Generation of accelerograms compatible with design specifications using information theory

This paper deals with the generation of seismic accelerograms which are compatible with a given response spectrum and other design specifications. The time sampling of the stochastic accelerogram yields a time series represented by a random vector in high dimension. The probability density function of this random vector is constructed using the maximum entropy (MaxEnt) principle under constraints defined by the available information (design specifications). In this paper, an adapted algorithm is proposed to identify the Lagrange multipliers introduced in the MaxEnt principle to take into account the constraints. This algorithm is based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Itô stochastic differential equation in order to estimate the integrals in high dimension of the problem. The constraints related to a seismic accelerogram are developed explicitly. This methodology is validated through an application for which the available information is related to the variance of each component of the random vector representing the accelerogram, statistics on the response spectrum, on the peak ground acceleration, on the cumulative absolute velocity and on the end-values for the velocity and for the displacement.     

基于小波变换的拟合规范反应谱多维地震动模拟

本文提出一种基于小波变换的拟合规范反应谱的多维地震动模拟算法。首先将规范反应谱推广到三维相关设计反应谱,然后将已有的三维地震动加速度时间历程曲线分解为一系列不同频段上的地震动分量,调整每一个地震动分量的幅值使其在相应的频率范围内拟合设计反应谱,最后经过调整后的地震动分量进行重构得到更新的地震动时间历程曲线。将该时间历程曲线的反应谱与目标反应谱进行比较,重复该过程直到误差位于特定的范围内。该方法可以保留原始地震动的局部时-频特性,为多维地震动的模拟提供了一种新的方法。     

Wavelet‐based characterization of design ground motions

With the recent emergence of wavelet‐based procedures for stochastic analyses of linear and non‐linear structural systems subjected to earthquake ground motions, it has become necessary that seismic ground motion processes are characterized through statistical functionals of wavelet coefficients. While direct characterization in terms of earthquake and site parameters may have to wait for a few more years due to the complexity of the problem, this study attempts such characterization through commonly available Fourier and response spectra for design earthquake motions. Two approaches have been proposed for obtaining the spectrum‐compatible wavelet functionals, one for input Fourier spectrum and another for input response spectrum, such that the total number of input data points are 30–35% of those required for a time‐history analysis. The proposed methods provide for simulating ‘desired non‐stationary characteristics’ consistent with those in a recorded accelerogram. Numerical studies have been performed to illustrate the proposed approaches. Further, the wavelet functionals compatible with a USNRC spectrum in the case of 35 recorded motions of similar strong motion durations have been used to obtain the strength reduction factor spectra for elasto‐plastic oscillators and to show that about ±20% variation may be assumed from mean to 5 and 95% confidence levels due to uncertainty in the non‐stationary characteristics of the ground motion process. Copyright © 2002 John Wiley & Sons, Ltd.     

Wavelet‐based simulation of spectrum‐compatible aftershock accelerograms

In damage‐based seismic design it is desirable to account for the ability of aftershocks to cause further damage to an already damaged structure due to the main shock. Availability of recorded or simulated aftershock accelerograms is a critical component in the non‐linear time‐history analyses required for this purpose, and simulation of realistic accelerograms is therefore going to be the need of the profession for a long time to come. This paper attempts wavelet‐based simulation of aftershock accelerograms for two scenarios. In the first scenario, recorded main shock and aftershock accelerograms are available along with the pseudo‐spectral acceleration (PSA) spectrum of the anticipated main shock motion, and an accelerogram has been simulated for the anticipated aftershock motion such that it incorporates temporal features of the recorded aftershock accelerogram. In the second scenario, a recorded main shock accelerogram is available along with the PSA spectrum of the anticipated main shock motion and PSA spectrum and strong motion duration of the anticipated aftershock motion. Here, the accelerogram for the anticipated aftershock motion has been simulated assuming that temporal features of the main shock accelerogram are replicated in the aftershock accelerograms at the same site. The proposed algorithms have been illustrated with the help of the main shock and aftershock accelerograms recorded for the 1999 Chi–Chi earthquake. It has been shown that the proposed algorithm for the second scenario leads to useful results even when the main shock and aftershock accelerograms do not share the same temporal features, as long as strong motion duration of the anticipated aftershock motion is properly estimated. Copyright © 2008 John Wiley & Sons, Ltd.     

Wavelet-based generation of spectrum-compatible time-histories

This paper deals with the well-known problem of generating spectrum-compatible synthetic accelerograms for the linear and non-linear time-history analyses of structural systems. A wavelet-based procedure has been used to decompose a recorded accelerogram into a desired number of time-histories with non-overlapping frequency contents, and then each of the time-histories has been suitably scaled for matching of the response spectrum of the revised accelerogram with a specified design spectrum. The key idea behind this iterative procedure is to modify a recorded accelerogram such that the temporal variations in its frequency content are retained in the synthesized accelerogram. The proposed procedure has been illustrated by modifying five recorded accelerograms of widely different characteristics such that those are compatible with the same USNRC design spectrum.     

地震波时变修正Kanai-Tajimi非平稳随机模型的建立

利用谐小波变换对实际强震记录的时变谱进行估计,并统计分析了远场3类不同场地上地震波的时变谱特征,分析发现对于硬场地上的远场地震波在时域内平稳段较短,下降段衰减较快,而在频域内则具有较大的中心频率和较宽的频带.利用均匀调制非平稳模型和时变修正Kanai-Tajimi非平稳模型模拟地震波的时变谱,把非线性函数的参数识别问题转化成求解无约束优化问题,利用拟牛顿迭代法求得最优解,得到3类不同场地上这两种模型的参数具体取值以及参数函数集的具体表达式.为了定量地确定模拟模型的精度,定义了误差函数,验证了所提时变谱参数识别方法的精度,给出了与建筑抗震规范相对应的不同场地不同烈度下多遇和罕遇地震的谱强度因子的大小.最后提出了利用求解时变线性微分方程组来合成非平稳地震波的方法.     

Simulation and generation of spectrum-compatible ground motions based on wavelet packet method

This paper deals with the problem of generating spectrum-compatible artificial accelerograms for seismic dynamic analysis of engineering projects. A wavelet-packet-based, two-step procedure for the issue is proposed. The first step is to generate acceleration time history that could account for temporal and frequency non-stationarities of recorded ground motions. The second step is to decompose it into a desired number of wavelet packet vectors with high frequency resolution and non-overlapping frequency contents. Then each wavelet packet vector is scaled suitably and iteratively for the response spectrum of the simulated accelerogram to fit a specified design spectrum. The advantages of this procedure are that it can simulate user-specified acceleration time history with only 6 input parameters and the adjusted accelerogram has similar characteristics to the recorded one. The proposed procedure has been illustrated by simulating and modifying acceleration time history that are compatible with two different design spectrums for nuclear power plants. In addition, iterative efficiency of the method is investigated by simulating and adjusting acceleration time history for 100 successive times. The maximum relative error of the 76 period control points can reach 6% or below. Results show that the proposed method is effective and practical to generate and find spectrum-compatible ground motions with both stochastic and deterministic aspects.     

Calculation of free field response spectrum of a non-homogeneous soil deposit from bed rock response spectrum

In this paper, a method to determine free field response spectrum of a soil deposit from a specified bed rock response spectrum is presented. This method treats the earthquake motion as if it was a stationary Gaussian random process but to account for the non-stationary character, an approximate method is used. The soil deposit is assumed to have mechanical properties (strength, shear modulus, etc.) increasing with some power exponent of depth. This layer overlies either a compliant elastic half space or a layer with shear modulus increasing linearly with depth.To demonstrate the validity and usefulness of this approach, two examples are presented. The first one consists in the transfer, from bed rock to free surface of a given soil profile, of the response spectrum derived from an accelerogram used to generate the Eurocode 8 response spectrum. The obtained free field response spectrum is compared to the one obtained by using a wave propagation program. The second example consists in the validation of this method with experimental records.     

A generalization of the Drenick–Shinozuka model for bounds on the seismic response of a Single-Degree-Of-Freedom system

This paper deals with seismic excitation of linearly elastic structures. It is well known that dynamical structural response is very sensitive to random fluctuations of the excitation; the consequence is that the identification of the forcing function on the basis of a few ‘global’ parameters does not allow to predict exhaustively stresses in seismically excited structures. In the paper, a convex model is established to treat uncertainty associated with the ‘details’ of the excitation, in order to set bounds on the response parameters of a SDOF system, assuming that only rough information is available for expected earthquakes at a given site. In particular, we assume that the maximum expected ‘energy’ of the accelerogram, and the maximum ‘distance’ of its power spectrum from the target spectrum, typical for the site under construction, are specified. © 1998 John Wiley & Sons, Ltd.     

New method of generating spectrum compatible accelerograms using neural networks

A new method is proposed for generating artificial earthquake accelerograms from response spectra. This method uses the learning capabilities of neural networks to developed the knowledge of the inverse mapping from the response spectra to earthquake accelerogram. In the proposed method the neural networks learn the inverse mapping directly from the actual recorded earthquake accelerograms and their response spectra. A two-stage approach is used. In the first stage, a replicator neural network is used as a data compression tool. The replicator neural network compresses the vector of the discrete Fourier spectra of the accelerograms to vectors of much smaller dimension. In the second stage, a multi-layer feed-forward neural network learns to relate the response spectrum to the compressed Fourier spectrum. A simple example is presented, in which only 30 accelerograms are used to train the two-stage neural networks. This example demonstrates how the method works and shows its potential. © 1998 John Wiley & Sons, Ltd.     

Calculation of selected ordinates of fourier spectra

A method is presented for calculating single or, by repeated use, selected ordinates of Fourier spectra rapidly and efficiently. The approach differs from standard methods in that any frequency consistent with the interval of digitization may be chosen and records of arbitrary length may be analysed. The method is based on the relation between Fourier spectra of an accelerogram and the final response of an undamped oscillator to the same accelerogram. This relation is reviewed and extended to aid the development of the computing method and to assist in the interpretation of Fourier spectrum techniques in earthquake engineering. Because only the terminal values of the response of an undamped oscillator are required to define the Fourier spectra, repeated application of superposition is used to form equivalent excitations with durations of only one-quarter of the period of the oscillator.     

Eurocode 8-compatible synthetic time-series as input to dynamic analysis

Nonlinear dynamic analysis of existing or planned structures often requires the use of accelerograms that match a target design spectrum. Here, our main concern is to generate a set of motions with a good level of fit to the Eurocode 8 design spectra for France. Synthetic time series are generated by means of a non-stationary stochastic method. To calibrate the input parameters in the stochastic approach, we select a reference set of accelerograms for a Eurocode 8 type B site category from the PEER Ground-Motion Database, which are then adjusted to the target spectrum through wavelet addition. Then, we compute nonlinear seismic responses of a soil column, including pore pressure effects, and brittle and ductile structures to the stochastic time-series, the natural accelerograms and time-series generated using stationary stochastic approaches. The results of these calculations reveal considerable variability in response despite the similarities in terms of spectral acceleration.     

Modal-based ground motion selection procedure for nonlinear response time history analysis of high-rise buildings

The selection of representative input ground motions (IGMs) is important for a proper nonlinear response time history analysis (NLRHA) of modern structures. The prevailing IGM selection procedure requires that the response spectra of selected ground motions are matched with the code-specified design spectra, while the effect of the frequency contents combination in the time domain on the multimode interactions is not considered. Ignoring the effect of the frequency contents combination in the time domain of IGMs may cause significant variations in the analysis results for selected IGMs, although they are matched to the same design spectrum. In this paper, a modal-based ground motion selection (MGMS) procedure is proposed as a supplement to spectrum matching-based IGM selection procedures for selecting proper IGMs that can sufficiently induce the multimode interactions. In the proposed procedure, three equivalent single-degree-of-freedom (ESDOF) systems are developed by pushover analysis. NLRHA is then conducted for these ESDOF systems with a set of 20 seed IGMs chosen by the spectrum-matching–based selection procedure. Finally, seven IGMs are selected from the seed IGMs for NLRHA in the full structural model. To verify MGMS, seismic demands of high-rise buildings were computed by NLRHA with seven MGMS-selected IGMs, seven IGMs with closest spectrum matching, and groups of seven randomly selected IGMs derived from three different sets of 20 seed IGMs. The computed seismic demands with MGMS-IGMs show very good agreement with the mean demands determined using the whole set of seed IGMs, while the deviation is much lesser compared with those groups of randomly selected IGMs.     

Numerical simulation of ground acceleration spectra and accelerograms for engineering application

A numerical approach to the earthquake ground motion analysis is proposed for regions where no accelerograms are available. Using Haskell matrix techniques, the response spectra of a layered substratum for SV waves were calculated and then multiplied by the spectra corresponding to Brune's type pulses. The ground acceleration spectra were obtained for different angles of pulse incidence at the substratum base. The spectrum shape depends upon the substratum response and the pulse shape, while its level was related to the maximum ground acceleration corresponding to the expected maximum intensity. Transformation of the ground spectra into the time domain produced numerical accelerograms for horizontal and vertical components and for different angles of pulse incidence. Finally, a standard statistical procedure was applied to obtain the design response spectra used in engineering applications.     

考虑超随机特性的人工地震动合成

文中根据自相关函数随机噪声部分的2个重要性质提出了自相关函数随机噪声部分的迭代生成算法,并给出了以确定性自相关函数为目标函数,考虑随机噪声部分影响的人工合成地震动方法.本文的研究结果表明地震动加速度的平方和（SS）比峰值加速度（PGA）更好地量度了地震地面运动强度.文中用蒙特卡罗方法分析了自相关函数噪声项对人工合成地震动幅值和反应谱的影响：由于自相关函数的随机噪声项对地震动总功率或平方和的贡献为0,因此随机噪声项对合成地震动幅值的影响不大,但由于自相关函数随机噪声项明显改变了地震动功率谱在频域上的分布特征,使原本光滑的平均反应谱出现了明显的波动,从而在一定程度上提高了平均反应谱的峰值,使自相关函数噪声部分对平均反应谱也有一些影响.     

平稳随机地震地面运动过程模型及其统计特征

地震地面运动过程具有强烈的随机性,应用随机理论对实际工程结构进行地震可靠性分析和抗震设计与加固时都需要建立合理的随机地震地面运动模型,本文选择3种典型的随机地震动模型,即理想白噪声模型、金井清模型和改进的金井消模型,分析了它们的物理概念、频域特征以及适用范围。引入状态向量,建立状态方程．通过复振型叠加法分析了地震地面运动过程的时域统计特性,推导出3种随机地震动模型的相关函数的解析表达式．这些结果可为结构随机地震反应时域分析和抗震可靠性评估提供基础。     

Aseismic design implications of near-fault san fernando earthquake records

Near-fault records of the 1971 San Fernando earthquake contain severe, long duration acceleration pulses which result in unusually large ground velocity increments. A review of these records along with the results of available theoretical studies of near-fault ground motions indicates that such acceleration pulses may be characteristic of near-fault sites in general. The results of an analytical study of a building severely damaged during the San Fernando earthquake indicate that such severe, long duration acceleration pulses were the cause of the main features of the observed structural damage. The implications of such pulses on current aseismic design methods, particularly those used to establish design earthquakes, are examined for buildings located near potential earthquake faults. Analytical studies of the non-linear dynamic response of single and multiple degree-of-freedom systems to several near-fault records, as well as to a more standard accelerogram, indicate that at near-fault sites: (a) very large displacement ductilities may result for current levels of code design forces; (b) smoothed elastic design response spectra should reflect the larger ground velocities that may occur; and (c) peak inelastic response cannot reliably be inferred from elastic response predictions.     

几条地震波的归一化时-频反应谱分析

时-频反应谱是地震动幅值、频谱和持时三要素构成的空间三维谱.基于此,本文提出归一化时-频反应谱定义与计算方法,计算三条典型地震波的归一化时-频反应谱,对比分析表明:不同地震记录的时-频反应谱的幅值在时间和周期两个轴上的分布差别很大,具有不同时-频反应谱的地震波可能对结构地震响应产生不同影响;对12层钢筋混凝土框架结构模型进行弹塑性时程分析,通过结构地震反应、结构损伤曲线与输入地震动的归一化时-频反应谱对比,发现结构最大反应并不一定是造成结构倒塌的直接原因,用结构弹性阶段反应最大值进行抗震设计存在一定局限性,从而证明归一化时-频反应谱可有效用来分析地震动特性和结构破坏机理.     

数字化噪声对强震记录的影响及其消除方法

本文详细地分析了强震加速度记录的数字化噪声。分析表明:数字化噪声由数字化设备的系统误差和操作者的随机读数误差迭加而成,随机数字化误差是具有各态历经性质的,其振幅按高斯规律分布的平稳随机过程,在其频谱组成中,长周期分量占明显的优势,因此将对二次积分加速度记录的位移曲线产生严重的影响。 研究表明:随机数字化噪声位移主要分布在周期大于25秒的频段,对加速度记录来说,分布在周期小于25秒的频段内,其随机噪声是相当小的(假定记录纸速为1厘米/秒)。因此,利用数字滤波技术,可以除去数字化加速度记录中的大部份随机数字化噪声。 作为实例,对一个典型的强震加速度记录进行了滤波,给出了低噪声的加速度记录和由此算出的位移曲线,且和未经滤波的相应记录及其位移进行了比较。      

弹性能量半径演化谱及其在多自由度体系地震反应计算中的应用

目前用于结构抗震设计的反应谱仅能反映峰值反应,无法体现反应值随时间的变化。文中提出一种弹性能量半径演化谱,可反映线性单自由度体系弹性能量(即动能与弹性势能之和)随地震持时的变化,且其峰值近似等于结构峰值位移。文中给出了利用地震动演化功率谱得到该演化谱的方法并进一步发展了一种计算线性多自由度体系地震位移反应的新方法。通过两座框架结构的地震反应计算,将新方法与传统振型组合法及时程分析法的计算结果进行对比,发现对于振型稀疏结构,新方法计算结果与SRSS法接近;而对于振型密集结构,新方法计算结果较CQC法更精确,且避免了CQC法相关系数的复杂计算。