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.     

Generation of spectrum compatible accelerograms

In this paper a new method is presented for generating earthquake accelerograms which have pre-established response spectra. The non-stationary random nature and other salient features of the accelerograms can be taken care of by the procedure developed. The method leads to a sample spectrum which lies above the given spectrum. The generation of records to suit several spectra simultaneously can also be handled by this approach. The method is detailed first. This is followed by several numerical examples.     

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.     

HORIZONTAL-TO-VERTICAL SPECTRUM RATIO OF EARTHQUAKE GROUND MOTION FOR SITE CHARACTERIZATION

Nakamura's method, which uses a horizontal-to-vertical Fourier spectrum ratio of microtremor, has become popular to determine the predominant period and amplification of a site. In this study, this method is extended for earthquake ground motion recordings using new strong motion data recorded by JMA-87-type accelerometers. From the analysis of these accelerograms, horizontal-to-vertical Fourier spectrum ratios of a site for different earthquakes are also found to be stable irrespective of magnitude, distance and depth. To establish this fact, attenuation relations of velocity response spectra for horizontal and vertical components are derived for three damping ratios (0, 2 and 5 per cent) using the JMA data. Then the horizontal-to-vertical ratios of the velocity response spectra are obtained. The results show that the horizontal and vertical velocity response spectra are dependent on magnitude, distance and depth, but that their ratios are almost independent of magnitude, distance and depth. However, since the current data set consists of mostly intermediate to far field data, this observation should be limited to records of these distance ranges. Introducing station coefficients, representing site amplification, to this relation yields the value comparable to the horizontal-to-vertical Fourier spectrum ratio at a specific site. The stability of the spectrum ratio is explained by the transfer function between the ground surface and stiff-soil outcrop due to S-wave propagation. These results suggest that site amplification characteristics can be evaluated by one-point two-component surface recordings of earthquake ground motion, in a similar manner as proposed by Nakamura for microtremor. © 1997 by John Wiley & Sons, Ltd.     

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.     

Parametric modeling of earthquake response spectra

A mathematical model for the response spectra is determined using statistical analysis. The form of the model is first established using fifty computer simulated accelerograms. The final form is then used on twenty-five accelerograms from fifteen past United States earthquakes. This model smooths out peaks and valleys which are characteristic of the response spectrum of any single earthquake. Thus it serves as a ‘smooth design spectrum’ and can be used to approximate structural response to a future seismic event.     

Computation of response spectra from mining tremors using neural networks

Underground coal and copper ore exploitation in two Polish mining regions causes mining tremors and a series of other negative phenomena in the environment. Although these tremors are strictly connected with human activity, they differ considerably from other paraseismic vibrations. The moment of their occurrence is not to be foreseen likewise for earthquakes. The main problem discussed in the paper was formulated as the neural network evaluation of a relation between mining tremor energies, epicentral distances and acceleration response spectra. Back-propagation neural networks with Resilient back-propagation learning method were used. Each input vector included information about the mining tremor energy and the epicentral distance. Values of acceleration response spectrum were expected as the outputs of neural networks. Neurally evaluated spectra were compared with spectra computed on the basis of experimental data. After the network is trained and tested, it can be used for mapping of new data of mining tremor energies and epicentral distances into the spectra. Then, what is the substantial advantage of neural approach, the prediction of acceleration response spectra can be performed without recording of surface vibrations. In the light of the results, it is visible that the presented way of computation of acceleration response spectra can be peculiarly applied to prognosis of mining tremors influences on structures.     

地震动随机函数模型研究(Ⅰ)——模型建立

基于随机过程的随机函数解释,发展了一种随机地震动模型.模型包括两个部分,分别是基于理论物理关系的Fourier幅值谱模型和基于经验关系的Fourier相位谱模型.基于拟加速度谱概念建立的幅值谱模型能够反映强震记录的幅值特性,而Fourier相位谱模型则利用累积相位谱的单值连续特性,以线性多项式与三角级数组合的形式给出.模拟记录与实测记录对比结果显示两者不仅在波形结构上相似性良好,而且反应谱层次亦吻合良好.     

Estimation of strength reduction factors via normalized pseudo‐acceleration response spectrum

Estimation of design forces in ductility‐based earthquake‐resistant design continues to be carried out with the application of response modification factors on elastic design spectra, and it remains interesting to explore how best to estimate strength reduction factors (SRFs) for a design situation. This paper considers the relatively less explored alternative of modelling SRF spectrum via a given response spectrum. A new model is proposed to estimate the SRF spectrum in terms of a pseudo‐spectral acceleration (PSA) spectrum and ductility demand ratio with the help of two coefficients. The proposed model is illustrated for an elasto‐plastic oscillator, in case of 10 recorded accelerograms and three ductility ratios. The proposed model is convenient and is able to predict SRF spectrum reasonably well, particularly at periods up to 1.0 s. Coefficients of the proposed model may also be determined in case of a given design spectrum when there is uncertainty in SRF spectrum due to uncertainty in temporal characteristics of the ground motion. This is illustrated with the help of 474 accelerograms recorded in western U.S.A. and different scaled PSA spectra. It is shown that probabilistic estimates may be obtained in this situation for SRF spectrum by assuming the error residuals to be log normally distributed with period‐dependent parameters. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

适用于结构时程分析法的输入地震波

本文对建筑结构抗震设计时程法所需的输入地震波提出一种基于规范反应谱的、与设防烈度、场地条件、设计近震或远震、结构自振特性有关的选择原则和方法。按远、近震和四类场地标定了反应谱、延性谱和积累损伤谱。通过对六幢不同高度的剪切和弯曲型结构模型的弹塑性分析,表明离差很小。建议在进行结构时程法分析时,按地震加速度反应谱特定的分布规律选择4条加速度记录作为输入计算。两个实际的例子表明按上述方法计算的结果与按底部剪力法计算的结果基本相符。     

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.     

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.     

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.     

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.     

神经网络方法在地震预报研究中的初步应用

本文把神经网络方法引进地震预报研究当中。使用地震频次，最大震级，平均震级，等价地震次数等多项地震活动性指标作为神经网络的输入，未来时段内的最大地震震级作为其输出，可以对某一固定地区的最大地震震级作出中近期预报。选用的神经网络模型为含两个中间层的前向模型，并采用ＢＰ算法。所得结果表明，用神经网络方法可以在一定精度范围内使震级预报的内检符合率达到１００％，在本文的例子中，外推预报准确率达到６０％以上。     

Hysteretic energy spectrum and damage control

The inelastic response of single‐degree‐of‐freedom (SDOF) systems subjected to earthquake motions is studied and a method to derive hysteretic energy dissipation spectra is proposed. The amount of energy dissipated through inelastic deformation combined with other response parameters allow the estimation of the required deformation capacity to avoid collapse for a given design earthquake. In the first part of the study, a detailed analysis of correlation between energy and ground motion intensity indices is carried out to identify the indices to be used as scaling parameters and base line of the energy dissipation spectrum. The response of elastoplastic, bilinear, and stiffness degrading systems with 5 per cent damping, subjected to a world‐wide ensemble of 52 earthquake records is considered. The statistical analysis of the response data provides the factors for constructing the energy dissipation spectrum as well as the Newmark–Hall inelastic spectra. The combination of these spectra allows the estimation of the ultimate deformation capacity required to survive the design earthquake, capacity that can also be presented in spectral form as an example shows. Copyright © 2001 John Wiley & Sons, Ltd.     

基于强震记录的核电厂抗震标准反应谱研究

依据基岩场地上的汶川地震强震记录,分析了地震动地面峰值和核电站抗震标准反应谱的特性,证明了在推导和使用标准反应谱时所考虑的地面峰值加速度与地面峰值速度之比(PGA/PGV)受地面峰值加速度和震中距的影响,将对标准反应谱形状产生明显的影响.另外还发现了基岩场地的竖向峰值加速度可能要远比通常认为水平向峰值加速度的2/3大....