共查询到20条相似文献，搜索用时 125 毫秒
1.
George Christakos 《Mathematical Geology》1985,17(5):489-515
Parameter estimation has become increasingly interesting the last few decades for a variety of engineering topics. In such situations, one may face problems like (a) how to estimate parameters for which erroneous measurements are available (direct estimation), or (b) how to estimate coefficients of some process model governing a geological phenomenon when these coefficients are inaccessible or difficult to access by direct investigation (inverse estimation or identification). Both these problems are examined in this presentation from a modern stochastic viewpoint, where parameters sought are interpretated mathematically as random functions, generated and estimated in space or time with the aid of recursive models. Advantages of this methodology are remarkable, from both theoretical and physical points of view, as compared to conventional statistics or nonrecursive estimators. Particularly it may offer more accurate estimators, better representation of spatial variation, and a means of overcoming difficulties such as excessive computational time or computer storage. To test effectiveness of this type of estimation, a series of representative case studies from geotechnical practice have been computed in detail. 相似文献
2.
When estimating the mean value of a variable, or the total amount of a resource, within a specified region it is desirable to report an estimated standard error for the resulting estimate. If the sample sites are selected according to a probability sampling design, it usually is possible to construct an appropriate design-based standard error estimate. One exception is systematic sampling for which no such standard error estimator exists. However, a slight modification of systematic sampling, termed 2-step tessellation stratified (2TS) sampling, does permit the estimation of design-based standard errors. This paper develops a design-based standard error estimator for 2TS sampling. It is shown that the Taylor series approximation to the variance of the sample mean under 2TS sampling may be expressed in terms of either a deterministic variogram or a deterministic covariance function. Variance estimation then can be approached through the estimation of a variogram or a covariance function. The resulting standard error estimators are compared to some more traditional variance estimators through a simulation study. The simulation results show that estimators based on the new approach may perform better than traditional variance estimators. 相似文献
3.
We consider numerical identification of the piecewise constant permeability function in a nonlinear parabolic equation, with the augmented Lagrangian method. By studying this problem, we aim at also gaining some insight into the potential ability of the augmented Lagrangian method to handle permeability estimation within the full two-phase porous-media flow setting. The identification is formulated as a constrained minimization problem. The parameter estimation problem is reduced to a coupled nonlinear algebraic system, which can be solved efficiently with the conjugate gradient method. The methodology is developed and numerical experiments with the proposed method are presented. 相似文献
4.
Normal and lognormal estimation 总被引：3，自引：0，他引：3
Jean-Michel M. Rendu 《Mathematical Geology》1979,11(4):407-422
A comprehensive theoretical study of the problem of estimation of regionalized variables with normal or lognormal distribution is presented. Unbiased linear estimators are derived, under both assumptions that the population mean is known and unknown, and their error variance is calculated. The minimum variance kriging estimators are studied in more detail and are compared with the conditional expectations. The emphasis is on the study of lognormally distributed variates. The derived mathematical formulas are applicable to the optimal contouring of sample values with the appropriate distribution, as well as the optimal estimation of blocks of ore in mineral deposits. 相似文献
5.
Disjunctive kriging, universal kriging, or no kriging: Small sample results with simulated fields 总被引：3，自引：0，他引：3
This paper provides a comparison between linear (universal) and nonlinear (disjunctive) kriging estimators when they are computed from small samples chosen randomly on simulated stationary and nonstationary fields. Point estimation results are reported. In all cases considered, kriging estimators were found better than a local mean estimator, with universal kriging either better than or as good as disjunctive kriging. The latter, which is suited to handle stationary fields, did not provide more accurate estimates because the use of small samples led to inconsistencies in the assumed bivariate model. Universal kriging was particularly better with nonstationary fields. 相似文献
6.
Muhammad Nauman Malik Mehdi Murtuza Iqbal Asif Bakar Muhammad Saifullah Abu Brahim Aissa Dk Nur Afiqah Jalwati Puteri Amer Farhan Rafique 《地下水科学与工程》2014,7(4):373-382
In many circumstances involving heat and mass transfer issues, it is considered impractical to measure the input flux and the resulting state distribution in the domain. Therefore, the need to develop techniques to provide solutions for such problems and estimate the inverse mass flux becomes imperative. Adaptive state estimator (ASE) is increasingly becoming a popular inverse estimation technique which resolves inverse problems by incorporating the semi-Markovian concept into a Bayesian estimation technique, thereby developing an inverse input and state estimator consisting of a bank of parallel adaptively weighted Kalman filters. The ASE is particularly designed for a system that encompasses independent unknowns and /or random switching of input and measurement biases. The present study describes the scheme to estimate the groundwater input contaminant flux and its transient distribution in a conjectural two-dimensional aquifer by means of ASE, which in particular is because of its unique ability to efficiently handle the process noise giving an estimation of keeping the relative error range within 10% in 2-dimensional problems. Numerical simulation results show that the proposed estimator presents decent estimation performance for both smoothly and abruptly varying input flux scenarios. Results also show that ASE enjoys a better estimation performance than its competitor, Recursive Least Square Estimator (RLSE) due to its larger error tolerance in greater process noise regimes. ASE’s inherent deficiency of being slower than the RLSE, resulting from the complexity of algorithm, was also noticed. The chosen input scenarios are tested to calculate the effect of input area and both estimators show improved results with an increase in input flux area especially as sensors are moved closer to the assumed input location. 相似文献
7.
Muhammad Malik Nauman Murtuza Mehdi Asif Iqbal Muhammad Saifullah Abu Bakar Brahim Aissa Dk Nur Afiqah Jalwati Puteri Amer Farhan Rafique 《地下水科学与工程》2019,(4):373-382
In many circumstances involving heat and mass transfer issues,it is considered impractical to measure the input flux and the resulting state distribution in the domain.Therefore,the need to develop techniques to provide solutions for such problems and estimate the inverse mass flux becomes imperative.Adaptive state estimator(ASE)is increasingly becoming a popular inverse estimation technique which resolves inverse problems by incorporating the semi-Markovian concept into a Bayesian estimation technique,thereby developing an inverse input and state estimator consisting of a bank of parallel adaptively weighted Kalman filters.The ASE is particularly designed for a system that encompasses independent unknowns and/or random switching of input and measurement biases.The present study describes the scheme to estimate the groundwater input contaminant flux and its transient distribution in a conjectural two-dimensional aquifer by means of ASE,which in particular is because of its unique ability to efficiently handle the process noise giving an estimation of keeping the relative error range within 10%in 2-dimensional problems.Numerical simulation results show that the proposed estimator presents decent estimation performance for both smoothly and abruptly varying input flux scenarios.Results also show that ASE enjoys a better estimation performance than its competitor,Recursive Least Square Estimator(RLSE)due to its larger error tolerance in greater process noise regimes.ASE's inherent deficiency of being slower than the RLSE,resulting from the complexity of algorithm,was also noticed.The chosen input scenarios are tested to calculate the effect of input area and both estimators show improved results with an increase in input flux area especially as sensors are moved closer to the assumed input location. 相似文献
8.
J.-J. Song 《Rock Mechanics and Rock Engineering》2006,39(2):131-146
Summary. Mauldon (1998) suggested end-point estimators of areal frequency and mean trace length for a planar sampling window which
were recently proved to be unbiased maximum likelihood estimators by Lyman (2003). The present paper is to expand the concept
and applicability of the end-point estimators to those for a general non-planar sampling window. The generalized end-point
estimators are verified and its applicability for variable discontinuity orientation is checked by Monte Carlo simulation.
Standard deviation of estimation error and estimation efficiency of areal frequency and mean trace length are also considered. 相似文献
9.
Highly Robust Variogram Estimation 总被引：5，自引：0，他引：5
Marc G. Genton 《Mathematical Geology》1998,30(2):213-221
The classical variogram estimator proposed by Matheron is not robust against outliers in the data, nor is it enough to make simple modifications such as the ones proposed by Cressie and Hawkins in order to achieve robustness. This paper proposes and studies a variogram estimator based on a highly robust estimator of scale. The robustness properties of these three estimators are analyzed and compared. Simulations with various amounts of outliers in the data are carried out. The results show that the highly robust variogram estimator improves the estimation significantly. 相似文献
10.
Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties
such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task.
Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to
overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable
before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference
have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering.
In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of
them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most
common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal
densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational
cost significantly, using only the time needed to obtain a sample of the posterior probability density function. The use of
the information theory principles for the experimental design and for the ill-posedness diagnosis is also introduced. Finally,
a case study based on a highly instrumented well test found in the literature is presented. The results obtained are compared
with the ones computed by the maximum likelihood estimation approach. 相似文献
11.
In this paper, a Bayesian framework is introduced for pattern modeling and multiple point statistics simulation. The method presented here is a generalized clustering-based method where the patterns can live on a hyper-plane of very low dimensionality in each cluster. The provided generalizationallows a remarkable increase in variability of the model and a significant reduction in the number of necessary clusters for pattern modeling which leads to more computational efficiency compared with clustering-based methods. The Bayesian model employed here is a nonlinear model which is composed of a mixture of linear models. Therefore, the model is stronger than linear models for data modeling and computationally more effective than nonlinear models. Furthermore, the model allows us to extract features from incomplete patterns and to compare patterns in feature space instead of spatial domain. Due to the lower dimensionality of feature space, comparison in feature space results in more computational efficiency as well. Despite most of the previously employed methods, the feature extraction filters employed here are customized for each training image (TI). This causes the features to be more informative and useful. Using a fully Bayesian model, the method does not require extensive parameter setting and tunes its parameters itself in a principled manner. Extensive experiments on different TIs (either continuous or categorical) show that the proposed method is capable of better reproduction of complex geostatistical patterns compared with other clustering-based methods using a very limited number of clusters. 相似文献
12.
Kingshuk Roy Choudhury 《Mathematical Geosciences》2009,41(5):535-553
Finite strain estimation is a widely used technique for the study of rock deformation in structural geology. One particular
algorithm proposed by Shimamoto and Ikeda uses the ‘average shape matrix’ of deformed markers. This paper provides a detailed
error analysis for resulting strain estimates in two dimensions. When the number of markers exceeds 100, estimators of components
of the strain tensor are shown to have an approximately Gaussian distribution with variances that increase with their mean.
Equal variance estimators are obtained by applying a log transform for the elongation and an arcsin transformation for the
orientation estimates. Confidence interval formulae for strain tensor components are proposed. Lithology specific constants
arising in these formulae are estimated from undeformed samples. The results are validated by application to simulated data
as well as observational data from thin sections of sandstone sampled from SE Ireland. 相似文献
13.
This study compares kriging and maximum entropy estimators for spatial estimation and monitoring network design. For second-order
stationary random fields (a subset of Gaussian fields) the estimators and their associated interpolation error variances are
identical. Simple lognormal kriging differs from the lognormal maximum entropy estimator, however, in both mathematical formulation
and estimation error variances. Two numerical examples are described that compare the two estimators. Simple lognormal kriging
yields systematically higher estimates and smoother interpolation surfaces compared to those produced by the lognormal maximum
entropy estimator. The second empirical comparison applies kriging and entropy-based models to the problem of optimizing groundwater
monitoring network design, using six alternative objective functions. The maximum entropy-based sampling design approach is
shown to be the more computationally efficient of the two. 相似文献
14.
Zekai Sen 《Mathematical Geology》1989,21(8):891-903
The cumulative semivariogram approach is proposed for modeling regionalized variables in the geological sciences. This semivariogram is defined as the successive summation of half-squared differences which are ranked according to the ascending order of distances extracted from all possible pairs of sample locations within a region. This procedure is useful especially when sampling points are irregularly distributed within the study area. Cumulative semivariograms possess all of the objective properties of classical semivariograms. Classical semivariogram models are evaluated on the basis of the cumulative semivariogram methodology. Model parameter estimation procedures are simplified with the use of arithmetic, semilogarithmic, or double-logarithmic papers. Plots of cumulative semivariogram values vs. corresponding distances may scatter along a straight line on one of these papers, which facilitates model identification as well as parameter estimation. Straight lines are fitted to the cumulative semivariogram scatter diagram by classical linear regression analysis. Finally, applications of the methodology are presented for some groundwater data recorded in the sedimentary basins of the Kingdom of Saudi Arabia. 相似文献
15.
A conceptual framework for quantitative estimation of physical vulnerability to landslides 总被引：5，自引：0，他引：5
The paper illustrates a method for scenario-based, quantitative estimation of physical vulnerability of the built environment to landslides. The rationale and main features of the procedure are presented in the context of quantitative risk estimation. Vulnerability is defined quantitatively as a function of landslide intensity and the susceptibility of vulnerable elements. Reference terminology is presented and discussed. Models for the quantification of intensity and susceptibility for some categories of elements at risk such as structures and persons are proposed. An example application is illustrated. 相似文献
16.
W. E. Bardsley 《Mathematical Geology》1988,20(5):513-528
Engineering and scientific approaches to design magnitude estimation are briefly revisited. Some defense is offered for use of annual maxima in design as if they were variables from a common distribution. However, to assume any particular form of distribution tail beyond the largest data value is not justifiable, regardless of the degree of data support over the main body of the distribution. An alternative approach to the design problem is suggested through use of parameter-free nonparametric estimation using the kernel method. Some simulation results are presented which suggest that the parameter-free approach is worthy of further development. A particular advantage of nonparametric methods is that competing estimators can be checked against parametric distributions, leading to a progressive improvement in estimator accuracy.This paper was presented (by title) at Engineering Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987. 相似文献
17.
At various stages of petroleum reservoir development, we encounter a large degree of geological uncertainty under which a rational decision has to be made. In order to identify which parameter or group of parameters significantly affects the output of a decision model, we investigate decision-theoretic sensitivity analysis and its computational issues in this paper. In particular, we employ the so-called expected value of partial perfect information (EVPPI) as a sensitivity index and apply multilevel Monte Carlo (MLMC) methods to efficient estimation of EVPPI. In a recent paper by Giles and Goda, an antithetic MLMC estimator for EVPPI is proposed and its variance analysis is conducted under some assumptions on a decision model. In this paper, for an improvement on the performance of the MLMC estimator, we incorporate randomized quasi-Monte Carlo methods within the inner sampling, which results in an multilevel quasi-Monte Carlo (MLQMC) estimator. We apply both the antithetic MLMC and MLQMC estimators to a simple waterflooding decision problem under uncertainty on absolute permeability and relative permeability curves. Through numerical experiments, we compare the performances of the MLMC and MLQMC estimators and confirm a significant advantage of the MLQMC estimator. 相似文献
18.
Simultaneous parameter identification of a heterogeneous aquifer system using artificial neural networks 总被引：2，自引：1，他引：1
An artificial neural network (ANN) model is proposed for the simultaneous determination of transmissivity and storativity
distributions of a heterogeneous aquifer system. ANNs may be useful tools for parameter identification problems due to their
ability to solve complex nonlinear problems. As an extension of previous study—Karahan H, Ayvaz MT (2006) Forecasting aquifer
parameters using artificial neural networks, J Porous Media 9(5):429–444—the performance of the proposed ANN model is tested
on a two-dimensional hypothetical aquifer system for transient flow conditions. In the proposed ANN model, Cartesian coordinates
of observation wells, associated piezometric heads and observation time are used as inputs while corresponding transmissivity
and storativity values are used as outputs. The training, validation and testing processes of the ANN model are performed
under two scenarios. In scenario 1, all the sampled data are used through the simulation time. However, in the scenario 2,
there are data gaps due to irregular observations. By using the determined synaptic network weights, transmissivity and storativity
distributions are predicted. In addition, the performance of the proposed ANN is tested for different noise data conditions.
Results showed that the developed ANN model may be used in simultaneous aquifer parameter estimation problems. 相似文献
19.
Zekâi Sen 《Mathematical Geology》1992,24(4):417-435
The standard cumulative semivariograms (SCS), obtained analytically from the currently employed stationary stochastic processes, provide a basis for the model identification and its parameter as well as regional correlation estimations. The analytical solutions for different stationary stochastic processes such as independent (IP), moving average (MA), autoregressive (AR), and autoregressive integrated moving average ARIMA (1,0,1) processes give rise to different types of SCSs which can be expressed in terms of the autocorrelation structure parameters only. The SCSs of independent and MA processes appear as linear trends whereas other type of processes have SCSs which are nonlinear for short distances but become linear at large distances. Irrespective of the stationary stochastic process type the linear portions of SCSs have unit slopes. The vertical distance between these linear portions and that of the IP cumulative semivariogram (CS), provide an indicator for measuring the regional correlation. In the case of stationary processes, the straight line portions of any CS are parallel to each other. Hence, it is possible to identify the model from the sample CS. Finally, necessary procedures are provided for the model parameters estimation. The methodology developed, herein, is applied to some hydrochemical ions in the groundwater of the Wasia aquifer in central part of Kingdom of Saudi Arabia. 相似文献
20.
The continuous ranked probability score (CRPS) is a much used measure of performance for probabilistic forecasts of a scalar observation. It is a quadratic measure of the difference between the forecast cumulative distribution function (CDF) and the empirical CDF of the observation. Analytic formulations of the CRPS can be derived for most classical parametric distributions, and be used to assess the efficiency of different CRPS estimators. When the true forecast CDF is not fully known, but represented as an ensemble of values, the CRPS is estimated with some error. Thus, using the CRPS to compare parametric probabilistic forecasts with ensemble forecasts may be misleading due to the unknown error of the estimated CRPS for the ensemble. With simulated data, the impact of the type of the verified ensemble (a random sample or a set of quantiles) on the CRPS estimation is studied. Based on these simulations, recommendations are issued to choose the most accurate CRPS estimator according to the type of ensemble. The interest of these recommendations is illustrated with real ensemble weather forecasts. Also, relationships between several estimators of the CRPS are demonstrated and used to explain the differences of accuracy between the estimators. 相似文献