POINT-ESTIMATE MOMENT-BASED RELIABILITY ANALYSIS

In moment-based reliability analysis, the probability of failure is calculated from a probability distribution fitted to the first few calculated moments of a limit state function. The calculation of the moments and the distributions fitting in the analysis are described. We suggest using the point estimate method to calculate the moments of the limit state function. A probability distribution from the Gram-Charlier series type A distributions or the Johnson family of distributions is selected to fit the calculated moments. The method, in general, does not require knowledge of the probability distributions of the basic random variables involved in the limit state function but their statistical moments. The method is simple to implement and can be used directly with an available deterministic computer program because it does not require iteration or derivatives of the limit state function.     

基于Beta分布的改进的一次可靠度法研究

为了提高一次可靠度方法的计算精度和计算效率,文章利用Beta分布拟合了功能函数中的随机变量的概率分布,利用VBA语言给出了将Beta分布和对数正态分布转化为标准正态分布的方法,采用蒙特卡洛模拟法比较了采用不同概率分布的一次可靠度计算精度。算例分析表明:当功能函数中随机变量服从对数正态分布时,失效概率被高估;当随机变量服从正态分布时失效概率被低估。利用本文提出的Beta分布拟合随机变量的概率不仅大大提高了计算精度,而且在保证迭代收敛的前提下提高了计算效率。     

Exposure to the mixtures of organic compounds in homes in Japan

The aim of the study reported herein was to characterize occupants' simultaneous exposure to mixtures of organic compounds in homes. Statistical distributions for concentrations of 28 organic compounds (17 VOCs and 11 aldehydes) measured in 1417 homes were generated to analyze concentration distributions. Three candidate distributions were identified for fitting the measured data: log-normal, exponential and gamma distributions. It appears from the results of fitting tests that gamma distributions are capable of representing 28 compound concentrations. Probability distributions show that formaldehyde and acetaldehyde ranged from 25 to 220 microg/m3 at 90% probabilities and most VOCs ranged from 3 to 80 microg/m3 at 90% probabilities. In order to characterize the occupant's exposure to the mixtures, the joint probability distributions of organic compounds were generated from the best-fitted distributions of individual compounds under the assumption that concentrations of organic compounds are mutually independent in homes. These joint distributions provided the statistical data for characterizing the occupant's exposure to the mixtures of organic compounds in homes. PRACTICAL IMPLICATIONS: Occupants often encounter not just one compound in indoor environments, but many compounds due to their concurrent emissions from several sources. This paper describes characteristics of statistical distributions for concentrations of 17 VOCs and 11 aldehydes in homes in Japan. After applying a probability model to the occupants' simultaneous exposure to mixtures of organic compounds, the authors interpret the current state of the occupant's exposure to the mixtures within homes using joint probability distributions of 28 organic compounds.     

Determining the probability distribution of rework costs in construction and engineering projects

Rework arises due to design errors, changes and omissions during design and has been found to contribute to 52% of a project's cost overrun. The statistical characteristics of rework costs experienced from contract award in 276 construction and engineering projects were analysed. The skewness and kurtosis values of rework costs are computed to determine if the empirical distribution of the data follows a normal distribution. The empirical distributions for rework costs are found to be non-Gaussian. Theoretical probability distributions are fitted to the rework data. The Kolmogorov–Smirnov and Anderson–Darling non-parametric tests are used to determine the ‘Goodness of Fit’ of the selected probability distributions. A Generalised Pareto probability function is found to provide the best overall distribution fit for rework costs. The Generalised Pareto distribution is used to calculate the probability of rework being experienced for the selected sample. Projects with a contract value <A$1million had higher rework probabilities than that of >A$101 million. Larger projects may be better managed and longer completion times provide an opportunity to make adjustments to facilitate cost control. The anticipation that rework will occur using the probabilities that are derived can enable a quantitative risk assessment to be undertaken prior to the commencement of construction.     

Subjective probabilities for earthquake damage and loss

This paper presents a method for developing consensus probability distributions of damage from subjective probability densities provided by individual experts. The method employs Bayesian statistical theory and incorporates weighting of expert judgements in evaluating the consessus distributions. Earthquake ground motion vs. damage relationships are developed in the form of damage probability matrices using Gaussian quadrature methods. The main advantage of this approach over existing distribution discretization techniques is that no error is introduced in the mean value of the random variable and errors in the variance are reduced significantly with even a small number of value-probability pairs. As a consequence, expected loss estimates obtained by the proposed method contain no error due to discretization. The results from this paper are particularly useful for forecasting damage and losses in geographical areas with large numbers of structures and with a variety of engineering characteristics.     

Multivariate distributions of maxima and extremes for Gaussian vector-processes

A new class of multivariate extensions of probability distributions related to local maxima and extremes for scalar Gaussian processes are considered. Joint statistics of the radius vector magnitude and the corresponding direction vector constitute the basis for the present approach. The asymptotic behaviour of the distributions is also investigated. The influence from basic process characteristics on the shape of the density functions are studied. Application of the extreme value distributions for evaluation of reliability is discussed. Numerical results are presented for a specific example. Finally, the relevance of the so-called expected extreme hypersurfaces is illustrated in connection with a given design formulation.     

Maximum entropy probability distributions for flood frequency analysis

It is customary to assume a frequency distribution in flood frequency analysis. The parameters of the distribution are estimated by using observed or transformed data. The fitted distribution is then used to estimate the magnitudes of floods of different frequencies.

The maximum entropy (ME) probability distribution is defined as the 'minimally prejudiced probability distribution which maximizes the entropy subject to constraints supplied by the given information'. In spite of many attractive features of the ME distribution, it has not been used in its general form in practice. The main reason for not using the ME distribution in its general form is that the parameter estimation problem associated with the ME distribution is not easy. Recently this problem has been solved and an algorithm has been developed to estimate the parameters of the ME distribution.

The objective of the research reported in the present paper is to fit ME distributions to flood data. The ME distributions are compared with other well known distributions. The computational aspects and selection of orders of distributions are also discussed. The ME distribution is shown to be versatile and fits a variety of flood data very well.     

Estimation of train derailment probability using rail profile alterations

Investigation of train derailment is a complicated job that occurs in special points with special characteristics. It depends on several variables so for successful predication, exact estimation of all effective parameters is required. Instead of this complicated job, usually a time history of variables and statistic distribution can be used. According to statistic distributions, exact determination of train derailment is practically impossible and therefore a probability function should be utilised. Angle of wheel flange, friction coefficient, axle load and train speed are effective parameters in investigation of train derailment probability. In this paper, by using statistical distributions, aforementioned parameters are investigated and derailment probability is calculated using reliability theory. To describe extra capabilities of model, derailment probability is calculated in three different curves of railway network considering real geometrical specifications of curves, amount of wear in rail profiles measured by EM120 track recording cars, axle load and operation speed.     

考虑概率分布影响的低概率水平边坡可靠度分析

目前考虑土体参数空间变异性的边坡可靠度分析所研究的边坡几何尺寸相对较小。为有效地分析考虑参数空间变异性的几何尺寸相对较大的边坡可靠度问题,提出了基于多重响应面与子集模拟的边坡可靠度分析方法。以一个坡高为24 m的两层非均质黏土边坡为例验证了提出方法的有效性,并探讨了正态、对数正态、极值I型、Gamma和Beta这5种概率分布类型对边坡可靠度的影响。结果表明,提出方法具有以下优势:1可以有效地计算考虑多参数空间变异性的低概率水平边坡可靠度;2可以较好地解决几何尺寸相对较大的边坡可靠度问题;3有较高的参数敏感性分析计算效率,可为调查概率分布类型和波动范围等参数统计特征对边坡可靠度的影响提供技术支持。此外,参数概率分布类型对边坡可靠度具有重要的影响,常用的正态和对数正态分布分别用于表征参数概率分布特征时,可能会分别高估和低估边坡失效概率。     

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.     

Impact of translation approach for modelling correlated non-normal variables on parallel system reliability

The adequacy of two approximate methods based on incomplete information, namely method P and method S, for constructing multivariate distributions with given marginal distributions and covariance has not been studied systematically. This article aims to study the errors of the method P and method S. First, the method P and method S as well as the exact method are presented. Second, the performance of the two approximate methods is evaluated based on their abilities to match exact solutions for system probabilities of failure. Finally, an illustrative example of a parallel system is investigated to demonstrate the errors associated with the two methods. The results indicate that the errors in system probabilities of failure for the two methods highly depend on the level of system probability of failure, the performance function underlying the system, and the degree of correlation. Such errors increase greatly with decreasing system probabilities of failure. When the target system probability of failure is larger than 1.0E?03, the system probabilities of failure obtained from the two methods and the exact method are of the same order of magnitude. The maximum error in the system probability of failure may not be associated with a large correlation. It can happen at an intermediate correlation.     

生活垃圾土性指标概率特性

通过室内试验 ,进行了北京生活垃圾有机物含量成份分析 ,物理力学指标测定 ,并统计分析土性参数的变异性和概率分布。研究表明 ,垃圾场地的均匀性较差 ,参数的变异性较大 ,其土工问题需要用概率方法来分析     

压剪应力条件下岩体裂纹扩展概率模型研究

经典Ｗｅｉｂｕｌ统计断裂理论从统计的角度建立了拉剪应力条件下裂纹扩展的统计断裂模型。而岩体工程中的断续节理岩体的裂纹有相当一部分是处于压剪应力作用下,应用经典Ｗｅｉｂｕｌ统计断裂理论建立的裂纹扩展概率模型是不适宜的。本文对断续节理岩体中压剪应力条件下裂纹扩展的随机性从断裂力学角度进行了研究,建立了压剪应力条件下裂纹的断裂力学概率模型,并讨论了节理岩体的失效概率与裂纹几何、力学各参数之间的关系。     

An evaluation of the self-determined probability-weighted moment method for estimating extreme wind speeds

For the estimation of probability distribution parameters, the method of self-determined probability-weighted moments (SD-PWM) has previously been introduced as a refinement on the original method of probability-weighted moments (PWM). Tables have been created summarizing the solution of the relevant equations for certain probability distributions, but application of these is awkward. In addition, certain associated algorithms are difficult to interpret and contain formulations that do not appear to properly enforce the definitions of self-determined probability-weighted moments. Therefore, new algorithms have been developed to both clarify and simplify the determination of SD-PWM parameter estimates. As an application of the SD-PWM algorithms, the estimation of extreme wind speeds is considered using the Gumbel and generalized extreme value (GEV) distributions. The estimation results are compared to similar results obtained via PWM, the method of moments and the maximum likelihood method. The analyses suggest SD-PWM may be a reasonable tool for analyzing the ability of a particular distribution to describe a sample. Relative to the method of moments and PWM estimates, the SD-PWM estimates compare well based on fits of the cumulative distributions. While the SD-PWM estimates exhibit increased variability relative to the method of moment (MOM) estimates, SD-PWM wind speed estimates are generally conservative relative to the MOM estimates.     

Risk Assessment of Hydrogen Fuel Cell Electric Vehicles in Tunnels

The need to understand the risks and implications of traffic incidents involving hydrogen fuel cell electric vehicles in tunnels is increasing in importance with higher numbers of these vehicles being deployed. A risk analysis was performed to capture potential scenarios that could occur in the event of a crash and provide a quantitative calculation for the probability of each scenario occurring, with a qualitative categorization of possible consequences. The risk analysis was structured using an event sequence diagram with probability distributions on each event in the tree and random sampling was used to estimate resulting probability distributions for each end-state scenario. The most likely consequence of a crash is no additional hazard from the hydrogen fuel (98.1–99.9% probability) beyond the existing hazards in a vehicle crash, although some factors need additional data and study to validate. These scenarios include minor crashes with no release or ignition of hydrogen. When the hydrogen does ignite, it is most likely a jet flame from the pressure relief device release due to a hydrocarbon fire (0.03–1.8% probability). This work represents a detailed assessment of the state-of-knowledge of the likelihood associated with various vehicle crash scenarios. This is used in an event sequence framework with uncertainty propagation to estimate uncertainty around the probability of each scenario occurring.     

地基沉降泊松曲线拟合的概率方法

在线性加载过程中,地基沉降的发展曲线呈S型,可用泊松曲线来描述这一过程。基于贝叶斯理论,提出采用概率的方法来估计泊松曲线的参数。与以往方法不同,所提出的方法得到的是参数的分布。计算出参数的后验分布后,可进行沉降预测分布的计算。实例分析表明,所提出的方法所得结果合理可信,且包含了参数更为丰富的信息,是一种优越于传统方法的方法,值得推广应用。     

岩土参数概率分布类型及其选择标准

 岩土参数的概率分布类型对风险评价和可靠度分析具有相当大的影响,对其研究是一项基础性的重要工作。从分析总结各种概率分布类型的产生背景、所描述对象的物理意义着手,将其分门别类,发现大致有5大系列,即Bernoulli分布系列、Poisson分布系列、极值分布系列、中心极限分布系列和用于统计分析的分布系列。然后研究岩土参数被建模为随机变量时影响其不确定性的因素,得出用中心极限分布系列对其描述较为合理,在此基础上,详尽地对比隶属于中心极限分布系列的正态、对数正态分布的各种特性,提出在二者之间如何选择的标准,即当变异系数小于30%且偏度系数小于0.025时选择正态分布,反之,选择对数正态分布。另外,论证泊松比更适合建模为b 分布的事实。最后,用一统计实例诠释本文所提观点的正确性。研究成果对岩土工程的风险评价和可靠度分析具有重要的参考价值。     

Logistic regression modelling of storm-induced shallow landsliding in time and space on natural terrain of Lantau Island,Hong Kong

This study is aimed at developing a method for modelling the probability of landsliding using a geographical information system (GIS), rainstorm events and associated landslide distributions, with an attempt to assess where landslides are likely to occur when certain rainstorm events happen. This research focuses on the natural terrain of Lantau Island, Hong Kong. In order to derive a logistic regression model for statistical prediction of the probability of landsliding, topographic attributes derived from digital elevation model (DEM) data are combined with a variety of other digital datasets including 24 h rainfall, lithology and vegetation cover in a GIS. The model was then applied to given rainstorm events and rainfalls of a variety of periods of return time in order to predict the probability of landsliding on natural slopes in space and time. The modelling techniques described here can be used to develop effective mitigation strategies.     

Estimating the frequency distributions of PM10 and PM2.5 by the statistics of wind speed at Sha-Lu,Taiwan

The frequency distribution of air pollutant concentration varies with the meteorological conditions and pollutant emission level. There exists a simple relation between the frequency distribution of wind speed and frequency distribution of air pollutant concentration. The concentration of air pollutant, C, at cumulative probability, p, is inversely proportional to the wind speeds, u, at probability of (100 - p) when the distributional types and shape factors of both data are the same. The relationship is shown as K=Cp u(100 - p), where K is constant. In this study, three theoretical distributions (log-normal, Weibull and type V Pearson distributions) are selected to fit the measured data of PM10, PM2.5 and wind speed. The frequency distributions of air pollutants can be estimated from the simple relationship of air pollutant concentration and wind speed. The results show that the log-normal distribution is the best one to represent the data of PM10, PM2.5 and wind speed. The K values of PM10 and PM2.5 are nearly constant from the 30-80th percentiles. It was also found that the distributions of PM10 and PM2.5 can be successfully estimated from the distribution of wind speed. The Kolmogorov-Smirnov (K-S) test shows that there is no significant discrepancy between the estimated and measured distribution of PM10 and PM2.5 at the 95% confidence level. Therefore, the distribution of air pollutants is easily estimated when the wind speed data are known.