In the present paper, a dimension-reduction modeling method is proposed for a dual stochastic dynamic system of non-stationary ground motion stochastic processes and stochastic structures. In the proposed method, the random variables describing the stochastic ground motions and structural parameters are respectively represented by the functions of one elementary random variable, resulting in the entire stochastic dynamic system can be represented by merely two elementary random variables. Since the number of elementary random variables needed is extremely small, the set of representative points in regard to the elementary random variables can thus be selected by number theoretical method. Benefiting from the proposed method, it can be conveniently combined with the probability density evolution method to realize the dynamic response analysis and dynamic reliability evaluation of nonlinear stochastic structures. The seismic response analysis of an eight-storey reinforced concrete frame structure with random parameters subjected to non-stationary stochastic ground motions are investigated as case studies. Numerical results fully demonstrated the effectiveness of the proposed method
