- 15.Elishakoff, I.: Are probabilistic and antioptimization methods interrelated? In: Elishakoff, I. (ed.) Whys and Hows in Uncertainty Modeling: Probability Fuzziness and Anti-Optimization, Springer, Wien (1999)Google Scholar
- 16.Ziegler F.: Private communication (2010)Google Scholar
- 17.Entropy (information theory) From Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Entropy_%28information_theory%29