Safety assessment of infrastructures using a new Bayesian Monte Carlo method

A recently developed Bayesian Monte Carlo (BMC) method and its application to safety assessment of structures are described in this paper. We use a one-dimensional BMC method that was proposed in 2009 by Rajabalinejad in order to develop a weighted logical dependence between successive Monte Carlo simulations. Our main objective in this research is to show that the extended BMC can dramatically improve simulation efficiency by using prior information from modelling and outcomes of preceding simulations. We provide theory and numerical algorithms for an extended BMC method for multi-dimensional problems, integrate it with a probabilistic finite element model and apply these coupled models to assessment of reliability of a flood defence for the 17th Street Flood Wall system in New Orleans. This is the first successful demonstration of the BMC method to a complex system. We provide a comparison of the numerical efficiency for the BMC, Monte Carlo (MC) and Dynamic Bounds methods that are used in reliability assessment of complex infrastructures.     

影响b值计算误差的Monte Carlo实验研究

本文假设地震的发生与时间的关系遵循稳态泊松模型,假设地震震级M服从参数为1/β的指数分布,其中β=b/loge,在此基础上生成地震目录.用最小二乘法估算b值,分别从样本数量、震级间隔、震级误差三方面分析b值误差的大小.统计分析结果表明,b值的标准偏差随着样本数量的增多而减小;随着震级间隔的增大而减小;震级误差使b值的标准误差变大.本文可以为利用真实地震目录求b值时选择适当的方法提供参考.     

Simulating hourly rainfall occurrence within an equatorial rainforest,Borneo Island / Simulation de l'occurrence de pluie horaire au sein de la forêt équatoriale,Ile de Bornéo

Abstract

The ability to simulate characteristics of the diurnal cycle of rainfall occurrence, and its evolution over the seasons is important to the forecasting of hydrological impacts resulting from land-use and climate changes within the humid tropics. This stochastic modelling study uses a generalized linear model (GLM) solution to second-order Markov chain models, as these discrete models are better at describing binary occurrence processes on an hourly time-scale than continuous-time approaches such as stochastic state-space models. We show that transition probabilities derived by the Markov chain method need to be time-varying rather than stationary to simulate the evolution of the diurnal cycle of rainfall occurrence over a Southeast Asian monsoon sequence. The conceptual and pragmatic links between discrete diurnal processes and continuous processes occurring over seasonal periods are thereby simulated within the same model.     

Statistical analysis of the effects on overland flow of spatial variability in soil hydraulic conductivity / Analyse statistique des effets de la variabilité spatiale de la conductivité hydraulique du sol sur l'écoulement de surface

Abstract

The effects of spatial variation of the saturated hydraulic conductivity (K _s ) of the soil on the variation of overland flow were tested by analysing 2000 synthetic rainfall—runoff events, all generated from real, observed rainfall events but with runoff modelled by a two-dimensional distributed model using different spatially variable K _s fields in a small (12 ha) agricultural catchment. The purpose is to determine the influence of spatial variation in K _s on runoff generation. The statistical measures used to describe the variation in the generated K _s were its coefficient of variation and correlation length. Both of these had two levels of typical values obtained from field measurements in other studies. The storms were analysed at a general event level, first using simple graphical and statistical methods and then using analysis of variance (ANOVA). The observed scale of the spatial variation of K _s does cause statistically significant variation in overland flow. The graphical analysis showed that the first flow peak in a multi-event storm had the largest variation and that differences were greater in the rising part of the hydrograph than in its recession. The greatest variation in overland flow was produced by the combination of the greater coefficient of variation and the longer correlation lengths. The smallest variation in overland flow was produced by the combination of the smaller coefficient of variation and the shorter correlation lengths. ANOVA showed that the coefficient of variation and correlation length alone did not explain all the variation of the total flow. ANOVA was not very useful due to the many restrictive assumptions that were not satisfied by the nature of the data and therefore analysis methods with less restrictive assumptions need to be tested.     

An approach for the determination of precipitation input for worst-case flood modelling

ABSTRACT

There is a lack of suitable methods for creating precipitation scenarios that can be used to realistically estimate peak discharges with very low probabilities. On the one hand, existing methods are methodically questionable when it comes to physical system boundaries. On the other hand, the spatio-temporal representativeness of precipitation patterns as system input is limited. In response, this paper proposes a method of deriving spatio-temporal precipitation patterns and presents a step towards making methodically correct estimations of infrequent floods by using a worst-case approach. A Monte Carlo approach allows for the generation of a wide range of different spatio-temporal distributions of an extreme precipitation event that can be tested with a rainfall–runoff model that generates a hydrograph for each of these distributions. Out of these numerous hydrographs and their corresponding peak discharges, the physically plausible spatio-temporal distributions that lead to the highest peak discharges are identified and can eventually be used for further investigations.

Editor A. Castellarin; Associate editor E. Volpi     

利用蒙特卡罗方法的剩余静校正及其应用

针对剩余静校正问题,讨论了统计方法中的蒙特卡罗法用于反射波能量最大化剩余静校正的方法。分别论述了反射波叠加能量最大化法和蒙特卡罗方法,以及蒙特卡罗方法如何应用于剩余静校正的计算中,并用实例说明了该方法的效果。通过实际应用蒙特卡罗剩余静校正方法,解决了经野外静校正后残留的剩余静校正问题,并通过与其他剩余静校正方法的实际应用对比,说明了蒙特卡罗剩余静校正方法的优势。对于大剩余量的静校正问题,蒙特卡罗剩余静校正方法仍然可以很好的解决,并且不会产生串相位问题,说明蒙特卡罗剩余静校正方法是可靠的。     

Computer Monte Carlo simulation in quantitative resource estimation

The method of making quantitative assessments of mineral resources sufficiently detailed for economic analysis is outlined in three steps. The steps are (1) determination of types of deposits that may be present in an area, (2) estimation of the numbers of deposits of the permissible deposit types, and (3) combination by Monte Carlo simulation of the estimated numbers of deposits with the historical grades and tonnages of these deposits to produce a probability distribution of the quantities of contained metal.Two examples of the estimation of the number of deposits (step 2) are given. The first example is for mercury deposits in southwestern Alaska and the second is for lode tin deposits in the Seward Peninsula.The flow of the Monte Carlo simulation program is presented with particular attention to the dependencies between grades and tonnages of deposits and between grades of different metals in the same deposit.     

地基承载力上限分析中的Monte Carlo搜索技术

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。     

A Probabilistic Model for Fatigue Crack Propagation Analysis

A simple probabilistic model for predicting crack growth behavior under random loading is pre-sented.In the model,the parameters c and m in the Paris-Erdogan Equation are taken as random variables,and their stochastic characteristic values are obtained through fatigue crack propagation tests on an offshorestructural steel under constant amplitude loading.Furthermore,by using the Monte Carlo simulation tech-nique,the fatigue crack propagation life to reach a given crack length is predicted.The tests are conducted toverify the applicability of the theoretical prediction of the fatigue crack propagation.