Spectral Estimation of Irregularly Sampled Nonstationary Multidimensional Processes by Time-Varying Periodogram

A multidimensional version of the time varying periodogram has been developed. The estimation method based on the multidimensional time-varying periodogram has been applied to a nonstationary multidimensional storm model. This work proposes that the multidimensional time varying periodogram is capable of estimating nonstationary spectral density functions in space and time.     

Spectral Estimation in Space and Time Domain by Nonstationary Minimum Variance Spectral Estimator

A multidimensional version of the nonstationary minimum variance spectral estimator has been developed. The numerical results have shown that this method has more resolution power than the conventional nonstationary spectral estimation methods based on periodograms. The application of the spectral estimation method to an irregularly sampled multidimensional nonstationary rainfall mode is also investigated. The other advantage of this spectral estimation method is that it does not require window selection.     

非平稳条件下北京市最大月降水量频率特征分析

为探究气候变化下极端降水的频率变化特征,基于北京市22个雨量站实测月降水量数据,以时间为协变量构建平稳和非平稳GEV模型,对北京市最大月降水量序列(极值降水序列)进行模拟和频率分析,并采用Bootstrap方法对频率分析结果的不确定性进行评价.结果表明:所有极值降水序列的最优概率分布模型均为非平稳GEV模型,该模型能够...     

Multidimensional spectrum estimation for nonstationary processes

A spectrum estimation method for multidimensional nonstationary processes has been developed. The estimation method has been applied to a nonstationary two-dimensional random field. The numerical findings show that the results of the estimations are about what can be expected from a multidimensional estimation for a nonstationary process.     

Practical Calculation of Non-Gaussian Multivariate Moments in Spatiotemporal Bayesian Maximum Entropy Analysis

During the past decade, the Bayesian maximum entropy (BME) approach has been used with considerable success in a variety of geostatistical applications, including the spatiotemporal analysis and estimation of multivariate distributions. In this work, we investigate methods for calculating the space/time moments of such distributions that occur in BME mapping applications, and we propose general expressions for non-Gaussian model densities based on Gaussian averages. Two explicit approximations for the covariance are derived, one based on leading-order perturbation analysis and the other on the diagrammatic method. The leading-order estimator is accurate only for weakly non-Gaussian densities. The diagrammatic estimator includes higher-order terms and is accurate for larger non-Gaussian deviations. We also formulate general expressions for Monte Carlo moment calculations including precision estimates. A numerical algorithm based on importance sampling is developed, which is computationally efficient for multivariate probability densities with a large number of points in space/time. We also investigate the BME moment problem, which consists in determining the general knowledge-based BME density from experimental measurements. In the case of multivariate densities, this problem requires solving a system of nonlinear integral equations. We refomulate the system of equations as an optimization problem, which we then solve numerically for a symmetric univariate pdf. Finally, we discuss theoretical and numerical issues related to multivariate BME solutions.     

基于Halphen分布和最大熵的洪水频率分析

设计洪水估算值对水利水电工程的设计规划至关重要,其关键是选择合适的分布线型和参数估计方法。目前采用单一的频率曲线进行水文分析计算,其设计结果具有较大的不确定性。引入Halphen分布函数进行洪水频率分析,并提出了基于最大熵原理的参数估计方法。利用丹江口水库1929~2014年的年最大日流量资料系列,分析检验Halphen分布的拟合效果,并与传统的分布进行比较。结果表明,Halphen函数具有灵活的形式和较好的尾部特征,适合于水文频率分析,其拟合结果基本优于其他的传统分布。     

Complementary Entropy and Wavelet Analysis of Drilling-Ability Data

The paper combines wavelet and entropy analysis of nonstationary drilling-ability data in order to obtain optimum information on the mechanical behavior of different geological formations. Both methods are multiscale in nature, and while entropy analysis provides information on stationary subdomains, wavelet analysis identifies dominant scales or range of scales at which the entropy analysis is most useful. The combination of the techniques yields relatively simple results that can aid the drilling process by providing information on delays to be expected.     

Texture Segmentation Based on Image Model and Neural Network

INTRODUCTIoNImagetextureanalysisisanimportantpartofresearchin-tocomputervision.Forobjectidentificationandunderstand-ing,textureanalysisisthebasisoftheresearchwork.Ingeneral,texturecanberegardedasakindofstructurethatconsistsofmanytextureelementsorpatternswhicharemoreorlesssimilar,i.e.,primitivesthatformtexturesandspatialdependenceorinteractionbetweentheprimitives.Ex-tensiveresearchhasbeendoneintextureanalysis,andrefer-ence(Haralick,l979)hasmadeathoroughsurvey.Amongthesetextureanalysismetho…     

基于Petri网的地质灾害事件空间复杂结构模拟与分析系统

地球系统中各种空间对象在时空及功能上的直接或间接的依赖关系是研究各种复杂问题的出发点, 模拟和分析这些对象之间的直接和间接制约关系往往是认识复杂系统和进行空间决策的基础, 如在地震、洪水、火灾等突发性事件发生过程中各种应急设施和部门的相互影响和制约往往是复杂的、不协调的关系.由此产生的级联效应往往会造成意想不到的严重后果.如何提高对灾害效应的认识, 预警预报灾害的级联效应是提高灾害预防和应急反应能力的重要基础.在研究灾害事件中相关对象之间的空间复杂结构的基础上, 通过建立定量关系来表示对象之间的相互关系, 采用模糊Petri网技术模拟对象之间的级联效应.以四川汶川大地震后堰塞湖的空间复杂结构为例, 动态模拟堰塞湖的潜在级联效应, 推测出易受影响的堰塞湖, 从而为有效防治地震后的次生灾害提供一种理论与技术思路.该方法和技术同样可以用于其他地学复杂系统结构的模拟和分析.      

计算相关距离的神经网络方法

通过对GRNN网络分析, 导出了网络参数spread与平方指数相关函数参数r0之间的关系, 提出了基于GRNN的计算相关距离和拟合相关曲线的方法。研究表明,在最优spread参数条件下GRNN网络能够较为准确地映射实测土性曲线的变化特征,反映土性空间的相关特征。     

基于典型饱水砂岩样品的多维空间多元统计密度反演方法

实测数据资料、岩石物理学和多维空间多元统计思想的结合,有助于定量解析数据,减少岩石骨架、流体信息预测的风险性。运用典型饱水砂岩样品(韩德华G组砂岩样品)的密度、黏土含量和孔隙度实测数据,反演石英、黏土和流体的密度,所得反演结果符合实际情况,得到的拟合密度与实测密度相关系数可达0.985 5。所提出的密度反演方法的核心是多维空间多元统计思想与质量守恒定律相结合;与传统二维空间二元回归的密度反演方法对比结果表明,该方法不仅可以避免回归运算中奇异点的影响,而且得到的拟合密度与实测密度呈更为显著的相关关系。反演结果的均值与实际值相对误差在2%左右,准确度高,证明了方法的合理有效性。     

Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method

The space domain version of the turning bands method can simulate multidimensional stochastic processes (random fields) having particular forms of covariance functions. To alleviate this limitation a spectral representation of the turning bands method in the two-dimensional case has shown that the spectral approach allows simulation of isotropic two-dimensional processes having any covariance or spectral density function. The present paper extends the spectral turning bands method (STBM) even further for simulation of much more general classes of multidimensional stochastic processes. Particular extensions include: (i) simulation of three-dimensional processes using STBM, (ii) simulation of anisotropic two- or three-dimensional stochastic processes, (iii) simulation of multivariate stochastic processes, and (iv) simulation of spatial averaged (integrated) processes. The turning bands method transforms the multidimensional simulation problem into a sum of a series of one-dimensional simulations. Explicit and simple expressions relating the cross-spectral density functions of the one-dimensional processes to the cross-spectral density function of the multidimensional process are derived. Using such expressions the one-dimensional processes can be simulated using a simple one-dimensional spectral method. Examples illustrating that the spectral turning bands method preserves the theoretical statistics are presented. The spectral turning bands method is inexpensive in terms of computer time compared to other multidimensional simulation methods. In fact, the cost of the turning bands method grows as the square root or the cubic root of the number of points simulated in the discretized random field, in the two- or three-dimensional case, respectively, whereas the cost of other multidimensional methods grows linearly with the number of simulated points. The spectral turning bands method currently is being used in hydrologic applications. This method is also applicable to other fields where multidimensional simulations are needed, e.g., mining, oil reservoir modeling, geophysics, remote sensing, etc.     

熵值理论和改进BP网络在湖泊富营养化评价中的应用研究

针对湖泊型饮用水源地水体污染、富营养化加剧的问题,引入熵值理论,建立单指标营养状态指数(TSI)和熵权藕合的湖泊综合营养状态指数模型(STSI),计算得到湖泊综合富营养状态指数判断湖泊富营养综合状态;基于神经网络仿真理论和Matlab软件系统,采用附加动量法和自适应学习速率改进BP算法,建立5-3-1结构型式的BP网络模型对湖泊富营养状态进行仿真预测。综合富营养化指数模型及改进BP模型应用于评价及预测固城湖富营养状态,并对模型评价结果进行验证。结果表明,改进BP网络模型可以有效地综合判断水体状态,为富营养评价及预测提供新的方法。     

Using the Entropy of Curves to Segment a Time or Spatial Series

The concept of the thermodynamics of curves is used to analyze change in the variability of time or spatial series. More specifically, the entropy of a curve makes it possible to divide a nonstationary random field, because of a change in variance, into subdomains where data are said to be stationary. It is demonstrated that for time and spatial series the entropy of a curve is the slope of the cumulative sum of absolute differences. Numerical simulations show the efficiency of this tool. It can be shown that the presence of a linear or quadratic trend is without effect on the localization of the stationary subdomains. A practical case is studied with data collected from a tunnel boring machine where several parameters are recorded. This analysis can bring more information on the mechanical behavior of the different geological formations and explain or justify unplanned delays.     

Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics

In many earth sciences applications, the geological objects or structures to be reproduced are curvilinear, e.g., sand channels in a clastic reservoir. Their modeling requires multiple-point statistics involving jointly three or more points at a time, much beyond the traditional two-point variogram statistics. Actual data from the field being modeled, particularly if it is subsurface, are rarely enough to allow inference of such multiple-point statistics. The approach proposed in this paper consists of borrowing the required multiple-point statistics from training images depicting the expected patterns of geological heterogeneities. Several training images can be used, reflecting different scales of variability and styles of heterogeneities. The multiple-point statistics inferred from these training image(s) are exported to the geostatistical numerical model where they are anchored to the actual data, both hard and soft, in a sequential simulation mode. The algorithm and code developed are tested for the simulation of a fluvial hydrocarbon reservoir with meandering channels. The methodology proposed appears to be simple (multiple-point statistics are scanned directly from training images), general (any type of random geometry can be considered), and fast enough to handle large 3D simulation grids.     

渗流场随机性的随机有限元分析

基于一阶Taylor随机有限元法,推导出相应的渗流场随机分析中渗流响应量（水头和水力梯度）的随机响应公式,进而实现三维稳定渗流场随机有限元分析,并编制了相应的程序。在分析中,将渗流区域材料的渗透张量视为三维各向异性随机场,利用三维可分离向量随机场的局部平均法对随机场进行离散,根据参数选取的不同,可以离散出不同数量的随机变量。最后,给出一个算例,对离散出随机变量数量不同的情况分别进行随机分析,将分析结果和仅仅将渗透张量视为三维随机变量得到的结果对比,验证了所提方法的可行性。     

Modeling soil variability as a random field

The observed variability in the spatial distribution of soil properties suggests that it is natural to describe such distribution as a random field. One of the ways to study engineering problems in such a stochastic setting is by the use of the Monte-Carlo simulation procedure. Application of this technique requires the capability to generate a large number of realizations of a given random field. A numerical procedure for the generation of such realizations in two-dimensional space is introduced as a finite difference approximation of a stochastic differential equation. The equation used was that suggested by Heine (1955). The resulting procedure is essentially similar to other autoregressive procedures used for the same purpose (Whittle, 1954; Smith and Freeze, 1979). However, contrary to these procedures, the present one is defined in terms of physically significant parameters:r ₀, the autocorrelation distance;, the discretization size; and the standard deviation, . Formulating the simulation procedure in terms of the physically significant parameters (r ₀,, ) greatly simplifies the task of generating realizations that are compatable with a given soil deposit.     

Neural network prediction of the reliability of heterogeneous cohesive slopes

The reliability of heterogeneous slopes can be evaluated using a wide range of available probabilistic methods. One of these methods is the random finite element method (RFEM), which combines random field theory with the non‐linear elasto‐plastic finite element slope stability analysis method. The RFEM computes the probability of failure of a slope using the Monte Carlo simulation process. The major drawback of this approach is the intensive computational time required, mainly due to the finite element analysis and the Monte Carlo simulation process. Therefore, a simplified model or solution, which can bypass the computationally intensive and time‐consuming numerical analyses, is desirable. The present study investigates the feasibility of using artificial neural networks (ANNs) to develop such a simplified model. ANNs are well known for their strong capability in mapping the input and output relationship of complex non‐linear systems. The RFEM is used to generate possible solutions and to establish a large database that is used to develop and verify the ANN model. In this paper, multi‐layer perceptrons, which are trained with the back‐propagation algorithm, are used. The results of various performance measures indicate that the developed ANN model has a high degree of accuracy in predicting the reliability of heterogeneous slopes. The developed ANN model is then transformed into relatively simple formulae for direct application in practice. Copyright © 2016 John Wiley & Sons, Ltd.     

基于信息熵与多重分形理论的非均匀流动分析

根据粘土和壤土中非均匀水流运动的示踪试验, 研究了土壤水非均匀流动模式, 并基于信息熵与多重分形理论探讨了多孔介质中流动的非均匀性质.不同土质试验研究的分析结果表明, 各深度信息熵与特征长度具有相反的变化趋势.非均匀流动多重分形特性分析表明, 非均匀流动分布具有很强的自相似性, 但并不是在所有研究尺度范围内都满足标度不变性, 在显色比例相近的情况下, 壤土和粘土中水流运动标度不变性的范围表现出显著的差异.