随机结构分析的扩阶系统方法(Ⅰ)——扩阶系统方程

本文提出了一类新的随机结构分析方法——扩阶系统方法。文中首先论述了随机函数空间中的正交展开与次序正交展开概念。利用随机函数空间中的正交分解原理,证明了扩阶系统方程的正确性。     

Wavelet-vaguelette decomposition of spatiotemporal random fields

A wavelet-based orthogonal decomposition of the solution to stochastic differential/pseudodifferential equations of parabolic type is derived in the cases of random initial conditions and random forcing. The family of spatiotemporal models considered can represent anomalous diffusion processes when the spatial operator involved is a fractional or multifractional pseudodifferential operator. The results obtained are applied to the generation of the sample paths of Gaussian spatiotemporal random fields in the family studied.     

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.     

Conditional components for simulation of vector random fields

Conditional component random fields (CC) based on Cholesky decomposition of the multivariate spectra are introduced in this study to develop a new method for conditional simulation of vector attributes in environmental and geological phenomena. The CC are independent random fields with covariance models obtained from projections and conditioning in the frequency domain. The approach is to simulate one attribute in the physical space and use the results to estimate the other attributes in the frequency domain. Then, a CC for the next attribute is simulated and projected on the other attributes. In general, any attribute is built as the sum of inverse Fourier transform of the orthogonal projection of previous simulated CC plus a last CC simulated in the physical space. This simulation approach continues in this fashion for several attributes and the order of them may be changed for different realizations. This method allows for data conditioning and simulation. A simplified version for intrinsically correlated random fields allows for an approach that avoids the frequency domain.     

动态随机有限元法

本提出分析了不确定性结构随机动力响应的一种新的数据方法－－动态随机有限元法。经的特点是引入反映结构振动特征的动态形函数,中引出了相应的计算列式。算例表明,本方法的计算效率及数值精度均优于一般的随机有了限元法,具有应用前景。     

A) A. I. H. S. / A) A. I. H. S.

Abstract

A new method is presented to generate stationary multi-site hydrological time series. The proposed method can handle flexible time-step length, and it can be applied to both continuous and intermittent input series. The algorithm is a departure from standard decomposition models and the Box-Jenkins approach. It relies instead on the recent advances in statistical science that deal with generation of correlated random variables with arbitrary statistical distribution functions. The proposed method has been tested on 11 historic weekly input series, of which the first seven contain flow data and the last four have precipitation data. The article contains an extensive review of the results.

Editor D. Koutsoyiannis

Citation Ilich, N., 2014. An effective three-step algorithm for multi-site generation of stochastic weekly hydrological time series. Hydrological Sciences Journal, 59 (1), 85–98.     

随机结构动力可靠度分析的极值概率密度方法

提出了随机结构动力可靠度分析的极值概率密度方法。基于概率密度演化的基本思想,构造一个虚拟随机过程,使得随机结构动力反应的极值为该虚拟随机过程的截口随机变量。进而．采用概率密度演化方法,建立概率密度演化方程并求解给出随机结构动力反应的极值分布。在安全域内积分即可给出结构动力可靠度,当安全界限为随机变量时,采用这一方法几乎不增加额外的工作量,与随机模拟结果的比较表明,本文建议方法具有良好的精度和效率。     

THE EFFECTS OF INACCURATE INPUT PARAMETERS ON DEPOSITION OF SUSPENDED SEDIMENT

I.~OntjcnONEngineeringPredictionsofsedimenttransPOrtinopen-Channelsystems,especiallyifunsteadyflowconditionmustbeconsidered,isfraughtwithambigUityduetospatialandtemporalvariability,measurementerrors,lumtedsamplingoftheParameters,bounceandscallconditionS,andsink/sourcetenns.Duringrecentyearsmanysophisticatedmathematicalmodelshavebecomeavailabletocalculateunsteadyflowinone,tWoorthreedimensionS.ThesemodelswillbecoupledwithtranSportequationSforbedloadorsuSpendedloadtocalculateforexamplelongt…     

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.     

考虑岩土介质随机特性的工程场地地震动相干函数研究

将随机结构正交展开理论和随机振动分析的虚拟激励原理运用于场地波动有限元分析，形成了一种可以考虑岩土介质随机特性对工程场地地震动相干函数影响的分析方法。实例分析表明，非严格均匀分布的随机介质场地对场地表面的迟滞相干函数值有重要影响，这种影响可由场地的随机影响因子来衡量，在进行工程场地地震动随机场研究时应当考虑场地介质随机特性的影响。     

Risk assessment of an interacting structure–soil system due to liquefaction

The present study deals with the non‐linear stochastic dynamic analysis of a soil–structure interacting system. The ultimate objective is to determine the risk of damage to the system due to liquefaction under a wide range of earthquake intensities. A Monte Carlo simulation approach is followed in conjunction with advanced finite element procedures. The stochastic spatial variability of soil properties and the randomness of the seismic excitation are taken into account in order to estimate the statistics of the response, measured in terms of uniform foundation settlement and tilting. Specifically, soil properties are modelled as non‐Gaussian random fields and seismic excitations as non‐stationary random processes. The probabilistic characteristics of the stochastic field modelling soil properties are established from in situ tests. The risk of damage to the soil–structure system due to liquefaction is assessed by establishing fragility curves, which are of paramount importance for risk assessment and management studies of such systems. Fragility curves express the probability of exceeding various thresholds in the response. The relative effect of the variability of various soil parameters on the variability of the response is also examined. Copyright © 2002 John Wiley & Sons, Ltd.     

A conceptually based stochastic point process model for daily stream‐flow generation

Based on the stochastic and phenomenological aspects of hydrological processes, a conceptually based stochastic point process (SPP) model for daily stream‐flow generation is proposed in this paper. In which, storms are defined by a stochastic point process with marked values. All the random variables defining the process are assumed to be mutually independent, which constitutes a compound Poisson point process. The direct surface runoff is regarded as occurring from storage in a cascade of surface linear reservoirs and is responsible for the short‐term variation of the daily stream flows. The baseflow component is considered as coming from subsurface/groundwater storage and is responsible for the long‐term persistence of the storm time‐series. This type of model is proposed as a more realistic model of daily stream flow than models based on pure stochastic processes. Studies on the instantaneous unit hydrograph and the mechanism of baseflow could thereby provide some parameters for this model. Copyright © 2002 John Wiley & Sons, Ltd.     

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。     

Coherency matrix-based proper orthogonal decomposition with application to wind field simulation

Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.     

Statistical analysis on energy field of seismicity in Ningxia and its neighborhood region

IntroductionOneofnotablefeaturesofseismicityistherandomoccurrenceofearthquakesinspaceandtime.Oneessentialelementofseismicityisthatearthquakereleasedenergycanbetakenastherandomfunctionsofspatialandtemporalcoordinates.Therandomfunctioncanbecalledseismicityenergystochasticfieldorearthquakeenergyfield.Sincetheseismicityisrelatedinspaceandtime,usingtheconceptofstochasticfield,thetotalfeatureofregionalseismicactivitycanbeconsidered,ratherthanthestatisticsofasingleearthquakeinthepast.Therefore,thefe…     

Stochastic dynamic analysis of a layered half-space

A stochastic thin-layer method is developed for the analysis of wave propagation in a layered half-space. A random field of shear moduli in the layered system is considered in terms of multiple correlated random variables. Expanding the random moduli and uncertain responses by means of Hermite polynomial chaos expansions and applying the Galerkin method in the spatial as well as stochastic domains, stochastic versions of thin-layer methods for a layered half-space in plane strain and antiplane shear are obtained. In order to represent the infinite half-space, continued-fraction absorbing boundary conditions are included in the thin-layer models of the half-space. Using these stochastic methods, dynamic responses of a layered half-space subjected to line loads are examined. Means, coefficients of variance, and probability density functions of the half-space responses with a varying correlation coefficient of the shear moduli are computed and verified by comparison with Monte Carlo simulations. It is demonstrated that accurate probabilistic dynamic analysis is possible using the developed stochastic thin-layer methods for a layered half-space.     

多年冻土区桩基础桥墩随机地震反应分析

将随机振动理论、粘弹性边界条件的二维波动法以及结构动力分析有限元法结合起来，考虑场地地震动为零均值的高斯平稳随机过程，对青藏铁路多年冻土区桩基础桥墩进行了随机地震反应分析，计算了9度地震作用下桥墩随机地震响应最大值的均值和均方差，分析了冻土层及桥墩高度对桥墩随机地震响应的影响。     

宁夏及邻近地区地震活动能量场的统计分析

应用随机函数理论,将区域地震活动能量看作是空间和时间的随机函数,采用自然正交函数展开的分析方法,对宁夏及邻近地区小地震活动场的特征进行了研究．重点分析了场的主要部分,即前几个典型场的时间权重系数的时间变化,发现它们在中强地震发生前数值有较大幅度的升、降变化,显示出了与区域及其周围中强地震相关的变化特性．从宁夏地区的震例看,地震能量随机场的自然正交函数展开方法是一种值得探索的地震分析预测方法．      

平稳随机激励下随机结构非线性动力响应分析

为了在结构强震灾变过程模拟中正确反映结构参数的随机性并准确界定结构失效模式,提出一种平稳随机激励下随机结构非线性动力响应分析的简化方法.首先运用点估计法将复合非线性随机系统转化为一系列平稳随机激励下的确定性非线性结构,然后再应用成熟的等效线性化方法计算出平稳随机激励下非线性结构动力响应的各阶矩.文末进行了算例分析与验证...     

Fluid flow dynamics under location uncertainty

We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition is reminiscent in spirit to the classical Reynolds decomposition. However, the random velocity fluctuations considered here are not differentiable with respect to time, and they must be handled through stochastic calculus. The dynamics associated with the differentiable drift component is derived from a stochastic version of the Reynolds transport theorem. It includes in its general form an uncertainty dependent subgrid bulk formula that cannot be immediately related to the usual Boussinesq eddy viscosity assumption constructed from thermal molecular agitation analogy. This formulation, emerging from uncertainties on the fluid parcels location, explains with another viewpoint some subgrid eddy diffusion models currently used in computational fluid dynamics or in geophysical sciences and paves the way for new large-scales flow modeling. We finally describe an applications of our formalism to the derivation of stochastic versions of the Shallow water equations or to the definition of reduced order dynamical systems.