A fuzzy random approach of stochastic seismic response spectrum analysis

The primary objective of the present study is to explore a new definition of seismic response spectrum, where the uncertainty, that strongly affects the system and excitation parameters, is treated by fuzzy random theory. The proposed work is based on a simultaneous probabilistic and credibilistic representation of uncertainty used in a specific variety generally known as fuzzy probabilistic approach. The standard stochastic approaches normally consider the ground acceleration as the only source of uncertainty modeled as a stochastic process with deterministic structural parameters. But, in reality the parameters of the ground acceleration have a fuzzy credibilistic nature. In the present study, a methodology is proposed to describe the ground motion model that considers the credibilistic nature of the parameters involved. At the same time, the structural parameters are also considered to be fuzzy type, in order to take into account properly the level of approximation that affects their determinations. Thereby, a fuzzy version of the classical stochastic response spectrum evaluation of linear systems is obtained. The consistency of fuzzy stochastic response spectrum obtained by the proposed approach is studied with respect to available non-probabilistic formulations reported in the literature.