数值积分权函数法推求P-Ⅲ型分布参数

一、问题的提出水文计算中,当水文变量的总体分布函数形式确定之后,问题就归结为推求总体分布函数所含的参数,即参数估计问题。通常,需要估计的参数有均值(X)、变差系数(C_V)和偏态系数(C_)。水文计算中很少采用矩法和极大似然法。除极大似然法在C_较大时无解外,主要是由于两种方法都存在较大的计算误差,其中以矩法     

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。     

Г分布保证修正值系数В的确定

本文用统计试验法,对Γ分布估算了水文频率计算中适线法结果的保证修正值系数B,并绘制了用绝对值和最小法及最小二乘法适线的B值诺模图。其应用范围为C_s=0～6及p=0.01%～20%。为便于检读,也列出了此两法的B值表。     

基于次序统计量理论的洪水频率分析方法研究

针对目前参数估计方法存在稀遇洪水频率设计值偏大的问题,提出采用基于数值次序统计量期望值的适线法计算洪水频率设计初始值;针对目前参数估计方法存在常遇洪水频率设计值偏小的问题,提出采用周文德公式修正目前频率设计偏小的情形,计算洪水频率设计修正值;针对目前传统方法计算洪水频率设计值抽样误差大的问题,提出采用基于数值次序统计量标准差的方法计算洪水频率设计保证值。定量分析表明,提出的基于数值次序统计量期望值的优化适线法具有良好的无偏性和有效性;寸滩站洪水频率设计修正值大于频率设计初始值,且两者偏差随着频率减小而减小;寸滩站洪水频率设计保证值明显大于修正值。     

水文频率分析中抽样误差的统计试验研究

基于统计试验方法,探讨水文频率分析中抽样误差的分布问题。试验结果表明:小样本容量时,设计值抽样误差存在"系统性"偏小,误差均值小于零,随样本容量的增加,偏差逐渐缩小,趋于零均值正态分布;当Cv、Cs值较大时,抽样误差明显增大,小样本情况下还须额外考虑抽样误差均值的修正。     

加权核密度估计在洪水频率分析中的应用

本文引进加权核密度估计方法,研究洪水频率的分析计算;运用统计试验方法,同目前广泛认同的参数估计方法中线性矩法相比,结果表明:线性矩法及加权核密度估计法推求出的设计值的无偏性相当,但加权核密度估计方法的有效性较线性矩法好.最后还与普通的非参数密度函数估计方法对比,结果表明加权核密度估计方法推求出的设计值的无偏性及有效性都较好;尤其是有效性精度较高.因此,加权核密度估计是一种有应用和研究价值的方法.     

拓扑克里格法与普通克里格法在区域洪水频率分析中的比较研究

依据北江(珠江流域支流)流域6个水文测站年最大洪峰流量资料,分别用Top-kriging(拓扑克里格法)和普通克里格法进行区域洪水频率估计。采用均方根误差作为频率分布线型拟合优度指标。运用线性矩法进行单站洪水频率分析,确定10、50、100、1000年一遇设计洪水值。在此基础上,从Topkriging和普通克里格法设计洪水估计不确定性和相对线性矩法单站洪水频率的估计误差两个方面比较Top-kriging和普通克里格法。结果表明:(1)Top-kriging法是更好的线性无偏估计,相比普通克里格法更适合于区域洪水频率估计;(2)Top-kriging法设计洪水估计不确定性明显小于普通克里格法;(3)Top-kriging法设计洪水估计结果更接近线性矩法单站洪水频率分析结果。     

基于随机加权先验的P-Ⅲ分布参数贝叶斯估计

研究随机加权先验法进行P-Ⅲ分布参数贝叶斯估计。应用随机加权法确定分布参数的先验分布,MCMC自适应采样算法(AM)进行参数的后验分布采样,并与矩法、极大似然法和概率权重矩法等传统水文频率分析方法进行比较。实例表明,AM方法估算参数下,实测样本与对应频率设计值离差平方和最小,是一种可行的水文频率分析途径。     

基于随机加权先验的P-Ⅲ分布参数贝叶斯估计

研究随机加权先验法进行P-Ⅲ分布参数贝叶斯估计。应用随机加权法确定分布参数的先验分布,MCMC自适应采样算法(AM)进行参数的后验分布采样,并与矩法、极大似然法和概率权重矩法等传统水文频率分析方法进行比较。实例表明,AM方法估算参数下,实测样本与对应频率设计值离差平方和最小,是一种可行的水文频率分析途径。     

可考虑历史洪水信息的广义极值分布线性矩法的研究

在水文及其他行业中广义极值分布(GEV)是一种较为常用的分布线型,包括极值Ⅰ型、极值Ⅱ型和极值Ⅲ型分布.在介绍了该分布线性矩与其参数关系后,给出了有效的可以考虑历史洪水信息的线性矩公式,并对由线性矩推求分布密度函数中k值作了改进.通过统计试验计算分析了线性矩在该分布中的统计性能及历史洪水公式的适用性,并与绝对值准则和平方和准则两种不同优化适线法、矩法作了比较.统计试验表明,改进k值计算后的线性矩法略优于传统线性矩法.从总体上讲,改进k值计算后的线性矩法优于平方和准则适线法及矩法,其参数及设计值的不偏性很好,与绝对值准则适线法总体上相当.     

用蒙特卡洛模拟法计算正交最小二乘法拟合参数的标准偏差

介绍了一种计算正交最小二乘法拟合参数标准偏差的新方法－蒙特卡洛模拟法，并以电子探针微区分析技术分析环境样品的数据为例，对用于计算经典最小二乘法回归系数标准偏差的公式法和蒙特卡洛模拟法进行了比较。计算结果表明，两者完全相符，蒙特卡洛模拟法的计算结果正确、可靠。考察了模拟次数对计算结果的影响。模拟次数大于500时，计算结果趋于稳定，计算所需时间在1min以内。拟合方差与回归系数标准偏差存在明显的相关关系。线性模型能解释的方差越大，回归系数标准偏差越小。蒙特卡洛模拟法特别适合于非线性模型拟合参数标准偏差的计算。     

The evaluation of the probability of rock wedge failure using the point estimate method

In a probabilistic analysis of rock slope stability, the Monte Carlo simulation technique has been widely used to evaluate the probability of slope failure. While the Monte Carlo simulation technique has many advantages, the technique requires complete information of the random variables in stability analysis; however, in practice, it is difficult to obtain complete information from a field investigation. The information on random variables is usually limited due to the restraints of sampling numbers. This is why approximation methods have been proposed for reliability analyses. Approximation methods, such as the first-order second-moment method and the point estimate method, require only the mean and standard deviation of the random variable; therefore, it is easy to utilize when the information is limited. Usually, a single closed form of the formula for the evaluation of the factor of safety is needed for an approximation method. However, the commonly used stability analysis method of wedge failure is complicated and cumbersome and does not provide a simple equation for the evaluation of the factor of safety. Consequently, the approximation method is not appropriate for wedge failure. In order to overcome this limitation, a simple equation, which is obtained from the maximum likelihood estimation method for wedge failure, is utilized to calculate the probability of failure. A simple equation for the direct estimation of the safety factors for wedge failure has been empirically derived from failed and stable cases of slope, using the maximum likelihood estimation method. The developed technique has been applied to a practical example, and the results from the developed technique were compared to the results from the Monte Carlo simulation technique.     

Regional frequency analysis of daily rainfall extremes using L-moments approach

Daily extreme precipitation values are among environmental events with the most disastrous consequences for human society. Information on the magnitudes and frequencies of extreme precipitations is essential for sustainable water resources management, planning for weather-related emergencies, and design of hydraulic structures. In the present study, regional frequency analysis of maximum daily rainfalls was investigated for Golestan province located in the northeastern Iran. This study aimed to find appropriate regional frequency distributions for maximum daily rainfalls and predict the return values of extreme rainfall events (design rainfall depths) for the future. L-moment regionalization procedures coupled with an index rainfall method were applied to maximum rainfall records of 47 stations across the study area. Due to complex geographic and hydro-climatological characteristics of the region, an important research issue focused on breaking down the large area into homogeneous and coherent sub-regions. The study area was divided into five homogeneous regions, based on the cluster analysis of site characteristics and tests for the regional homogeneity. The goodness-of-fit results indicated that the best fitting distribution is different for individual homogeneous regions. The difference may be a result of the distinctive climatic and geographic conditions. The estimated regional quantiles and their accuracy measures produced by Monte Carlo simulations demonstrate that the estimation uncertainty as measured by the RMSE values and 90% error bounds is relatively low when return periods are less than 100 years. But, for higher return periods, rainfall estimates should be treated with caution. More station years, either from longer records or more stations in the regions, would be required for rainfall estimates above T=100 years. It was found from the analyses that, the index rainfall (at-site average maximum rainfall) can be estimated reasonably well as a function of mean annual precipitation in Golestan province. Index rainfalls combined with the regional growth curves, can be used to estimate design rainfalls at ungauged sites. Overall, it was found that cluster analysis together with the L-moments based regional frequency analysis technique could be applied successfully in deriving design rainfall estimates for northeastern Iran. The approach utilized in this study and the findings are of great scientific and practical merit, particularly for the purpose of planning for weather-related emergencies and design of hydraulic engineering structures.     

模糊加权优化适线法的改进及统计特征分析

水文序列长度有限,频率曲线参数估计存在抽样误差,采用加权适线法能够很好地减小误差。模糊加权优化适线法的诺模图长度有限,而且隶属度函数不是以样本无穷大为前提,对模糊加权优化适线法改进,提出半降正态分布的隶属度函数,运用大样本统计试验方法延长诺模图。以理想数据、蒙特卡洛随机数和实测序列对改进的方法检验,以无偏性和有效性为评价指标,运用评分法和百分率法对统计结果分析评价。结果表明改进的模糊加权优化适线法的统计特性好,适线精度高,能够促进模糊加权优化适线法在实际工程中的推广应用。     

暴雨频率分布线型优选方法的研究

本文将四阶线性矩检验法引入暴雨频率分布线型的选择,分析四阶线性矩检验法作为暴雨频率分布线型的选择准则的适用性,并与国内外其他4种常用的选优统计量得出的结果进行比较.四阶线性矩检验法的结果表明三参数的对数正态分布与各流域的实测暴雨资料拟合最好,这与其他4种方法的结论基本一致,很好地鏊别了暴雨频率的分布线型,四阶线性矩检验法可以作为检验暴雨频率分布线型选择的方法,四阶线性矩检验法扩展了暴雨线型检验的方法.     

Estimation of Areal Frequency and Mean Trace Length of Discontinuities Observed in Non-Planar Surfaces

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.     

Assessing flood inundation mapping through estimated discharge using GIS and HEC-RAS model

Water discharge is the main parameter in hydraulic modeling for flood hazard assessment. However, the unavailability of data on discharge and observed river morphologies resulted in erroneous calculations and irregularities in flood inundation mapping. The objectives of this study are (i) to investigate uncertainties of hydraulic parameters (width, cross-sectional depth, and channel slope) used in discharge equation and (ii) to examine the influence of estimate discharge on water extent and flood depth with different boundary conditions on interferometric synthetic aperture radar (IFSAR) and modified IFSAR DEMs. Sensitivity analysis was conducted with the Monte Carlo simulation method to generate random data combinations. Bjerklie’s equation was used to calculate discharge based on the three variables, and Manning’s n was substituted into the Hydrologic Engineering Center River Analysis System (HEC-RAS) model. TerraSAR-X was used to distinguish existing flood water bodies and normal water extent. The uncertainty of the combined variables was assessed with the likelihood measures such as F-statistic, mean absolute error, root mean square error, and Nash–Sutcliffe efficiency which compares observed and predicted inundated area as well as flood water depth simulated using the HEC-RAS model.     

System reliability analysis of slopes using multilayer perceptron and radial basis function networks

This paper presents a system reliability analysis method for soil slopes on the basis of artificial neural networks with computer experiments. Two types of artificial neural networks, multilayer perceptrop (MLP) and radial basis function networks (RBFNs), are tested on the studied problems. Computer experiments are adopted to generate samples for constructing the response surfaces. On the basis of the samples, MLP and RBFN are used for establishing the response surface to approximate the limit state function, and Monte Carlo simulation is performed via the MLP and RBFN response surfaces to estimate the system failure probability of slopes. Experimental results on 3 examples show the effectiveness of the proposed methodology.     

Importance sampling based algorithm for efficient reliability analysis of axially loaded piles

In reliability analysis, the crude Monte Carlo method is known to be computationally demanding. To improve computational efficiency, this paper presents an importance sampling based algorithm that can be applied to conduct efficient reliability evaluation for axially loaded piles. The spatial variability of soil properties along the pile length is considered by random field modeling, in which a mean, a variance, and a correlation length are used to statistically characterize a random field. The local averaging subdivision technique is employed to generate random fields. In each realization, the random fields are used as inputs to the well-established load transfer method to evaluate the load–displacement behavior of an axially loaded pile. Failure is defined as the event where the vertical movement at the pile top exceeds the allowable displacement. By sampling more heavily from the region of interest and then scaling the indicator function back by a ratio of probability densities, a faster rate of convergence can be achieved in the proposed importance sampling algorithm while maintaining the same accuracy as in the crude Monte Carlo method. Two examples are given to demonstrate the accuracy and the efficiency of the proposed method. It is shown that the estimate based on the proposed importance sampling method is unbiased. Furthermore, the size of samples can be greatly reduced in the developed method.