Simulation of Nonseparable Nonstationary Spatially Varying Ground Motions with an Enhanced Interpolation Approximation Approach

Abstract

An enhanced interpolation approach is developed for simulating nonseparable nonstationary ground motions on the basis of the spectral representation method, which mainly contains two steps of interpolations and an optimization. Firstly, the interpolation technique is utilized to reduce the Cholesky decomposition time of the lagged coherence matrix. The square root of the evolutionary power spectral density is then decoupled into several time and frequency discrete functions using the proper orthogonal decomposition (POD) interpolation technique, which results in the availability of the fast Fourier transform (FFT) technique in the simulation. Compared with existing decoupling schemes, the POD interpolation achieves a significant efficiency improvement with a slight accuracy reduction. Finally, the simulation formula is further optimized to reduce the number of FFT operations. The accuracy and efficiency of this method are verified with the numerical examples of nonstationary ground motions simulation. Results show that the error introduced by two-step interpolations is fairly small and the simulation agrees with the targets very well. Furthermore, the efficiency generating sample function is significantly enhanced.