Estimating probability curves of rock variables using orthogonal polynomials and sample moments

A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.

Computer program of nonlinear, curved regression for ‘probacent’-probability equation in biomedicine

On the basis of experimental observations on animals, applications to clinical data on patients and theoretical statistical reasoning, the author developed a com-puter-assisted general mathematical model of the ‘probacent’-probability equation, Equation (1) and death rate (mortality probability) equation, Equation (2) derivable from Equation (1) that may be applica-ble as a general approximation method to make use-ful predictions of probable outcomes in a variety of biomedical phenomena [1-4]. Equations (1) and (2) contain a constant, γ and c, respectively. In the pre-vious studies, the author used the least maximum- difference principle to determine these constants that were expected to best fit reported data, minimizing the deviation. In this study, the author uses the method of computer-assisted least sum of squares to determine the constants, γ and c in constructing the ‘probacent’-related formulas best fitting the NCHS- reported data on survival probabilities and death rates in the US total adult population for 2001. The results of this study reveal that the method of com-puter-assisted mathematical analysis with the least sum of squares seems to be simple, more accurate, convenient and preferable than the previously used least maximum-difference principle, and better fit-ting the NCHS-reported data on survival probabili-ties and death rates in the US total adult population. The computer program of curved regression for the ‘probacent’-probability and death rate equations may be helpful in research in biomedicine.

Regionalization of Rainfall Intensity-Duration-Frequency (IDF) Curves in Botswana

A regional analysis of design storms, defined as the expected rainfall intensity for given storm duration and return period, is conducted to determine storm Rainfall Intensity-Duration-Frequency (IDF) relationships. The ultimate purpose was to determine IDF curves for homogeneous regions identified in Botswana. Three homogeneous regions were identified based on topographic and rainfall characteristics which were constructed with the K-Means Clustering algorithm. Using the mean annual rainfall and the 24 hr annual maximum rainfall as an indicator of rainfall intensity for each homogeneous region, IDF curves and maps of rainfall intensities of 1 to 24 hr and above durations were produced. The Gamma and Lognormal probability distribution functions were able to provide estimates of rainfall depths for low and medium return periods (up to 100 years) in any location in each homogeneous region of Botswana.

Probability Distribution of SARS-Cov-2 (COVID) Infectivity Following Onset of Symptoms: Analysis from First Principles

The phasing out of protective measures by governments and public health agencies, despite continued seriousness of the coronavirus pandemic, leaves individuals who are concerned for their health with two basic options over which they have control: 1) minimize risk of infection by being vaccinated and by wearing a face mask when appropriate, and 2) minimize risk of transmission upon infection by self-isolating. For the latter to be effective, it is essential to have an accurate sense of the probability of infectivity as a function of time following the onset of symptoms. Epidemiological considerations suggest that the period of infectivity follows a lognormal distribution. This proposition is tested empirically by construction of the lognormal probability density function and cumulative distribution function based on quantiles of infectivity reported by several independent investigations. A comprehensive examination of a prototypical ideal clinical study, based on general statistical principles (the Principle of Maximum Entropy and the Central Limit Theorem) reveals that the probability of infectivity is a lognormal random variable. Subsequent evolution of new variants may change the parameters of the distribution, which can be updated by the methods in this paper, but the form of the probability function is expected to remain lognormal as this is the most probable distribution consistent with mathematical requirements and available information.

区域地质灾害易发性评价的证据权法原理与实践

在阐述证据权法概念与原理的基础上,以西北黄土高原滑坡、崩塌地质灾害高易发的兰州市区为评价区,详解基于证据权法的区域地质灾害易发性评价的技术流程,利用GIS工具,开展评价指标选取与相关性分析、证据因子权重与后验概率分析、评价模型检验、易发程度评价。分析结果显示,坡度、坡向、地层岩性、断层、绿化灌溉、土地利用类型等地质灾害影响因素之间呈无相关或弱相关性,符合相互独立的要求,组成的模型ROC曲线(接受者操作特征曲线)AUC值(曲线下面积)为0.85,具有较高的预测精度。理论与实践表明,与其他统计学方法相比,证据权法同时考虑了评价指标中存在地质灾害与不存在地质灾害2种情况,避免了当地质灾害不存在时权重偏大导致结果失真的问题。证据权法结果为地质灾害发生的绝对概率,可以作为不同区域、地区的地质灾害易发程度对比的依据。

基于改进PRM算法的机器人路径规划

概率路线图(Probabilistic Roadmap, PRM)算法是移动机器人领域常用的路径规划算法。针对传统PRM算法存在采样点分布不均匀、路线图构建效率低以及路径冗余不平滑等问题,提出了一种改进PRM算法。使用二维Sobol序列优化采样策略,保证采样点全局均匀分布,优化采样点的覆盖面积,提高了采样点的质量;其次,对采样点进行邻域分类并施加连接约束,使相邻邻域采样点进行连接,减少路线图的大小,提高了路线图的构图和搜索效率;接着,使用节点平移优化算法优化节点位置,使优化路径符合实际空间中的最优路径;最后,使用贝塞尔曲线平滑路径拐点,使生成的路径更符合机器人的实际运动约束。大量仿真实验结果表明,改进PRM算法可以有效提升规划路径的质量且受采样点数量的影响较小。相比于传统PRM算法和其他改进PRM算法,提出的PRM算法在路径长度、运行时间和成功率上具有明显优势。

基于CB-RRT^(*)算法的滩涂履带车路径规划

针对滩涂履带车在受潮汐影响的滩涂环境中进行长时间勘测作业的需求,提出柯西贝塞尔快速搜索随机树星(Cauchy Bessel Rapidly-exploring Random Tree Star,CB-RRT^(*))算法进行路径规划。为规划出安全路径,基于全局地图和潮汐数据,并通过滩涂履带车到分界区的距离构建出滩涂预测模型;为提高滩涂履带车移动到目标点需进行多次路径规划的速度,对初始路径的关键树节点使用柯西概率密度函数进行采样缩小采样范围来提高节点的利用率,进而提高算法的收敛性;在重选父节点过程中考虑最大转角约束设定相应系数,并使用连续二次贝塞尔曲线进行拼接的方式来生成路径,达到提高路径平滑度的目的和解决平滑后路径与原路径偏差过大造成的安全性问题。仿真实验结果表明,CB-RRT^(*)算法在静态滩涂环境和动态滩涂环境中,能大大提高算法的收敛性和路径的平滑性,且保证路径长度最优,研究内容可以保证滩涂履带车在各种滩涂环境中进行长时间安全作业。

COVID-19对太湖重金属污染及水生生态风险的影响

自COVID-19爆发以来,人类生活和经济受到很大负面影响,但同时疫情期间自然环境得到一定改善.为探究COVID-19管控对太湖重金属污染和水生生态风险的影响,将疫情期间(2021.6—2021.7)和爆发前(2019.9—2020.1)太湖重金属污染和水生生态风险进行对比分析,并通过PCAAPCS-MLR(主成分-绝对主因子分析-多元线性回归受体模型)对重金属进行定量源解析.结果表明,疫情期间太湖重金属污染水平和对水生生物的生态风险皆显著降低,降幅分别为39.9%—92.8%和0.19%—87.66%.整体水质优良比例提升了33.65%.重金属中受影响最大的元素为铜和铬.定量源解析结果表明,工业源对铜和铬的贡献率分别为79.75%和84.26%,疫情期间工业活动的减少是太湖重金属污染和生态风险降低的主要原因.为更好地管控太湖重金属污染和保护太湖水生生物,建议优先监管太湖周边电镀、冶炼和化学三大工业企业铜和铬的排放.

基于三相动态谐波分析的电能表误差检测方法

在检测电能表误差时,原始信号中谐波的干扰会导致检测结果与实际情况存在较大偏差。为此,提出基于三相动态谐波分析的电能表误差检测方法。在谐波分析阶段,考虑到谐波的动态属性会导致三相信号的采样执行效果难以达到同步,构建了余弦组合窗——旁瓣最低与最速下降窗,利用其对电能表离散信号进行截取,以此避免信号能量向临近谱线泄漏,再利用离散傅里叶变换对信号进行处理,实现对谐波的提取。在误差检测阶段,以离散随机信号的概率密度函数为导向,采用最优直方图曲线拟合法对其加以分析,并结合标准情况下电能表信号的分布状态,实现对误差的计算。在测试结果中,电能表误差检测结果的偏差始终稳定在3.0%以内。

肇庆市中心城区暴雨强度公式研究及应用

采用年最大值法挑选肇庆市中心城区降水样本,并尝试用皮尔逊Ⅲ型、耿贝尔型、指数分布型3种概率分布函数进行拟合试验,结果表明:皮尔逊Ⅲ型和耿贝尔型通过KS检验;耿贝尔型暴雨强度的精度误差较皮尔逊Ⅲ型为优,最终获得耿贝尔型暴雨强度公式。根据公式计算单一重现期暴雨强度发现,1h降水量达50mm的重现期为2年以内,即每年都会发生;24h降水量达暴雨量级的重现期为2年以内,即每年都会发生;特大暴雨量级的降水的重现期为50年以上。在面对超百年一遇的极端降雨时,需要完善应急管理措施;在预测有强降雨过程来临时,及时做好城市排水管道、调蓄池、行泄通道的调度。

基于高斯混合模型及EM算法的建筑工程数据预警治理方法

结合初期雨水调蓄大直径顶管工程的实际设计及施工经验,对软弱地层条件下长距离大直径平行双管曲线顶管在设计及施工过程中存在的重点难点问题进行总结,并对顶管过程中的顶力及管周摩阻力做了深入分析研究,有针对性地提出了相应的解决方案,使该顶管工程顺利贯通。建筑工程行业在现代社会中发挥着重要的经济和社会作用,然而,它也伴随着诸多风险和不确定性。为了有效地管理和预测这些风险,本文提出了一种基于高斯混合模型(GMM)和期望最大化(EM)算法的数据预警治理方法。该方法旨在通过对建筑工程数据的建模和分析,提前识别潜在的问题和风险,从而改善工程项目的管理和决策。

二连盆地巴音都兰凹陷B51井区白垩系阿四段扇三角洲前缘沉积特征

在岩心观察和粒度分析的基础上,结合录井、测井、地震等资料,对二连盆地巴音都兰凹陷B51井区下白垩统阿四段扇三角洲前缘沉积特征、分布规律与发育模式进行了研究。研究结果表明:(1)巴音都兰凹陷B51井区阿四段发育砂砾岩相、砂岩相、粉砂岩相、泥岩相等四大类,可进一步划分为13个小类,粒度概率累计曲线表现为悬浮一段式、低斜两段式、高斜两段式、滚动-跳跃-悬浮三段式4种类型,具有箱形、钟形、漏斗形、指形、平直形5种测井相标志,发育前积、丘状、杂乱状、亚平行状4种地震相。(2)研究区阿四段扇三角洲前缘发育水下分流主河道、水下分流河道、河口坝、水下分流间湾、席状砂和远砂坝6种沉积微相,纵向上可分为Ⅰ,Ⅱ,Ⅲ共3个砂组,Ⅱ砂组和Ⅲ砂组沉积时期,扇三角洲前缘砂体分布广泛,水下分流主河道和水下分流河道发育;Ⅰ砂组沉积时期,湖盆范围最大,砂体变细、变薄。(3)研究区阿四段自下而上表现为水进沉积序列,发育退积型扇三角洲前缘,预测B51-71井区和B51-74井区发育的水下分流主河道和水下分流河道为利储集相带,B51-19井区发育的河口坝为较有利的储集相带。

Development of damage probability matrices based on Greek earthquake damage data

A comprehensive study is presented for empirical seismic vulnerability assessment of typical structural types, representative of the building stock of Southern Europe, based on a large set of damage statistics. The observational database was obtained from post-earthquake surveys carried out in the area struck by the September 7, 1999 Athens earthquake. After analysis of the collected observational data, a unified damage database has been created which comprises 180,945 damaged buildings from/after the near-field area of the earthquake. The damaged buildings are classified in specific structural types, according to the materials, seismic codes and construction techniques in Southern Europe. The seismic demand is described in terms of both the regional macroseismic intensity and the ratio αg/ao, where αg is the maximum peak ground acceleration （PGA） of the earthquake event and ao is the unique value PGA that characterizes each municipality shown on the Greek hazard map. The relative and cumulative frequencies of the different damage states for each structural type and each intensity level are computed in terms of damage ratio. Damage probability matrices （DPMs） and vulnerability curves are obtained for specific structural types. A comparison analysis is fulfilled between the produced and the existing vulnerability models.

Probability Distribution and Their Non-linear Relationship between Node Degree and Clustering Coefficient of Aviation Network of China Based on Complex Network

In order to reveal the complex network feature of aviation network of China,probability distribution of node degree and clustering coefficient of aviation network of China was researched according to statistics data of civil aviation of China.It was verified that node degree had power function probability distribution.Clustering coefficient of nodes with exponential function probability distribution was discovered.It was found that node degree and clustering coefficient had single peak nonlinear relationship.At the left side of the peak,there is no certain relationship between them.At the right side of the peak,clustering coefficient became smaller with the rise of node degree and there was negative exponential function relationship between them by regression analysis.

土水特征的试验研究及概率分析

【目的】土水特征曲线(SWCC)是非饱和土力学中的重要曲线,用于表征土体吸力-含水率的关系。而土水特征试验往往耗时耗力,提高SWCC试验效率具有现实意义。【方法】联合采用渗析法与滤纸法可获取全吸力范围内的SWCC。为了在确保试验精度的前提下提高试验效率,以合肥地区黏性土为研究对象,在大量试验研究的基础上,采用4种方案对渗析法与滤纸法的试验数据点进行组合(渗析法及滤纸法所有数据点;渗析法数据点;渗析法所有数据点及一个低吸力的滤纸法数据点;渗析法所有数据点及一个高吸力的滤纸法数据点),研究数据组合方案对SWCC拟合结果的影响。【结果】结果显示:最优的数据组合方案是渗析法所有数据点加上滤纸法的最高吸力点;与基于所有试验数据点的方法相比,二者SWCC拟合参数的统计特征十分接近。在此基础上,计算得到了合肥地区4个工地的黏性土SWCC参数的概率统计特征。【结论】结果表明:需要进行大量SWCC试验时,在不影响试验精度的情况下,可减少滤纸法的试验数据点,采用渗析法所有数据点及一个高吸力的滤纸法数据点的方案以获取SWCC,可有效提高试验效率。

道路急弯路段追尾冲突分析预测

为实现急弯路段的追尾碰撞风险主动防控,提出了一种基于多源数据融合的追尾冲突动态预测方法。首先,基于无人机、毫米波雷达等采集的车辆运行数据,提出了适用于急弯路段交通流特征的追尾冲突判别模型及冲突等级阈值划分标准,分析了急弯路段的追尾冲突空间分布特征。然后,筛选车型、大车比率、断面速度差等13个交通流特征指标作为输入变量,以粒子群算法为基础,分别构建了其与BP神经网络、随机森林、支持向量机算法的追尾冲突动态组合预测模型,并根据混淆矩阵和曲线下面积评估各模型的预测性能,利用黑箱解释方法分析冲突发生概率的显著性影响因素及影响程度。结果表明:相较于平直或一般弯道路段,急弯路段的追尾冲突TTC(Time to Collision)值更小,出弯缓和曲线段冲突更为严重,且弯道内侧碰撞风险最高;粒子群-随机森林模型的追尾冲突预测性能最佳,灵敏度达90.70%;急弯路段追尾冲突受车辆平均车头间距的影响程度最大,当平均车头间距为25 m左右时,冲突发生概率最小,向心加速度均值、速度均值等因素亦对其有显著影响。

二维曲线型随机变量函数的概率分布

给出了二维曲线型随机变量函数的密度函数计算公式,丰富了二维曲线型随机变量的理论和方法,具有一定的理论价值.

基于Pavlou方法的焊接结构疲劳寿命预测

变幅载荷作用下的疲劳寿命预测一直是焊接结构完整性评估的重要内容.基于Pavlou提出的疲劳损伤区概念,采用BS7608标准中推荐的S-N曲线,运用有限元热传导分析技术,提出了一种焊接结构疲劳寿命的预测方法.针对承载型十字焊接接头、非承载型十字焊接接头和对接焊接接头,开展了二级变幅载荷谱块的拉伸疲劳试验,分别采用Miner模型、M-H模型和Pavlou方法估算了试件的疲劳寿命.结果表明,Pavlou方法的预测精度明显高于其它2种模型,预测寿命与试验寿命误差散射图中数据点的分布形态更加合理,验证了Pavlou方法的精确性和有效性.进一步讨论了焊接接头S-N曲线存活率对疲劳寿命预测精度的影响,提出2.3%存活率可以获得较为满意的预测结果.

密度造型方法的初步探索

传统的自由曲线造型系统,可描述为“(离散的)控制顶点序列,关于(离散的)基函数序列,进行(离散的)加权平均”。现打破其离散属性,改变为连续属性,即将描述改为“(连续的)曲线,关于(连续的)函数族,进行(连续的)积分平均”。相应的变化,类似于概率论中,离散型随机变量使用分布律定义的数学期望,变为连续型随机变量使用概率密度函数定义的数学期望,因此,这种连续属性的造型方法称为密度造型方法。其中,连续的曲线,称为控制曲线;连续的函数族,称为基密度函数。为了初步探索密度造型方法,定义了其模型,并尝试构造了一种满足非负、规范、对称性质的1次与2次的基密度函数,进一步研究了基密度的导数,以及对应随机变量的任意阶矩函数的情况。在密度造型的过程中,输入可以是任意次数的多项式甚至非多项式的参数曲线,输出的造型曲线是次数分别不超过1和2的多项式曲线。密度造型的曲线具备凸包、仿射不变和对称等性质。

弯坡路段多模式失效概率与轿车单车事故的关系

为促进可靠性分析(概率几何设计)在公路安全设计及事故预测中的应用,通过建立事故预测模型将轿车多模式失效概率与轿车事故之间建立关系。首先,以多模式失效为切入点,基于单个轿车在弯坡路段可能的3种失效模式(侧滑、侧翻、视距不足)建立多模式失效系统;其次,以华盛顿州10241起弯坡路段的轿车单车事故为研究对象,通过蒙特卡罗法和宽界限法求解系统的多模式失效概率;最后,将多模式失效概率、公路因素作为解释变量建立负二项模型、随机效应负二项模型、随机参数负二项模型3种事故预测模型,挖掘多模式失效概率与轿车单车事故之间的关系。结果表明:3种事故预测模型中随机参数负二项模型的拟合最优;当考虑多模式失效概率时,公路几何因素对轿车单车事故的影响被削弱;除两个暴露变量外,多模式失效概率对轿车单车事故的影响最大;多模式失效概率与轿车单车事故的拟合曲线近似为线性,且拟合曲线的截距不为0。该研究成果可用于公路的可靠性设计中。