Explicit fuzzy analysis of systems with imprecise properties

This paper presents a practical approach based on High Dimensional Model Representation (HDMR) for analyzing the response of structures with fuzzy parameters. The proposed methodology involves integrated finite element modelling, HDMR based response surface generation and explicit fuzzy analysis procedures. The uncertainties in the material, loading and structural properties are represented using convex normal fuzzy sets. HDMR is used to express the response of the system in a separable closed-form expression as a linear combination of the fuzzy variables through the definition of intervening variables, then using the transformation technique the bounds on the response at each α-level are obtained. The merit of the proposed methodology is computational efficiency without compromise on accuracy in addition to fixing the dependency problem associated with the nonlinearity of the function, and this is demonstrated through some numerical examples.