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1.
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。 相似文献
2.
Efficient reliability method for implicit limit state surface with correlated non‐Gaussian variables 
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下载免费PDF全文 In contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u‐space), the reliability analysis that is simply realized in the original space (x‐space, non‐Gaussian type) would be more efficient for practical use, for example, with the Low and Tang's constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for first‐order reliability method is derived in this paper. Also, the new algorithm is simply formulated in x‐space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non‐Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed‐form solution. With the aid of numerical differentiation analysis in x‐space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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以模糊随机变量理论为指导,视模糊随机变量的均值为模糊数,基于小样本理论推导了均值模糊数模糊变化范围与样本数的关系式。采用截集敏感性分析法进行了边坡稳定的模糊随机有限元可靠度分析,得到了边坡的模糊随机可靠指标及模糊滑面的位置,研究了样本数与边坡模糊随机可靠指标的关系。分析表明,基于模糊随机变量理论的模糊随机可靠度分析方法是随机可靠度分析方法的自然推广;模糊随机可靠指标与样本数有关,随着样本数的改变,模糊随机可靠指标的中值也会发生微小变化,不是定值;在相同的置信度情况下,模糊随机可靠指标的变化范围随着样本数的增加而减小,可通过增加样本数的方式来减小模糊随机可靠指标的模糊性。 相似文献
4.
针对特定场地下土工构筑物的正常使用极限状态,采用近年发展的几何可靠性方法计算了多种构筑物的可靠度指标。考虑同一场地下的钻孔灌注桩、抗浮锚杆和CFG桩单桩加载变形测试曲线的离散性,各曲线回归参数呈现差异并可作为随机变量,进而探讨了各曲线回归参数间的相关性及联合分布特性。基于这些回归参数的联合发散概率密度等值线,即随机变量刚好达到极限承载能力状态,该几何可靠性算法可在随机变量的原始空间求得土工构筑物的可靠度指标。通过比对该几何可靠度指标与常规的一次可靠性算法成果,验证了该几何可靠性计算技术的可行性。计算表明,几何可靠性评价模型实施简便,易于被工程技术人员接受。 相似文献
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Efficient Probabilistic Algorithm Illustrated for a Rock Slope 总被引：7，自引：0，他引：7
B. K. Low 《Rock Mechanics and Rock Engineering》2008,41(5):715-734
Summary A new spreadsheet-based algorithm for the first-order reliability method (FORM) is illustrated for a two-dimensional rock
slope of Hong Kong. The new algorithm combines inverse distribution functions and a refined Newton method with the automatic
constrained-optimization search of the design point in the original space of the random variables; it obviates the need for
computations of equivalent normal means and equivalent normal standard deviations. In the rock slope analysis, the versatile
4-parameter beta distribution is used in lieu of a truncated normal distribution. Probabilities of failure inferred from reliability
indices are compared with those from Monte Carlo simulations. The effects of parametric correlations on the required reinforcing
force for a target reliability index value are studied. The intuitive perspective of an expanding equivalent dispersion ellipsoid
in the original space of the basic random variables is also described as it is the basis from which the new approach evolved.
Author’s address: Dr. Bak Kong Low, School of Civil and Environmental Engineering, Nanyang Technological University, Block
N1 #1b-40, 50 Nanyang Avenue, 639798 Singapore 相似文献
6.
SVM在地下工程可靠性分析中的应用 总被引：4，自引：0，他引：4
将支持向量机应用到地下工程可靠性分析中,通过将支持向量机分别与一阶二次矩和蒙特卡洛结合,提出了基于支持向量机的可靠性分析方法,利用数值模拟构造学习样本,通过支持向量机学习,建立变形与随机变量之间映射关系的支持向量机表达,进而实现隧道极限状态函数及其偏导数的显式表达,从而计算隧道的可靠性指标。该方法避免了传统可靠性分析的缺点。算例分析结果表明,该方法计算效率高、结果可靠,对含有大量随机变量的复杂岩土工程可靠性分析具有很大的潜力,具有广泛的应用前景和工程价值。 相似文献
7.
针对基坑工程中岩土参数存在随机性和变异性的特点,基于响应面重构法、遗传算法和禁忌搜索方法研究了土钉墙边坡可靠性分析方法。考虑土钉的加固作用,建立了适用于土钉墙边坡任意形状滑面安全系数计算的改进Morgenstern-Price法。基于响应面原理,将改进Morgenstern-Price法取代传统响应面法中的有限单元法来随机抽样构造响应面函数,建立了一种近似的土钉墙边坡可靠度计算方法。以土体的抗剪强度指标 、 为随机变量,提出了一种能同时确定土钉墙边坡最小可靠度指标 及相应最危险滑面的全局优化计算方法--土钉墙可靠性分析自适应禁忌搜索遗传算法（ATSGA）。结合算例,分别以土钉墙边坡的最小可靠度指标和最小中值安全系数为目标函数,采用ATSGA法搜索其相应的最危险滑动面,结果表明,二者相差较大。 相似文献
8.
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. 相似文献
9.
Slope reliability analysis by updated support vector machine and Monte Carlo simulation 总被引：1，自引：0，他引：1
This paper presents a new methodology for slope reliability analysis by integrating the technologies of updated support vector machine (SVM) and Monte Carlo simulation (MCS). MCS is a powerful tool that may be used to solve a broad range of reliability problems and has therefore become widely used in slope reliability analysis. However, MCS often involves a great number of slope stability analysis computations, a process that requires excessive time consumption. The updated SVM is introduced in order to build the relationship between factor of safety and random variables of slope, contributing to reducing a large number of normal computing tasks and enlarging the problem scale and sample size of MCS. In the algorithm of the updated SVM, the particle swarm optimization method is adopted in order to seek the optimal SVM parameters, enhancing the performance of SVM for solving complex problems in slope stability analysis. Finally, the integrating method is applied to a classic slope for addressing the problem of reliability analysis. The results of this study indicate that the new methodology is capable of obtaining positive results that are consistent with the results of classic solutions; therefore, the methodology is proven to be a powerful and effective tool in slope reliability analysis. 相似文献
10.
Correlated random variables are commonly involved in probabilistic slope stability analysis, such as reliability analysis of slopes with spatially variable soil properties. This paper proposes a simple Correlated Sampling Technique (CST) for generating samples of correlated random variables. The CST firstly produces correlated standard-normally distributed samples through linear combinations of independent standard-normally distributed samples. Correlated arbitrarily distributed samples can then be obtained by the Nataf transformation. The CST was combined with FOSM (named CST-based FOSM) for probabilistic slope stability analysis. The slope reliabilities of a single-layered cohesive soil slope and a high earth and rockfill dam were analyzed to illustrate the CST-based FOSM. These illustrative examples indicated that the CST-based FOSM can accurately estimate the slope reliability indices with considerably fewer simulations (especially in the case of low failure probability) compared with direct MCS, and the slope reliability was sensitive to the correlation of the strength parameters. 相似文献
11.
基于LSSVM与MCS的路基沉降可靠度分析 总被引：1，自引：0，他引：1
提出了一种计算路基沉降可靠度的新方法。基于FLAC中的修正剑桥模型,以最小二乘支持向量机为核心技术,结合蒙特卡罗法构建计算模型。由于修正剑桥模型参数较多,对模型参数进行了敏感性分析,将对沉降影响较大的参数确定为随机变量。选取训练样本对支持向量机进行训练,按照随机变量的概率分布进行抽样,馈送到最小二乘支持向量机得到相应的响应值,用Matlab编制程序完成可靠度计算,并进行了算例分析。计算结果表明,蒙特卡罗法结合支持向量机的沉降可靠度计算方法应用于公路软基沉降可靠度计算是可行的。 相似文献
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在广义随机空间中直接建立验算点的迭代公式,可以方便地解决含相关随机变量的结构可靠度计算问题。在广义随机空间中推导了一种收敛性较好的验算点迭代公式,并应用于边坡稳定的可靠度分析。针对卡基娃混凝土面板堆石坝地震工况坝坡稳定的可靠度分析表明:(1)由于安全系数法采用的输入参数为确定值,故不能考虑参数随机波动的影响。可靠度分析能够反映参数随机性的影响,这对于深入评估工程安全与抗风险能力是有益的。(2)通过引入条件概率方法考虑地震和坝坡失稳同时发生的概率得到的结构可靠指标将提高,而提高的幅度与地震发生概率的大小有关。(3)堆石非线性强度指标具有正相关性,考虑强度指标的相关性将提高边坡稳定的可靠度。 相似文献
13.
Ji Yuan Iason Papaioannou Daniel Straub 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2019,13(1):20-33
Rainfall-induced landslides occur during or immediately after rainfall events in which the pore water pressure builds up, leading to shallow slope failure. Thereby, low permeability layers result in high gradients in pore water pressure. The spatial variability of the soil permeability influences the probability such low permeability layers, and hence the probability of slope failure. In this paper, we investigate the influence of the vertical variability of soil permeability on the slope reliability, accounting for the randomness of rainfall processes. We model the saturated hydraulic conductivity of the soil with a one-dimensional random field. The random rainfall events are characterised by their duration and intensity and are modelled through self-similar random processes. The transient infiltration process is represented by Richards equation, which is evaluated numerically. The reliability analysis of the infinite slope is based on the factor of safety concept for evaluating slope stability. To cope with the large number of random variables arising from the discretization of the random field and the rainfall process, we evaluate the slope reliability through Subset Simulation, which is an adaptive Monte Carlo method known to be especially efficient for reliability analysis of such high-dimensional problems. Numerical investigations show higher probability of slope failure with increased spatial variability of the saturated hydraulic conductivity and with more uniform rainfall patterns. 相似文献
14.
A data driven multivariate adaptive regression splines (MARS) based algorithm for system reliability analysis of earth slopes having random soil properties under the framework of limit equilibrium method of slices is considered. The theoretical formulation is developed based on Spencer method (valid for general slip surfaces) satisfying all conditions of static equilibrium coupled with a nonlinear programming technique of optimization. Simulated noise is used to take account of inevitable modeling inaccuracies and epistemic uncertainties. The proposed MARS based algorithm is capable of achieving high level of computational efficiency in the system reliability analysis without significantly compromising the accuracy of results. 相似文献
15.
The first-order reliability method (FORM) is used to calculate the reliability index of a circular tunnel subjected to a hydrostatic stress field. The random variables are first assumed to follow the normal distribution. Comparison between analysis using negatively correlated and uncorrelated friction angle and cohesion indicates that the results of reliability analysis are conservative if negative correlation among strength parameters is not modeled. The reliability analysis involving correlated non-normal distributions is also investigated. The probability density functions are obtained from reliability indices and compared to those generated from Monte Carlo simulations. Reliability-based design of tunnel support pressure is also illustrated. 相似文献
16.
Probabilistic analysis of underground rock excavations using response surface method and SORM 总被引：6，自引：0，他引：6
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. 相似文献
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After careful analyses of the popular Monte Carlo method and geometric method in reliability analysis, the misuse of Monte Carlo method with several non-uniform distribution random variables is pointed out. As a result, a correct procedure sampling procedure of Monte Carlo method is presented. Meanwhile, in order to satisfy the needs of practice in reliability analysis, an extended geometrical optimized method(EGOM) is proposed, its procedure under conditions of correlation and non-normal distribution variable is also presented. Furthermore, several examples from others’ reliability analysis practice with the proposed EGOM prove its correctness and effectiveness. 相似文献
20.
This paper aims to provide a stochastic response surface method (SRSM) that can consider non-Gaussian dependent random variables under incomplete probability information. The Rosenblatt transformation is adopted to map the random variables from the original space into the mutually independent standard normal space for the stochastic surrogate model development. The multivariate joint distribution is reconstructed by the pair-copula decomposition approach, in which the pair-copula parameters are retrieved from the incomplete probability information. The proposed method is illustrated in a tunnel excavation example. Three different dependence structures characterized by normal copulas, Frank copulas, and hybrid copulas are respectively investigated to demonstrate the effect of dependence structure on the reliability results. The results show that the widely used Nataf transformation is actually a special case of the proposed method if all pair-copulas are normal copulas. The effect of conditioning order is also examined. This study provides a new insight into the SRSM-based reliability analysis from the copula viewpoint and extends the application of SRSM under incomplete probability information. 相似文献