先验概率分布及似然函数模型的选择对边坡可靠度评价影响的定量评估

受工程勘察成本及试验场地限制,可获得的试验数据通常有限,基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是,目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布,似然函数为多维正态分布,这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型,以一个不排水黏土边坡为例,采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明：参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响,选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险,选用对数正态分布获得的边坡可靠度计算结果居中。相比之下,似然函数的影响更加显著。与其他类型似然函数相比,由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时,获得与场地信息更为吻合的计算结果。另外,构建似然函数时不同位置处测量误差之间的自相关性对边坡后验失效概率也具有一定的影响。     

子波估计及极大似然反褶积方法稳健性讨论

利用极大似然反褶积提取鲁棒性地震子波的方法进行了研究，并讨论了极大似然反褶积的稳健性。理论分析表明，在理想条件下极大似然反褶积是无偏估计，而且还是一致估计，这一结论可以由所提取的地震子波得到验证。实际地震资料的处理结果分析表明，极大似然反褶积具有很好的稳健性。应当指出，为保证地震子波的鲁棒性，极大似然反褶积子渡时窗应尽量满足统计条件，以提高极大似然反褶积的稳健性。     

估计地层中化石属种数目的统计数学模型

应用二项分布的参数极大似然估计法，计算地层中化石属种数目的估计值，得出在彼此相距不远的n个或可列个剖面上取样的一般估计式：NA=[r(s1 s2 ΛΛ sn)/k1 k2 ΛΛ kn]。通过实例检验其有效性的基础上，从理论上提出诸如此类的统计数学模型。     

水文频率分析中参数估计SAGA-ML方法的研究

建立基于模拟退火遗传算法(Sjmualted Annealing Genetic Algorithm,SAGA)的改进极大似然法,即将似然函数相反数求解极小值的表达式作为目标函数,依据矩法估计参数取值范围作为约束条件,然后应用SAGA进行参数估计.与常规极大似然法思路有本质不同,改进极大似然法通过遗传算法进行参数优化.通过蒙特卡罗试验,验证了改进极大似然法在参数估计和不同频率设计值估计两个方面均具有很好的准确性,与基于最大熵原理的方法效果相当,优于其他方法;同时该方法不受线型类型、参数数目和约束条件的限制;可以避免应用常规极大似然法时出现似然方程无解等情况;且求解过程简便快捷,使极大似然法在理论上和实际应用中都成为有效的方法.     

混合极值理论及最大似然法估计东南沿海各地震区地震危险性

将东南沿海地区划分成七个地震区带,利用历史及现代地震资料,运用混合极值理论及最大似然法分析了各个地震区带的地震危险性.并采用预测检验的方法确定了各个地震区带的危险阈值,对各地震区未来三年的中小地震及未来五年的中强地震的危险性分别给出了定量的估计.     

基于BUS方法的无限长边坡可靠度更新

某一特定岩土场地的试验数据、监测资料和观测信息等通常十分有限,然而贝叶斯方法却可充分利用有限的场地信息克服试验数据样本量较小的不足。为有效估计有限样本条件下参数统计特征,提出了基于结构可靠度方法和贝叶斯更新(BUS)的边坡可靠度更新方法,通过融入直剪试验数据更新无限长边坡可靠度验证了提出方法的有效性,并系统探讨了岩土体参数先验信息如试验样本量、概率分布和似然函数模型对边坡可靠度更新的影响规律。结果表明:BUS方法能够考虑岩土体参数概率分布和似然函数模型的影响,融入有限的场地信息准确地估计参数统计特征和更新边坡可靠度,为解决有限样本条件下边坡可靠度更新问题提供了一条有效的途径。土体参数概率分布对边坡可靠度更新结果(参数后验均值、标准差以及更新的失效概率)具有重要的影响,基于常用的正态和对数正态分布的边坡可靠度更新结果偏于保守,相比之下,似然函数模型对边坡可靠度更新结果的影响相对较小。此外,岩土体参数不确定性和更新的边坡失效概率均随着试验样本量的增大而减小,但当样本量增大到一定程度时它们的变化不大。     

线性矩法与常规矩法对太湖流域降雨频率分析的比较研究

介绍了线性矩法的基本理论,并与常规矩法进行了初步的比较与分析,说明了其理论上的优越性;以太湖流域的雨量资料为例,选取4个站点分别应用线性矩法和常规矩法估计其不同重现期下年极值降雨频率设计值;最后,利用Monte Carlo方法对太湖流域内96个站点数据进行模拟,比较线性矩法和常规矩法所估计的统计参数。结果表明:线性矩法估计的参数在精确性、不偏性及稳健性方面较常规矩法更优。     

极大熵准则在降雨强度-历时-频率模型参数估计中的应用

根据频率与重现期的关系推导出三类常用降雨强度-历时-频率模型的无条件及条件概率分布(概率密度)函数及与模型相对应的约束。极大熵与极大似然准则产生一致估计,本文尝试基于极大熵准则建立降雨强度-历时-频率模型参数估计的优化模型,应用模拟退火算法求解该优化模型。根据比较发现,极大熵估计有时比常用的极大似然估计和最小二乘估计更精确。     

极值降水对雄安新区年径流总量控制率的影响研究

径流总量控制是低影响开发雨水系统构建的重要控制目标之一.为研究极值降水对年径流总量控制率的影响,首先对雄安新区雄县、容城、安新三个站点年径流总量控制率对应的设计降雨量进行推求,分析设计降雨量与控制率的关系并对雄安新区雨水径流源头控制效果分区进行验证,再利用广义帕累托分布和轮廓似然法估计3个站点不同重现期的降水值以分析极...     

基于自适应贝叶斯更新方法的岩土参数概率分布推断

合理推断岩土参数概率模型是岩土工程可靠度分析与风险评估的重要一步,目前大多基于现场或室内试验数据推断岩土参数概率分布。提出了岩土力学参数概率分布推断的自适应贝叶斯更新方法,建立了定量的子集模拟计算终止条件,构建了岩土参数概率分布推断及可靠度分析框架,并给出了计算流程。以台湾3号高速公路滑坡及不排水饱和黏土边坡为例验证了提出方法的有效性,并探讨了子集模拟每层样本数目对岩土参数概率分布推断的影响。结果表明:与最大似然和马尔可夫链蒙特卡洛方法相比,提出的方法计算效率高,编程较为简便,可为解决低接受概率水平岩土参数概率分布推断问题提供一个有效的工具。子集模拟每层随机样本数目对概率分布推断具有一定的影响,随着样本数目的增加,岩土参数后验统计特征和子集模拟阈值均逐渐收敛。此外,可根据互补累积分布函数随子集模拟阈值的变化关系来验证所建立的定量的子集模拟计算终止条件的合理性。     

On tail estimation: An improved method

A step is described toward better statistical treatment of data for tail estimation. The classical extreme value theory together with its practical inefficiency for tail inference are discussed briefly. The threshold method that utilizes available information in a more efficient manner is described, and its relation to extreme value theory is mentioned. Some comparison is also made using two sets of published data.     

Application of statistical geo-spatial information technology to soil stratification in the Seoul metropolitan area

Typical geotechnical testing results reflect the level of soil uncertainty, which requires statistical corrections of the data for an appropriate engineering decision. This study proposes frameworks to detect outlying data points using statistical analyses, the cross-validation-based method and the generalised extreme value distribution-based method. The borehole data regarding soil depth distribution in a central area of Seoul, South Korea are assessed to validate the aforementioned methods for comparison with the distribution-based method and the Moran scatterplot method. The results show that the proposed methods enable more reliable spatial distributions to be achieved with a quantitative evaluation of local reliability.     

Statistics for Modeling Heavy Tailed Distributions in Geology: Part II. Applications

In this paper, we present three diverse types of applications of extreme value statistics in geology, namely: earthquakes magnitudes, diamond values, and impact crater size distribution on terrestrial planets. Each of these applications has a different perspective toward tail modeling, yet many of these phenomena exhibit heavy or long tails which can be modeled by power laws. It is shown that the estimation of important tail characteristics, such as the extreme value index, is directly linked to the interpretation of the underlying geological process. Only the most extreme data are useful for studying such phenomena, so thresholds must be selected above which the data become power laws. In the case of earthquake magnitudes, we investigate the use of extreme value statistics in predicting large events on the global scale and for shallow intracontinental earthquakes in Asia. Large differences are found between estimates obtained from extreme value statistics and the usually applied standard statistical techniques. In the case of diamond deposits, we investigate the impact of the most precious stones in the global valuation of primary deposits. It is shown that in the case of Pareto-type behavior, the expected value of few extreme stones in the entire deposit has considerable influence on the global valuation. In the case of impact crater distributions, we study the difference between craters distributions on Earth and Mars and distributions occurring on other planets or satellites within the solar system. A striking result is that all planets display the same distributional tail except for Earth and Mars. In a concluding account, we demonstrate the apparent loghyperbolic variation in all of the above-mentioned examples.     

Uncertainty, subjectivity, experience: a comparative pilot study

Mean tendencies and variances of ad hoc mean estimates (field estimates) of some engineering geological parameters were compared to statistically obtained reference values. The latter correspond to the “best” estimates in the sense of approximating so-called reality (Einstein and Baecher, 1982. Probabilistic and statistical methods in engineering geology. Problem statement and introduction to solution. Rock Mech., Suppl. 12: 47–61; Einstein and Baecher, 1983. Probabilistic and statistical methods in engineering geology. Specific methods and examples, Part I: Exploration. Rock Mech. Rock Eng., 16: 39–72). The study was carried out by means of a demoscopic field study on 43 engineering geologists. “Professional experience” was examined by comparing the estimation results of two trial groups, one consisting of people with several years of professional experience, the other one consisting of university students. The biases of the ad hoc estimates due to subjectivity and the limitation of working time at the selected reference outcrops follow statistically describable trends and thus can be analyzed by univariate and multivariate methods. Some geological and psychological hypotheses concerning the mean estimation trends, correlations and discriminations are postulated. Implications on commonly used field estimation methods are discussed.     

IDW矿石品位估值结果的不确定性评价

作为一种常用的矿石品位估值方法, 距离幂次反比(inverse distance weighting, 简称IDW)计算结果的可信度难以评估.对此, 提出了一种基于统计学理论的解决途径. 将参与IDW估值的样品品位视为指示化阈值, 推导得出估值过程中其分配到的权重, 即为待估点取这样品值的概率. 基于这一结论构建出IDW估计值对应的条件累计分布函数(conditional cumulative distribution function, 简称CCDF), 从而完成待估位置矿石品位不确定性的建模. 以一典型矿区的实际矿体勘探数据为基础进行了对比测试. 针对每个估值点的CCDF进行了中位数、期望、方差等信息的提取, 验证表明这一方法的计算结果与样品数据的实际情况之间存在较好的吻合度. 在一定程度上说明了它在IDW品位估值结果不确定性评价方面的有效性.      

考虑历史洪水资料的期望概率权重矩法参数估计统计试验研究

为有效利用历史洪水资料,提高洪水资料系列参数的估计精度,研究期望概率权重矩法在广义极值分布参数估计中的应用。采用蒙特卡洛试验研究期望概率权重矩法的统计特性,并与部分概率权重矩法做比较。结果表明:期望概率权重矩法具有良好的稳定统计特性,并且是具有历史洪水资料系列进行参数估计的一种简单、稳定和有效的参数估计方法,具有推广意义。     

Bayesian Inference of Spatial Covariance Parameters

This paper shows the application of the Bayesian inference approach in estimating spatial covariance parameters. This methodology is particularly valuable where the number of experimental data is small, as occurs frequently in modeling reservoirs in petroleum engineering or when dealing with hydrodynamic variables in groundwater hydrology. There are two main advantages of Bayesian estimation: firstly that the complete distribution of the parameters is estimated and, from this distribution, it is a straightforward procedure to obtain point estimates, confidence regions, and interval estimates; secondly, all the prior information about the parameters (information available before the data are collected) is included in the inference procedure through their prior distribution. The results obtained from simulation studies are discussed.     

Prediction of oil or gas pool sizes when discovery record is available

The Upper Devonian Bashaw reef play of the Western Canada Basin was used to demonstrate: (1) estimation of pool size distribution by means of a discovery model, (2) the usefulness of a feedback mechanism in petroleum resources evaluations, and (3) enhancement of reliability by reducing uncertainty associated with estimates. The feedback mechanism presented herein allows us to challenge geological interpretations. For example, given the second largest pool size, the largest pool size can be estimated, and vice versa. In evaluations of petroleum resources, the uncertainty inherited from superpopulations is inevitably associated with the estimates. This type of uncertainty can be reduced to a certain extent if additional information is included in the estimation procedures and, consequently, the reliability of the estimates is enhanced. The additional information used may, for example, be the geological interpretation of a particular play. To achieve maximum effectiveness, resource evaluation methods should possess these types of flexibility. This study also estimated, with a 90% probability, that the remaining potential in the Bashaw reef play ranges from 32 to 50 millions of cubic meters (200 to 300 MM bbl) of oil in place.