基于正交Hilbert时变功率谱的多分量完全非平稳地震动模拟及验证

Simulation and verification of multivariate fully non-stationary earthquake ground motions using orthogonal Hilbert spectra

提出基于正交Hilbert时变功率谱的多分量完全非平稳地震动模拟方法,该方法在确定描述各分量间相关性的互协方差函数时,假定各分量采用一组相同的随机相位偏差。分别以EL Centro地震动加速度时程记录南北分量和Northridge地震Newhall台站实测三分量地震动加速度时程记录为单、多分量地震动时程模拟对象,模拟生成具有完全非平稳特征的单、多分量地震动时程;采用Hilbert时频谱、累积归一化Arias强度指标、加速度反应谱、Renyi熵和分形维数等指标验证模拟生成的地震动时程的有效性。研究结果表明:与基于Hilbert时变功率谱生成的单、多分量地震动时程相比,基于正交Hilbert时变功率谱生成的单、多分量非平稳地震动时程能更真实地描述实测地震动记录的强度和频率非平稳特性。

A multi-component time-frequency non-stationary ground motion simulation method by using the orthogonal Hilbert time-varying power spectrum(i.e.the orthogonal Hilbert spectra)was proposed.In this proposed method,an assumption that a set of the same random phase deviation to determine the cross-covariance function for describing the correlation between the components of multi-component non-stationary ground motion was adopted.Taking the north-south component of the EL Centro earthquake acceleration time history(i.e.the EL Centro N-S component)and the tri-directional components of the Northridge earthquake acceleration time history measured at Newhall station(i.e.the Northridge-Newhall tri-directional components)as the simulation objects of the single and multi-component ground motions,the single-component and multi-component ground motions with time-frequency non-stationary characteristics were respectively obtained.Then,the Hilbert time-frequency spectrum,the cumulative normalized Arias intensity index,the acceleration response spectrum,Renyi entropy and the fractal dimension were used to verify the validity of the simulated ground motions.The results show that compared with the single and multi-component ground motions simulated by using the Hilbert spectra,the simulated single-and multi-component ground motions by using the orthogonal Hilbert spectra can more accurately describe the strength and frequency non-stationary characteristics of the recorded ground motions.