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.     

Simulation of three-dimensional strong ground motions along principal axes,San Fernando earthquake

Power spectral density which describes frequency content is considered one of the most significant properties to be taken into account when generating ground motions through the use of stochastic processes. Using a smoothed and normalized Fourier amplitude spectrum, frequency content for components of motion along a set of principal axes is estimated. Fourier amplitude spectra obtained by this moving-window technique are presented which show the time dependency of frequency content for motions produced by the San Fernando earthquake of 9 February 1971. A mathematical model to simulate ground motion processes is proposed for which both the intensity and frequency content are non-stationary. Using this mathematical model with parameter characteristics along principal axes similar to those of the motions recorded during the San Fernando earthquake, three-dimensional ground motions are synthetically generated. The properties of the simulated motions show general characteristics similar to the characteristics observed in real accelerograms. The suggested model is considered adequate for engineering purposes.     

A procedure for simulating synthetic accelerograms compatible with correlated and conditional probabilistic response spectra

The modeling of seismic load is a major topic that has to be addressed thoroughly in the framework of performance based seismic analysis and design. In this paper, a simple procedure for simulating artificial earthquake accelerograms matching the statistical distribution of response spectra, as given by median ground motion prediction equations, the standard deviation and correlation coefficients, is proposed. The approach follows the general ideas of the (natural) ground motion selection algorithms proposed by Baker [4] and Wang [43] but using simulated (artificial) “spectrum-compatible” accelerograms. This allows to simulate spectrum-compatible accelerograms featuring variability similar to the one of recorded accelerograms when the match of median and ±1 standard-deviation response spectra is imposed by the regulator. The procedure is illustrated by an application to the NGA ground motion data and models.     

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.     

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.     

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.     

Stochastic earthquake response of secondary systems in base-isolated structures

This paper studies the stochastic responses of secondary systems in base-isolated shear beam structures. A number of base isolation systems such as the laminated rubber bearing (LRB), the resilient-friction base isolator (R-FBI) with or without sliding upper plate, and the EDF system are considered. The stochastic models for the El Centro 1940 and the Mexico City 1985 earthquakes which preserve the non-stationary evolutions of amplitude and frequency content of ground accelerations are used as earthquake excitations. The technique of equivalent linearization is utilized and the mean-square response statistics of secondary systems and primary structure are evaluated. The accuracy of the linearization scheme is verified by comparison with the Monte Carlo simulation results. Statistically estimated peak responses of the secondary system are evaluated and the results are compared with the response spectra for actual earthquake accelerograms. It is shown that the use of base isolation systems, generally, provides considerable protection for structural contents. In particular, the LRB system is remarkably effective in reducing responses of secondary systems. Results for the Mexico City earthquake show that the base-isolated structures are sensitive to long period ground excitations.     

Physically compliant,conditionally simulated spatially variable seismic ground motions for performance‐based design

The performance‐based design of lifeline systems requires spatially variable seismic excitations at the structures' supports that are consistent with prescribed seismic ground motion characteristics and an appropriate spatial variability model—such motions can be obtained through conditional simulation. This work revisits the concept of conditional simulation and critically examines the conformity of the generated motions with the characteristics of the target random field and observations from data recorded at dense instrument arrays. Baseline adjustment processing techniques for recorded earthquake accelerograms are extended to fit the requirements of simulated and conditionally simulated spatially variable ground motions. Emphasis is placed on the use of causal vs acausal filtering in the data processing. Acceleration, velocity and displacement time histories are evaluated in two example applications of the approach. The first application deals with a prescribed synthetic time history that incorporates nonstationarity in the amplitude and frequency content of the motions and depends on earthquake magnitude, source–site distance and local soil conditions; this example results in zero residual displacements. The second application considers as prescribed time history a recording in the vicinity of a fault and yields nonzero residual displacements. It is shown that the conditionally simulated time histories preserve the characteristics of the prescribed ones and are consistent with the target random field. The results of this analysis suggest that the presented methodology provides a useful tool for the generation of spatially variable ground motions to be used in the performance‐based design of lifeline systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of arma models to estimate earthquake ground motion and structural response

This paper deals with the use of ARMA models in earthquake engineering. Tools and methods applied to strong ground motion are discussed emphasizing simulation of probabilistic earthquake response spectra. The ARMA models are applied to Icelandic earthquake data and a tentative model for Icelandic earthquakes is presented. This model, which is derived using 54 accelerograms, is based on a low-order, time-invariant ARMA process excited by Gaussian white noise and amplitude modulated using a simple envelope function to account for the non-stationary characteristics. This simple model gives a reasonable fit to the observed ground motion. Further, this model produces accurate earthquake response spectra, which, combined with accompanying attenuation and duration formulae, might be useful in earthquake hazard and risk assessment.     

龙门山地区的kappa（κ0）模型及汶川MS8.0地震的强地震动模拟

在地震动模拟中,高频衰减参数（κ₀）是一个重要的参数,它控制了傅里叶谱高频部分的衰减特性.本文利用汶川M_S8.0地震和芦山M_S7.0地震主余震的1671组强震动观测记录,计算了龙门山地区50个断层距小于150 km的强震动台站的κ₀,基于随机有限断层法模拟了汶川地震中这些台站的加速度时程、傅里叶振幅谱和反应谱,并与前人的研究进行比较.结果表明,合理计算的κ₀可以有效地改善加速度时程振幅和高频谱（>1 Hz）的模拟结果.另一方面,本文基于κ₀与地形高程的相关性,建立了龙门山地区的κ₀经验模型.分别采用该经验模型和κ₀= 0.04 s模拟了汶川地震的峰值加速度分布,并与观测记录进行比较.结果表明,采用本文提出的κ₀模型可以更好地重现汶川地震的峰值加速度分布,特别是在断层破裂方向的反方向区域和山区.综上,汶川地震中山区的峰值加速度明显大于盆地地区的现象,不仅与断层破裂产状有关,还与山区和盆地地区的κ₀之间显著的差异有关.     

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.     

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。     

Influence of intensity of motion on the seismic response of structures with asymmetric force-deformation curves

Asymmetrically yielding single-degree-of-freedom elastoplastic systems are subjected to simulated accelerograms based on El Centro-NS, 1940 ground motion (wide frequency band) to calculate the corresponding ductility demands. Results are compared with those corresponding to simulated accelerograms of the SCT-EW, 1985 Mexico earthquake (narrow frequency band) obtained in a previous work. Results obtained reveal that the characteristics of the excitation influence the response of asymmetrically yielding structures and that the differences found on responses corresponding to both earthquakes are due to frequency content, duration and/or intensity of motion. The effect of the latter concepts is studied using modulating sinusoidal excitations as well as accelerograms recorded on soft and hard soils of Mexico City. Two alternate expressions are proposed to evaluate the increase in ductility demands of structures with asymmetric force-displacement curves with respect to symmetric ones. Those expressions take into account motion intensity and duration, as well as seismic design coefficient.     

Stochastic finite fault modelling of M w 4.8 earthquake in Kachchh, Gujarat, India

The modified stochastic finite fault modelling technique based on dynamic corner frequency has been used to simulate the strong ground motions of M _w 4.8 earthquake in the Kachchh region of Gujarat, India. The accelerograms have been simulated for 14 strong motion accelerographs sites (11 sites in Kachchh and three sites in Saurashtra) where the earthquake has been recorded. The region-specific source, attenuation and generic site parameters, which are derived from recordings of small to moderate earthquakes, have been used for the simulations. The main characteristics of the simulated accelerograms, comprised of peak ground acceleration (pga), duration, Fourier and response spectra, predominant period, are in general in good agreement with those of observed ones at most of the sites. The rate of decay of simulated pga values with distance is found to be similar with that of observed values. The successful modelling of the empirical accelerograms indicates that the method can be used to prepare wide range of scenarios based on simulation which provide the information useful for evaluating and mitigating the seismic hazard in the region.     

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.     

Statistical performance analysis of seismic‐excited structures with active interaction control

This paper presents a statistical performance analysis of a semi‐active structural control system for suppressing the vibration response of building structures during strong seismic events. The proposed semi‐active mass damper device consists of a high‐frequency mass damper with large stiffness, and an actively controlled interaction element that connects the mass damper to the structure. Through actively modulating the operating states of the interaction elements according to pre‐specified control logic, vibrational energy in the structure is dissipated in the mass damper device and the vibration of the structure is thus suppressed. The control logic, categorized under active interaction control, is defined directly in physical space by minimizing the inter‐storey drift of the structure to the maximum extent. This semi‐active structural control approach has been shown to be effective in reducing the vibration response of building structures due to specific earthquake ground motions. To further evaluate the control performance, a Monte Carlo simulation of the seismic response of a three‐storey steel‐framed building model equipped with the proposed semi‐active mass damper device is performed based on a large ensemble of artificially generated earthquake ground motions. A procedure for generating code‐compatible artificial earthquake accelerograms is also briefly described. The results obtained clearly demonstrate the effectiveness of the proposed semi‐active mass damper device in controlling vibrations of building structures during large earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

Empirical green's function corrected for source effect

One of the severe problems in the semi-empirical method for the prediction of strong ground motions is that there is no objective criterion for choosing empirical Green's functions. It is undesirable that synthesized strong ground motions are affected by the source process of an earthquake whose record is adopted as an empirical Green's function. Through the analysis of strong motion accelerograms of two aftershocks of the 1983 Japan Sea earthquakes, it is found that characteristics of the accelerograms are dependent on the moment rate function derived from teleseismic observations. A procedure is presented for removing the effect of the source process from observed strong motion accelerograms. The thus obtained empirical Green's function expresses approximately the impulse response of the medium between the earthquake source and the observation site.     

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.