非平稳地震动过程模拟方法(Ⅱ)

在总结回顾具有同一统计特征非平稳地震动过程模拟的研究基础上, 提出了一个模拟产生与某个给定地震动记录具有同一统计特征[CD2]时变功率谱的非平稳地震动过程的方法. 方法具有如下一些特点: 模拟产生的样本过程在幅值上和频率上均是非平稳的, 幅值和频率的非平稳性均取决于目标时变功率谱; 任意一个样本过程的时变功率谱未必符合目标谱, 但在统计意义上却严格符合目标谱. 最后, 论文以Landers地震的一个加速度记录为例对方法进行了验证.      

Simulation of non-stationary ground motion processes (II)

Introduction When doing Monte Carlo analysis of stochastic earthquake response of nonlinear structures, it is necessary to have a great number of ground motion processes with an identical statistical feature; In theoretical analysis of earthquake resistance of structures, to study the effect of one parameter, it is required to keep other parameters fixed, and it is often needed one set of ground motion proc-esses having an identical statistical feature; Similarly, while doing structural model…     

An evolutionary ground motion model for earthquake analysis of structures in zones with little history

Time history methods to perform structural dynamic analysis for vulnerability, seismic risk and structural performance studies are frequent in all kinds of projects. To apply these methods it is necessary to have earthquake acceleration records consistent with the seismic characteristics of the zone where the structure or facilities will be constructed. In regions where seismic activity is important but recorded history is scarce, the simulation of acceleration records becomes necessary.In the present work, a methodology to simulate artificial acceleration records is presented. This methodology is based on the theory of non-stationary random processes with evolutive power spectral density function. The random process model proposed uses the definition of the Boore power spectral density function, in order to take into account the seismic mechanism of the zone. The zone of Mendoza, in the province of Cuyo in Argentina close to the border with Chile, was selected to make applications of the theory. This zone was selected because it has important seismic activity but the information about this activity is scarce. To evaluate the performance of the method some response and seismic variables such as response spectra, Arias evolutionary intensity, and power spectra were computed. The results were compared with actual earthquake data obtained in the region.     

Structural response to non-stationary multiple-support random excitation

The seismic behaviour of large-size structures subjected to multiple-support excitation is studied by means of a random vibration approach. Ground motion is modelled as a non-stationary stochastic process having an evolutionary spectral density. To describe the spatial variability of the input motion a model is adopted which accounts for finite propagation velocity and for loss of correlation as a function of distance and frequency. Structural analysis is entirely performed in the frequency domain and full advantage is taken of FFT properties and capabilities. An example is given regarding the behaviour of a 800 m long viaduct. Results are shown in terms of response evolutionary spectral density, variance and reliability with respect to a fixed threshold.     

Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics

A method for generating an ensemble of orthogonal horizontal ground motion components with correlated parameters for specified earthquake and site characteristics is presented. The method employs a parameterized stochastic model that is based on a time‐modulated filtered white‐noise process with the filter having time‐varying characteristics. Whereas the input white‐noise excitation describes the stochastic nature of the ground motion, the forms of the modulating function and the filter and their parameters characterize the evolutionary intensity and nonstationary frequency content of the ground motion. The stochastic model is fitted to a database of recorded horizontal ground motion component pairs that are rotated into their principal axes, a set of orthogonal axes along which the components are statistically uncorrelated. Model parameters are identified for each ground motion component in the database. Using these data, predictive equations are developed for the model parameters in terms of earthquake and site characteristics and correlation coefficients between parameters of the two components are estimated. Given a design scenario specified in terms of earthquake and site characteristics, the results of this study allow one to generate realizations of correlated model parameters and use them along with simulated white‐noise processes to generate synthetic pairs of horizontal ground motion components along the principal axes. The proposed simulation method does not require any seed recorded ground motion and is ideal for use in performance‐based earthquake engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

On a continuous spectral algorithm for simulating non-stationary Gaussian random fields

This paper presents an algorithm for simulating Gaussian random fields with zero mean and non-stationary covariance functions. The simulated field is obtained as a weighted sum of cosine waves with random frequencies and random phases, with weights that depend on the location-specific spectral density associated with the target non-stationary covariance. The applicability and accuracy of the algorithm are illustrated through synthetic examples, in which scalar and vector random fields with non-stationary Gaussian, exponential, Matérn or compactly-supported covariance models are simulated.     

Non-stationary structural response with evolutionary spectra using seismological input model

A recently developed seismological model of ground motion is incorporated into the non-stationary random vibration theory making use of Priestley's evolutionary power spectral density. A general method of computing the input power spectrum is proposed and shown to reduce to the classical method when the input and the output are taken as stationary. Based on the concepts of Yang's non-stationary envelopes and first-passage reliability estimates via extreme point process, a statistical response spectrum for the pseudo-velocity is developed. Comparisons made among the results of non-stationary analysis with different modulating functions, and that of the stationary approximation, on SDOF linear structures with 5 per cent damping show that the type ofmodulating function chosen has little effect on the magnitudes of mean pseudo-velocities, provided the input power spectrum is properly scaled, and that the stationary approximation produces conservative results for structures with natural periods greater than 0.5 sec.     

时变地震谱估计的非参数方法评价及应用

针对工程中常见的非平稳地震动激励,进一步建立了时变功率谱估计的理论框架。首先,在多个样本情形下,采用信号处理中的时频分析方法对非平稳激励的时变谱估计理论进行了讨论。当激励样本数量有限时,对Priestley提出的估计方法进行了介绍。其次,以地震工程中常用的Kanai-Tajimi谱模型为目标,分别对均匀调制与一般调制谱的估计结果以及不同估计方法的精度与收敛性进行评价后,提出了能够方便工程应用的建议。最后,针对SMART-Ⅰ(Strong Motion Array in Taiwan,Phase Ⅰ)密集台阵第45次地震记录的多组三维样本,揭示了EW、NS、UD三个方向时变谱的典型特征以及各方向间的时变相干性。结果表明:与短时Fourier变换相比,复Morlet小波与广义谐和小波估计谱具有较好的精度与收敛性,Priestley方法估计单个样本具有优势;SMART-Ⅰ台阵地震动具有强度和频率的双重非平稳性,三个方向具有弱相干性。研究结论可为拓展谱估计理论的工程应用以及后续大跨结构多维多点非平稳地震响应的分析提供参考。     

时变功率谱空间变化性分析

基于我国台湾地区SMART-1密集台阵强震记录资料和Kameda的时变功率谱模型,利用多重滤波技术和非线性最小二乘法拟合得到每条记录的Kameda模型参数值;通过分析模型参数随频率变化的散点图分布规律,建立了时变功率谱模型参数随频率变化的随机模型。采用随机振动理论和多元统计分析方法,分析了沿波传播方向距离、垂直于波传播方向距离及测点所在位置土层厚度等局部空间位置变化对时变功率谱模型参数的影响规律,探讨了时变功率谱模型参数的空间分布形式,建立了各模型参数随空间坐标变化的随机预测模型,从而为重大工程多点输入地震动参数的确定和多点输入加速度时程的合成提供实用模型。     

Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades

Abstract

During recent decades, intensive research has focused on techniques capable of generating rainfall time series at a fine time scale that are (fully or partially) consistent with a given series at a coarser time scale. Here we theoretically investigate the consequences on the ensemble statistical behaviour caused by the structure of a simple and widely-used approach of stochastic downscaling for rainfall time series, the discrete Multiplicative Random Cascade. We show that synthetic rainfall time series generated by these cascade models correspond to a stochastic process which is non-stationary, because its temporal autocorrelation structure depends on the position in time in an undesirable manner. Then, we propose and theoretically analyse an alternative downscaling approach based on the Hurst-Kolmogorov process, which is equally simple but is stationary. Finally, we provide Monte Carlo experiments which validate our theoretical results.

Editor Z.W. Kundzewicz

Citation Lombardo, F., Volpi, E., and Koutsoyiannis, D., 2012. Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades. Hydrological Sciences Journal, 57 (6), 1052–1066.     

Use of the Fourier-Laplace transform and of diagrammatical methods to interpret pumping tests in heterogeneous reservoirs

Advances in computer power and in reservoir characterization allow simulation of pressure transients in complex reservoirs generated stochastically. Generally, interpretation of these transient gives useful information about the reservoir hydraulic properties: a major goal is to interpret these transients in the stochastic context. First we ensemble average the pressure over all the random permeability field realizations to derive an equation which drives the ensemble averaged pressure. We use the Fourier transform in space and the Laplace transform in time, in conjuction with a perturbation series expansion in successive powers of the permeability fluctuations to obtain an explicit solution. The Nth order term of this series involves the hydrodynamic interaction between N permeability heterogeneities and after averaging we obtain an expansion containing correlation functions of permeability fluctuations of increasing order.Next, Feynman graphs are introduced allowing a more attractive graphical interpretation of the perturbation series. Then series summation techniques are employed to reduce the graph number to be summed at each order of the fluctuation expansion. This in turn gives useful physical insights on the homogenization processes involved. In particular, it is shown that the sum of the so-called ‘one-particle irreducible graphs’ gives the kernel of a linear integro-differential equation obeyed by the ensemble average pressure. All the information about the heterogeneity structure is contained in this renormalized kernel, which is a limited range function.This equation on its own is the starting point of useful asymptotic results and approximations. In particular it is shown that interpretation of pumping tests yields the steady-state equivalent permeability after a sufficiently long time for an infinite reservoir, as expected.     

A modified method for simulating non-stationary multi-point earthquake ground motion

A spectral-representation-based algorithm is proposed to simulate non-stationary and stochastic processes with evolutionary power,according to a prescribed non-stationary cross-spectral density matrix. Non-stationary multi-point seismic ground motions at different locations on the ground surface are generated for use in engineering applications. First,a modified iterative procedure is used to generate uniformly modulated non-stationary ground motion time histories which are compatible with the prescribed power spectrum. Then,ground motion time histories are modeled as a non-stationary stochastic process with amplitude and frequency modulation. The characteristic frequency and damping ratio of the Clough-Penzien acceleration spectrum are considered as a function of time in order to study the frequency time variation. Finally,two numerical examples are presented to validate the efficiency of the proposed method,and the results show that this method can be effectively applied to the dynamic seismic analysis of long and large scale structures.     

全非平稳地震作用的结构随机反应与可靠度分析

在平稳地震动过程的Clough-Penzien功率谱基础上,采用林家浩非均匀调制函数建立全非平稳地震动过程的演变功率谱。根据我国现行的《建筑抗震设计规范》进行全非平稳地震动演变功率谱的参数识别研究。应用非平稳随机过程模拟的谱表示-随机函数方法,生成建筑结构抗震设计所用地震动的代表性样本集合。通过代表性样本集合的二阶统计值及地震反应谱与目标值的拟合比较,验证本文方法的有效性。最后结合概率密度演化方法,进行以层间位移角为控制准则的结构随机地震反应分析与抗震可靠度计算。     

Probabilistic representation and transmission of earthquake ground motion records

A relatively simple and straightforward procedure is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that allows its convenient use in later analytical random vibration response studies. The method is based on the spectral decomposition of the random process by the orthogonal Karhunen-Loeve expansion and the subsequent use of least-squares approaches to develop an approximating analytical fit for the data-based eigenvectors of the underlying random process. The resulting compact analytical representation of the random process is then used to derive a closed-form solution for the non-stationary response of a damped SDOF harmonic oscillator. The utility of the method for representing the excitation and calculating the mean-square response is illustrated by the use of an ensemble of acceleration records from the 1971 San Fernando earthquake.     

REDUCTION OF SERIALLY CORRELATED HYDROLOGIC DATA

Abstract

The need for specifying water availability in terms of its time sequence and distribution, rather than in terms of lumped quantities or flow duration, has given rise to data asquisition programs which use shorter sampling intervals. Shorter time intervals, in turn, has resulted in serially correlated observations. In order to determine the reliability of design variables derived from these observations, it is necessary to reduce these data to an equivalent series of independent observations, or find the effective lenght of the series.

A general parametric formula is developed for the effective number of observations for the second order autoregressive process, which has been found to apply to the series of mean daily river flows. Different values of the parameters were programmed in a digital computer to obtain tables for data reduction.     

A method for generating fully non-stationary and spectrum-compatible ground motion vector processes

Earthquake ground motion spatial variability can influence significantly the response of certain structures. In order to accurately evaluate probabilistic characteristics of the seismic response of structures, the Monte Carlo simulation technique is still the only universal method of analysis when strong nonlinearities and input uncertainties are involved. Consequently, realizations of ground motion time histories taking into account both time and spatial variability need to be generated. Furthermore, for some design applications, the generated time histories must also satisfy the provision imposed by certain seismic codes stating that they have to be also response-spectrum-compatible. For these purposes, a spectral-representation-based methodology for generating fully non-stationary and spectrum-compatible ground motion vector processes at a number of locations on the ground surface is proposed in this paper. The simulated time histories do not require any iterations on the individual generated sample functions so that Gaussianity and prescribed coherence are suitably preserved. The methodology has also the advantage of providing the fully non-stationary and spectrum-compatible cross-spectral density matrix of the ground motion time-histories that can be used for reliability studies in an analytic stochastic fashion.     

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.     

Calibration of a semi-distributed model for conjunctive simulation of surface and groundwater flows / Calage d’un modèle semi-distribué pour la simulation conjointe d’écoulements superficiels et souterrains

Abstract

Abstract A hydrological simulation model was developed for conjunctive representation of surface and groundwater processes. It comprises a conceptual soil moisture accounting module, based on an enhanced version of the Thornthwaite model for the soil moisture reservoir, a Darcian multi-cell groundwater flow module and a module for partitioning water abstractions among water resources. The resulting integrated scheme is highly flexible in the choice of time (i.e. monthly to daily) and space scales (catchment scale, aquifer scale). Model calibration involved successive phases of manual and automatic sessions. For the latter, an innovative optimization method called evolutionary annealing-simplex algorithm is devised. The objective function involves weighted goodness-of-fit criteria for multiple variables with different observation periods, as well as penalty terms for restricting unrealistic water storage trends and deviations from observed intermittency of spring flows. Checks of the unmeasured catchment responses through manually changing parameter bounds guided choosing final parameter sets. The model is applied to the particularly complex Boeoticos Kephisos basin, Greece, where it accurately reproduced the main basin response, i.e. the runoff at its outlet, and also other important components. Emphasis is put on the principle of parsimony which resulted in a computationally effective modelling. This is crucial since the model is to be integrated within a stochastic simulation framework.