Monte—Carlo法在地下工程可靠性分析中的应用研究

为了加速地下工程可靠性分析中Monte-Carlo法的收敛速度,根据NTM的均匀散布理论,将NT－net引入到Monte-Carlo方法的可靠性分析中,编制了相应的计算程序,通过对一具体工程实例的可靠性分析,将本文方法与普通的Monte-Carlo法进行了对比,本文方法显示了很好的优越性。     

基于弯矩和轴力随机相关特性的RC偏压构件可靠度分析

我国现行规范在分析混凝土偏心受压构件可靠度时,未考虑轴力和弯矩的随机相关特性。基于此,首先推导了弯矩和轴力间相关系数与对应荷载效应比值的函数表达式,得到了相关系数随荷载效应比值变化的规律。在此基础上定性分析了弯矩和轴力的随机相关特性对大偏压和小偏压两类构件失效概率的不同影响规律。采用Monte Carlo方法计算了当水...     

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.     

雅砻江某边坡稳定性蒙特卡洛模拟方法的改进

以雅砻江某边坡为例,对边坡岩土物理力学参数采用蒙特卡洛抽样,并且自编抽样数据与GEOSLOPE软件接入程序,借助GEOSLOPE软件逐次计算安全系数,得出安全系数均值、方差、失稳概率,同时将计算结果与GEOSLOPE软件自带蒙特卡洛计算结果进行对比,结果表明该方法计算结果优于传统计算结果。     

Multinormal integrals by importance sampling for series system reliability

A structural system with multi-failure modes can be modeled as a series system if it fails whenever any of the failure mode occurs. Applying FORM, failure probability of a series system can be expressed using a complementary standard multinormal integral. However, the integral is increasingly more difficult as the dimension increases. Importance sampling method can be used to deal with such multi-fold integration. Considering the fact that the optimal importance sampling function can be determined for a linear limit state function in a uncorrelated standard normal space, this paper proposes an importance sampling function for multinormal integral as a linear combination of such optimal sampling functions. The accuracy and applicability of the method are investigated using numerical examples.     

Effect of spatial variability on stability and failure mechanisms of 3D slope using random limit equilibrium method

It is well known that soils are prone to spatial non-uniformity, which affects evaluations of slope stability and failure mechanisms. This paper presents a probabilistic slope stability evaluation, considering the 3D spatial variation in the soil properties, by the random limit equilibrium method (RLEM). Specifically, 3D random fields of cohesion c, friction angle ?, and soil unit weight γ are generated using a fast Fourier transform. The RLEM is applied to evaluate the effects of the 3D spatial variability of the soil properties on slope stability and failure mechanisms. A Monte Carlo simulation is used to interpret the slope reliability and variation in slope failure dimension. Based on the critical slip surface passing different portions of a slope (slope base, inclined face, and crest), four main failure mechanisms (two base failures and two face failures), and one additional failure mechanism (toe failure), are identified for spatially variable slopes, and the corresponding distributions of the stability number (N_s) and sliding volume (V) are investigated in detail. The results show that the large variation in the soil properties induces changes in the failure mechanisms, and a threshold of c-? values is found for a shift from base failure to toe failure. Lastly, associated sensitivity studies are performed to explore the effects of the uncertainties of the input parameters on the uncertainty of the output. The results estimated by partial Spearman correlation coefficients show that cohesion has the greatest influence on the stability number, and that a positive influence of the unit weight, contributing to slope stability, is found for a base failure mechanism.     

基于子集模拟的边坡可靠度分析方法研究

边坡稳定受到诸多不确定性因素的影响,比如土体性质的空间变异性以及地层情况的不确定性。这些不确定性因素的影响可以通过蒙特卡洛模拟(Monte Carlo Simulation, MCS)进行定量地分析。MCS概念简单并具有广泛的适用性。但是,在小概率失效区域内,MCS计算效率很低,需要庞大的随机样本量来保证一定的计算精度。本文提出了一种实用的边坡可靠度分析方法。通过采用一种高级的MCS方法(Subset Simulation, 子集模拟)来提高小概率区域内的计算效率以及计算精度,并以EXCEL的表单环境为平台,联合使用Visual Basic Application(VBA)编写计算程序。在该程序中,子集模拟、边坡稳定的确定性分析和不确定性分析分别由三个相对独立的计算模块实现。最后,本文以James Bay 土坝为例,简明地说明了所提出方法的有效性,并探索了临界滑动面的不确定性对边坡可靠度分析的影响。     

不同设计配筋下大偏压RC柱承载力抗震可靠度

为研究偏心距随机特性对不同设计配筋下RC柱承载力抗震可靠度的影响规律,采用解析方法,推导了以多个无量纲化设计参数表达的大偏压RC柱失效方程和配筋影响系数计算式。考虑规范中的柱配筋率要求,分析了荷载效应比值等设计参数在常用取值范围内时配筋影响系数的变化规律。结合已有的水平地震作用、竖向重力荷载、混凝土强度和钢筋强度等参数的概率模型,并考虑偏心距的随机特性,采用Monte Carlo方法进行了大偏压RC柱可靠度分析。结果表明:不同设计参数组合下大偏压RC柱配筋影响系数的变化离散性较大;当配筋影响系数较小时,增加配筋对大偏压RC柱可靠指标的改善作用不大;当该系数较大时,增加配筋对可靠指标的提升效果较明显。     

A Monte Carlo method based on first- and second-order reliability approximations

A Monte Carlo sampling method based on both first- and second-order approximations to the failure region is proposed for the calculation of structural failure probabilities. The method applies to smooth failure surfaes and involves consideration of the hyperplane tangential to the failure surface at the design point and a hyperparabolic approximation to the failure surface. The efficiency of the method is illustrated with two examples and comparisons made with some other Monte Carlo methods.     

Numerical estimation and sensitivity analysis of the energy demand for six industrial buildings in France

When it comes to dealing with energy savings in buildings, studies almost systematically focus on the residential and tertiary building stocks while the industrial building stock is ignored. This study comes as a first step to move forward on this topic and its objectives are threefold: first to develop a simple methodology suitable for various industrial activities, then to analyse the distribution of the energy demand by use for six different cases and, finally, to carry out a sensitivity analysis. A first observation was that the energy demands for HVAC and lighting systems and the heat loads were of the same order of magnitude. The energy demand for heating and cooling was normally distributed, and the uncertainty on the results lay between ±20% and ±40% for most cases. The influence of six weather conditions was estimated for all of the six buildings and found to be significant, yet not uniformly.     

Application of line sampling simulation method to reliability benchmark problems

A procedure denoted as Line Sampling (LS) has been developed for estimating the reliability of static and dynamical systems. The efficiency and accuracy of the method is shown by application to the subset of the entire spectrum of the posed benchmark problems [Schuëller GI, Pradlwarter HJ, Koutsourelakis PS. Benchmark study on reliability estimation in higher dimensions of structural systems. In URL: http://www.uibk.ac.at/mechanik/Publications/benchmark.html. Institute of Engineering Mechanics, Leopold-Franzens University, Innsbruck, Austria, 2004], i.e. in particular linear systems with random properties. The notion of design point excitation for non-linear systems is discussed and its use extended for reliability estimations of conservative non-linear MDOF systems considering critical conditional excitation.For solving the hysteretic MDOF system with uncertain structural parameters subjected to general Gaussian excitation, however, the general applicable subset procedure [Au SK, Beck JL. Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 2001;16:263–277] has been used combined with Importance Sampling.     

随机有限层理论及其在地基沉降可靠度计算中的应用

基于比奥固结理论,将土体视为横观各向同性弹性体,土性参数考虑为随机变量,结合梯度优化法和有限层理论,推导出随机有限层的理论计算公式。根据理论推导,编制了随机有限层的计算程序,程序中采用了二级分层技术,使得计算更加合理。采用Matlab软件自带的GUI工具进行界面设计,利用Matlab与VisualC++接口技术,实现VisualC++和Matlab的混合编程,编制出可独立运行的随机有限层可视化程序。最后进行了算例分析,计算结果表明:这种方法是可行性,为地基沉降可靠度计算提供了一种新方法,值得进一步进行研究。     

非线性Mohr-Coulomb破坏准则下边坡可靠度上限

传统边坡可靠度分析往往在岩土参数服从线性Mohr-Coulomb(简称线性M-C)破坏准则的假设条件下进行,并且常常采用极限平衡法或有限元法计算安全系数。然而,岩土介质破坏准则具有一定的非线性。为能更加实际地描述岩土破坏机理和得到严格精确的解,基于非线性MohrCoulomb(简称非线性M-C)破坏准则,结合极限分析上限法和蒙特卡洛法,进行边坡可靠度上限分析。当非线性参数m=1时,与等效的线性M-C破坏准则进行对比计算,验证了方法的可行性。同时,将初始粘聚力、内摩擦角arctan(c0/σt)和非线性参数作为随机变量且服从截断正态分布,进行了参数变异性和敏感性影响分析。研究表明:非线性M-C破坏准则下,边坡可靠度随初始粘聚力、内摩擦角arctan(c0/σt)和非线性参数变异性的增大而减小;边坡可靠度随初始粘聚力和内摩擦角arctan(c0/σt)的增大而增大,随非线性参数的增大而减小。     

抗滑桩锚固深度的可靠性设计

以抗滑桩锚固深度确定的原则为基础,针对不同的锚固段地层及不同的地基系数形式,建立了锚固深度可靠性设计的数学模型。介绍了Monte Carlo法在该模型中的应用,实例分析了常规设计与可靠性设计的异同,认为可靠性设计把计算参数当作随机变量更切合于实际,而且还能得出抗滑桩所承担的风险水平,同时即使抗滑桩能满足常规设计的条件,也未必能满足可靠性设计的条件。     

A fast and efficient response surface approach for structural reliability problems

The reliability analysis of large and complex structural requires approximate techniques in order to reduce computational efforts to an acceptable level. Since it is, from an engineering point of view, desirable to make approximative assumptions at the level of the mechanical rather than the probabilistic modeling, simplifications should be carried out in the space of physically meaningful system- or loading variables.Within the context of this paper, a new adaptive interpolation scheme is suggested which enables fast and accurate representation of the system behavior by a response surface (RS). This response surface approach utilizes elementary statistical information on the basic variables (mean values and standard deviations) to increase the efficiency and accuracy. Thus the RS obtained is independent of the type of distribution or correlations among the basic variables which enables sensitivity studies with respect to these parameters without much computational effort.Subsequently, the response surface is utilized in conjunction with advanced Monte Carlo simulation techniques (importance sampling) to obtain the desired reliability estimates.Numerical examples are carried out in order to show the applicability of the suggested approach to structural systems reliability problems. The proposed method is shown to be superior both in efficiency and accuracy to existing approximate methods, i.e., the first order reliability methods.     

计算结构可靠指标的子域抽样法

提出了基于Monte Carlo法的用于结构可靠度计算的子域抽样法,其基本思想是以有界域模拟替代无界失效域。介绍了服从某种概率分布的变量在给定子区间内产生随机数的方法,并按照这种方法在选定的有界子区域内进行抽样模拟计算失效概率,并编制了仿真程序将抽样计算过程可视化。经算例验证,该算法抽样效率很高,且具有较高的模拟计算精度。     

结构系统可靠性理论的分析方法及进展

简要介绍了现代结构系统可靠性理论的发展概况 ,对各个时期有代表性的算法进行了比较系统的阐述。并对近年来流行的算法 ,如快速概率积分法、MonteCarlo模拟法、响应面法等进行重点介绍。在此基础上 ,探讨了当前研究工作中存在的一些共同问题 ,并对将智能化方法引进结构系统可靠性领域的运用和发展前景作了预测。     

数值模拟联合算法及其在润扬大桥可靠度评估中的应用

为了定量研究大跨桥梁在外界随机因素作用下的结构安全性,实现在线状态的可靠度评估,利用可靠度的随机有限元法对润扬大桥悬索桥在正常运营和损伤等多种工况下的结构可靠度进行了数值模拟和可靠度评估。分析中采用蒙特卡罗重要抽样法和中心复合响应面法的联合算法作为数值模拟的基本工具,介绍了联合算法的具体实现途径、随机变量的参数定义并对大跨桥梁基于可靠度指标的评估准则进行了讨论。得到了多个随机变量的概率灵敏度、主要失效模式所对应的可靠度指标及其相应的状态等级。算例分析结果表明,基于随机有限元的可靠度分析方法可以较好地描述大跨桥梁的非线性特征,联合算法的应用提高了可靠度分析的效率和精度,其结果为润扬大桥悬索桥的状态评估和健康监测提供了参考。     

建筑结构可靠度分析方法

介绍了建筑结构可靠度研究的意义,详细阐述了结构可靠度的基本计算方法,对矩法、响应面法、蒙特卡罗法等可靠度计算分析方法进行了分析,指出了各种方法的优点及适用范围,并对结构体系可靠度研究进行了展望.