计算近似失效概率的最大熵密度函数法

本文应用最大熵密度函数作为结构功能函数Ｚ的近似密度函数来计算结构的失效概率。最大熵密度函数以Ｚ的期望和高阶中心矩为约束条件加以拟合。文中着重研究了应用最优化方法和数值求积法确定最大熵密度函数的拉格朗日系数的方法,并给出了一个算例。算例表明,最大熵密度函数法的结果与其它三种方法非常接近。本文方法特别适用于基本随机变量为非正态分布的情况。     

Maximum entropy based finite element analysis of porous media

The maximum entropy theory has been used in a wide variety of physical, mathematical and engineering applications in the past few years. However, its application in numerical methods, especially in developing new shape functions, has attracted much interest in recent years. These shape functions possess the potential for performing better than the conventional basis functions in problems with randomly generated coarse meshes. In this paper, the maximum entropy theory is adopted to spatially discretize the deformation variable of the governing coupled equations of porous media. This is in line with the well-known fact that higher-order shape functions can provide more stable solutions in porous problems. Some of the benchmark problems in deformable porous media are solved with the developed approach and the results are compared with available references.     

厚圆柱扁壳位移型基本方程及控制方程分析

基于考虑横向剪切变形的厚壳位移型基本方程及扁壳基本假定,建立了以5个中面位移为5个独立变量的厚扁壳及厚圆柱扁壳位移型基本方程。对厚圆柱扁壳进行了动力分析,首先引入3个辅助位移函数,同时运用柯西-黎曼条件,将5个二阶微分方程变形为1个二阶和2个四阶过渡微分方程;然后引入另一辅助位移函数,建立其解耦的控制微分方程;最后利用4个辅助位移函数求出5个位移分量。结果表明,厚扁壳的位移型基本方程退化为厚圆柱扁壳及薄圆柱扁壳的位移型方程是正确的,且所推导的方程具有通用性。     

Stress evaluation of cooling towers subjected to uneven settlements with stochastic characteristics

Analytical methods to evaluate the maximum response of a rotational shell that is subjected to uneven settlements of a stochastic nature are presented. The settlements along the foundation ring are represented by a Fourier series. Each term in the series contains two coefficients: the amplitude and the phase angle. The phase angles are assumed to be random variables. Two cases are considered: when the amplitudes can be deterministically estimated, and when they are treated as random variables. In the first case, approximations of the maximum stresses in the shell are computed as a function of the standard deviations of the stresses and the predominant harmonic numbers. In the second case, the amplitude spectrum of the highest probability of occurance is obtained by the application of the maximum entropy principle that has been developed in the information sciences. Two other spectra that represent the limits of all possible spectra are generated by combining constraint equations and the maximum entropy principle.     

BuildOpt—a new building energy simulation program that is built on smooth models

Building energy simulation programs compute numerical approximations to physical phenomena that can be modeled by a system of differential algebraic equations (DAE). For a large class of building energy analysis problems, one can prove that the DAE system has unique solution that is once continuously differentiable in the building design parameters. Consequently, if building simulation programs are built on models that satisfy the smoothness assumptions required to prove existence of a unique smooth solution, and if their numerical solvers allow controlling the approximation error, one can use such programs with generalized pattern search optimization algorithms that adaptively control the precision of the solutions of the DAE system. Those optimization algorithms construct sequences of iterates with stationary accumulation points and have been shown to yield a significant reduction in computation time compared to algorithms that use fixed precision cost function evaluations.In this paper, we state the required smoothness assumptions and present the theorems that state existence of a unique smooth solution of the DAE system. We present BuildOpt, a detailed thermal and daylighting building energy simulation program. We discuss examples that explain the smoothing techniques used in BuildOpt. We present numerical experiments that compare the computation time for an annual simulation with the smoothing techniques applied to different parts of the models. The experiments show that high precision approximate solutions can only be computed if smooth models are used. This is significant because today's building simulation programs do not use such smoothing techniques and their solvers frequently fail to obtain a numerical solution if the solver tolerances are tight. We also present how BuildOpt's approximate solutions converge to a smooth function as the precision parameter of the numerical solver is tightened.     

多种微分方程数值计算方法分析

数值微分方程的数值解法是计算方法、数值分析理论中非常重要的内容,数值微分方法也是解决实际计算问题的重要方法。本文对几种常用的数值微分方法进行了简要的分析,并用这几种方法对具有光滑性质的被积函数进行数值计算,龙格-库塔方法和4阶阿达姆斯方法的数值计算稳定性和计算精度都比较好。     

极小曲面的Weierstrass表示与建筑造型

极小曲面广泛存在于自然界中,是平均曲率处处为0的一类重要曲面。其上含有多种相容的数学结构,可用不同的数学观点、方法来处理。局部上极小曲面定义为面积泛函的临界点,用变分方程或等价的欧拉—拉格朗日方程(二阶椭圆偏微分方程)表达。可用微分方程求其解析介或近似介,也可用变分方程求其近似介。极小映射是两个黎曼流形间的特殊映射,Weierstrass抛弃面积概念,从另外一个角度给出了极小曲面方程的通解。采用极小曲面Weierstrass表示,借助于计算机绘图技术可以获得各种精美的极小曲面图形。极小曲面在拓扑上可以有随心所欲的复杂,在几何上可以有令人难以琢磨的对称。这些图形在银屏上未显示前,大多无法事先想象出来。作为应用本文绘制了实射影平面在三维欧氏空间的最佳浸入Boy’s曲面的图形。还讨论了几种用极小曲面或调和曲面造型的建筑。     

不同通风方式的熵产数值模拟

利用热和流体流动控制方程,同时考虑了黏性耗散效应,以伴有温差的强迫对流空调房间为研究对象,分析讨论了不同通风方式在同一送风速度下熵产的分布情况。分析结果表明：熵产主要分布在送风口和回风口区域,最大熵产出现在送风口区域;模型1同侧上送下回通风方式的熵产的面积加权平均最小,模型3异侧下送上回通风方式的熵产的面积加权平均最大;无论哪种通风方式,在总熵产中,黏性熵产占绝对比重。     

基于SIMULINK的起重机起升机构动态仿真

就起重机机械起升机构多质点动力学系统建立了多质量多自由度的动力学模型，利用MATLAB／SIMULINK构造相应的仿真系统，采用自适应步长四阶Runge—Kutta法求解系统的微分方程组，对瞬间离地、悬空起动、空中制动等一系列典型工况进行动态仿真，对起升机构的动态性能进行了初步探讨并获得了有实用价值的成果。所得分析结论进一步完善了先前理论分析和数值计算研究成果，研究方法进一步提高了起升机构的建模精度。理论上可以考虑每一离散质点的运动从而使模型更加与实际系统一致。     

最大熵原理及应用

介绍信息论中的一个基本原理──最大熵原理，以及它在优化设计，气象学和统计力学等方面的应用．     

浅谈建筑之熵

人类对不同功能的建筑及其空间的需求导致了不同的建筑形态,建筑形态的不确定性造就了形形色色的建筑.从建筑形态的角度,借助“熵”的概念探讨建筑的基本属性,即建筑的不确定性.分别从熵增原理、耗散结构、最大熵原理等定律看待大量消耗能源和资源的建筑业,并对维特鲁威提的建筑三原则进行了分析.提出在开发设计阶段考虑负熵流入,同时以负熵最大化为目标,使建筑可持续发展,在此基础上建立生态建筑.     

Fourier-based maximum entropy method in stochastic dynamics

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bicki and Sobczyk has demonstrated the principle of maximum entropy is a powerful tool for solving stochastic differential equations. In particular, its use in connection with the moment equations generated by the Ito formula provides accurate estimations of the probability density evolution of some oscillators for which conventional methods such as the diverse closure schemes are not applicable. A major computational requirement of the method, however, lies in the need of calculating a large number of multidimensional integrals at each time step--a numerical task for which both accurate and economic algorithms are required. In this paper it is shown that conventional economic integration techniques often lead to numerical collapse of the solution, especially when dealing with highly nonlinear oscillators. A strategy that overcomes this difficulty is proposed. In essence, the integrals are reformulated in terms of multidimensional Fourier transforms, which are solved by an ad hoc FFT algorithm aimed at obtaining only one single “frequency” point. It is demonstrated that the numerical stability and the accuracy of the proposed algorithm are superior to those afforded by other integration schemes.     

基于隧道空间全波场二维数值模拟与特征分析

基于隧道地震波场二维数值模拟是研究隧道超前探测过程中地震波传播规律的基础,目前关于这方面的研究均建立在隧道侧壁观测系统的基础上,并且把隧道空间作为与周围地层具有同样弹性参数的均匀介质考虑,因此不能实现全波场模拟,与实际存在差异。基于实际隧道空间,建立了更加接近实际的隧道地质模型,实现了隧道空间的二维全波场模拟。通过二维全波场模拟及实例结果对比分析表明：① 采用空间四阶时间二阶交错网格有限差分法能有效实现基于隧道空气介质的二维全波场模拟;② 当地质界面倾角为90°时,掌子面附近激发的共激发点观测系统比侧壁的共接收点观测系统更有利于反射波的获取;③ 随着地质界面倾角的减小,界面同侧激发和接收的反射波能量增强;④对于局部地质体和大倾角地质界面,掌子面附近激发横波能量强于纵波,有利于横波成像。     

变截面高层建筑结构考虑楼板变形时的二阶分析

对考虑楼板变形的变截面框－剪结构的二阶分析问题建立了一个分段连续化的串并联模型，导出其二阶分析的微分方程组，用常微分方程求解器求解。讨论了影响二阶效应的一些因素。     

基于截尾概率分布的基坑突涌模糊可靠度分析

岩土工程可靠度分析中,计算参数具有随机性,稳定性评价具有模糊性。传统的Monte Carlo模拟方法计算可靠度时,往往假定参数概率分布在正负无穷之间分布,与真实情况不符,而且其计算效率也往往较低。规范推荐的基坑突涌验算公式,计算结果往往偏于保守。引入截尾概率分布的确定方法,对参数概率分布进行截尾处理;提出拉丁超立方抽样与最大熵原理结合来确定结构响应概率分布的方法,并将其与模糊可靠度原理结合,构建了基于抽样模拟的模糊可靠度计算模型;推荐了考虑土体抗剪强度的突涌验算公式。将所提方法应用于某深基坑工程突涌分析中,其结果表明,基于截尾分布的抽样可以有效避免参数抽样值为负数的情况,所提计算模型效率明显优于传统的Monte Carlo模拟方法,模糊可靠度的计算结果比经典可靠度更符合工程实际情况。     

Approximate analysis of tall buildings using sandwich beam models with variable cross‐section

In this paper an approximate method is carried out for determining the natural periods of multistory buildings subjected to earthquake. The building resists lateral forces through a combination of lateral resisting systems. These systems could be replaced by a cantilever Timoshenko or a sandwich beam with varying cross‐section that characterizes three kinds of stiffnesses: the global bending stiffness, the local bending stiffness and the shear stiffness. Using appropriate transformations, the differential equations for flexural and shear free vibration of a cantilever beam with variably distributed mass and stiffness are reduced to Bessel's equations and ordinary differential equations. The frequency equations can be solved by selecting suitable expressions such as exponential and power functions for stiffness and mass distribution along the height of the building. The calculated frequencies are combined appropriately by using approximate methods. Based on the fact that shear and bending deformations are all considered, the free vibration frequency of the structure could be calculated. The capability and accuracy of the proposed method are demonstrated by a numerical example in which finite element results are compared with the proposed methodology and other approximate methods. Copyright © 2007 John Wiley & Sons, Ltd.     

复合梁模态分析的一种里兹解法

就复合材料包覆钢筋混凝土梁(FRP-RC)提出了一种分析其振动特性的近似方法,基于摄动法的思想合理选择里兹函数,并利用最小势能原理来求解纤维复合材料包覆钢筋混凝土梁的模态特性。这一方法在等截面均匀梁的模态子空间内实施,它将FRP-RC梁无阻尼自由振动时复杂的变系数微分方程加以简化,转化成一代数方程组来求解。在此基础上,计算了该梁在不同约束条件下的自振频率,并与其它方法进行了对比。分析表明,利用本方法不仅可以简化计算过程,而且计算结果具有较高的精度,对同类问题具有适用性。     

BT工程项目风险分析和分配研究

近年来,BT模式在基础设施建设中大量运用,由于BT项目和基础设施的本身特点,使得BT项目运作过程不确定性加大,风险增加。加强风险管控,风险责任分配是保证项目成功运行的关键。通过分析基础设施建设BT项目的风险因素,构建了风险指标体系和风险分配评价标准,在此基础上运用多属性离差最大化和熵权法原理,建立了BT项目风险分配模型。最后通过算例说明模型的运用。研究表明,模型有助于确定BT项目风险责任的分配顺序和风险承担程度。     

熵权–集对分析模型探测堤坝渗漏

堤坝渗漏过程中水流携带的各种物质构成“信息流”,通过“信息流”中的“信息熵”可以确定地下流场的性质,其中运用水化学和环境同位素方法探测堤坝渗漏已经得到广泛应用。基于信息熵和集对分析系统理论,并结合水化学和环境同位素探测方法,建立了一种新的堤坝集中渗漏通道探测模型：熵权—集对分析模型。将PH,电导,Cl,δD和δO作为探测指标,依据探测指标和判断标准界限值的关系,对待测样本进行同一、差异和对立的集对分析,计算各探测指标联系度; 采用基于极大熵原理的熵权赋值法确定不同指标的权重,计算各样本综合联系度; 并据此将待测样本分类,进而确定钻孔内水的来源。最后将该模型应用于探测南方某水库堤坝渗漏问题,并利用流速和温度探测方法相互验证,分析表明：该模型探测结果跟流速和温度探测结果相吻合。     

Romberg extrapolations for numerical schemes solving stochastic differential equations

Let (X_t) be the solution of a stochastic differential system. We consider the following situations: computation of Eƒ(X_t) by a Monte-Carlo method (for example, computation of moments of the solution); integration of ƒ(·) with respect to the invariant probability law of (X_t) (when this process is ergodic); or of the upper Lyapunov exponent, by simulating a single trajectory.

We propose to perform an extrapolation between approximate values due to first-order schemes; we show that this algorithm (simpler to implement than second-order schemes) provides a second-order accuracy, and we give results of numerical tests.