Probabilistic analysis for the response of nonlinear base isolation system under the ground excitation induced by high dam flood discharge

According to theoretical analysis, a general characteristic of the ground vibration induced by high dam flood discharge is that the dominant frequency ranges over several narrow frequency bands, which is verified by observations from the Xiangjiaba Hydropower Station. Nonlinear base isolation is used to reduce the structure vibration under ground excitation and the advantage of the isolation application is that the low-frequency resonance problem does not need to be considered due to its excitation characteristics, which significantly facilitate the isolation design. In order to obtain the response probabilistic distribution of a nonlinear system, the state space split technique is modified. As only a few degrees of freedom are subjected to the random noise, the probabilistic distribution of the response without involving stochastic excitation is represented by the delta function. Then, the sampling property of the delta function is employed to reduce the dimension of the Fokker-Planck- Kolmogorov (FPK) equation and the low-dimensional FPK equation is solvable with existing methods. Numerical results indicate that the proposed approach is effective and accurate. Moreover, the response probabilistic distributions are more reasonable and scientific than the peak responses calculated by conventional time and frequency domain methods.