共查询到20条相似文献，搜索用时 421 毫秒
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集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)作为一种有效的数据同化方法,在众多数值实验中体现优势的同时,也暴露了它使用小集合估计协方差情况下精度较低的缺陷。为了降低取样噪声对协方差估计的干扰并提高滤波精度,应用局域化函数对小集合估计的协方差进行修正,即在协方差矩阵中以舒尔积的形式增加空间距离权重以限制远距离相关。在一个二维理想孔隙承压含水层模型中的运行结果表明,局域化对集合卡尔曼滤波估计地下水参数的修正十分有效,局域化可以很好地过滤小集合估计中噪声的影响,节省计算量的同时又可以防止滤波发散。相关长度较小的水文地质参数(如对数渗透系数)更容易受到噪声的干扰,更有必要进行局域化修正。 相似文献
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地学自由曲面径向基函数网络重建的详细算法 总被引：3，自引：0，他引：3
径向基函数(RadialBasisFunction,简称RBF)神经网络是一种理想的地学离散数据网格化工具,能够适应各种不同分布形式和边界条件的数据,收敛速度较快,可以逼近任何复杂曲面。这里详细介绍了RBF神经网络的算法。适当径向基函数的形式和偏差系数是使用RBF神经网络作地学曲面重建的关键。大量的实际数据验证结果表明,当选用Gauss型径向基函数时,一般可获得比较理想的网格化效果,同时具备"曲面平滑"和"拟合度高"的特点。 相似文献
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SOM-RBF神经网络模型在地下水位预测中的应用 总被引：1，自引：0，他引：1
利用自组织映射(SOM)聚类模型优化径向基函数神经网络(RBFN)隐层节点的方法,减小了RBFN由于自身结构问题在地下水水位预测中产生的误差。采用SOM对已有样本进行聚类,利用聚类后的二维分布图确定隐层节点的数目,并根据聚类结果计算径向基函数的宽度,确定径向基函数的中心,由此建立SOM-RBFN模型。以吉林市丰满区二道乡为例,采用2000—2009年观测的地下水位动态资料,利用SOM-RBFN模型对地下水位进行预测,验证其准确性,并分别以5、7、10a的地下水位动态数据为研究样本建立模型,考查样本数量对预测结果的影响。研究结果表明:SOM-RBFN模型预测地下水水位过程中,均方根误差(RMSE)的均值为0.43,有效系数(CE)的均值为0.52,均达到较高标准,因此SOM-RBFN模型可以作为有效而准确的地下水水位预测方法;同时RBF7的RMSE和CE均值分别为0.38和0.68,结果优于RBF5和RBF10,这就意味着在模型计算中样本数量不会直接影响预测结果的精度。 相似文献
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从热力学定律出发,利用自由能函数和耗散函数,通过严格的理论推导得到屈服函数、流动法则和硬化规律。在临界状态模型的框架内,将基于热力学基础的各向异性模型和特定的旋转硬化规律结合起来,提出了一种新的处理方法用来模拟密砂在三轴试验中的变形曲线。给定多组模型参数,计算排水和不排水三轴试验,并简单讨论了模型参数对曲线规律的影响,结果表明这种方法是有效的。通过屈服面在变形不同阶段采用不同的旋转方向,能够考虑密砂的复杂试验曲线特征,又由模型的热力学基础保证了屈服面和剪胀函数的协调。这种方法确定的模型结构严密,适应性强,可以描述大范围土体的特性,且简单易于使用。 相似文献
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朱永盛 《物探化探计算技术》1981,(2)
一、前言趋势分析是利用数理统计的方法和电子计算机研究化探分析数据在空间上的变化规律,即把样品中元素含量看成空间坐标的函数,用一定的数学公式计算出的数学面,来逼近观测数据所反映的面,这个数学面称为趋势面。对于一组化探分析数据所计算出的趋势值,可分解为趋势部分(反映区域性变化规律)和残差部分(反映局部范围的异常)以及随机因素所造成的偏倚,去掉随机因素的影响,更好地总 相似文献
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介绍了径向基函数神经网络的原理、训练算法,建立的径向基函数神经网络城市需水量预测模型具有较强的非线性处理能力和逼近能力,运算速度快、性能稳定,克服了BP神经网络学习过程的收敛过分依赖于初值和可能出现局部收敛的缺陷,预测精度较高,泛化能力强。 相似文献
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扩展有限元法是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法,其原理是在裂尖附近用一些奇异函数和沿裂纹面用阶跃函数加强传统有限元的基,以考虑跨过裂纹的位移场的不连续,该加强策略允许计算网格独立于不连续体几何。讨论了扩展有限元法的一些数值方面,主要包括：水平集法确定界面和加强节点与加强方式、裂尖加强范围的选择、J积分区域的确定和积分方案等。 相似文献
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本文介绍了前人对W(u)的几个数值逼近式,并提出了笔者对W(u)的契比晓夫及帕第逼近结果。众所周知,泰斯井函数W(u)的积分表达式为 相似文献
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资源量分类中勘查工程间距的确定方法研究 总被引：1，自引：0，他引：1
国内外的地质勘查规范中,对矿产资源量的分类(地质可靠程度)均有标准的定义,但没有确定资源量分类工程间距的定量方法,导致矿产勘查工作经常出现质量隐患。本文用变异函数模型统计学方法探讨这一问题。变异函数的变程反映了空间上区域化变量之间相关性的大小,当矿体样品品位服从正态分布时,正态分布函数位置参数μ等于样品平均品位,形状参数σ等于样品品位标准差,样品品位的方差等于变异函数的基台值;在拐点之间即区间(μ-σ,μ+σ],样品分布概率为0.6826,变异函数变程的0.6826倍(0.6826a)可作为划分控制资源量的分类工程间距;影响资源量分类可靠程度的主要因素是建立的理论变异函数模型的稳健性。 相似文献
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The majority of geostatistical estimation and simulation algorithms rely on a covariance model as the sole characteristic of the spatial distribution of the attribute under study. The limitation to a single covariance implicitly calls for a multivariate Gaussian model for either the attribute itself or for its normal scores transform. The Gaussian model could be justified on the basis that it is both analytically simple and it is a maximum entropy model, i.e., a model that minimizes unwarranted structural properties. As a consequence, the Gaussian model also maximizes spatial disorder (beyond the imposed covariance) which can cause flow simulation results performed on multiple stochastic images to be very similar; thus, the space of response uncertainty could be too narrow entailing a misleading sense of safety. The ability of the sole covariance to adequately describe spatial distributions for flow studies, and the assumption that maximum spatial disorder amounts to either no additional information or a safe prior hypothesis are questioned. This paper attempts to clarify the link between entropy and spatial disorder and to provide, through a detailed case study, an appreciation for the impact of entropy of prior random function models on the resulting response distributions. 相似文献
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The majority of geostatistical estimation and simulation algorithms rely on a covariance model as the sole characteristic of the spatial distribution of the attribute under study. The limitation to a single covariance implicitly calls for a multivariate Gaussian model for either the attribute itself or for its normal scores transform. The Gaussian model could be justified on the basis that it is both analytically simple and it is a maximum entropy model, i.e., a model that minimizes unwarranted structural properties. As a consequence, the Gaussian model also maximizes spatial disorder (beyond the imposed covariance) which can cause flow simulation results performed on multiple stochastic images to be very similar; thus, the space of response uncertainty could be too narrow entailing a misleading sense of safety. The ability of the sole covariance to adequately describe spatial distributions for flow studies, and the assumption that maximum spatial disorder amounts to either no additional information or a safe prior hypothesis are questioned. This paper attempts to clarify the link between entropy and spatial disorder and to provide, through a detailed case study, an appreciation for the impact of entropy of prior random function models on the resulting response distributions. 相似文献
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孙建国 《吉林大学学报(地球科学版)》2012,42(2):545-553
为了避开由大型代数方程组数值求解所带来的问题,将电场反射张量的基本概念和拟解析近似的基本思想引入到了直流电位场的数值模拟中,定义了体电位反射函数、面电荷反射函数和面电位反射函数等3个辅助函数,并给出了其在一般条件下的拟解析近似解和在简单条件下（均匀或点电流源背景场、均匀导电柱体或球体）的分析解。简单的对比分析证明：面电荷反射函数是异常体表面上自由面电荷密度的函数;在简单条件下,这种函数关系转化成为比例关系;类似的结论对于简单条件下的面电位反射函数也成立;然而,在一般条件下难以建立面电位反射函数和自由面电荷密度之间的明确关系。 相似文献
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This paper presents a consistent Bayesian solution for data integration and history matching for oil reservoirs while accounting for both model and parameter uncertainties. The developed method uses Gaussian Process Regression to build a permeability map conforming to collected data at well bores. Following that, an augmented Markov Chain Monte Carlo sampler is used to condition the permeability map to dynamic production data. The selected proposal distribution for the Markov Chain Monte Carlo conforms to the Gaussian process regression output. The augmented Markov Chain Monte Carlo sampler allows transition steps between different models of the covariance function, and hence both the parameter and model space are effectively explored. In contrast to single model Markov Chain Monte Carlo samplers, the proposed augmented Markov Chain Monte Carlo sampler eliminates the selection bias of certain covariance structures of the inferred permeability field. The proposed algorithm can be used to account for general model and parameter uncertainties. 相似文献
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On the Use of Non-Euclidean Distance Measures in Geostatistics 总被引：4，自引：0，他引：4
Frank C. Curriero 《Mathematical Geology》2006,38(8):907-926
In many scientific disciplines, straight line, Euclidean distances may not accurately describe proximity relationships among
spatial data. However, non-Euclidean distance measures must be used with caution in geostatistical applications. A simple
example is provided to demonstrate there are no guarantees that existing covariance and variogram functions remain valid (i.e.
positive definite or conditionally negative definite) when used with a non-Euclidean distance measure. There are certain distance
measures that when used with existing covariance and variogram functions remain valid, an issue that is explored. The concept
of isometric embedding is introduced and linked to the concepts of positive and conditionally negative definiteness to demonstrate
classes of valid norm dependent isotropic covariance and variogram functions, results many of which have yet to appear in
the mainstream geostatistical literature or application. These classes of functions extend the well known classes by adding
a parameter to define the distance norm. In practice, this distance parameter can be set a priori to represent, for example,
the Euclidean distance, or kept as a parameter to allow the data to choose the metric. A simulated application of the latter
is provided for demonstration. Simulation results are also presented comparing kriged predictions based on Euclidean distance
to those based on using a water metric. 相似文献
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The basic concepts of spectral and multiscale selective reconstruction of (geophysically relevant) vector fields on the sphere from error-affected data is outlined in detail. The reconstruction mechanism is formulated under the assumption that spectral as well as multiscale approximation is well-representable in terms of only a certain number of expansion coefficients at the various resolution levels. It is shown that spectral denoising by means of orthogonal expansions in terms of vector spherical harmonics reflects global a priori information of the noise (e.g., in form of a covariance tensor field), whereas multiscale signal-to-noise thresholding can be performed under locally dependent noise information within a multiresolution analysis in terms of spherical vector wavelets. An application of the multiscale formalism to Earth's magnetic field determination is presented. 相似文献
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随机模拟是地质统计方法的重要内容。在矿石品位估计方法中克里格方法作为一种无偏估计方法,常被用于矿石品位的估计。但克里格法估值存在平滑效应。作者在分析序贯高斯模拟和普通克里格法基本原理的基础上,运用序贯高斯模拟方法和普通克里格方法对某铁矿体内全铁(TFe)品位进行估计,给出了品位估计结果模型。研究从勘探线方向、垂直勘探线方向和竖直方向分别计算变差函数,对球状模型、指数模型、高斯模型的变差函数拟合效果进行了优选,结果表明球型模型拟合效果最好。针对序贯模拟和克里格品位估值效果进行了分析,结果显示:序贯高斯模拟结果在品位分布形态上更接近样品品位分布形态,其平滑效应更小;克里格方法估计与序贯高斯模拟方法相比仅在品位均值方面更接近样本品位均值。因此,认为序贯高斯模拟方法可以更好地刻画矿体内品位分布状态。 相似文献
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Computational power poses heavy limitations to the achievable problem size for Kriging. In separate research lines, Kriging algorithms based on FFT, the separability of certain covariance functions, and low-rank representations of covariance functions have been investigated, all three leading to drastic speedup factors. The current study combines these ideas, and so combines the individual speedup factors of all ideas. This way, we reduce the mathematics behind Kriging to a computational complexity of only $\mathcal{O}(dL^{*} \log L^{*})$ , where L ? is the number of points along the longest edge of the involved lattice of estimation points, and d is the physical dimensionality of the lattice. For separable (factorized) covariance functions, the results are exact, and nonseparable covariance functions can be approximated well through sums of separable components. Only outputting the final estimate as an explicit map causes computational costs of $\mathcal{O}(n)$ , where n is the number of estimation points. In illustrative numerical test cases, we achieve speedup factors up to 108 (eight orders of magnitude), and we can treat problem sizes of up to 15 trillion and two quadrillion estimation points for Kriging and spatial design, respectively, within seconds on a contemporary desktop computer. The current study assumes second-order stationarity and simple Kriging on a regular, equispaced lattice, without working with restricted neighborhoods. Extensions to many other cases are straightforward. 相似文献
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Olivier Dubrule 《Mathematical Geosciences》2017,49(4):441-465
Many variogram (or covariance) models that are valid—or realizable—models of Gaussian random functions are not realizable indicator variogram (or covariance) models. Unfortunately there is no known necessary and sufficient condition for a function to be the indicator variogram of a random set. Necessary conditions can be easily obtained for the behavior at the origin or at large distance. The power, Gaussian, cubic or cardinal-sine models do not fulfill these conditions and are therefore not realizable. These considerations are illustrated by a Monte Carlo simulation demonstrating nonrealizability over some very simple three-point configurations in two or three dimensions. No definitive result has been obtained about the spherical model. Among the commonly used models for Gaussian variables, only the exponential appears to be a realizable indicator variogram model in all dimensions. It can be associated with a mosaic, a Boolean or a truncated Gaussian random set. In one dimension, the exponential indicator model is closely associated with continuous-time Markov chains, which can also lead to more variogram models such as the damped oscillation model. One-dimensional random sets can also be derived from renewal processes, or mosaic models associated with such processes. This provides an interesting link between the geostatistical formalism, focused mostly on two-point statistics, and the approach of quantitative sedimentologists who compute the probability distribution function of the thickness of different geological facies. The last part of the paper presents three approaches for obtaining new realizable indicator variogram models in three dimensions. One approach consists of combining existing realizable models. Other approaches are based on the formalism of Boolean random sets and truncated Gaussian functions. 相似文献