Fast Simulation Of Non-stationary Process Based On Time-frequency Interpolation

High-rise buildings and long-span bridges are easy to be affected by wind-induced vibration due to their structural characteristics,leading to structural damage.At this time,the wind load plays a major role,even decisive.The non-stationary wind velocity and pressure can be obtained directly by field measurement.But the measured data of extreme winds are difficult to obtain.So the number of measured data which can be used for design and calibration is inadequate.Therefore,the simulation of nonstationary wind velocity field is very important to the nonlinear buffeting analysis of high-rise buildings and long-span bridges.However,a series of academic results have been made on the efficient decomposition and fast calculation of non-stationary wind velocity simulation in recent years.There are still some problems to be solved faced with non-stationary wind velocity field simulation in large scale civil engineering.This paper focuses on the fast simulation of non-stationary wind velocity field based on the spectral representation method.The main work and achievements are as follows:(1)The Cholesky decomposition method based on time-frequency interpolation is proposed.The core idea is to perform an interpolation operation in the time direction and the frequency direction,respectively.Much less time-frequency nodes need to be decomposed.The number of interpolation nodes is determined by parameter studying of error and running time.The numerical results show the time-frequency interpolation method has a good effect on accelerating the Cholesky decomposition.With the increase of the number of simulation points,it maintains a stable acceleration efficiency.Compared with the existing frequency interpolation scheme,it can save nearly 60% of the calculation time,while the calculation accuracy is similar.The interpolation in time direction does not lead to the obviously increase of the overall interpolation error.The time-frequency interpolation accelerating the Cholesky decomposition is suitable for simulating non-stationary wind velocity fields in large scale civil engineering.(2)Combined with the power spectrum matrix expressed by time-varying coherence matrix,a time-varying coherence matrix decomposition scheme based on time-frequency interpolation is proposed to replace the power spectrum matrix decomposition.The main idea is the decomposition results of time-varying coherence matrix are smoother,which are more conducive to combine with interpolation scheme.In the same case,much fewer interpolation nodes are needed in the proposed method.The numerical results show the reconstruction results of time-frequency interpolation are in good agreement with the target curves.(3)The proper orthogonal decomposition(POD)method is introduced to decouple the time-frequency parts of Cholesky decomposition results.An improved POD scheme is proposed to accelerate the harmonic superposition.The improved POD scheme can make full use of each set of time functions to consider the inconsistency of auto power spectrum at each simulating points.The numerical simulation results show that the interpolation algorithm and the POD algorithm can effectively combine with each other,greatly improving the simulation efficiency.The POD reconstruction results are in good agreement with the target curves.The combination method has a good application prospect for the simulation of multi-point non-stationary wind velocity fields.(4)Based on time-frequency interpolation and the improved POD scheme,a fast simulation method of spatial multi-point non-stationary ground motion is proposed considering time-invariant coherent function.When the decomposed power spectrum matrix is considered,the time-frequency interpolation combined with the improved POD scheme can be used.As for the decomposed time-invariant coherence matrix,the frequency interpolation combined with the reduced improved POD scheme can be used.The numerical results show the decomposition results of time-invariant coherence matrix of ground motion are relatively uniform,and only need to be interpolated in the frequency direction.The efficiency and accuracy of interpolation are significantly improved.On this basis,combined with POD scheme,the fast simulation of spatial ground motion can be realized.Furthermore,the validity of the proposed method is verified by different degrees of wave-passage effect.