共查询到20条相似文献，搜索用时 171 毫秒
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A stochastic approach to nonlinear unconfined flow subject to multiple random fields 总被引：3，自引：3，他引：0
Liangsheng Shi Jinzhong Yang Dongxiao Zhang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(6):823-835
In this study, the KLME approach, a moment-equation approach based on the Karhunen–Loeve decomposition developed by Zhang
and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random fields with known means and covariance functions. The F, R, H and Q are first decomposed into finite series in terms of Gaussian standard random variables by the Karhunen–Loeve expansion. The
hydraulic head h is then represented by a perturbation expansion, and each term in the perturbation expansion is written as the products of
unknown coefficients and Gaussian standard random variables obtained from the Karhunen–Loeve expansions. A series of deterministic
partial differential equations are derived from the stochastic partial differential equations. The resulting equations for
uncorrelated and perfectly correlated cases are developed. The equations can be solved sequentially from low to high order
by the finite element method. We examine the accuracy of the KLME approach for the groundwater flow subject to uncorrelated
or perfectly correlated random inputs and study the capability of the KLME method for predicting the head variance in the
presence of various spatially variable parameters. It is shown that the proposed numerical model gives accurate results at
a much smaller computational cost than the Monte Carlo simulation. 相似文献
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Sarino S. E. Serrano 《Stochastic Environmental Research and Risk Assessment (SERRA)》1990,4(2):151-160
Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement. 相似文献
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W. F. Curi T. E. Unny 《Stochastic Environmental Research and Risk Assessment (SERRA)》1995,9(2):133-149
The generation of the second and higher order moment equations for a set of stochastic differential equations based on Ito's differential lemma is difficult, even for small system of equations. From the knowledge of the statistical properties of the Gaussian white noises associated with the parameters and input coefficients of a set of stochastic differential equations of typeA.+B.Z=C(t), a way to automatically generate the second order moment equations in a computer is presented in this paper. The resulting set of first and second order moment equations is also presented in the same state-space form of the original set of stochastic differential equations through a vectorization of the correlation matrix, which takes advantage of its symmetry. The procedure involved here avoids the inversion of matrixA to apply Ito's differential lemma. Therefore, the presented numerical implementation reduces the computational effort required in the formulation and solution of the moment equations. Moreover, other robust and efficient numerical deterministic integration schemes can be equally applied to the solution of the moment equations. 相似文献
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Development of the instantaneous unit hydrograph using stochastic differential equations 总被引：1，自引：0，他引：1
Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement. 相似文献
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Two stochastic models are developed to describe the BOD output (i.e. effluent) variation of facultative aerated lagoons in series. One of the models uses the uncertainty analysis (UA) technique and the other is based on the moment equation solution methodology of stochastic differential equations (SDE's). The former considers a second-order approximation of the expectation (SOAE) and a first-order approximation of the variance (FOAV). The SDE model considers that output variability is accounted for by random variations in the rate coefficient. Comparisons are provided. Calibration and verification of the two models are aciieved by using field observations from two different lagoon systems in series. The predictive performances of the two models are compared with each other and with another SDE model, presented in a previous paper, that considers input randomness. The three methods show similar predictive performances and provide good predictions of the mean and standard deviation of the lagoon effluent BOD concentrations and thus are considered as appropriate methodologies. 相似文献
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A non-Gaussian closure scheme based on the Edgeworth expansion of the probability density function is used to study the response of a hysteretic structure under random parametric excitation. The system considered consists of a weightless mass supporting a concentrated mass and it is subjected to the vertical and horizontal components of the ground acceleration modeled as nonstationary Gaussian white noise processes. The material of the structure exhibits bilinear hysteretic behaviour. The equation governing the motion of the system is transformed into an Itô stochastic differential equation. A set of ordinary differential equations governing the response statistics are obtained. These form an infinite hierarchy of equations which must be truncated in order to solve for moments of any order. The Edgeworth expansion of the joint density is used to truncate this infinite hierarchy. Such a closure scheme appears desirable since for hysteretic systems an explicit expression of the probability density is required. A frequently used closure scheme based on Gaussian assumption underestimates the response. The non-Gaussian density can be used in reliability studies. 相似文献
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Jens R?der Raimon Tolosana-Delgado Fred A. Hamprecht 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(7):865-879
The aim of this paper is to compare four different methods for binary classification with an underlying Gaussian process with
respect to theoretical consistency and practical performance. Two of the inference schemes, namely classical indicator kriging
and simplicial indicator kriging, are analytically tractable and fast. However, these methods rely on simplifying assumptions
which are inappropriate for categorical class labels. A consistent and previously described model extension involves a doubly
stochastic process. There, the unknown posterior class probability f(·) is considered a realization of a spatially correlated Gaussian process that has been squashed to the unit interval, and
a label at position x is considered an independent Bernoulli realization with success parameter f(x). Unfortunately, inference for this model is not known to be analytically tractable. In this paper, we propose two new computational
schemes for the inference in this doubly stochastic model, namely the “Aitchison Maximum Posterior” and the “Doubly Stochastic
Gaussian Quadrature”. Both methods are analytical up to a final step where optimization or integration must be carried out
numerically. For the comparison of practical performance, the methods are applied to storm forecasts for the Spanish coast
based on wave heights in the Mediterranean Sea. While the error rate of the doubly stochastic models is slightly lower, their
computational cost is much higher. 相似文献
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平稳随机地震地面运动过程模型及其统计特征 总被引：8，自引：3，他引：5
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。 相似文献
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结构平稳随机地震反应时域分析:方法 总被引：3，自引：3，他引：3
给出了三种常用的随机地震地面运动过程模型,即理想白噪声模型、金井清模型、改进金井清模型的相关函数表达式.引入状态向量,在状态空间中建立地震地面运动激励下的结构振动方程,并求解出结构的复模态特性和复模态反应.利用复模态叠加法推导出线性时不变多自由度体系在这三种随机地震动激励下的平稳协方差反应的解析式,可在时域内直接计算结构随机反应的统计特征.该方法物理概念清晰,结论简便明确,可作为实际工程结构平稳随机地震反应的实用分析方法. 相似文献
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William Barham 《地球物理与天体物理流体动力学》2019,113(5-6):505-526
ABSTRACTA system of stochastic differential equations is formulated describing the heat and salt content of a two-box ocean. Variability in the heat and salt content and in the thermohaline circulation between the boxes is driven by fast Gaussian atmospheric forcing and by ocean-intrinsic, eddy-driven variability. The eddy forcing of the slow dynamics takes the form of a colored, non-Gaussian noise. The qualitative effects of this non-Gaussianity are investigated by comparing to two approximate models: one that includes only the mean eddy effects (the “averaged model”), and one that includes an additional Gaussian white-noise approximation of the eddy effects (the “Gaussian model”). Both of these approximate models are derived using the methods of fast averaging and homogenisation. In the parameter regime where the dynamics has a single stable equilibrium the averaged model has too little variability. The Gaussian model has accurate second-order statistics, but incorrect skew and rare-event probabilities. In the parameter regime where the dynamics has two stable equilibria the eddy noise is much smaller than the atmospheric noise. The averaged, Gaussian, and non-Gaussian models all have similar stationary distributions, but the jump rates between equilibria are too small for the averaged and Gaussian models. 相似文献
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N. D. Mtundu R. W. Koch 《Stochastic Environmental Research and Risk Assessment (SERRA)》1987,1(2):101-116
The dynamics of water within the unsaturated root zone of the soil are represented by a pair of stochastic differential equations (SDE's), one representing the so-called surplus state of the moisture and the other the deficit condition. The inputs to the model are the climatically controlled random infiltration events and evapotranspiration which are modeled as a compound Poisson process and a Wiener (Brownian motion) process, respectively.The solutions to these SDE's are not in close-form but sample functions are obtained by numerical integration. The moment properties of the soil moisture evolution process have also been derived analytically including the mean, variance, covariance and autocorrelation functions.To illustrate the model, climatic parameters representing the surplus and deficit cases and properties of clay loam soil have been used to numerically derived the corresponding sample functions. With proper selection of all the parameters, physically realistic sample trajectories can be obtained for the model. 相似文献
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R. Willis B. A. Finney M. McKee A. Militello 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(2):71-84
A new methodology is presented for the solution of the stochastic hydraulic equations characterizing steady, one-dimensional estuarine flow. The methodology is predicated on quasi-linearization, perturbation methods, and the finite difference approximation of the stochastic differential operators. Assuming Manning's roughness coefficient is the principal source of uncertainty in the model, stochastic equations are presented for the water depths and flow rates in the estuarine system. Moment equations are developed for the mean and variance of the water depths. The moment equations are compared with the results of Monte Carlo simulation experiments. The results confirm that for any spatial location in the estuary that (1) as the uncertainty in the channel roughness increases, the uncertainty in mean depth increases, and (2) the predicted mean depth will decrease with increasing uncertainty in Manning'sn. The quasi-analytical approach requires significantly less computer time than Monte Carlo simulations and provides explicit 相似文献
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Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. 相似文献
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滞变—摩擦基底隔震系统的随机地震反应分析 总被引：4，自引：0，他引：4
本建立了滞变－摩擦基底隔震系统在地震作用下的运动微分方程，并将地震地面运动模拟成均值为零的两次过滤Ｇａｕｓｓ白噪声过程。使用等效线性化方法求解了这种隔震系统的地震反应统计特征，并分析了这种隔震系统参数的变化对其反应统计特征的影响。 相似文献
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Based on the long period surface wave data recorded by the China Digital Seismograph Network (CDSN), theQ
R
of fundamental mode Rayleigh wave with periods from 10 s to 146 s is determined for the eastern Sino-Korean paraplatform
in this paper. TheQ
β
models of the crust and upper mantle are respectively obtained for the 4 paths, with the aid of stochastic inverse method.
It shows that in the eastern Sino-Korean paraplatform, the average crustalQ
β
is about 200, and that there exists a weak attenuation layer in the middle crust (about 10–20 km deep) which is possibly
related to earthquake-prone layer. A strong attenuation layer (lowQ) of 70 km thick extensively exists in the uppermost mantle, with the buried depth about 80 km. The averageQ
R
of fundamental mode Rayleigh wave is between the value of stable tectonic region and that of active tectonic region, and
much close to the latter.
Contribution No. 96A0001, Institute of Geophysics, SSB, China.
Funded by the Chinese Joint Seismological Science Foundation. 相似文献
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M. D. Ruiz-Medina J. M. Angulo R. Fernández-Pascual 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(3):273-281
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. 相似文献