Response of Structural Systems with Uncertain Parameters: A Comparative Study of Probabilistic and Fuzzy Sets Models

by Wei-Ling Chiang, Stanford Univ, United States,
Wei-min Dong, Stanford Univ, United States,
Haresh C. Shah, Stanford Univ, United States,

Abstract: Due to the limitation in space, this paper only presents the conclusions of a study on the response of structures with uncertain properties such as mass, stiffness and damping. In the original study, the effect of the uncertain parameters on the response and the effect of the modeling of the uncertainties on the response are investigated. In particular, two types of uncertainties are distinguished: random and fuzzy uncertainties. Two kinds of models are studied: probabilistic and fuzzy set models. The two approaches to uncertainty modeling are compared with regard to their impacts on the analysis and on the uncertain structural response obtained. The study considers free vibration, forced vibration with deterministic excitation, and forced vibration with Gaussian white noise excitation. It is concluded that, in general, fuzzy models are much easier to implement and the associated analysis easier to perform than their probabilistic counterparts. When the available data on the structural parameters are crude and do not support a rigorous probabilistic model, the fuzzy set approach should be considered in view of its simplicity.

Subject Headings: Fuzzy sets | Probability | Structural response | Model analysis | Parameters (statistics) | Uncertainty principles | Vibration | Structural models

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