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1.
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
2.
Probability levels, in the form of marginal cumulative distribution functions, are determined for the time it takes salt to
contact a casing, which penetrates a salt canopy, and the time it takes the casing to yield once salt has contacted the casing,
in support of through-salt well design activities required for deep-water, sub-salt environments. The finite-element method
coupled with an advanced reliability method is used to perform the analyses. Randomness caused by uncertainties in salt properties,
lithostatic stress, drilling-mud pressure, production temperature, and borehole ellipticity is handled by including statistics
and probability distributions for each of these random variables. The advanced reliability method takes full account of the
random variables and processes without Monte Carlo simulation, by using a method for assessing reliability statistics that
computes response probabilities in a direct and efficient manner. This advanced reliability method falls under the general
category of fast probability integration schemes. 相似文献
3.
Greco提出的临界滑裂面搜寻的Monte Carlo搜索技术具有原理简单、适应性强、搜索性能好及容易编程实现等优点,目前该类方法已在边坡稳定的优化计算中有许多成功的应用。为能够在多块体上限法求解地基极限承载力的优化计算中应用Monte Carlo搜索技术,基于上限法相容速度场的要求及地基承载力问题的特点,对Monte Carlo搜索技术实现中的目标函数、几何约束条件、初始破坏面的产生以及收敛准则等重新进行了设置。由于Monte Carlo搜索技术随机性的特点,某一次的搜索优化往往存在陷入局部极值的危险,为解决这一不足,采取了随机设置多次初始破坏面分别进行搜索优化的办法,计算表明,优化效果很好。通过对实际问题的计算以及对比发现,Monte Carlo搜索技术在此处多块体上限法求解地基承载力问题中的优化应用是相当成功的。此外,由于此处的优化是以破坏面上的节点为对象的,因此,不但可以方便地考虑三角形块体的优化,而且也可以方便地考虑四边形块体的优化问题,其适用性更强。 相似文献
4.
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
5.
Commodities such as oil and gas occur in isolated reservoirs or accumulations, more generically called basic units here. To understand a study area’s economic potential and to craft plans for exploration and development, resource analysts often aggregate (sum, accumulate) basic unit magnitudes in distinct spatial subsets of the study area and then appraise the total area’s potential by summing these intermediate sums. In a probabilistic approach, magnitudes are modeled as random variables. Some have asked, “Do different methods of partitioning basic units into subsets lead to different probability distributions for the sum of all basic unit magnitudes?” Any method of aggregation of basic unit magnitudes which obeys the rules of probability leads to the same probability distribution of the sum of all unit magnitudes as that computed by direct summation of all basic unit magnitudes. A Monte Carlo simulation of a synthetic example in which the magnitude of resource in each unit is marginally lognormal and pairwise correlations among basic unit magnitudes are specified illustrates key features of probabilistic aggregation. The joint distribution of certain pairs of aggregates are closely approximated by a bivariate lognormal distribution. 相似文献
6.
Geotechnical models are usually associated with considerable amounts of model uncertainty. In this study, the model uncertainty of a geotechnical model is characterised through a systematic comparison between model predictions and past performance data. During such a comparison, model input parameters (such as soil properties) may also be uncertain, and the observed performance may be subjected to measurement errors. To consider these uncertainties, the model uncertainty parameters, uncertain model input parameters and actual performance variables are modelled as random variables, and their distributions are updated simultaneously using Bayes’ theorem. When the number of variables to update is large, solving the Bayesian updating problem is computationally challenging. A hybrid Markov Chain Monte Carlo simulation is employed in this paper to decompose the high-dimensional Bayesian updating problem into a series of updating problems in lower dimensions. To increase the efficiency of the Markov chain, the model uncertainty is first characterised with a first order second moment method approximately, and the knowledge learned from the approximate solution is then used to design key parameters in the Markov chain. Two examples are used to illustrate the proposed methodology for model uncertainty characterisation, with insights, discussions, and comparison with previous methods. 相似文献
7.
Finding the critical slip surface and estimating the landslide volume are of primary importance for slope seismic design. However, this may be difficult due to the uncertainty of ground motions. To address this problem, a new method for calculating uncertainties is recommended in this paper, especially for the critical slip surface and landslide volume under random earthquake ground motions. Firstly, a series of intensity–frequency nonstationary random earthquake ground motions were generated based on an improved orthogonal expansion method. A given number of potential slip surfaces were set in a soil slope. Subsequently, the factor of safety (FOS) of each slip surface for all ground motions was calculated and the minimum FOS curves were obtained. It was found that the critical slip surfaces and failure times are uncertain under different earthquakes. The Monte Carlo method was used to verify the accuracy of probability density evolution method (PDEM), and the results of the PDEM and the Monte Carlo method are consistent, meaning that the PEDM has higher computational efficiency. Moreover, the distributions of earthquake-triggered landslide volume and landslide depth were analyzed by considering equivalent extreme events. Both landslide volume and depth exhibit a normal distribution for a homogeneous soil slope. The framework of this study is meaningful for slope seismic design in engineering, for example, the location of critical slip surface can be used for slope reinforcement, and the distribution of sliding volume can be used for disaster assessment. 相似文献
8.
In a probabilistic analysis of rock slope stability, the Monte Carlo simulation technique has been widely used to evaluate
the probability of slope failure. While the Monte Carlo simulation technique has many advantages, the technique requires complete
information of the random variables in stability analysis; however, in practice, it is difficult to obtain complete information
from a field investigation. The information on random variables is usually limited due to the restraints of sampling numbers.
This is why approximation methods have been proposed for reliability analyses. Approximation methods, such as the first-order
second-moment method and the point estimate method, require only the mean and standard deviation of the random variable; therefore,
it is easy to utilize when the information is limited. Usually, a single closed form of the formula for the evaluation of
the factor of safety is needed for an approximation method. However, the commonly used stability analysis method of wedge
failure is complicated and cumbersome and does not provide a simple equation for the evaluation of the factor of safety. Consequently,
the approximation method is not appropriate for wedge failure. In order to overcome this limitation, a simple equation, which
is obtained from the maximum likelihood estimation method for wedge failure, is utilized to calculate the probability of failure.
A simple equation for the direct estimation of the safety factors for wedge failure has been empirically derived from failed
and stable cases of slope, using the maximum likelihood estimation method. The developed technique has been applied to a practical
example, and the results from the developed technique were compared to the results from the Monte Carlo simulation technique. 相似文献
9.
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
10.
Two methods are compared for estimating the shape parameters of Pareto field-size (or pool-size) distributions for petroleum
resource assessment. Both methods assume mature exploration in which most of the larger fields have been discovered. Both
methods use the sizes of larger discovered fields to estimate the numbers and sizes of smaller fields: (1) the tail-truncated
method uses a plot of field size versus size rank, and (2) the log–geometric method uses data binned in field-size classes
and the ratios of adjacent bin counts. Simulation experiments were conducted using discovered oil and gas pool-size distributions
from four petroleum systems in Alberta, Canada and using Pareto distributions generated by Monte Carlo simulation. The estimates
of the shape parameters of the Pareto distributions, calculated by both the tail-truncated and log–geometric methods, generally
stabilize where discovered pool numbers are greater than 100. However, with fewer than 100 discoveries, these estimates can
vary greatly with each new discovery. The estimated shape parameters of the tail-truncated method are more stable and larger
than those of the log–geometric method where the number of discovered pools is more than 100. Both methods, however, tend
to underestimate the shape parameter. Monte Carlo simulation was also used to create sequences of discovered pool sizes by
sampling from a Pareto distribution with a discovery process model using a defined exploration efficiency (in order to show
how biased the sampling was in favor of larger fields being discovered first). A higher (more biased) exploration efficiency
gives better estimates of the Pareto shape parameters. 相似文献
11.
12.
Bayes约束随机场下坝基溶蚀区随机模拟方法及其影响分析 总被引：1，自引：0，他引：1
基于完全随机场模拟溶蚀岩体可能会高估其空间变异性和不能有效地利用溶蚀以外的地质信息和实践经验,提出用Bayes约束参数随机场模型描述坝基溶蚀区的随机模拟方法。引入Bayes公式,对溶蚀区域岩土参数的统计特性进行修正,反映出地质勘测的新增地质信息和试验参数信息,建立约束随机场,并在此基础上进行随机有限元分析,研究坝基溶蚀对大坝结构性态的作用效应。计算结果表明,相对于完全随机场模型,Bayes约束随机场模型更为客观地考虑了溶蚀岩体的空间变异性,有效地降低了溶蚀参数完全随机场下结构响应的模拟方差。在概率分析过程中,推荐蒙特卡洛响应面耦合方法（MC-RSM）作为适用于复杂工程的随机模拟方法,该方法能够代替直接MC法对同样力学机制的不断重复,减小计算时间成本。 相似文献
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15.
Dislocation modelling of an earthquake fault is of great importance due to the fact that ground surface response may be predicted by the model. However, geological features of a fault cannot be measured exactly, and therefore these features and data involve uncertainties. This paper presents a Monte Carlo based random model of faults with finite element method incorporating split node technique to impose the effects of discontinuities. Length and orientation of the fault are selected as random parameters in the domain model, and hence geometrical uncertainties are encountered. Mean and standard deviation values, as well as probability density function of ground surface responses due to the dislocation are computed. Based on analytical and numerical calculation of dislocation, two approaches of Monte Carlo simulations are proposed. Various comparisons are examined to illustrate the capability of both methods for random simulation of faults. 相似文献
16.
针对确定性模型难以描述含水层非均质空间分布的问题,提出基于随机理论的地下水环境风险评价方法。以矩形场地地下水污染风险评价为例,采用蒙特卡罗法生成大量渗透系数随机场,模拟含水层参数各种可能的非均质空间分布,在此基础上建立场地地下水流模型与溶质运移模型,分别计算污染物在地下水中的迁移转化情况。统计大量随机模拟中污染事故发生的频率,当模拟次数足够多时,污染频率收敛于污染概率,污染风险即通过污染概率体现出来。该方法将模型参数设为满足一定分布特征的随机变量,避免了确定性方法得出的武断的评价结果,可为工厂的选址、水源地的选址等工作提供科学指导。 相似文献
17.
Spatial risk analysis of Li-shan landslide in Taiwan 总被引：3，自引：0，他引：3
By coupling limit equilibrium analysis and Monte Carlo analysis with a geography information system (GIS), this study implements a method that can evaluate the risk (corresponding to probability of failure in this study) of landslide with consideration of spatial uncertainties. The GIS can adopt the three-dimensional information including surface topography, underground geomaterial distribution and groundwater level to determine slope profiles for analysis. Then the safety of defined slope can be evaluated by limit equilibrium analysis. In this study, the mechanical properties of geomaterial were considered as random variables instead of single values. The slope and groundwater profiles are also randomly adopted. Through a Monte Carlo sampling process, a distribution of safety factor and probability of failure can be determined. This probabilistic risk analysis approach was applied to Li-shan landslide in Central Taiwan.
Due to heavy rains, the sites near the highway 7A (mileage 73 k + 150) and the highway 8 (mileage 82 k) in the Li-shan Township began to subside in mid April 1990. Topography, geology, and groundwater condition of this area were first reviewed. Based on this review, together with field investigations and a series of limit equilibrium back analyses, a general hypothetic model was established to illustrate the failure mechanism of this landslide area. Then the developed probabilistic risk analysis model is applied to spatially evaluate the risk of this landslide area as well as the performance of the remediation treatment. 相似文献
18.
Two examples are given for comparing applications and limitations of four methods which can be used to deal with error propagation in geochemical calculations.The examples indicate that the Monte Carlo method can also be employed to evaluate the effect of covariance.A special function of the method for covariance matrix shown here can reveal the correlations of middle variables relative to the independent primary variables. 相似文献
19.
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