Seismic isolation has emerged as one of the most promising techniques for reducing destructive effects on
structures caused by strong earthquakes. Because of the uncertainty of earthquake, the seismic stochastic
analysis is a powerful tool in earthquake engineering, and attracted interests of many people in the past
decades. Reference (Jangid and Datta 1995) studied the influence of the eccentricity of a superstructure
on the responses of a base-isolated structure, the stochastic responses were obtained through solving the
Lyapunov equation, for which the computational efficiency quickly decreases when the number of
degrees of freedom of the structure increase.