水利水电工程岩基抗剪强度参数二维分布模型构造的Copula方法

基于国内103个水利水电工程1 174组岩基抗剪强度试验数据,采用Copula函数研究岩基抗剪强度参数联合分布模型,探讨水利水电工程中岩基抗剪强度参数联合分布模型构建方法。利用最小二乘法求出岩基抗剪强度参数试验数据的相关统计参数,基于AIC准则识别出岩基抗剪强度参数边缘分布。选择4种Copula函数构造岩基抗剪强度参数二维分布模型,探讨了基于Copula函数的岩基抗剪强度参数二维分布模型的优越性。结果表明:水利水电工程岩基抗剪强度参数存在明显的统计负相关性。Copula方法能够构造具有任意边缘分布和任意相关结构的岩基抗剪强度参数联合分布模型,它为构造抗剪强度参数联合分布模型提供了一种简便的工具。已知岩基抗剪强度参数的边缘分布函数和相关系数不能唯一确定岩基抗剪强度参数的联合概率分布模型,在抗剪强度参数边缘分布函数和相关系数完全相同的前提下,不同Copula函数建立的抗剪强度参数联合概率分布模型差异显著。与常用的抗剪强度参数二维正态分布模型相比,基于Copula函数的抗剪强度参数二维分布模型具有较强的灵活性,它能更好地拟合原始观测数据。水利水电工程中惯用小值平均法确定标准值,当摩擦系数取较小值时,不同Copula函数构造的黏聚力的条件累积分布函数差异显著,这将对抗剪强度参数标准值的选取以及相应的设计方案具有明显的影响。

基于贝叶斯理论的土体抗剪强度参数最优二维分布模型识别方法

提出了基于贝叶斯理论的土体抗剪强度参数最优二维分布模型的识别方法。首先,介绍了基于Copula函数的土体抗剪强度参数二维分布模型的表征方法。其次,采用蒙特卡洛模拟方法验证了贝叶斯理论识别最优二维分布模型的有效性,对比了贝叶斯独立识别、贝叶斯非独立识别、AIC一步识别,AIC两步识别4种识别方法的识别能力,分析了影响贝叶斯理论识别精度的主要因素。最后,搜集了29组实际工程土体抗剪强度参数试验数据,研究了贝叶斯独立识别和非独立识别在实际工程土体抗剪强度参数最优二维分布模型识别中的应用。结果表明,贝叶斯理论能够结合先验信息有效地识别表征土体抗剪强度参数最优二维分布模型;贝叶斯理论与AIC准则相较在小样本条件下的识别能力和识别精度方面优势明显;土体抗剪强度参数的样本数目、参数间相关性、备选二维分布模型集合以及先验信息都显著影响贝叶斯理论的识别精度。

基于二维指数条件分布的加速寿命模型

从概率意义上对寿命和应力之间的关系作了探索性研究。为了根据寿命和应力之间的概率相关性建立加速寿命模型,假设在给定应力条件下元件寿命服从指数分布,根据二维指数条件分布的定义和特性推导出一种BEC加速寿命模型。为了检验BEC模型的有效性,利用一组加速寿命试验数据,对BEC模型、Arrhenius模型、逆幂率模型进行了对比分析。结果表明,在加速应力范围,BEC模型能够正确描述寿命与应力之间的关系,与Arrhenius模型、IPL模型具有同等效力;而在正常应力范围,BEC模型的寿命外推精度低于Arrhenius模型和IPL模型。

MOS沟道和衬底电流的二维分布理论建模

小尺寸ＭＯＳ器件参量具有很强的分布效应，需要二维模型描述．本文从ｙ截面流函数方程求解获得了ＭＯＳ器件中的沟道电流和衬底电流二维分布解析模型．模型是横向场Ｅｙ（ｙ）和纵向场Ｅｘ（ｙ）的函数．二维分布模型载有较充分的物理过程，可以基本反映电流密度的实际分布．模型可应用于与电流路径相关的ＭＯＳ器件特性的研究；特别重要的应用领域是ＭＯＳ热载流子可靠性电子学中的栅电流分布建模．选用深亚微米ＭＯＳ器件的横向场Ｅｙ（ｙ）和纵向场Ｅｘ（ｙ）及ＩＤＳ模型，所建分布模型可应用于该尺寸区器件的沟道电流和衬底电流二维分布的描述．

基于二维极值分布的亳州地区强降水概率特征模拟

在全球气候变化的影响下,极端天气气候事件频繁发生。该文结合近年来极端天气气候变化研究中应用极值统计理论的新成果,采用亳州4个站建站以来汛期的实测降雨资料,探讨了二维Gumbel分布模型,在研究其经验频率和理论频率计算方法的基础上,根据随机变量的边缘分布和条件概率分布,分析了汛期最大强降水雨量及最大过程雨量的联合分布,建立了其联合重现期和条件重现期的分布模型,拟合效果很理想。

三峡库区滑坡土体抗剪强度参数相关性构建的最优Copula函数

Copula函数是一种将联合分布函数与各自边缘分布函数连接在一起的函数,已经成功应用在多个领域.本文为了研究表征抗剪强度参数间相关性的二维Copula函数分布模型最优化识别,在收集的滑坡土体参数基础上,采用K-S检验法确定了抗剪强度参数的最优边缘分布模型,并利用最小平方欧式距离识别出表征抗剪强度参数间相关结构最优的Copula函数.结果表明:Copula函数是构造土体抗剪强度参数c、φ之间联合分布函数的一种有效方法;基于核密度参数估计值的Gaussian Copula函数具有更好地描述参数间相关性的能力,构造方法具有计算简单、适用范围广以及能更好地模拟原始参数间相关性等优点,建议优先采用.该方法应基于监测数据计算后进行Copula函数选择,为工程计算参数选取提供一种新的途径.

重晶石掺量对重混凝土渗透性能的影响

试验通过二维随机分布模型模拟粗骨料在富勒级配下的分布状态,研究重晶石以20%、30%和40%替换普通卵石粗骨料对重混凝土渗透性能的影响.结果表明:随重晶石替换百分比的增加,混凝土内部流体速度场和相对水渗透系数明显下降,速度矢量的走向曲折变化,极大的提高了混凝土的抗渗透性能,但对内部压力场影响不大.

基桩正常使用极限状态失效概率区间估计方法

提出了基桩正常使用极限状态失效概率区间估计方法。首先,介绍了基桩标准化荷载-位移双曲线参数的定义,并给出了钻孔现浇灌注桩双曲线参数的现场试验数据。其次,采用Copula方法构造了双曲线参数的二维分布模型,并应用Bootstrap方法表征了双曲线参数二维分布模型的统计不确定性。最后,给出了考虑双曲线参数二维分布模型统计不确定性的基桩失效概率区间估计方法,并比较了基桩失效概率点估计和区间估计结果的优缺点。结果表明:基于有限双曲线参数试验数据估计的样本均值、标准差、Kendall秩相关系数和AIC值具有较大的变异性,这种变异性进一步导致双曲线参数的二维分布模型存在明显的统计不确定性。通过考虑双曲线参数二维分布模型的统计不确定性,基桩失效概率可以表示为具有一定置信度水平的置信区间。基桩失效概率的区间估计相比点估计能更加合理地表征基桩的真实可靠度水平。

基于投影变换判断导弹残骸落区安全性能的算法

为实现定量判断导弹残骸落区安全性问题,设计了地球投影变换的相关算法并推导了从地理坐标系到切平面二维坐标系的转化过程,提出了一种判断确定两多边形交集区域范围的算法,快速判断确定了相应残骸落区和规避区域在二维坐标系上的交集区域,通过构建二维正态分布模型快速计算交集区域概率,并将交集区域概率与设置阈值比较,定量判断出了导弹残骸落区内相应规避区域的安全性。算例结果表示,该算法易于实现,计算精度较高,能够较大程度上降低残骸落区内规避区域的转移损失,具有一定的实际应用价值。

人机交互中的移动目标选择

针对人机交互中移动目标选择的不确定性问题,提出三高斯落点分布模型。首先介绍三高斯落点分布模型原理,比较与其他模型的关系,并对模型进行拓展;进而从用户界面角度介绍三高斯落点分布模型的应用;最后对未来移动目标选择不确定性进行思考。

Analytical solution of vacuum preloading technology combined with electroosmosis coupling considering impacts of distribution of soil’s electrical potential

Combining vacuum preloading technology and electroosmosis can improve the treatment effect of soft soil foundation by utilizing the advantages of both methods.Many studies indicate that the soil electrical potential is non-linearly distributed in the treatment process by the combined method.However,in the previous theoretical study,the non-linear-distribution impacts of soil’s electrical potential on soft soil foundation treatment have not been considered.It is always assumed to be linear distribution,which is different from the experimental results.In this paper,the coupling consolidation model of this technology under the two-dimensional plane strain condition is initially established;and the well resistance effect,the vacuum load decreasing along the soil depth and the non-linear variation of electrical potential in the soil are considered.Then,the analytical solutions of the average excess pore water pressure and soil’s consolidation degree in the anode affected area are acquired based on the soil’s electrical potential distribution.Finally,the rationality of the analytical solution is testified by conducting an experimental model test,which proves the scientificity of the analytical solution.The analytical solution is adopted to better predict the dissipation of excess pore water pressure and soil consolidation degree when using the combined technology.This study can provide a reference with more accuracy for the engineering practices of this combined technology in the future.

Steady-State Properties of Driven Polydisperse Granular Mixtures

We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions,driven by a homogeneous heat bath at zero gravity.The width of particle size distribution is characterized by the only parameter,namely,the fractal dimension D.The energy dissipation of the mixture is increased as D increases or as e decreases.Furthermore,it is found that the steady-state properties of the mixture such as the collision rate,granular temperature,kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.

TWO-DIMENSIONAL FINITE ELEMENT MODEL OF TEMPERATURE DISTRIBUTION IN DERMAL TISSUES OF EXTENDED SPHERICAL ORGANS OF A HUMAN BODY

In the present study the thermal model of skin and subdermal tissues （SST） of human breast have been developed. The human breast is assumed to be spherical in shape with upper hemisphere projecting out from the trunk of the body and lower hemisphere is considered to be a part of the body core. The upper hemisphere represents the breast and its SST region is divided into three layers namely epidermis, dermis and subdermal tissues. The inner part of the breast represents the core/shell of the breast. The outer surface of the breast is assumed to be exposed to the environment from where the heat loss takes place by conduction, convection, radiation and evaporation. The heat transfer from core to the surface takes place by thermal conduction and blood perfusion. Also metabolic activity takes place at different rates in different SST layers of the breast. Boundary conditions have been framed on the basis of physical conditions. A finite element model has been developed for a two-dimensional steady state case.

Two-dimensional finite element model to study temperature distribution in peripheral regions of extended spherical human organs involving uniformly perfused tumors

Temperature as an indicator of tissue response is widely used in clinical applications. In view of above a problem of temperature distribution in peripheral regions of extended spherical organs of a human body like, human breast involving uniformly perfused tumor is investigated in this paper. The human breast is assumed to be spherical in shape with upper hemisphere projecting out from the trunk of the body and lower hemisphere is considered to be a part of the body core. The outer surface of the breast is assumed to be exposed to the environment from where the heat loss takes place by conduction, convection, radiation and evaporation. The heat transfer from core to the surface takes place by thermal conduction and blood perfusion. Also metabolic activity takes place at different rates in different layers of the breast. An elliptical-shaped tumor is assumed to be present in the dermis region of human breast. A finite element model is developed for a two-dimensional steady state case incorporating the important parameters like blood flow, metabolic activity and thermal conductivity. The triangular ring elements are employed to discretize the region. Appropriate boundary conditions are framed using biophysical conditions. The numerical results are used to study the effect of tumor on temperature distribution in the region.