非平稳地震动的双调制模型研究

地震动是工程结构地震反应研究与抗震设计的基础,要分析工程系统的性能,必须要把地震动作为随机过程来建立可靠的模型。本文通过对非平稳过程演变谱的研究,给出双调制函数,建立了双调制非平稳地震地面运动模型。结合双调制函数和三角级数法生成人工地震波,通过对人工波频率和强度的非平稳性研究验证了双调制模型的有效性。同时本文给出了双调制非平稳地震激励的结构响应虚拟激励算法,得到响应的时变功率谱。分析表明,该模型具有明确的物理意义,且更符合实际,为结构抗震可靠性分析提供了一种较好的地震动模型。     

爆炸地震动的反应谱拟合

本文提出采用拟动力试验方法解决爆破工程和防护工程中由于炸药爆炸和核爆炸地震动而引起的安全问题和结构抗震问题,并提出采用该方法时应解决的爆炸地震动的设计反应谱和爆炸地震动人工模拟的反应谱拟合技术。     

基于能量的平稳地震动功率谱转换关系持时取值研究

功率谱密度函数与反应谱的转换关系广泛应用于随机振动分析和人工地震动合成过程中,地震动持时对转换结果有着重要的影响。依据傅里叶幅值谱精确计算输入能量谱方法,并结合功率谱与幅值谱的关系,建立了与功率谱相对应的输入能量谱。以大量地震动记录统计得到的输入能量谱作为参考,提出了功率谱与设计谱转换过程中持时的确定方法。以Ⅱ类场地为例,选择了多条天然地震动记录和谱匹配时域调整记录进行统计计算,确定了合理的持时取值,通过人工合成记录验证了持时取值的合理性。     

基于震源机制且考虑场地土分层差异效应的多点地震动:理论与程序开发

结合前人工作,首先形成了适用于我国目标场地的基于震源机制,且考虑局部场地效应的地表多点地震动具体生成途径,包括:(1)依据随机振动理论建立能够反映包含多个土层在内的局部场地整体过滤效应的传递函数,(2)基于本文作者改进的过滤函数而得到的适用于我国目标场地的基岩谱,进而通过分区建立局部场地的整体传递函数以反映不同场地土之间的差异性,(3)在前人工作基础上考虑了场地的非平坦性因素,(4)为了程序编制方便,给出了多土层过滤后相位角变化的显示表达式;然后,依据上述理论框架成功实现了程序MEMSV2011.6(Multi-support Earthquake Motions Simulation Version 2011.6)的编制和可视化运行,该程序可直接生成界面图形并输出数据文件,具体功能包括:设置震源参数、分区输入土层参数、计算并显示土层传递函数、设定非平稳参数、调控频率、生成多点地震动时程、验证多点地震动间的相干性以及拟合规范(桥梁、建筑和电力设施)反应谱等;最后,以一桥梁土层为算例,利用该程序生成了目标场地基于震源机制的地表多点地震动,并分析了地表地震动对场地土和震中距因素的敏感性。本文内容具有坚实理论基础和实用性,可直接为工程提供参考。     

多水平成层的非均匀介质圆弧形峡谷地下多点地震动模拟

开发了考虑圆弧场地水平多分层效应的地下多点地震动模拟可视化程序,验证其可靠性。首先,描述了给出的圆弧场地多分层效应的SH波动散射频域解,其本质是突破了传统均匀介质和分层不穿越峡谷前提的局限性;其次,利用从水平地表到峡谷表面再到地下土层的传递函数,通过两次传递得到了圆弧峡谷地下的目标功率谱和反应谱;进而,具体描述所导出的圆弧场地平-凹相关性的相干函数及其推导过程;最后,基于上述理论,开发了多层状的非均匀圆弧场地的多点地震动模拟程序,给出了模拟结果与目标功率谱、反应谱和相干函数的拟合对比,验证了该理论和程序的合理性和可靠性,便于所发展理论和方法的实用化和推广。     

考虑半覆水圆弧相变场地特征的地下多点地震动模拟方法与程序开发

建立了同时引入土壤介质相变和半覆水圆弧地形因素的场地模型,并给出了地下多点地震动模拟的理论框架,开发了依据本文理论的程序并予以可靠性验证。首先,基于探明的波场分布得到了SV波入射半覆水圆弧相变场地的频域解;其次,获得依据频域解的场地传递函数并求解出地下自功率谱,建立了基于所得到的地下相干函数的地下互功率谱,由此构建出地下功率谱矩阵;最后,实现频域模型向时域信号转化（即多点地震动时程曲线）,进而基于上述理论进行可视化程序开发。通过数值算例进一步阐明了本研究的意义,结果表明,（1）地下与地表多点地震动在能量分布上存在显著差异,说明了研究的必要性;（2）生成地震动的拟合功率谱和拟合相干函数与理论值吻合较好,表明了结果的合理性;（3）可视化程序界面简洁,参数输入及调整方便,后处理结果显示清晰,反映出程序的便捷及适用性。     

基于S变换的非平稳随机过程演变功率谱密度估计

提出了一种基于S变换的估计Priestley非平稳随机过程演变功率谱密度的方法。此方法的根本在于,相对于S变换的"变换核",Priestley非平稳随机过程的调制函数为慢变函数。因此,非平稳随机过程的S变换可视为相位修正后的另一非平稳随机过程。推导出了对应于特定频率点的S变换瞬时均方值和非平稳随机过程演变功率谱密度之间的关系式。将功率谱密度函数表达为有限个频率点的级数展开,通过求解一组代数方程,就能得到级数展开中每个频率点的时变系数,由此,可给出非平稳随机过程的演变功率谱密度。由于级数展开中的高斯形状函数不依赖于时间,因此,本文所提算法具有较高的计算效率。最后,给出了均匀调制和非均匀调制非平稳随机过程演变功率谱估计的算例。     

六分量地震动实测记录的时频特征分析

至今国内外对地震动的三个平动分量已进行了较为充分的研究,但对含三个转动分量的六分量地震动记录的研究尚显不足.利用我国台湾东部HGSD台站在2007-2008年间的52次地震的六分量地震动的实测记录,分析了平动分量中竖向地震动与水平向地震动峰值比和转动分量中扭转地震动与摇摆地震动的角速度峰值比随震中距的变化.在此基础上,选择一组典型的含三个转动分量的六分量地震动记录,采用正交化HHT(Hilbert-Huang Transform)法对各分量的时频特征进行了对比分析.结果表明:在近震区域存在较大的竖向地震动,扭转分量的角速度峰值总体上大于摇摆分量的角速度峰值;各个分量上的能量分布存在差异,转动分量的卓越频带较平动分量宽;转动分量中的摇摆分量较扭转分量含有更多的高频成分.     

非平稳非高斯湿下击暴流风雨荷载的模拟

为模拟湿下击暴流风雨荷载,使用时变平均风速和调制的kaimal谱数值模拟具有非平稳非高斯特征的下击暴流脉动风速。从模拟结果可以看出,模拟的脉动风速相关函数明显具有时变的特征,而且瞬时相关函数均与目标函数吻合,因此模拟的脉动风速具有非平稳的目标特性;与此同时,在任意时刻,目标函数也与模拟的脉动风速概率密度函数吻合,表明模拟的脉动风速也具有非高斯的目标特性。因此,所采用的非平稳非高斯过程模拟方法有效可行。针对雨滴冲击荷载,首先对单个雨滴运动分析,推导出单个雨滴的冲击力,进而运用单位体积雨滴谱将单个雨滴冲击扩展到大量雨滴的冲击状态。结果表明,风速对雨滴冲击荷载的影响大,雨荷载变化趋势基本与风速一致,说明湿下击暴流的雨滴冲击作用主要由风速拖拽所致;此外,通过改变降雨强度发现,随着降雨强度增大,雨滴冲击力的变化趋势几乎不变,但峰值增大。     

用互谱密度函数估算两同频振动信号的相位差

根据振动实验教学中数字信号分析系统的需要,提出了用互谱密度函数估算两个同频信号相位差的方法,提高了测量精度. 应用于振动实验教学,取得了良好的效果.     

Stochastic modeling for starting-time of phase evolution of random seismic ground motions

In response to the challenge inherent in classical high-dimensional models of random ground motions, a family of simulation methods for non-stationary seismic ground motions was developed previously through employing a wave-group propagation formulation with phase spectrum model built up on the frequency components' starting-time of phase evolution. The present paper aims at extending the formulation to the simulation of non-stationary random seismic ground motions. The ground motion records associated with N—S component of Northridge Earthquake at the type-II site are investigated. The frequency components' starting-time of phase evolution of is identified from the ground motion records, and is proved to admit the Gamma distribution through data fitting. Numerical results indicate that the simulated random ground motion features zero-mean, non-stationary, and non-Gaussian behaviors, and the phase spectrum model with only a few starting-times of phase evolution could come up with a sound contribution to the simulation.     

Simplified method for simulation of ergodic spatially correlated seismic ground motion

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.     

Probabilistic models and simulation methods for seismic ground acceleration

Probabilistic models of seismic ground acceleration are reviewed. The review includes uniformly modulated, oscillatory, amplitude and phase modulated, ARMA, and other processes. Moreover, a novel and general nonstationary Gaussian model is presented. The model consists of a superposition of harmonics with correlated Gaussian amplitudes. The harmonic frequencies and the amplitude probabilistic characteristics depend on the duration and the correlation of the target seismic ground motion, respectively. The model can be generalized to represent the seismic ground motion at two or more sites. Methods are also presented for generating realizations of the probabilistic models in the paper. The methods are applied to demonstrate the generation of artificial seismic ground motions and to evaluate the usefulness of various probabilistic models in earthquake engineering.Invited lecture presented at the 6th Italian National Conference on Earthquake Engineering, Perugia, 13–15 October, 1993     

爆炸地震波模拟研究

基于能够描述爆炸地震波的非平稳随机过程模型进行爆炸地震波的模拟研究。基于爆炸地震能量守恒以及经验关系,提出了能够考虑装药量和爆距影响的爆炸地震波功率谱密度和幅值包络线模型,并且利用实测的爆炸试验数据,对模型参数进行标定,给出单点、两点（微差）和多点（微差）爆炸地震波实用模拟方法。结果表明模拟得到的爆炸地震波时程能够很好地再现爆炸地震波的一些特性。     

Instantaneous spectrum estimation of earthquake ground motions based on unscented Kalman filter method

Representing earthquake ground motion as time varying ARMA model,the instantaneous spectrum can only be determined by the time varying coefficients of the corresponding ARMA model.In this paper,unscented Kalman filter is applied to es- timate the time varying coefficients.The comparison between the estimation results of unscented Kalman filter and Kalman filter methods shows that unscented Kalman fil- ter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter,and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions nd to identify the systems with nonlinearity or abruptness.Moreover,the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power of ARMA model which was usually ignored in former studies has great effect on the estima- tion precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.     

NUMERICAL SIMULATION OF INSECT FLIGHT

In the non-inertial coordinates attached to the model wing, the two-dimensional unsteady flow field triggered by the motion of the model wing, similar to the flapping of the insect wings, was numerically simulated. One of the advantages of our method is that it has avoided the difficulty related to the moving-boundary problem. Another advantage is that the model has three degrees of freedom and can be used to simulate arbitrary motions of a two-dimensional wing in plane only if the motion is known. Such flexibility allows us to study how insects control their flying. Our results show that there are two parameters that are possibly utilized by insects to control their flight: the phase difference between the wing translation and rotation, and the lateral amplitude of flapping along the direction perpendicular to the average flapping plane.