时变地震谱估计的非参数方法评价及应用

针对工程中常见的非平稳地震动激励,进一步建立了时变功率谱估计的理论框架。首先,在多个样本情形下,采用信号处理中的时频分析方法对非平稳激励的时变谱估计理论进行了讨论。当激励样本数量有限时,对Priestley提出的估计方法进行了介绍。其次,以地震工程中常用的Kanai-Tajimi谱模型为目标,分别对均匀调制与一般调制谱的估计结果以及不同估计方法的精度与收敛性进行评价后,提出了能够方便工程应用的建议。最后,针对SMART-Ⅰ(Strong Motion Array in Taiwan,Phase Ⅰ)密集台阵第45次地震记录的多组三维样本,揭示了EW、NS、UD三个方向时变谱的典型特征以及各方向间的时变相干性。结果表明:与短时Fourier变换相比,复Morlet小波与广义谐和小波估计谱具有较好的精度与收敛性,Priestley方法估计单个样本具有优势;SMART-Ⅰ台阵地震动具有强度和频率的双重非平稳性,三个方向具有弱相干性。研究结论可为拓展谱估计理论的工程应用以及后续大跨结构多维多点非平稳地震响应的分析提供参考。

Evaluation and Application of Non-parametric Approachfor Time-varying Seismic Spectral Estimation

This study aims to establish an integrated theoretical framework of a time-varying power spectral density (PSD) estimation for non-stationary earthquake ground motion excitations. First, time-frequency analysis methods, including the short-time Fourier transform, complex Morlet wavelet, and generalized harmonic wavelet transforms, are adopted to estimate the time-varying PSD in the presence of multiple samples. Priestley''s estimation method is also introduced when the number of samples is limited. Second, by regarding the uniformly modulated and general modulated non-stationary Kanai-Tajimi models as the target seismic spectrum, a comparative study and an evaluation of the accuracy and the convergence of different time-varying PSD estimation approaches are performed. The guidance suggestions of the estimation method and the principle of parameter selection are also proposed herein to facilitate engineering application. Finally, a group of samples from three directions, including EW, NS, and UD of the 45th earthquake recorded in Strong Motion Array in Taiwan, Phase I or SMART-I, are used to reveal the typical transient features of the time-varying PSD and the coherence function among different directions. The results show that the complex Morlet wavelet and the generalized harmonic wavelet transforms exhibit a better performance compared to the short-time Fourier transform. The Priestley method also has advantages to one available sample. The earthquake ground motions of SMART-I exhibit dual non-stationary properties of intensity and frequency, and the three directions show a weak coherence. The research conclusions could also extend the application of spectral estimation theory in engineering and provide references for a further study on the multi-dimension and multi-point non-stationary seismic random response of large-span structures.