基于相位差谱的时-频非平稳人造地震动的反应谱拟合

本文根据相位差谱对地震动时程非平稳性的影响，反应谱、功率谱和傅里叶幅值谱间的数学关系以及加速度时程单谐波分量对反应谱拟合精度和拟合效率的作用，提出了一种可直接拟合目标反应谱的具有时－频非平稳性的人工地震动的高效方法，算例说明了其有效性。

基于调频率的时-频非平稳地震动生成

动力时程分析是研究地震作用下结构响应的有效途径,而输入的地震动时程对计算结果有重要影响。实际地震动是时-频非平稳的随机过程,而目前用于结构动力时程分析的人工波多为时域非平稳频域平稳的时间时程。本文采用增加频率调制过程的方法对生成人工波的传统三角级数模型进行了改进,可使生成的地震动时程不仅是强度非平稳的,而且频率成分也是随时间变化的。改进方法生成的时-频非平稳地震动时程更接近于真实的地震动记录,且能很好地拟合目标反应谱,对工程实践具有重要意义。

基于相位差谱的时─频非平稳人造地震动的生成

本文首先考察了地震动加速度时程在时域和频域上的非平稳性，通过实例分析说明地震动加速度时程 的非平稳性不能由相位谱的概率分布唯一决定，进而阐明了相位差谱是影响地震动非平稳的决定性因素。经 统计检验确定了脉动相位差的概率分布模型，利用相位差谱的数字特征与地震特性参数之间的统计关系，给 出了基于相位差谱的地震动时程生成方法。最后，通过对计算实例的分析，证实了此方法能够反映并模拟实 际地震动的时─频非平稳性。

一种时频非平稳人造地震动的生成及反应谱拟合方法

本文从数学角度介绍了相位差谱影响地震动非平稳性的机理，及结合大量实际地震波的统计数据，得到了相位差民地震特性参数之间的统计关系（只限其岩情况），同时给出了基于相位差谱的地震动人工生成及反应谱拟合的方法与步骤。最后，通过对计算实例的分析，证实了此方法能够反映模拟实际地震动的时－频非平稳性。

频率非平稳地震动对大坝非线性响应的影响

采用传统三角级数模型和基于调频率的时-频非平稳地震动生成方法合成的人工波作为输入时程对某大坝进行动力时程分析比较,结果表明,地震动时程的频率非平稳特性对结构非线性地震响应的影响不可忽略,现阶段用于动力时程分析的人工波大多只是幅值非平稳的均匀调制过程,可能低估了结构在真实地震情况下的反应,使结构的抗震设计偏于危险。

桥梁结构非平稳随机抗震分析

基于平稳地震动过程的Kanai-Tajimi功率谱密度函数,建立了一类时-频非平稳地震动过程的演变功率谱模型.结合公路工程抗震规范和非平稳过程模拟的随机函数-谱表示方法,生成了610条桥梁抗震设计所用的地震动概率模型的代表性时程集合,通过代表性时程的均值、标准差及平均反应谱值与目标值的比较验证了本文方法的有效性.在此基础上,结合概率密度演化方法,对范和港跨海斜拉桥随机地震反应与抗震可靠度进行了精细化的分析,为桥梁结构抗震分析提供参考.

Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function（IFDF） to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

Fractional S transform-Part 1:Theory

The S transform, which is a time-frequency representation known for its local spectral phase properties in signal processing, uniquely combines elements of wavelet transforms and the short-time Fourier transform （STFT）. The fractional Fourier transform is a tool for non-stationary signal analysis. In this paper, we define the concept of the fractional S transform （FRST） of a signal, based on the idea of the fractional Fourier transform （FRFT） and S transform （ST）, extend the S transform to the time-fractional frequency domain from the time- frequency domain to obtain the inverse transform, and study the FRST mathematical properties. The FRST, which has the advantages of FRFT and ST, can enhance the ST flexibility to process signals. Compared to the S transform, the FRST can effectively improve the signal time- frequency resolution capacity. Simulation results show that the proposed method is effective.

空间变异地震作用下大型连续刚构桥的延性性能研究

本文在前人工作的基础上提出了一种直接生成具有时－频非平稳特性的空间变异地震动的方法，即随机过程理论与相位差谱相结合的方法。此方法由于引入了相位差概念并结合已有的自功率谱、相干函数、视速度模型，从而使得生成具有时－频非平稳特性的空间变异地震动的过程更为直接和简便。最后通过几个合成示例说明了这种方法的有效性，可以用于结构多点输入地震反应分析。

Study of seismic spectrum decomposition based on CEEMD

Empirical mode decomposition( EMD) is a powerful tool of time-frequency analysis. EMD decomposes a signal into a series of sub-signals,called Intrinsic mode functions( IMFs). Each IMF contains different frequency components which can deal with the nonlinear and non-stationary of signal. Complete ensemble empirical mode decomposition( CEEMD) is an improved algorithm,which can provide an accurate reconstruction of the original signal and better spectral separation of the modes. The authors studied the decomposition result of a synthetic signal obtained from EMD and CEEMD. The result shows that the CEEMD has suitability in spectrum decomposition time-frequency analysis. Compared with traditional methods,a higher time-frequency resolution is obtained through verifying the method on both synthetic and real data.

Sparse time-frequency representation of nonlinear and nonstationary data Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data. These methods are inspired by the empirical mode decomposition method （EMD） and the recently developed compressed （compressive） sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a（t） cos（0（t））}, where a is assumed to be less oscillatory than cos（θ（t）） and θ ＇≥ 0. This problem can be formulated as a nonlinear ι0 optimization problem. We have proposed two methods to solve this nonlinear optimization problem. The first one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit. Convergence analysis has been carried out for the nonlinear matching pursuit method. Some numerical experiments are given to demonstrate the effectiveness of the proposed methods.

基于小波消噪的EMD模型在GPS振动信号处理中的应用

经验模式分解和小波分解是当前有效处理非平稳信号的两种时频分析方法,它们各具有其优缺点,适用于不同的应用。从对GPS振动信号的预处理、时域和频域处理入手,结果分析表明,对GPS振动信号先进行小波滤波消除随机噪声的干扰,再应用经验模式分解更有利于变形特征信息的分离和提取,提取的信号与振动平台记录数据更加吻合。