Reliability analysis using radial basis function networks and support vector machines

To reduce computational costs in structural reliability analysis, utilising approximate response surface functions for reliability assessment has been suggested. Based on the similarities of two adaptive and flexible models, the radial basis function neural network (RBFN) and support vector machine (SVM), the derivatives of the approximate functions of RBFN and SVM models with respect to basic variables are given, and two RBFN-based RSMs (RBFN-RSM1, RBFN-RSM2) and two SVM-based RSMs (SVM-RSM1, SVM-RSM2) are studied. The similarities and differences of these methods are reviewed, and the applicability of these methods is illustrated using five examples. It is shown that there is no obvious difference between RBFN-based RSMs and SVM-based RSMs, and the number of samples needed in RBFN/SVM-RSM2 is smaller than that of RBFN/SVM-RSM1.     

边坡可靠度分析的支持向量机法

提出了基于支持向量机（SVM）的边坡可靠度分析新算法。该方法采用均匀设计确定样本点,通过一定数量的确定性计算来训练SVM,拟合边坡的功能函数;采用一阶可靠度方法（FORM）和迭代算法优化SVM模型,获得可靠度指标和验算点信息;在SVM模型基础上进一步通过二阶可靠度方法（SORM）和蒙特卡罗模拟（MCS）计算边坡的失稳概率。以两个典型边坡为例,通过与其他方法比较,证明了该方法的准确性和高效性。结果表明：提出的在标准正态空间（U空间）中取样并构建SVM,在原始空间（X空间）中计算功能函数的算法,有效地解决了具有相关非正态分布变量的可靠度分析问题,并且可很容易扩展到SORM的计算。算例结果证明,该方法的精度高于FORM;而效率优于MCS。分析过程中,边坡安全系数计算和可靠度分析相互独立。因此,该方法既适用于具有显式功能函数的简单问题,也适用于需要软件计算安全系数的实际边坡问题。     

土工格栅加筋橡胶砂强度特性试验研究

橡胶砂作为轻质、耗能填料在土木工程中有广泛的应用前景,但其强度往往会随橡胶含量的增大而降低。土工格栅常用于对散体材料的加筋补强,研究土工格栅对橡胶砂强度特性的加筋效应具有重要意义。基于三轴压缩试验,对3种不同格栅布置方式（1、2、3层）下的干燥橡胶砂强度特性展开研究,重点考察加筋层数对不同围压（50、100、200 kPa）下、不同配比（0%、10%、20%、30%、40%）橡胶砂的强度参数,如峰值强度、似黏聚力、内摩擦角的影响规律。结果表明：土工格栅加筋橡胶砂的强度参数,包括峰值强度、似黏聚力、内摩擦角,相对于未加筋橡胶砂均有明显提高,提高幅度随土工格栅加筋层数的增加而增大,随着围压的降低而增大;土工格栅对配比为20%橡胶砂的强度加筋效应最为明显;土工格栅加筋橡胶砂的强度参数恢复系数与加筋密度之间呈良好的线性关系;土工格栅加筋橡胶砂的强度特性可由试验所得的经验恢复函数较好地估计。     

Reliability analysis of a large-scale landslide using SOED-based RSM

A design matrix in response surface method (RSM) that satisfies the orthogonality is very useful because the mean square error can be minimized, so that the response surface is more precise. But the orthogonality of a second-order design matrix in conventional RSM cannot be satisfied. In this paper, a second-order orthogonal experimental design (SOED)-based RSM is proposed by considering the orthogonality of high-order design matrix. The SOED is constructed by changing the length of star points, and the main characteristic of SOED is that the design matrix is diagonal. When the high-order terms are considered in the SOED-based RSM, a globe optimal solution can be found. As the regression equation is determined, the reliability index can be analyzed by the normalized distance between the mean value of the performance function and the critical limit state of the safety factor. A practical large-scale landslide with two slip surfaces is taken to verify the applicability and precision of the proposed method in detail. It is found that the SOED-based response surface is more rigorous than the conventional RSM.     

基于响应面法的边坡稳定二阶可靠度分析

提出了基于响应面法的边坡稳定二阶可靠度分析的实用算法。选择U空间中的随机变量,通过空间变换和相关矩阵分解,计算试验点的功能函数;通过迭代算法构造响应面、以确保通过最小的计算量获得最优精度,并在此基础上进行FORM/SORM计算。以一岩石边坡的平面滑动问题为例,通过与蒙特卡洛模拟、FORM及随机响应面法的比较,证明了该方法的准确性和高效性。分析了参数的相关性及试验点取值范围对计算结果的影响,讨论了可靠度分析结果中参数敏感性和物理属性问题。该方法可为实际边坡问题的可靠度分析提供参考,并可以用来进行基于可靠度分析的加固设计。     

橡胶砂动剪模量和阻尼比循环单剪试验研究

对7种不同配比的橡胶颗粒-砂混合物（简称橡胶砂）进行了循环单剪试验,得出了4种不同竖向固结压力p下不同配比橡胶砂的动剪模量和阻尼比的变化规律。研究表明：同一固结压力下,橡胶颗粒的增多使得应力-应变曲线明显降低,动剪模量衰减,阻尼比和隔震消能能力提高;同一配比下,橡胶砂的应力-应变曲线和动剪模量随固结压力的增大而增大,而阻尼比则随着固结压力的增大略有降低;橡胶颗粒含量的增加,会使得动剪模量归一化 曲线衰减更早,更有利于橡胶砂的隔震应用;与已有研究的对比分析表明,该试验结果与已有文献的试验结果吻合良好,橡胶砂混合物的动剪模量和阻尼比受试验方法的影响不大。     

System reliability analysis of slopes using multilayer perceptron and radial basis function networks

This paper presents a system reliability analysis method for soil slopes on the basis of artificial neural networks with computer experiments. Two types of artificial neural networks, multilayer perceptrop (MLP) and radial basis function networks (RBFNs), are tested on the studied problems. Computer experiments are adopted to generate samples for constructing the response surfaces. On the basis of the samples, MLP and RBFN are used for establishing the response surface to approximate the limit state function, and Monte Carlo simulation is performed via the MLP and RBFN response surfaces to estimate the system failure probability of slopes. Experimental results on 3 examples show the effectiveness of the proposed methodology.     

Probabilistic analysis of underground rock excavations using response surface method and SORM

Probabilistic analysis of underground rock excavations is performed using response surface method and SORM, in which the quadratic polynomial with cross terms is used to approximate the implicit limit state surface at the design point. The response surface is found using an iterative algorithm and the probability of failure is evaluated using the first-order and the second-order reliability method (FORM/SORM). Independent standard normal variables in U-space are chosen as basic random variables and transformed into correlated non-normal variables in the original space of random variables for constructing the response surface. The proposed method is first illustrated for a circular tunnel with analytical solutions considering Mohr–Coulomb (M–C) and Hoek–Brown (H–B) yield criteria separately. The failure probability with respect to the plastic zone criterion and the tunnel convergence criterion are estimated from FORM/SORM and compared to those obtained from Monte Carlo Simulations. The results show that the support pressure has great influence on the failure probability of the two failure modes. For the M–C model, the hypothesis of uncorrelated friction angle and cohesion will generate higher non-performance probability in comparison to the case of negatively correlated shear strength parameters. Reliability analyses involving non-normal distributions are also investigated. Finally, an example of a horseshoe-shaped highway tunnel is presented to illustrate the feasibility and validity of the proposed method for practical applications where numerical procedures are needed to calculate the performance function values.     

基于上限分析的边坡稳定可靠性评估

从塑性极限分析出发,基于上限分析构建边坡极限状态可靠度计算模型;针对状态函数高度非线性导致常规可靠度方法求解时存在困难的问题,将响应面模型作为极限状态函数与可靠度计算间"桥梁",利用二次正交原理优化取样点,建立考虑参数相关性的二次响应面替代函数。利用JC法直接求得边坡可靠指标的一个上限解,讨论了单个及多个参数变异性对边坡可靠度的影响。     

边坡失效概率估计的高斯过程动态响应面法

针对传统响应面法在求解具有高度非线性隐式功能函数边坡可靠性问题上的局限性,采用适用于处理高维度、小样本、非线性回归问题的高斯过程回归模型构建隐式功能函数的响应面,将高斯过程响应面与蒙特卡罗模拟法相结合,通过构造合理的迭代方式,在利用高斯过程回归模型的不确定性评价功能获取最优采样点的基础上,实现了高斯过程响应面动态更新,由此提出了边坡失效概率快速估计的高斯过程动态响应面法。利用数值算例验证了该方法的有效性,在此基础上对3个边坡算例进行了可靠性分析。结果表明,与传统响应面法相比较,该方法计算精度与计算效率明显较高,易于与既有的边坡分析软件相结合,且实现容易,适用于边坡可靠性的快速分析。     

Probabilistic assessment of tunnel convergence considering spatial variability in rock mass properties using interpolated autocorrelation and response surface method

This study aims at the probabilistic assessment of tunnel convergence considering the spatial variability in rock mass properties. The method of interpolated autocorrelation combined with finite difference analysis is adopted to model the spatial variability of rock mass properties. An iterative procedure using the first-order reliability method(FORM) and response surface method(RSM) is employed to compute the reliability index and its corresponding design point. The results indicate that the spatial variability considerably affects the computed reliability index. The probability of failure could be noticeably overestimated in the case where the spatial variability is neglected. The vertical scale of fluctuation has a much higher effect on the probabilistic result with respect to the tunnel convergence than the horizontal scale of fluctuation. And the influence of different spacing of control points on the computational accuracy is investigated.     

考虑参数空间变异性的非饱和土坡可靠度分析

在考虑多个土体参数空间变异性的基础上,提出了基于拉丁超立方抽样的非饱和土坡稳定可靠度分析的非侵入式随机有限元法。利用Hermite随机多项式展开拟合边坡安全系数与输入参数间的隐式函数关系,采用拉丁超立方抽样技术产生输入参数样本点,通过Karhunen-Loève展开方法离散土体渗透系数、有效黏聚力和内摩擦角随机场,并编写了计算程序NISFEM-KL-LHS。研究了该方法在稳定渗流条件下非饱和土坡可靠度分析中的应用。结果表明：非侵入式随机有限元法为考虑多个土体参数空间变异性的非饱和土坡可靠度问题提供了一种有效的分析工具。土体渗透系数空间变异性和坡面降雨强度对边坡地下水位和最危险滑动面位置均有明显的影响。当降雨强度与饱和渗透系数的比值大于0.01时,边坡失效概率急剧增加。当土体参数变异性或者参数间负相关性较大时,忽略土体参数空间变异性会明显高估边坡失效概率。     

Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables

This paper proposes a stochastic response surface method for reliability analysis involving correlated non-normal random variables, in which the Nataf transformation is adopted to effectively transform the correlated non-normal variables into independent standard normal variables. Transformations of random variables that are often used in reliability analyses in terms of standard normal variables are summarized. The closed-form expressions for fourth to sixth order Hermite polynomial chaos expansions involving any number of random variables are formulated. The proposed method will substantially extend the application of stochastic response surface method for reliability problems. An example of reliability analysis of rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed stochastic response surface method. The results indicate that the proposed stochastic response surface method can evaluate the reliability of rock slope stability involving correlated non-normal variables accurately and efficiently. Its accuracy is shown to be higher than that for the first-order reliability method, and it is much more efficient than direct Monte-Carlo simulation. The results also show that the number of collocation points selected should ensure that the Hermite polynomial matrix has a full rank so that different order SRSMs can produce a robust estimation of probability of failure for a specified performance function. Generally, the accuracy of SRSM increases as the order of SRSM increases.     

Representing the geological body heterogeneous property field using the quadratic generalized tri-prism volume function model (QGTPVF)

3D geological modeling should be an effective tool for accurately representing the geometric structure boundary and internal property fields of geological body. However, conventional methods have rarely focused on the expression of geological heterogeneous properties, known as 4D modeling. A volume function is defined as a piecewise mathematic function that describes a parameterized geological property field and created by fitting the property functions of certain 3D voxels. The quadratic generalized tri-prism volume function (QGTPVF) model is proposed for representing geological property fields with a sedimentary strata structure based on the volume function method and generalized tri-prism (GTP) voxel model. A QGTPVF is designed for borehole sample points, and it interpolates geological properties by fitting quadratic volume functions combined with the influence of geological geometric structure constraints, including stratum interfaces and fault planes. This research mainly focuses on the QGTPVF definition and fitting method, single GTP volume function is a continuous quadratic function, and a property smoothing along directionally adjacent bedding GTPs method is also studied, so geological property field is also expressed by the smooth function. A preprocessing method of faults geological structures is given, and the general framework QGTPVF is also discussed for practical applications. The QGTPVF model could be converted to tetrahedron voxel and 3D grid models for calculation and analysis easily. An example on a porosity property field is studied to verify the method’s accuracy and reliability by comparing to Kriging and inverse distance weighted interpolation methods, and the result of accuracy and time complexity are better, so the QGTPVF provides a new solution for modeling geological property fields.     

基于整体稳定性分析法的边坡临界滑动面搜索

临界滑动面搜索是边坡稳定分析中很重要的内容,针对现有方法的不足,提出了一种新的搜索方法。基于边坡稳定性的整体分析法,建立了确定临界滑面的非线性优化模型。该模型将滑面离散点的纵坐标和安全系数都视为独立变量,目标函数取为安全系数本身,约束条件是平衡方程组和滑面凸性。由于目标函数是线性函数,约束条件至多是二次多项式,非线性程度较低,可采用经典优化算法和常见的非线性优化工具求解,比如Matlab。通过实例分析并与传统的滑面搜索方法进行对比表明,所建议的方法在数值稳定性及收敛性方面均具有优势。     

表面波法确定卵石土地基承载力模型研究

利用统计学的原理,对卵石土地基动力触探击数和剪切波速的关系进行了研究,推导了它们之间的二次多项式、幂函数和指数函数回归方程。通过对比研究发现,二者之间具有良好的指数函数相关关系。为了验证该指数函数回归模型的可行性,选择了相似场地进行面波检测试验,试验结果与勘探结果完全吻合。研究结果表明,应用表面波法不但可以进行卵石土地基分层,而且还可以定量地评价其地基承载力。     

边坡危险滑动面及稳定安全系数的力学解析方法

为了分析边坡的稳定性,提出了一种基于极限平衡理论的分析方法。假定坡体为只受重力作用的弹性体,通过弹性力学解析解求得应力分布,将滑动面用分段二次多项式函数表示,当分段间隔足够小时,这种表示方式可以描述任意曲面形状,根据坡体滑面所满足的Mohr-Coulomb准则,定义边坡稳定安全系数,其为多项式系数的函数。通过混和罚函数优化方法可以求出最危险滑动面对应的多项式系数,获得边坡的稳定安全系数,从而判定边坡的稳定性。所提出的方法与以往方法不同,不用将滑体划分成垂直条块,不用假定滑面上的法向应力分布形式,而直接利用已有的坡体弹性应力解。算例表明:本文方法所得到的结果与简化Bishop法和有限元强度折减法获得的结果非常接近,且基本介于有限元法和简化Bishop法之间。     

改进响应面法及其在倾斜荷载桩可靠度分析中的应用

针对结构可靠度分析中常用的二次函数响应面法的不足,提出一种采用髙次响应面函数和利用JC法几何性质原理确定迭代中心点准则的响应面法。在此基础上,将该法应用于倾斜荷载桩的可靠性分析,计算了基于桩顶水平位移过大和桩身材料屈服这两种失效模式下的基桩可靠度,并连同蒙特卡罗法和二次函数响应面法的计算结果进行了比较。计算表明,改进的响应面法减少了计算的迭代次数,有效地提高了计算精度和数值试验的稳定性,可用于大型复杂结构的可靠性分析。     

岩土力学数值模拟结果的概率评估方法研究

提出了一种用于评估多参数随机变异情况下岩土力学非线性数值模拟结果可靠性的多维高效直接积分型随机分析方法.它首先根据多维积分理论和可靠性分析的直接积分法确定多维随机输入参数的计值点;然后利用非线性数值模拟方法,比如有限元法或有限差分法等,完成所有计值点上的计算任务,据此就可以利用多维高效积分程序计算待评估响应量的前几阶矩(一般包括1～6阶矩);最后利用多种方法,包括曲线拟合法、加权余量法及最大熵法计算响应量的概率分布,并据此算出响应量的概率置信区间,用于定量评估响应量的可靠性.数值算例表明,此法具有精度和计算效率较高的优点.     

基于多项式拟合模型的GPS高程转换方法研究

在详细论述GPS高程转换基本原理的基础上,利用二次多项式模型,对区域高程异常进行了拟合分析,并进行了精度评定。结果显示,利用二次多项式模型进行GPS高程转换能够取得较好的结果,参与建模的点位拟合精度较高,而远离建模点分布区域的点位拟合精度相对较低,建模点的选取能够对GPS高程拟合结果产生重要影响。