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 spatially correlated accelerograms

For the seismic analysis of complex or nonlinear extended structures, it is useful to generate a set of properly correlated earthquake accelerograms that are consistent with a specified seismic hazard. A new simulation approach is presented in this paper for the generation of ensembles of spatially correlated accelerograms such that the simulated motions are consistent with (i) a parent accelerogram in the sense of temporal variations in frequency content, (ii) a design spectrum in the mean sense, and (iii) with a given instantaneous coherency structure. The formulation is based on the extension of stochastic decomposition technique to wavelet domain via the method of spectral factorization. A complex variant of the modified Littlewood-Paley wavelet function is proposed for the wavelet-based representation of earthquake accelerograms, such that this explicitly brings out the phase information of the signal, besides being able to decompose it into component time-histories having energy in non-overlapping frequency bands. The proposed approach is illustrated by generating ensembles of accelerograms at four stations.     

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。     

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.     

Simulation of artificial earthquakes

A procedure is developed for the simulation of artificial earthquake accelerograms, The time variation of amplitude and frequency content is preserved in the simulation procedure. Sixteen artificial earthquake accelerograms are simulated and compared with a target accelerogram. The time variation of amplitude and frequency content for 26 historical earthquake accelerograms is characterized.     

The use of optimization to construct critical accelerograms for given structures and sites

In this paper a methodology has been presented for constructing the most critical accelerogram from among a be class of candidate accelerograms for a given site and structure. This most critical accelerogram could be used to assess seismic resistance of a structure with a high level of confidence. Specifically, the method superimposes accelerograms recorded at similar sites to create the candidate accelerograms, then uses optimization and approximation techniques find the most critical accelerogram. The most critical accelerogram is defined as the one which maximizes damage is structure, as computed by non-linear dynamic structural analysis, as well as satisfies constraints on ground parameters to ensure credibility. The damage has been defined as cumulative inelastic energy dissipation or sure of interstorey drifts. The method is applied to ten examples in the paper.     

BUILDING DUCTILITY DEMAND: INTERPLATE VERSUS INTRAPLATE EARTHQUAKES

The inelastic seismic response behaviour for a range of simplified single-degree-of-freedom models has been analysed using 180 random phase angle synthetic accelerograms with different frequency contents and different durations and 105 real accelerograms collected from different regions worldwide. Results from the analyses have identified that the frequency content of the excitation can greatly influence the ductility demand ratio due to inelastic amplification effects. Consequently, results derived from intraplate earthquake records (typically of higher frequency content) were generally different to those from interplate records. However, the commonly used El Centro accelerogram has significantly lower ductility demand in the low period range than the average of records with similar elastic response spectral shape. Apart from this, there was little evidence to suggest any inherent differences in the inelastic response behaviour of buildings from intraplate and interplate earthquakes which possessed similar frequency content. Thus, the average ductility demand ratios from future earthquakes in an area can be predicted by interpolation of the results presented in this paper assuming the elastic response spectrum has been defined. Ductility demand ratios derived from the synthetic accelerograms and the real accelerograms with similar frequency content have been shown to be consistent. However, results from synthetic records derived for the idealised code design spectra (such as the Uniform Building Code and the Australian Standard AS1170.4) indicate a significantly higher ductility demand in the long period range.     

强震加速度记录的数据处理方法

本文用数值积分法,对RDZ1-12-66型自动触发电流计记录式强震仪的幅频响应失真进行校正。并采用高通数字滤波的方法,修正加速度图的零线.为此编制了计算机程序,绘制了修正后的加速度、速度和位移时程曲线.计算了修正前后加速度图的傅氏谱。同时,对这些结果加以讨论。 修正后的加速度图,精确地表示了仪器基本频带在0.09HZ和25HZ之间的绝对地面加速度。      

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.     

The generation of spectrum compatible accelerograms for the design of nuclear power plants

Based on the main features of the computer program THGE, the paper reviews the techniques which are available for the construction of an accelerogram whose response spectrum matches a design spectrum. First, a sample accelerogram is generated as the product of the stationary random sequence by a deterministic shape function. It is assumed that the spectral properties of the stationary process have been determined in a previous step, in order to lead to the design spectrum as expected maximum responses of a set of single degree of freedom oscillators. The principal properties of the Fast Fourier Transform which is used for this first step are reviewed. The paper then describes the procedures which are available, both in the frequency domain and in the time domain, to improve the agreement between the response spectrum and the target. It also discusses some related issues, such as the response spectrum calculations, the statistical dependence between the three earthquake components, the duration of the time history, the variability of the secondary response to various samples and the generation of an accelerogram whose response spectra envelop a set of design spectra. The point of view adopted is the one of the structural engineer.     

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.     

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets： artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011 -2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals' response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.     

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。      

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

The seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.     

A non-parametric wave type based model for real-time prediction of strong ground motion accelerogram

A wave type based method for real-time prediction of strong ground motion (SGM) accelerogram is developed. Real-time prediction of SGM is requested in predictive building control systems to trigger and control actuator systems achieving the goal of reduction of the structural deformations during an on-going earthquake. It is well known that SGM is a classic example of non-stationary stochastic process with temporal variation of both amplitude and frequency content. The developed non-parametric model considers the non-homogeneity of the seismic process which contains different wave types with the individual frequency contents and time-dependency amplitude distribution pattern. Therefore, an important part of the method is to detect dominant seismic wave phases. Prediction of seismic signal is undertaken by applying frequency adaptive windowing approach, which leads to predict the on-coming signal in time window t+Δt based on the measured data in the time window t. Besides use of the frequency adaptive windowing, constant windowing and semi-adaptive windowing approaches are deployed. The results show that use of the adaptive time windows relevant to dominant frequency of the signal will enable the model to catch and predict the most dominant frequencies. Performance of the proposed model is verified by the use of 97 free-field accelerograms, which were applied to train and validate the prediction model. The selected accelerograms were measured above the soil type C and D according Eurocode 8 and their Moment magnitude are ranging between 6.2 and 7.7. The learning capability of the radial basis function Artificial Neural Network is used to reconstruct the SGM accelerogram. The most significant advantage of the proposed model is the concept of wave type based modeling which has the advantage of a conceptual physical modeling of the seismic process. Comparison of the real-time predicted and the observed accelerograms shows a high correlation when the frequency adaptive approach is applied. This paper lays a foundation for more effective use of real-time predictive control systems and potential for future extension in active structural control as well as in real-time seismology.     

根据渐进谱的统计规律生成地震加速度时程

基于美国西部80条基岩上的近场强震记录, 采用Nakayama方法生成记录的渐进谱, 并参照Kameda方式,用统计方法建立了根据震级、距离等地震参数预测渐进谱的统计模型. 提出一种以渐进谱为目标谱的生成幅值和频率非平稳地震加速度时程的迭代方法. 由于考虑了渐进谱幅值和相位的相互影响,所生成的时程的相位也是时频非平稳的,并在相位调整中识别了相位谱增量符号以加速迭代收敛进程. 最后根据统计回归的目标渐进谱模型和本文提出的拟合目标渐进谱的方法,可生成不同震级、距离条件下的幅值和频率均非平稳的地震加速度时程.      

Earthquake accelerogram simulation with statistical law of evolutionary power spectrum

By using the technique for evolutionary power spectrum proposed by Nakayama and with reference to the Kameda formula, an evolutionary spectrum prediction model for given earthquake magnitude and distance is established based on the 80 near-source acceleration records at rock surface with large magnitude from the ground motion database of western U.S.. Then a new iteration method is developed for generation of random accelerograms non-stationary both in amplitude and frequency which are compatible with target evolutionary spectrum. The phase spectra of those simulated accelerograms are also non-stationary in time and frequency domains since the interaction between amplitude and phase angle has been considered during the generation. Furthermore, the sign of the phase spectrum increment is identified to accelerate the iteration. With the proposed statistical model for predicting evolutionary power spectra and the new method for generating compatible time history, the artificial random earthquake accelerograms non-stationary both in amplitude and frequency for certain magnitude and distance can be provided.     

Rocking strong earthquake accelerations

In this paper, the method presented by Lee and Trifunac (1985) for generating synthetic torsional accelerograms has been extended to the estimation of synthetic rocking accelerograms and of their response spectra. Results from our previous regression analyses for the characterization of strong shaking in terms of (1) earthquake magnitude and epicentral distance, or (2) Modified Mercalli Intensity at the site are utilized here again. The effects of geologic environment, in terms of site parameters or the representative depth of sediments, which influence amplification, and the dispersive properties of ground motion are also included. The synthetic rocking accelerogram is then constructed from the horizontal and vertical acceleration components.     

Generating multiple spectrum compatible accelerograms using stochastic neural networks

A new neural‐network‐based methodology for generating artificial earthquake spectrum compatible accelerograms from response spectra was proposed in 1997, in which, the learning capabilities of neural networks were used to develop the knowledge of the inverse mapping from the response spectra to earthquake accelerograms. Recently, this methodology has been further extended and enhanced. This paper presents a new stochastic neural network that is capable of generating multiple earthquake accelerograms from a single‐response spectrum. A new stochastic feature to the neural network has been combined with a new scheme for data compression using the replicator neural networks developed in the original method. A benefit of this extended methodology is gaining efficiency in compressing the earthquake accelerograms and extracting their characteristics. The proposed method produces a stochastic ensemble of earthquake accelerograms from any response spectra or design spectra. An example is presented that used 100 recorded accelerograms to train the neural network and several design spectra and response spectra to test this improved methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

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.