Theory of fuzzy random vibration with fuzzy parameters

In this paper, based on our previous papers [1–4], the general theory of fuzzy random vibration with fuzzy parameters is studied. In order to better describe the random excitation with fuzziness in mathematics, first, the random variable and random process with a fuzzy parameter are defined and their probability distributions and statistical moments are discussed. Secondly, by simulating the fuzzy random excitation as a random process with a fuzzy parameter, the fundamental method and numerical method are presented for analysing the fuzzy random response of linear or nonlinear oscillators subjected to this kind of excitation. Finally, the methods are applied to the fuzzy random vibration of aseismic structures and a concrete example is given.This paper is supported by the Natural Science Foundation of China.