基于MATLAB的平面框架结构位移可靠度分析研究

基于结构可靠度分析数值模拟方法———蒙特卡罗法和响应面法的基本原理,利用MATLAB软件对一榀2跨3层框架在水平荷载作用下进行位移可靠度分析,分别采用了直接抽样蒙特卡罗法、响应面法、响应面—蒙特卡罗法、响应面—重要抽样蒙特卡罗法编制相应的计算程序,得到了结构水平位移最不利点的失效概率和可靠指标。计算结果表明,利用MATLAB可以编制结构可靠度分析程序,计算速度较快,数据合理,并为复杂结构的可靠性分析提供参考。     

基于响应面法的大跨度悬索桥可靠度分析研究

为解决传统响应面法在分析大型复杂结构可靠度时可能遇到的不收敛或者误差较大的问题,通过对迭代步长取值的改进,提出了基于改进响应面的悬索桥结构可靠度分析方法。以某大跨度悬索桥为分析对象,分别采用改进响应面法和基于响应面的蒙特卡罗法分析了扁平钢箱梁的静力可靠度。计算结果表明,采用改进响应面法可以较准确地计算悬索桥在活荷载作用下的静力可靠指标,而基于响应面的蒙特卡罗法计算误差较大。另外,分析结果还表明,悬索桥的可靠指标计算应考虑几何非线性的影响。     

基于MATLAB的可靠度分析算法的性能比较

简要介绍和讨论可靠度分析算法原理;基于结构可靠度分析方法:一次二阶矩法、JC法、蒙特卡罗法、重要抽样法、响应面法的基本原理,利用MATLAB软件对两个算例编制了相应计算程序,并对计算结果进行了比较。计算结果的比较表明,利用MATLAB编制的程序进行结构可靠度计算,可节约大量运算时间,并能得到较为有效的、合理的结果。     

JC法在柔性路面结构可靠度计算中的应用

本文对目前研究的柔性路面结构可靠度的计算方法进行了讨论.在近十年的研究工作中,对于柔性路面结构可靠度的计算,我们采用过直接蒙特卡罗法、蒙特卡罗模拟统计分析法等,经过新近一些比较分析,发现采用JC法比较合适.该法不仅符合我国《工程结构可靠度设计统一标准(GB 50153-92)》推荐的方法,而且计算速度快,适应性好,精度又能满足工程设计的要求,故而推荐在今后柔性路面结构可靠度计算中采用.     

下穿高速双孔并行隧道可靠度分析

针对地下结构可靠度分析中功能函数不能显示表达的特点,提出基于三维有限元的可靠度分析方法。以下穿高速双孔并行隧道为例,根据三维有限元计算结果,分别以DP2与DP3准则作为塑性屈服的判定准则,采用遗传算法选取样本点构建二次响应面模型,通过对Monte Carlo法,基于BP神经网络的Monte Carlo法,中心点法,JC法和遗传算法得出的可靠度指标的比较分析,得出遗传算法的运用可显著提高响应面模型的逼近精度,中心点法计算出的可靠度指标误差较大,Monte Carlo法、BP-Monte Carlo法、JC法及遗传算法求得的可靠度指标精度相近,JC法因操作简便、计算精度高可广泛用于地下结构的可靠度分析。基于遗传算法选取的样本点构建响应面模型,以JC法计算地下结构的可靠度分布,得出在公路线荷载作用下,衬砌上下两侧向内变形,上下两侧围岩应力释放多,可靠度相应增大;衬砌左右两侧向外变形,左右两侧围岩应力增大,可靠度相应减小;并行隧道的相互影响导致邻近另一隧道侧的衬砌可靠度较小。     

工程结构可靠度理论综述

文章论述了工程结构可靠度理论的基本概念,总结了结构可靠度国内外研究现状;针对一次二阶矩法、响应面法及蒙特卡罗法三种常用的可靠度计算方法,分析研究了各个计算方法的特点。     

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.     

结构可靠度算法的比较

讨论了现有结构可靠度的计算方法,介绍了JC法、二次二阶矩的ESORM法、一次渐近积分法、序列响应面法、Monte Carlo法以及直接重要抽样的Monte Carlo法,通过算例,对这些方法的精度以及适用范围作了分析,为可靠度的计算提供了一个有价值的参考。     

边坡可靠度分析的随机响应面法及程序实现

提出分析相关非正态变量可靠度计算问题的随机响应面法,采用Nataf变换成功地解决输入变量相关时随机响应面法的配点问题及可靠度计算问题。推导4～6阶Hermite随机多项式展开的解析表达式,并编写基于C#语言的随机响应面法计算程序。以岩质边坡平面滑动破坏模式为例证明随机响应面法在边坡可靠度分析中的有效性。研究结果表明,基于Nataf变换的随机响应面法能够有效分析含有相关非正态变量的边坡可靠度问题。随机响应面法的计算精度优于传统的FORM方法,其计算效率高于传统的蒙特卡罗模拟方法,其收敛性在数学意义上是有保证的。随机多项式展开的阶数几乎对边坡安全系数均值的估计没有影响,但是在边坡失效概率的计算中要选择适当的随机多项式展开的阶数。在基于随机响应面法的可靠度分析框架内,边坡安全系数计算和可靠度分析2个过程分开独立进行,同时计算安全系数和失效概率能够更加系统地进行边坡稳定性分析。研究成果为拓展随机响应面法在边坡可靠度分析中的应用奠定了一定的基础。     

结构可靠度分析的实用方法研究

现有的结构可靠度分析方法较多,文中系统地介绍了结构点可靠度的计算方法并对其进行了分类概括和评述,着重对一次二阶矩法、高次高阶矩法、帕罗黑莫法、蒙特卡罗法、响应面法和随机有限元法进行了分析。为人们在进行结构可靠度计算时提供了一个有价值的参考。     

Reliability analysis and inspection updating by stochastic response surface of fatigue cracks in mixed mode

The analysis of engineering structures under fatigue crack growth aims at ensuring an appropriate reliability level over the entire operational lifetime. This paper deals with a new approach, namely the Stochastic Response Surface, to couple finite element analysis and reliability methods. The stochastic collocation method provides an explicit expression of the limit state function related to fatigue failure. This expression is used in first and second order reliability methods in order to compute the failure probability at a given structural age. When inspection is carried out, the structural reliability can be easily updated in terms of the observed crack length. Two numerical applications dealing with fatigue crack growth are presented to illustrate the proposed method, showing its performance in terms of numerical efficiency and accuracy.     

CQ2RS: a new statistical approach to the response surface method for reliability analysis

Assessing the reliability of a complex structure requires a deal between reliability algorithms and numerical methods used to model the mechanical behavior. The Response Surface Method (RSM) represents a convenient way to achieve this purpose. The interest of such a method is that the user is allowed to choose and check the computed mechanical experiments. Nevertheless, this choice in an optimal way turns out to be not always an easy task. This paper proposes a response surface method named CQ2RS (Complete Quadratic Response Surface with ReSampling) allowing to take into account the knowledge of the engineer on one hand and to reduce the cost of the reliability analysis using a statistical formulation of the RSM problem on the other hand. Some academic and industrial examples illustrate the efficiency of the method.     

A sequential response surface method and its application in the reliability analysis of aircraft structural systems

The reliability analysis of aircraft structural systems is difficult to evaluate due to the complexity of the g-function g(x), the probability density function ƒ(x) and the dimension m of the problem. In many cases, the g-function can be very complex and the number of evaluation of g(x) may dominate the computation cost. Response Surface Methods may alleviate the problem by giving a simple approximation, g′(x), to the true g-function, which can then be used instead of g(x) for the reliability analysis.In this paper, a new Sequential Response Surface Method together with Monte Carlo Importance Sampling (MCIS) is suggested. Based on the method, a reliability analysis program RSM for aircraft structural systems is developed.Several examples are presented to illustrate the method.     

Moment methods for structural reliability

First-order reliability method (FORM) is considered to be one of the most reliable computational methods. In the last decades, researchers have examined the shortcomings of FORM, primarily accuracy and the difficulties involved in searching for the design point by iteration using the derivatives of the performance function. In order to improve upon FORM, several structural reliability methods have been developed based on FORM, such as second-order reliability method (SORM), importance sampling Monte-Carlo simulation, first-order third-moment reliability method (FOTM), and response surface approach (RSA). In the present paper, moment methods for structural reliability are investigated. Five moment method formulas are presented and investigated, and the accuracy and efficiency of these methods are demonstrated using numerical examples. The moment methods, being very simple, have no shortcomings with respect to design points, and requires neither iteration nor the computation of derivatives, and thus are convenient to be applied to structural reliability analysis.     

外加预应力加固RC梁挠度计算的可靠度分析

以外加预应力加固RC梁挠度计算的工程实例,应用改进一次二阶矩法建立基于挠度计算的极限状态方程,通过四次迭代计算,得到外加预应力加固RC梁挠度计算的可靠度指标,并与一次二阶矩法得到的结果进行对比,结论表明,应用改进一次二阶矩法计算得到的可靠度指标具有更好的精度。     

蒙特卡罗法理论及其在ANSYS中的实现

综述了计算可靠性的方法——蒙特卡罗法的基本理论,介绍了其在有限元程序ANSYS的实现,对两跨6层的平面框架进行了可靠性分析,并得到理想的分析结果.有限元程序ANSYS的使用,方便的实现了MCM分析,计算机软件和硬件发展将推动MCM进行可靠性分析的实际应用范围和深度.     

A hybrid approach to detect crack parameters using measured natural frequencies in thin walled angle section steel beams

Present study outlines a hybrid approach using Finite Element Method (FEM)–Response Surface Method (RSM)–Genetic Algorithm (GA) to predict the crack parameters, namely crack position and crack depth ratio with the help of only the measured natural frequencies of cracked thin walled beams. Numerical experimental trials of cracked beams have been conducted based on design of experiment (DOE) approach using an improved Finite element model. The improvement has been achieved by consideration of warping stiffness in cracked angle section beam. Thereafter, regression analysis has been conducted to construct Response Surface Function (RSF). Optimum crack parameters were then calculated using GA by minimizing an objective function which has been formed as the root mean square (RMS) of the residuals between RSFs and measured frequencies. Results of the study indicate that, the proposed approach performs with excellent accuracy and it does not require the response of an uncracked beam as benchmark information.     

Prediction of the combination of failure modes for an arch bridge system

An innovative prediction method for the combination of failure modes of an arch bridge is proposed for its probabilistic risk assessment and is compared with the conventional system reliability analysis method. The suggested method reveals various combinations of failure modes in significantly reduced time and efforts in comparison to the previous permutation method or the conventional system reliability analysis method. Additionally, the suggested method can be used for the verification of the system reliability with more specific predictions of the failure modes.Component reliabilities of girders have been evaluated by using response surfaces of the design variables at the selected critical sections, i.e. the maximum shear and negative moment locations. Response Surface Method (RSM) is successfully applied for the reliability analyses of complex structure with relatively small probability of failure. Previous methods such as Monte Carlo Simulations or First Order Second Moment method cannot easily calculate the derivative terms of implicit limit state functions. Hence, the target bridge system is modeled as a series-connection system for the analysis of its system reliability. The upper and lower bound of the probabilities of failure for the structural system have been evaluated and are compared with the suggested prediction method for all possible combination of failure modes.     

A new look at the response surface approach for reliability analysis

Closed-form mechanical models to predict the behaviour of complex structural systems often are unavailable. Although reliability analysis of such systems can be carried out by Monte Carlo simulations, the large number of structural analyses required results in prohibitively high computational costs. By using polynomial approximations of actual limit states in the reliability analysis, the number of analyses required can be minimized. Such approximations are referred to as Response Surfaces. This paper briefly describes the response surface methodology and critically evaluates existing approaches for choosing the experimental points at which the structural analyses must be performed. Methods are investigated to incorporate information on probability distributions of random variables in selecting the experimental points and to ensure that the response surface fits the actual limit state in the region of maximum likelihood. A criterion for reduction in the number of experiments after the first iteration is suggested. Two numerical examples show the application of the approach.