Simulating the particle size distribution of rockfill materials based on its statistical regularity

The particle size distribution of rockfill is studied by using granular mechanics, mesomechanics and probability statistics to reveal the relationship of the distribution of particle size to that of the potential energy intensity before fragmentation, which finds out that the potential energy density has a linear relation to the logarithm of particle size and deduces that the distribution of the logarithm of particle size conforms to normal distribution because the distribution of the potential energy density does so. Based on this finding and by including the energy principle of rock fragmentation, the logarithm distribution model of particle size is formulated, which uncovers the natural characteristics of particle sizes on statistical distribution. Exploring the properties of the average value, the expectation, and the unbiased variance of particle size indicates that the expectation does notequal to the average value, but increases with increasing particle size and its ununiformity, and is always larger than the average value, and the unbiased variance increases as the ununiformity and geometric average value increase. A case study proves that the simulated results by the proposed logarithm distribution model accord with the actual data. It is concluded that the logarithm distribution model and Kuz-Ram model can be used to forecast the particle-size distribution of inartificial rockfill while for blasted rockfill, Kuz-Ram model is an option, and in combined application of the two models, it is necessary to do field tests to adjust some parameters of the model.

Evaluation of Probability Distribution Functions for Modeling Forest Tree Diameters on Agricultural Landscapes in Ogun State, Nigeria

The use of probability distribution functions for describing tree diameter at breast height provides useful information for forest resource evaluation and quantification. A series of probability distribution functions have been widely developed and applied for managing forest trees in conventional forest reserves without much consideration for trees outside forest reserves. The aim of this study is to evaluate and propose a suitable probability distribution function for trees in Agricultural landscapes. The study examined 3-parameter lognormal, Lognormal, 3-parameter Gamma, Gamma, 3-parameter Weibull and Weibull distribution functions, using the Maximum Likelihood method for fitting tree diameter at breast height. Three hundred and thirty-two temporary farmlands were randomly selected from which stem diameter of all living trees, with diameter ≥ 10.0 cm, were measured. Results of the statistical analysis showed that the 3-parameter lognormal distribution gave a superior description of the stem diameter with the least values of Anderson Darling (1.627) and Akaike Information Criterion (5962.0) statistics. Hence, the 3-parameter lognormal distribution function was found suitable for the stem diameter of trees in Agricultural landscapes in the study area.

Nonequilibrium Statistical Nature of Intergranular Brittle Fracture in Polycrystal

The brittle fracture probability and reliability are obtained in terms of dislocation mechanism of microcrack evolution. The statistical distribution functions and statistical deviations of elongation, strength, plastic work, crack extension force, fracture foughness, critical and crack length, can be derived in a unified fashion.

Wave Energy Estimation by Using A Statistical Analysis and Wave Buoy Data near the Southern Caspian Sea

Statistical analysis was done on simultaneous wave and wind using data recorded by discus-shape wave buoy. The area is located in the southern Caspian Sea near the Anzali Port. Recorded wave data were obtained through directional spectrum wave analysis. Recorded wind direction and wind speed were obtained through the related time series as well. For 12-month measurements（May 25 2007-2008）, statistical calculations were done to specify the value of nonlinear auto-correlation of wave and wind using the probability distribution function of wave characteristics and statistical analysis in various time periods. The paper also presents and analyzes the amount of wave energy for the area mentioned on the basis of available database. Analyses showed a suitable comparison between the amounts of wave energy in different seasons. As a result, the best period for the largest amount of wave energy was known. Results showed that in the research period, the mean wave and wind auto correlation were about three hours. Among the probability distribution functions, i.e Weibull, Normal, Lognormal and Rayleigh, ＂Weibull＂ had the best consistency with experimental distribution function shown in different diagrams for each season. Results also showed that the mean wave energy in the research period was about 49.88 k W/m and the maximum density of wave energy was found in February and March, 2010.

The Distribution of the Concentration Ratio for Samples from a Uniform Population

In the present paper we derived, with direct method, the exact expressions for the sampling probability density function of the Gini concentration ratio for samples from a uniform population of size n = 6, 7, 8, 9 and 10. Moreover, we found some regularities of such distributions valid for any sample size.

Robust and Efficient Reliability Estimation for Exponential Distribution

In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.

L-Moments and TL-Moments as an Alternative Tool of Statistical Data Analysis

Moments and cumulants are commonly used to characterize the probability distribution or observed data set. The use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. The moment method does not always produce satisfactory results. It is difficult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very different from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are often considerably less accurate than those obtained using other methods, particularly in the case of small samples. The present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics.

On the Relationship between Statistical and Phenomenological Models of the Thermodynamic Systems

The paper deals with the performing of a critical analysis of the problems arising in matching the classical models of the statistical and phenomenological thermodynamics. The performed analysis shows that some concepts of the statistical and phenomenological methods of describing the classical systems do not quite correlate with each other. Particularly, in these methods various caloric ideal gas equations of state are employed, while the possibility existing in the thermodynamic cyclic processes to obtain the same distributions both due to a change of the particle concentration and owing to a change of temperature is not allowed for in the statistical methods. The above-mentioned difference of the equations of state is cleared away when using in the statistical functions corresponding to the canonical Gibbs equations instead of the Planck’s constant a new scale factor that depends on the parameters of a system and coincides with the Planck’s constant in going of the system to the degenerate state. Under such an approach, the statistical entropy is transformed into one of the forms of heat capacity. In its turn, the agreement of the methods under consideration in the question as to the dependence of the molecular distributions on the concentration of particles, apparently, will call for further refinement of the physical model of ideal gas and the techniques for its statistical description.

基于多保真度模型的高比例新能源配电网潮流不确定性表征方法

在能源生产和消费低碳化转型的背景下,如何量化源-荷不确定性的影响,高效、准确地实现配电网潮流不确定性表征,对配电网的安全、可靠运行具有重要意义。该文从计算效率和准确性两方面出发,将现有基于概率潮流的不确定性表征方法分为高、低保真度模型两类,综合分析了两种方法存在的问题。在此基础上,提出一种基于多保真度模型的高比例新能源配电网潮流不确定性表征方法,以实现潮流状态变量矩信息的高精度估计与概率分布函数的刻画。在矩信息估计方面,提出结合高、低保真度模型特点的最优输入样本数量分配方法,在给定总计算负担下实现了输出变量矩信息的无偏估计。在概率分布函数刻画方面,提出基于综合启动函数的概率分布函数刻画方法,利用多保真度模型提供的先验信息,提升概率分布函数拟合的准确性。通过118节点配电网的仿真计算,验证所提方法的有效性。

基于智能电表量测的配电网线路异常参数辨识及定位方法

为提高配网线路参数质量,提出一种基于智能电表量测的配网线路异常参数辨识及定位方法。该方法把传统辨识算法的非线性辨识方程求解问题转化成参数最优分布的推断问题,进而在参数辨识的基础上,利用概率统计法进行异常参数定位。首先,给定线路参数初始分布,利用马尔科夫链蒙特卡洛方法生成参数样本,并通过树状结构估计方法和损失函数进行参数分布更新,并以损失函数结果收敛时的参数分布期望作为线路参数辨识值;其次,计算线路参数相对偏移距离,通过概率统计方法判断辨识数据是坏数据或异常参数,并将坏数据直接剔除;最后,计算分析反映线路参数错误的异常因子,进行线路异常参数定位。通过实际29节点的10 kV馈线展示了参数辨识的流程,并通过实际97节点的10 kV馈线进行异常参数定位,证明了所提方法的可行性与有效性。

基于概率统计的压缩机可靠性研究

在统计国家管网现场大型离心压缩机机组2006~2022年运行故障数据的基础上,对数据进行清洗,将离心压缩机系统分为多个子系统进行概率统计,通过历史故障数据进行经验分布拟合与检验,建立了整个离心压缩机及其部件故障数据计算模型。除工艺系统服从对数正态分布外,其他服从双参数Weibull分布;所建立的计算模型都有95%以上的置信区间。

海洋环境噪声空间相关系数的统计特性

由于海洋环境的复杂性和随机性,实测海洋环境噪声空间相关系数同样具备随机性。本文利用南海浅海海洋环境噪声数据,分析比较了窄带以及宽频带海洋环境噪声空间相关系数统计特性,计算了海洋环境噪声空间相关系数的估计误差。结果表明:实测海洋环境噪声相关函数样本服从正态分布,噪声相关系数样本服从截断正态分布;带宽越宽,海洋环境噪声空间相关系数概率密度分布越集中,在数据量一定的条件下,宽频带噪声空间相关系数的估计精度高于窄带噪声。

生物氧化预处理过程pH值随机分布控制方法研究

生物氧化预处理过程中氧化槽pH值是影响细菌活性的关键因素之一,而pH值输出形态分布不符合高斯分布,使传统的均值和方差难以描述输出pH值分布,本文提出一种对矿浆输出pH的概率密度函数(PDF)统计信息控制方法。首先,采用B样条逼近矿浆输出pH值的PDF统计信息;其次,针对权值向量之间的关系,利用动态神经网络(DNN)建立控制输入和权值向量之间的非线性动态模型,基于建立pH的PDF统计信息权值模型,设计滑模变结构控制器,通过构造Lyapunov函数进行稳定性分析;最后,实现输出PDF统计信息对目标PDF统计信息的跟踪。仿真结果验证了所提方法的有效性,为生物氧化预处理过程提供了新方法。

Comparison of Block Design Nonparametric Subset Selection Rules Based on Alternative Scoring Rules

This article compares the size of selected subsets using nonparametric subset selection rules with two different scoring rules for the observations. The scoring rules are based on the expected values of order statistics of the uniform distribution (yielding rank values) and of the normal distribution (yielding normal score values). The comparison is made using state motor vehicle traffic fatality rates, published in a 2016 article, with fifty-one states (including DC as a state) and over a nineteen-year period (1994 through 2012). The earlier study considered four block design selection rules—two for choosing a subset to contain the “best” population (i.e., state with lowest mean fatality rate) and two for the “worst” population (i.e., highest mean rate) with a probability of correct selection chosen to be 0.90. Two selection rules based on normal scores resulted in selected subset sizes substantially smaller than corresponding rules based on ranks (7 vs. 16 and 3 vs. 12). For two other selection rules, the subsets chosen were very close in size (within one). A comparison is also made using state homicide rates, published in a 2022 article, with fifty states and covering eight years. The results are qualitatively the same as those obtained with the motor vehicle traffic fatality rates.

桥梁监测数据的车辆荷载效应分析与预测方法研究

桥梁监测积累了大量数据,通过对这些数据的深入分析和挖掘,可进一步掌握桥梁结构受力状态,对桥梁养护决策具有重要意义。从车辆荷载效应分析入手,提出了一种基于监测数据概率分析的桥梁安全评估方法。在经验模态分解(EMD)的基础上从原始监测数据中分离出车辆荷载产生的瞬态效应,并进行统计分析,获取每日最大挠度的概率分布,利用平稳随机过程外推其一段时期内的最大值概率分布,从而获得桥梁今后一段时间内车辆荷载效应的最大值,并与设计值进行对比分析,为在役桥梁的科学养护提供可靠的预测依据。

基于数字孪生的云网智能运维技术研究

云网融合的加速发展,既推动着通信网络数字化和智能化转型升级,也带来了云网运维复杂性不断提高的问题。尽管近年来通过各种智能化技术手段取得了一定进展,使网络管理控制变得更加敏捷和高效,但大规模云网设施仍然面临着运行维护过程中效率低、周期长和成本高等挑战。针对上述挑战,该文提出基于数字孪生的自适应探测、双重评估、优化调整三种智能运维的技术,旨在提高云网运维的效率并帮助预测网络异常。在自适应探测技术中,利用数据统计方法构建历史时序数据样本,通过算法选择适应的概率分布,预测故障发生的概率。双重评估技术中,通过对孪生系统和物理系统进行双重评估,验证故障原因并进行故障朔源。优化调整技术中,通过张量分解处理大数据,优化数据样本,并通过机器学习训练样本数据来优化调整智能运维模型。实验验证表明,该技术能够预测网络异常、快速定位故障,并优化调整系统,从而实现智能运维的目标。

数据透视方法下的充电桩低频辐射特性分析

GB/T 18487.2—2017新增对充电桩设备低频电磁辐射发射的具体要求,但大量测试数据仅以“频率-幅度”二维数据表格的形式记录和呈现。为直观获得大样本直流充电桩低频辐射干扰的分布特点和趋势,采用数据透视的分析方法对大样本数据进行分析。将直流充电桩关键字作为信息标签,针对信息标签对测试数据进行筛选排序、分类汇总和交互式查询。通过平面投影、直方图、区间化幅度概率分布等数据可视化方法,呈现大样本数据的统计特性。采用数据透视方法进行直流充电桩低频辐射特性分析,以直观获得样本数据的统计规律。该规律能够为统计产品特性、提高产品性能提供直观的参考依据。数据透视分析方法同样适用于其他测试数据的统计特性分析。

基于长期监测数据的混凝土箱梁温度梯度取值研究

为研究矮塔斜拉桥混凝土箱梁施工期的温度梯度取值,文中以广东东平水道矮塔斜拉桥为研究对象,详细分析了一年施工期内混凝土箱梁的实测温度结果,通过假设检验、参数估计、极值分析等统计学方法进行温度样本数据分析。结果表明,箱梁顶底板东西两侧的温差分布不同,特别是顶板的东西两侧温差累计概率分布差异较大;箱梁顶板最大正温差出现在西侧位置处,最大负温差出现在东侧,而底板最大负温差与最大正温差均出现在东侧;箱梁混凝土顶板的梯度升降标准值可偏于安全地,取22.5℃,梯度降温可以取9.0℃,底板的梯度升降标准值可偏于安全地,取5.5℃,梯度降温可以取4.0℃。

苏通大桥扁平钢箱梁温度场长期监测与统计分析

以苏通大桥斜拉桥的扁平钢箱梁为研究对象,基于结构健康监测系统对其温度场进行长期监测。根据温度监测结果对扁平钢箱梁的温度分布特性进行分析,重点研究扁平钢箱梁的横向温差和竖向温差分布特征,在此基础上采用统计学方法建立了扁平钢箱梁温度以及温差的概率分布模型,确定了具有一定重现期的钢箱梁温度和温差标准值。分析结果表明,扁平钢箱梁顶板与底板之间存在较大的竖向温差,顶板存在一定的横向温差,底板的横向温差可以忽略;扁平钢箱梁温度均可以通过2个正态分布函数的加权和来描述其概率密度分布,横向温差和竖向温差均可以通过2个威布尔分布函数的加权和来描述其概率密度分布。

最小二乘法的创立及其思想方法

目的探讨最小二乘法的历史发展过程及其创立者的思想与方法。方法历史考察与数理分析。结果勒让德在先驱者解线性方程组的基础上,以整体的思想方法创立了最小二乘法;高斯由寻找随机误差函数为突破,以独特的概率思想导出了正态分布,详尽地阐述了最小二乘法的理论依据。结论两位数学大师异曲同工地谱写了数理统计学的新篇。相比之下,高斯把最小二乘法推进得更远、更深刻,这极大地促进了数理统计学的发展。