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1.
F.-C. Wu C.-K. Wang 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(6):359-375
Higher-order approximation techniques for estimating stochastic parameter of the non-homogeneous Poisson (NHP) model are
presented. The NHP model is characterized by a two-parameter cumulative probability distribution function (CDF) of sediment
displacement. Those two parameters are the temporal and spatial intensity functions, physically representing the inverse of
the average rest period and step length of sediment particles, respectively. Difficulty of estimating the parameters has,
however, restricted the applications of the NHP model. The approximation techniques are proposed to address such problem.
The basic idea of the method is to approximate a model involving stochastic parameters by Taylor series expansion. The expansion
preserves certain higher-order terms of interest. Using the experimental (laboratory or field) data, one can determine the
model parameters through a system of equations that are simplified by the approximation technique. The parameters so determined
are used to predict the cumulative distribution of sediment displacement. The second-order approximation leads to a significant
reduction of the CDF error (of the order of 47%) compared to the first-order approximation. Error analysis is performed to
evaluate the accuracy of the first- and second-order approximations with respect to the experimental data. The higher-order
approximations provide better estimations of the sediment transport and deposition that are critical factors for such environment
as spawning gravel-bed. 相似文献
2.
L. Klimeš 《Studia Geophysica et Geodaetica》2006,50(3):417-430
Explicit equations for the spatial derivatives and perturbation derivatives of amplitude in both isotropic and anisotropic
media are derived. The spatial and perturbation derivatives of the logarithm of amplitude can be calculated by numerical quadratures
along the rays.
The spatial derivatives of amplitude may be useful in calculating the higher-order terms in the ray series, in calculating
the higher-order amplitude coefficients of Gaussian beams, in estimating the accuracy of zero-order approximations of both
the ray method and Gaussian beams, in estimating the accuracy of the paraxial approximation of individual Gaussian beams,
or in estimating the accuracy of the asymptotic summation of paraxial Gaussian beams. The perturbation derivatives of amplitude
may be useful in perturbation expansions from elastic to viscoelastic media and in estimating the accuracy of the common-ray
approximations of the amplitude in the coupling ray theory. 相似文献
3.
The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function (CDF) of the performance variable. The failure probability is obtained as the value of the complement CDF at a specif ied threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function (CGF) of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and effi ciency of the proposed methodology. 相似文献
4.
The common-reflection-surface (CRS) stack can be viewed as a physically justified extension of the classical common-midpoint (CMP) stack, utilizing redundant information not only in a single, but in several neighboring CMP gathers. The zero-offset CRS moveout is parameterized in terms of kinematic attributes, which utilize reciprocity and raypath symmetries to describe the two-way process of the actual wave propagation in active seismic experiments by the propagation of auxiliary one-way wavefronts. For the diffraction case, only the attributes of a single one-way wavefront, originating from the diffractor are sufficient to explain the traveltime differences observed at the surface. While paraxial ray theory gives rise to a second-order approximation of the CRS traveltime, many higher-order approximations were subsequently introduced either by squaring the second-order expression or by employing principles of optics and geometry. It was recently discovered that all of these higher-order operators can be formulated either for the optical projection or in an auxiliary medium of a constant effective velocity. Utilizing this duality and the one-way nature of the CRS parameters, we present a simple data-driven stacking scheme that allows for the estimation of the a priori unknown excitation time of a passive seismic source. In addition, we demonstrate with a simple data example that the output of the suggested workflow can directly be used for subsequent focusing-based normal-incidence-point (NIP) tomography, leading to a reliable localization in depth. 相似文献
5.
The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies
the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation
from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies.
It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied.
The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation.
We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray)
approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic
common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order
perturbations of travel time. 相似文献
6.
《Advances in water resources》2005,28(10):1032-1039
An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. 相似文献
7.
Response uncertainty evaluation and dynamic reliability analysis corresponding to classical stochastic dynamic analysis are usually restricted to the uncertainties of the excitation. The inclusion of the parameter uncertainties contained in structural properties and excitation characteristics has become an increasingly important problem in many areas of dynamics. In the present paper, a point estimate procedure is proposed for the evaluation of stochastic response uncertainty, and a response surface approach procedure in standard normal space is proposed for analysis of time-variant reliability analysis for hysteretic MDF structures having parameter uncertainties. Using the proposed procedures, the response uncertainties and time-variant reliability can be easily obtained by several repetitions of stochastic response analysis under given parameters without conducting sensitivity analysis, which is considered to be one of the primary difficulties associated with conventional methods. In the time-variant reliability analysis, the failure probability can be readily obtained by improving the accuracy of the first-order reliability method using the empirical second-order reliability index. The random variables are divided into two groups, those with CDF and those without CDF. The latter are included via the high-order moment standardization technique. A numerical example of a 15F hysteretic MDF structure that takes into account uncertainties of four structural parameters and three excitation characteristics is performed, based on which the proposed procedures are investigated and the effects of parameter uncertainties are discussed. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
8.
G. Christakos C. T. Miller D. Oliver 《Stochastic Environmental Research and Risk Assessment (SERRA)》1993,7(3):213-239
As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations. 相似文献
9.
In this paper sediment yield data, measured from 1978 to 1994 in two small Calabrian basins (W2 and W3) reafforested with eucalyptus trees (Eucalyptus occidentalis Engl.), and the Modified Universal Soil Loss Equation (MUSLE) applied in a distributed form are used to evaluate the anti-erosive effects of eucalyptus cover. At first step the sediment yield measurements observed in W2 basin are used to estimate a single cover management factor representative of the eucalyptus coppice and equal to the median value (0·164) of the cover management factor values calculated for each runoff event. Then, the reliability of the selected representative cover management factor is verified on W3 by comparing the cumulative distribution function (CDF) of the measured sediment yield with the CDF of the calculated one. Finally, the temporal analysis of the crop and management factor is developed searching, at monthly and annual scale, the correlation between crop anti-erosive effectiveness and rainfall erosivity index. © 1998 John Wiley & Sons, Ltd. 相似文献
10.
P. C. D. Milly 《Surveys in Geophysics》1991,12(1-3):145-154
Most combination equations for evaporation rely on a linear expansion of the saturation vapor-pressure curve around the air temperature. Because the temperature at the surface may differ from this temperature by several degrees, and because the saturation vapor-pressure curve is nonlinear, this approximation leads to a certain degree of error in those evaporation equations. It is possible, however, to introduce higher-order polynomial approximations for the saturation vapor-pressure curve and to derive a family of explicit equations for evaporation, having any desired degree of accuracy. Under the linear approximation, the new family of equations for evaporation reduces, in particular cases, to the combination equations of H. L. Penman (Natural evaporation from open water, bare soil and grass,Proc. R. Soc. London, Ser. A
193, 120–145, 1948) and of subsequent workers. Comparison of the linear and quadratic approximations leads to a simple approximate expression for the error associated with the linear case. Equations based on the conventional linear approximation consistently underestimate evaporation, sometimes by a substantial amount. 相似文献
11.
The common ray approximation considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common ray approximation.We derive the equations for estimating the travel-time errors due to the isotropic and anisotropic common ray approximations of the coupling ray theory. These equations represent the main result of the paper. The derivation is based on the general equations for the second-order perturbations of travel time. The accuracy of the anisotropic common ray approximation can be studied along the isotropic common rays, without tracing the anisotropic common rays.The derived equations are numerically tested in three 1-D models of differing degree of anisotropy. The first-order and second-order perturbation expansions of travel time from the isotropic common rays to anisotropic-ray-theory rays are compared with the anisotropic-ray-theory travel times. The errors due to the isotropic common ray approximation and due to the anisotropic common ray approximation are estimated. In the numerical example, the errors of the anisotropic common ray approximation are considerably smaller than the errors of the isotropic common ray approximation.The effect of the isotropic common ray approximation on the coupling-ray-theory synthetic seismograms is demonstrated graphically. For comparison, the effects of the quasi-isotropic projection of the Green tensor, of the quasi-isotropic approximation of the Christoffel matrix, and of the quasi-isotropic perturbation of travel times on the coupling-ray-theory synthetic seismograms are also shown. The projection of the travel-time errors on the relative errors of the time-harmonic Green tensor is briefly presented. 相似文献
12.
《Advances in water resources》1998,22(4):319-332
The equation describing the ensemble-average solute concentration in a heterogeneous porous media can be developed from the Lagrangian (stochastic–convective) approach and from a method that uses a renormalized cumulant expansion. These two approaches are compared for the case of steady flow, and it is shown that they are related. The cumulant expansion approach can be interpreted as a series expansion of the convolution path integral that defines the ensemble-average concentration in the Lagrangian approach. The two methods can be used independently to develop the classical form for the convection–dispersion equation, and are shown to lead to identical transport equations under certain simplifying assumptions. In the development of such transport equations, the cumulant expansion does not require a priori the assumption of any particular distribution for the Lagrangian displacements or velocity field, and does not require one to approximate trajectories with their ensemble-average. In order to obtain a second-order equation, the cumulant expansion method does require truncation of a series, but this truncation is done rationally by the development of a constraint in terms of parameters of the transport field. This constraint is less demanding than requiring that the distribution for the Lagrangian displacements be strictly Gaussian, and it indicates under what velocity field conditions a second-order transport equation is a reasonable approximation. 相似文献
13.
Muhammad Umer Altaf Arnold W. Heemink Martin Verlaan Ibrahim Hoteit 《Ocean Dynamics》2011,61(8):1093-1105
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in
the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the
timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method,
simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses
objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference
method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration
parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the
algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce
these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed
proper orthogonal decomposition-based calibration method. The main findings are: (1) The SPSA method gives comparable results
to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used
to estimate large number of parameters. 相似文献
14.
In this paper, a stochastic approach for obtaining damage-based inelastic seismic spectra is proposed. The Park and Ang damage model, which includes displacement ductility and hysteretic energy, is adopted to take into account the cumulative damage phenomenon in structural systems under strong ground motions. Differently from previous studies in this field, damage-based seismic spectra are obtained by means of peak theory of stochastic processes. The following stochastic inelastic seismic spectra are constructed and then analyzed: damage-based displacement and acceleration inelastic spectra, damage-based response modification factor spectra, damage-based yield strength demand spectra and damage-based inelastic displacement ratio spectra. 相似文献
15.
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
16.
17.
1 INTRODUCTIONThe prediction of future impacts on terrestrial ecosystems by atmospheric, climatic and land-usechanges is the aim of watershed management. Meeting these requirements scientists, managers and policymakers try to achieve the sustainable management of the vitally important resources of watersheds due toan integrated ecosystem approach at the catchment scale. As composite landscapes often have a highdegree of contingency between its elements, the transport over these landscape s… 相似文献
18.
This paper outlines the application of a new data‐based mechanistic (DBM) modelling methodology to the characterization of the sediment transmission dynamics in a small upland reservoir, Wyresdale Park, Lancashire. The DBM modelling strategy exploits advanced statistical procedures to infer the dynamic model structure and its associated parameters directly from the instrumented data, producing a parametrically efficient, continuous time, transfer function model which relates suspended sediment load at the reservoir inflow to the outflow at the event scale. The associated differential equation model parameters have physical attributes which can be interpreted in terms of sediment transmission processes and associated reservoir trap efficiency. Sedigraph analysis suggests that wind‐induced resuspension episodically supplies an additional load to the reservoir outlet. The stochastic nature of the DBM model makes it ideal for evaluating the effects of uncertainty through Monte Carlo simulations (MCS) for discharge and sediment transmission. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
19.
对于用高阶偏微分方程进行地震偏移,本文提出一种分裂算法。有限差分法目前只能解波动方程的二阶和三阶的近似方程的偏移问题,更高阶的近似方程还没有一种有效的解法。利用高阶方程进行偏移会提高偏移的精度和效果。本文就是为了解决这个问题所进行的探索。 本文阐述了分裂算法的原理,并给出了应用该算法解决偏移问题的实例。 相似文献
20.
When using global navigation satellite systems (GNSSs) for high-precision measurements, one should consider high-order errors. The ionospheric second-order error caused by the geomagnetic field is approximately proportional to the total electron content. Therefore, this error can be taken into account by modifying the coefficients in an “ionosphere-free” combination of GNSS measurements at two frequencies. This study checks the approximations underlying this modification. We reveal that these approximations are valid and the results depend weakly on the accuracy of ionospheric parameters used a priori for calculating the coefficients of the modified two-frequency formula. In addition, we investigate how the choice of a model of the Earth’s magnetic field affects the second-order ionospheric error. 相似文献