Structural eigenvalue analysis under the constraint of a fuzzy convex set model
In small-sample problems, determining and controlling the errors of ordinary rigid convex set models are difficult. Therefore, a new uncertainty model called the fuzzy convex set (FCS) model is built and investigated in detail. An approach was developed to analyze the fuzzy properties of the structural eigenvalues with FCS constraints. Through this method, the approximate possibility distribution of the structural eigenvalue can be obtained. Furthermore, based on the symmetric F-programming theory, the conditional maximum and minimum values for the structural eigenvalue are presented, which can serve as non-fuzzy quantitative indicators for fuzzy problems. A practical application is provided to demonstrate the practicability and effectiveness of the proposed methods.
KeywordsStructural eigenvalue Fuzzy Convex set Conditional extreme Symmetric F-programming
This work was supported by the National Natural Science Foundation of China (Grant 51509254).
- 1.Atluri, S.N.: Methods of Computer Modeling in Engineering & the Sciences. Tech Science Press, Palmdale (2005)Google Scholar
- 27.Yang, L.B., Gao, Y.Y.: The Principle and Application of Fuzzy Mathematics. Press of South China University of Technology, Guangzhou (2005) (in Chinese)Google Scholar
- 28.Li, Y.H., Huang, H.Z., Liu, Z.H.: Convex model in robust reliability analysis of structure. J. Basic Sci. Eng. 12, 383–391 (2004) (in Chinese)Google Scholar
- 29.Li, K.F.: Study on the non-probabilistic reliability methods for structures based on info-gap theory. Dissertation for doctoral degree. Naval University of Engineering, Wuhan (2012) (in Chinese)Google Scholar
- 31.Qiu, Z.P.: Convex Method Based on Non-probabilistic Set-Theory and Its Application. National Defense Industry Press, Beijing (2005)Google Scholar