响应面方法在边坡稳定可靠度分析中的应用

以Janbu法为例，研究隐式功能函数边坡工程稳定可靠度计算方法。首先分析非圆弧滑动边坡变形力学模式安全系数计算步骤和过程，提出采用类似力学模式的安全系数计算作为试验手段。借用响应面思想，利用试验结果拟合近似安全系数计算方程从而替代隐式方程，并建立近似极限状态方程。利用其计算可靠度指标和验算点，然后将安全系数计算近似方程、隐函数计算方程和验算点结合起来，确定新的展开点和抽样点，并进行近似方程再拟合、可靠度指标的循环计算直到收敛。这些研究构成状态方程为隐函数时的可靠度近似计算方法。最后通过不同计算方法的对比，验证该近似方法的准确性和合理性，并采用近似方程分析灰木露天矿边坡的稳定可靠性。     

基于响应面与重要性抽样的岩土工程可靠度分析方法研究

 由于功能函数非线性强且难以显式表达,岩土工程可靠度分析以往多采用响应面方法解决,但其求解的可靠度指标为几何可靠度。阐明几何可靠度与一般可靠度的实质和两者之间的差异,指出对于功能函数非线性较强的岩土工程问题,采用几何可靠度指标存在较大误差,需进行改进。然后引入V空间重要抽样方法将基本变量随机空间通过Rosenblatt变换和线性正交变换转换至V空间,在响应面方法得到岩土工程的设计验算点及其附近的响应面的基础上,采用重要性抽样方法求解岩土工程可靠度。几个数值算例和工程实例的对比分析表明该方法可行、有效、精度较高,适用于非线性强的岩土工程可靠度求解。     

管片衬砌结构可靠度分析的优化方法

从结构可靠度指标的几何意义出发,推导了管片衬砌结构可靠度指标计算的优化模型,在此基础上研制了基于复形优化思想的数值计算程序。算例表明,管片衬砌结构可靠度指标优化模型无需功能函数对变量求偏导数,将当量标准正态变量在验算点上的值用原始变量统计特征值和验算点的坐标来表示,就避免了每次迭代时要进行R-F变换,提高了计算效率,且精度较高。该优化模型对功能函数非线性程度高、隐式表示的管片衬砌结构可靠度分析比较适用,为地下结构可靠度分析提供了一种新的选择。     

基于遗传算法的重力坝多滑面稳定可靠度分析

重力坝坝基的抗滑稳定是大坝设计中首先要解决的关键问题,但是以往的坝基深层抗滑稳定可靠度研究中关于多滑面情况的研究成果偏少,主要原因是多滑面稳定可靠度计算的功能函数往往为隐式非线性,问题相对复杂、计算求解困难。根据可靠指标的几何涵义,将可靠度计算作为优化问题求解,从而引入遗传算法,提出基于遗传算法的重力坝坝基深层抗滑稳定可靠度计算方法。该方法避免功能函数需要表达为显式函数的限制,从而能够克服现行设计标准或规范中一次二阶矩方法适用性的不足,可用于多滑面情况的重力坝坝基抗滑稳定可靠度研究。算例和工程实例分析表明,该方法计算工作量少,精度和计算效率高,能同时满足具有显式或隐式功能函数的复杂工程结构可靠度计算,体现出常规可靠度计算方法不具备的优势,可为重力坝稳定安全评价方法的深入研究与重力坝结构设计提供新的思路和技术支撑。     

稳定性系数为隐式函数的边坡可靠度近似计算方法

分析发现在大多数情况下,边坡滑动模式的稳定性系数计算是一个隐函数。导致了在其相应的可靠度研究中建立显式的极限状态方程是不可能的。为了解决这一问题,以边坡稳定性分析的郎畏勒计算模式为例,研究了一种改进的响应面方法。在该方法中,采用郎畏勒分析模式的稳定性系数隐式计算方法取代经典响应面方法的有限元数值模拟计算;为了消除经典方法可靠度指标求解过程中方程线性化带来的误差,研究了采用梯度最速下降法最优化方法求解验算点的过程和步骤。然后给出了改进后的响应面方法近似显式函数拟合和可靠度指标的工作流程,最后采用改进的方法分析一个工程实例。改进的响应面计算过程比经典方法简单适用,工作量较小,具有理论意义和工程应用前景。     

改进的一次二阶矩法在隧道可靠度中的应用

在隧道衬砌结构可靠度分析中,基于一次二阶矩中心点法在基本变量的概率分布若为非正态分布或为非对数正态分布以及结构功能函数为非线性函数时,中心点法计算结果与实际出入较大。通过引入分离函数式对一次二阶矩法进行的线性化处理,结合蒙特卡罗-有限元法计算荷载作用效应的统计特征,从设计验算点开始进行迭代,并利用Mathematica辅助编程对隧道结构可靠度指标进行求解。计算结果表明:改进一次二阶矩法与分位点法相比具有更令人满意的精度,实用性好,适用于隧道及地下工程结构的可靠度分析。     

边坡可靠性评价的向量投影响应面研究及应用

岩土体的力学参数存在一定的随机性,当进行边坡稳定可靠性评价时,当功能函数不能用显式表达时,响应面法成为计算可靠度指标的重要方法。将向量投影响应面法与有限元强度折减法相结合,研究隐式功能函数边坡工程稳定可靠度计算方法。首先利用强度折减法结果拟合稳定系数计算方程从而代替隐式方程,并建立极限状态方程,然后进行向量投影以确定展开点和抽样点,进行近似方程的拟合、验算点和可靠度指标的计算,直到计算达到收敛。通过与不同计算方法进行对比,表明区别于通常以插值点为中心展开生成样本点的向量投影取样法的准确性和合理性,该方法可使可靠性分析次数显著减少,改善了对非线性程度较高的极限功能函数求解可靠指标的收敛性。同时,将该方法应用于杭兰高速公路大水田边坡的稳定可靠性分析当中。     

适用于边坡可靠度计算的改进二次二阶矩法

可靠性分析方法能够考虑边坡坡体材料及赋存环境的不确定性,在边坡稳定性评估中逐渐占据一定地位.常见可靠度计算方法中,二次二阶矩法所涉及的偏导数解析求解思路对功能函数要求严格,极大限制了该方法解决边坡可靠性问题的能力.利用数值差分原理,推导出功能函数在验算点处对基本随机变量的一阶、二阶及二阶混合偏导数近似计算公式;基于所推...     

基于神经网络和改进JC法的预应力混凝土连续梁桥可靠度研究

由于预应力混凝土连续梁桥极限状态功能函数不能显式表达,导致其可靠度求解困难。本文将BP神经网络与改进JC法引入预应力混凝土连续梁桥可靠度分析领域,首先利用BP神经网络对结构功能函数进行拟合,将高度非线性的极限状态方程显式化,然后采用改进JC法全局搜索验算点并求解可靠度指标,并采用算例来验证该方法的精度和效率。然后以一座预应力混凝土连续梁桥为例,计算结构的可靠指标。计算分析结果表明,BP神经网络和改进JC法能很好地应用于预应力混凝土连续梁桥的可靠度分析,能够弥补传统可靠度分析方法的不足,并且满足工程精度要求。     

基于组合拱理论隧道锚喷支护稳定可靠度求解的一维积分方法

基于组合拱原理和剪切滑移破坏模型,导出隧道锚喷支护结构功能函数。该函数表现为高度非线性隐式特征,同时基本参数间存在相关性,导致其可靠度求解困难。首先,引入基于半解析的Nataf变换以消除基本参数相关性的影响,将原始随机变量导入到标准正态空间中。其次,根据统计矩点估计法原理,依靠基本随机变量统计特征导出功能函数统计特征的矩估计公式。最后,根据统计矩与其变量的关系,以功能函数的前四阶矩为约束,基于最大熵理论导出功能函数的概率密度函数。构建基于组合拱理论的隧道锚喷支护稳定可靠度求解的一维数值积分方法。通过数值算例验证其准确性,最后分析荆竹山公路隧道支护结构的稳定可靠度,展示该方法的应用前景。     

Reliability analysis of ground–support interaction in circular tunnels using the response surface method

The first-order and the second-order reliability method (FORM/SORM) are used to evaluate the failure probability of three performance functions of the ground–support interaction in circular tunnels subjected to hydrostatic stresses. The response surface method (RSM) is used to enable reliability analysis of the implicit convergence-confinement method. The friction angle, cohesion and elastic modulus of the rock mass are considered as basic random variables and are first assumed to obey normal distributions. The quadratic polynomial with cross terms is employed as response surface function to approximate the limit state surface (LSS) at the design point. The strategies for the RSM are presented. The failure probability with respect to different criteria are obtained from FORM/SORM and compared to those generated from Monte Carlo simulations. The results show that the support installation position has great influence on the probability of the three failure modes under consideration. Comparison between analysis using correlated and uncorrelated friction angle and cohesion indicates that the influence of the correlation on the reliability analysis depends on the support installation position and the orientation of the LSS. The reliability analysis involving correlated non-normal distributions and the reliability-based design of the support are also investigated.     

Reliability analysis of tunnel using least square support vector machine

In the reliability analysis of tunnels, the limited state function is implicit and nonlinear, and is difficult to apply based on the traditional reliability method, especially for large-scale projects. Least squares support vector machines (LS-SVM) are capable of approximating the limited state function without the need for additional assumptions regarding the function form, in comparison to traditional polynomial response surfaces. In the present work, the LS-SVM method was adapted to obtain the limited state function. An LS-SVM-based response surface method (RSM), combined with the first-order reliability method (FORM), is proposed for use in tunnel reliability analysis and implementation of the method is described. The reliability index obtained from the proposed method applied to particular tunnel configurations under different conditions shows excellent agreement with Low and Tang’s (2007) method and traditional RSM results, and indicates that the LS-SVM-based RSM is an efficient and effective approach for reliability analysis in tunnel engineering.     

Structural reliability analysis for implicit performance functions using artificial neural network

The Monte-Carlo simulation (MCS), the first-order reliability methods (FORM) and the second-order reliability methods (SORM), are three reliability analysis methods that are commonly used for structural safety evaluation. The MCS requires the calculations of hundreds and thousands of performance function values. The FORM and SORM demand the values and partial derivatives of the performance function with respect to the design random variables. Such calculations could be time-consuming or cumbersome when the performance functions are implicit. Such implicit performance functions are normally encountered when the structural systems are complicated and numerical analysis such as finite element methods has to be adopted for the prediction.To address this issue, this paper presents three artificial neural network (ANN)-based reliability analysis methods, i.e. ANN-based MCS, ANN-based FORM, and ANN-based SORM. These methods employ multi-layer feedforward ANN technique to approximate the implicit performance functions. The ANN technique uses a small set of the actual values of the implicit performance functions. Such a small set of actual data is obtained via normal numerical analysis such as finite element methods for the complicated structural system. They are used to develop a trained ANN generalization algorithm. Then a large number of the values and partial derivatives of the implicit performance functions can be obtained for conventional reliability analysis using MCS, FORM or SORM. Examples are given in the paper to illustrate why and how the proposed ANN-based structural reliability analysis can be carried out. The results have shown the proposed approach is applicable to structural reliability analysis involving implicit performance functions. The present results are compared well with those obtained by the conventional reliability methods such as the direct Monte-Carlo simulation, the response surface method and the FORM method 2.     

大跨度悬索桥颤振可靠度分析的改进响应面法

介绍一种新的计算悬索桥颤振可靠度方法——改进响应面法。该方法利用传统响应面法将极限状态方程近似表达为简单的多项式形式,有效地解决FORM和SORM无法求解隐式极限状态方程的可靠度问题。另外,改进响应面法的使用还能有效地利用现有的确定性颤振分析软件。通过引入有限元方法,改进响应面法可应用于悬索桥颤振可靠度问题。通过使用重要抽样技术,提高改进响应面法的计算效率和计算精度,有效地解决传统响应面法在结构可靠度较大或失效概率较低时出现的迭代不收敛问题。数值算例验证该方法的效率和精度。最后,用该方法计算江阴长江大桥的颤振可靠度,结果表明基于经验公式的改进响应面法会过高地估计大跨度悬索桥的颤振可靠度。实际的悬索桥颤振可靠度应该采用基于有限元法的改进响应面法进行计算。     

Probabilistic evaluation for the implicit limit-state function of stability of a highway tunnel in China

This paper presents a practical algorithm for the first-order reliability method (FORM) to deal with the implicit nature of a limit-state function (LSF) in reliability assessment of stability of a working highway tunnel, which is constructed in a mountainous area in China. First, a mechanical model to determine the LSF that is not explicitly known with complex non-linear behaviour is formulated for the primary support provided by the combination of shotcrete and rockbolts. After reviewing concisely the basic concepts relevant to the FORM, the central difference approximation is subsequently introduced to estimate the partial derivatives of the LSF. By consideration of Taylor’s formula, this LSF can be transformed into an equation involving a single unknown described as the reliability index, and then the resulting solution procedure for determination of the reliability index can be rendered based on the derivation rule of compound function. A flow for tunnel reliability problem posed by the implicit LSF in applying the FORM is further developed. Eventually, the proposed methodology for the LSF in the non-explicit circumstance is used to perform the probabilistic evaluation for such a working tunnel where the choices of values of step length coefficient affecting the calculation results are suggested. Comparisons are made with the Monte-Carlo simulation method (MCSM) to assess the computational accuracy and efficiency of the algorithm proposed in this paper. It is shown that the MCSM used to obtain the “exact” solutions entails the formidable computational effort, whereas the current algorithm that alleviates the computational labour dramatically can provide an efficient way of implementing reliability calculations for the implicit LSF and offer results which are found to be in satisfactory agreement with the “exact” ones when the step length coefficient is properly taken.     

边坡可靠度分析的高斯过程方法

针对传统边坡可靠度分析方法的局限性,将高斯过程机器学习与重要抽样方法相结合,提出了边坡可靠度分析的高斯过程方法。利用极限平衡分析构造少量的学习样本,采用基于统计学习原理的高斯过程模型重构边坡隐式功能函数,实现边坡功能函数及其偏导数的显式表达,并构造合理的迭代方式,在计算过程中不断提升高斯过程模型对失效概率贡献较大区域的重构精度,进而应用重要抽样法计算边坡的失效概率与可靠指标。研究结果表明,该方法是可行的,具有较高的计算精度和效率。     

Reliability-based design optimization using convex linearization and sequential optimization and reliability assessment method

In this study, an effective method for reliability-based design optimization (RBDO) is proposed enhancing sequential optimization and reliability assessment (SORA) method by convex linearization. In SORA, reliability estimation and deterministic optimization are performed sequentially. And the sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the process of finding reliability information. In this study, the convex linearization is constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. So no additional evaluation of the probabilistic constraint is required in the deterministic optimization in SORA. The proposed RBDO method is applied to numerical examples and compared to various RBDO methods. It is shown that the proposed method is very efficient with similar accuracy.     

Response surface augmented moment method for efficient reliability analysis

The reliability analysis procedure based on design of experiment (DOE) is combined with the response surface method (RSM) for numerical efficiency. Instead of using the inefficient full factorial DOE, a response surface is constructed initially based on the data on the axial experimental points and updated successively by adding one more experimental point selected using an influence index, until the probability is converged. It is calculated using the Pearson system and the four statistical moments obtained from the experimental data complemented by the response surface. During the update of a response surface, cross product terms can be added into the formulation. The number of updating steps is finite, since the points to be added are selected among the set of points of full factorial design. The performance of the proposed method is tested with several examples containing various types of distributions. It is shown that the probability converges early in the process and thus the amount of calculation is only a small fraction of that of a full factorial design. This is comparable or even better than any other methods including FORM for a moderate number of random variables tested.     

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.     

Flutter reliability analysis of suspension bridges

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first-order reliability method (FORM) and the importance sampling updating method. The method is especially applicable for the reliability evaluation of complex structures of which the limit state surfaces are not known explicitly. After the accuracy and efficiency of the method are demonstrated through numerical examples, the method is used to estimate the flutter reliability of a suspension bridge. The uncertainties such as material properties, geometric parameters, structural damping ratio, flutter derivatives and extreme wind velocity at the bridge site are considered. The example suspension bridge is the Jiang Yin Bridge with a main span length of 1385 m built in China. The results show that the proposed method based on an empirical formula in which the limit state function is explicitly represented as a function of variables overestimates the flutter reliability of suspension bridges. The actual flutter reliability should be more accurately analyzed using the proposed method based on the deterministic finite element method in which the limit state function is implicitly represented as a function of variables. Finally, the most influential random variables on flutter reliability of suspension bridges are identified by using a sensitivity analysis.