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.     

Stochastic methods for safety assessment of the flood defense system in the Scheldt Estuary of the Netherlands

In this study, we address the effective method to apply a novel reliability method integrated with finite element models to the safety assessment of pilot site Scheldt in the Netherlands. This site was considered as one of the three main pilot sites in Europe to assess the application of newly suggested techniques in order to reduce and manage the flood risk in the Floodsite project. , 2004–2009). The novel method of dynamic bounds (DB) is applied to this site after a successful experience in (Rajabalinejad in Reliability methods for finite element models, 1 edn. IOS Press, Amsterdam, 2009). In this study, the bi-functional response of the finite element model is considered, and the dimensional uncertainty is defined presenting the expected uncertainty for a certain dimension in the DB method. The uncertainty is used as a judgment tool to choose the dimension for the DB method for the desired accuracy. The results obtained by applying this technique are presented in this paper.     

洪涝灾害风险评估与分区研究进展

在全球气候变化和城市化进程不断加快的背景下,城市洪涝灾害频发,造成严重的经济损失和人员伤亡问题。对近年来中国典型城市洪涝灾害进行系统整理介绍,说明洪涝灾害带来的人员伤亡和经济损失巨大。风险评估作为一种非工程性防洪措施,是城市洪涝风险管理的首要工作,精确、高效的把握洪灾过程等特征可以为防灾减灾工作提供科学依据。对城市洪涝风险评估与分区的概念和内容进行系统梳理,常用的风险评估方法有数理统计法、不确定性分析法、遥感影像评估法、指标体系评估法、情景模拟评估法；风险分区常用方法有阈值法、经验公式法和物理机制法。论述了城市洪涝风险评估与分区常用方法的应用范围、优缺点及其发展前景。     

Bayesian analysis of data and model uncertainty in 3D seismic travel-time tomography

We present a probabilistic analysis of seismic travel-time equations using the Bayesian Method. The assessment of models and data is crucial in 3D seismic travel-time tomography, and a method quantitatively assess the quality of both the data and the model is necessary in order to attain the most realistic results. The Bayesian method that we propose here is more effective than the frequentist approach, both in analysis time and uncertainty minimization, when processing large sets of tomographic data.     

淮河息县站流量概率预报模型研究

应用美国天气局采用的由Roman Krzysztofowicz开发的贝叶斯统计理论建立概率水文预报理论框架，即以分布函数形式定量地描述水文预报不确定度，研究了淮河息县站流量概率预报模型。理论和经验表明，概率预报至少与确定性预报一样有价值，特别当预报不确定度较大时，概率预报比现行确定性预报具有更高的经济价值。     

Flood hazard assessment in the Kujukuri Plain of Chiba Prefecture,Japan, based on GIS and multicriteria decision analysis

A simple flood hazard assessment based on GIS and multicriteria decision analysis was presented, and the sensitivity analysis was applied to evaluate the uncertainty of input factors. The location chosen for the study is the Kujukuri Plain, Chiba Prefecture, Japan. The model incorporates six factors: river system, elevation, depression area, ratio of impermeable area, detention ponds, and precipitation. A hazard map for the year 2004, as an example, was obtained. The method of analytic hierarchy process was applied to calculate the weighting values of each factor. The hazard map was compared with the actual flood area, and good coincidence was found between them. The relative importance and uncertainty of the six input factors and weights were evaluated by using the global sensitivity analysis, i.e., extended FAST method, and the results showed a robust behavior of the model. The flood hazard assessment method presented here is meaningful for the flood management and environment protection in the area under the similar condition as this study.     

Determination of failure probabilities of flood defence systems with improved dynamic bounds method

In this paper, we describe the computational framework of a novel method for solving the challenging problem of probabilistic finite elements. The method is called Improved Dynamic Bounds (IDB) and was developed recently to improve the efficiency of the dynamic bounds. The IDB is used in finite element numerical models to calculate time-dependent failure analyses of structures. In applications, the IDB can speed up the overall simulation process by several orders of magnitude. In applications controlled by two influential variables (e.g, two-dimensional problem), the computational efficiency is improved by a factor of 769 according to Rajabalinejad (2009). Applications of IDB indicate the method is most efficient for problems where the number of influential variables are limited. This is often the case for geotechnical and coastal flood defence systems. The IDB method is applied in this paper to the 17th Street Flood Wall, a component of the flood defence system (levee infra-structure) that failed during the Hurricane Katrina, to calculate the failure probability of an I-wall.     

Editorial

The assessment of rock-fall hazards is subject to significant uncertainty, which is not fully considered in general practice and research. This paper reviews and classifies the various sources of the uncertainty. Taking a generic framework for risk assessment as source, a probabilistic model is presented that consistently combines the different types of uncertainties, in order to obtain a unified estimate of rock-fall risk. An important aspect of the model is that it allows for incorporating all available information, including physical and empirical models, observations and expert knowledge, by means of Bayesian updating. Detailed formulations are developed for various types of information. Finally, two examples considering rock-fall risk on roads, with and without protection structures, illustrate the application of the probabilistic modeling framework to practical problems.     

Impact on loss/risk assessments of inter-model variability in vulnerability analysis

Fragility curves (FCs) constitute an emerging tool for the seismic risk assessment of all elements at risk. They express the probability of a structure being damaged beyond a specific damage state for a given seismic input motion parameter, incorporating the most important sources of uncertainties, that is, seismic demand, capacity and definition of damage states. Nevertheless, the implementation of FCs in loss/risk assessments introduces other important sources of uncertainty, related to the usually limited knowledge about the elements at risk (e.g., inventory, typology). In this paper, within a Bayesian framework, it is developed a general methodology to combine into a single model (Bayesian combined model, BCM) the information provided by multiple FC models, weighting them according to their credibility/applicability, and independent past data. This combination enables to efficiently capture inter-model variability (IMV) and to propagate it into risk/loss assessments, allowing the treatment of a large spectrum of vulnerability-related uncertainties, usually neglected. As case study, FCs for shallow tunnels in alluvial deposits, when subjected to transversal seismic loading, are developed with two conventional procedures, based on a quasi-static numerical approach. Noteworthy, loss/risk assessments resulting from such conventional methods show significant unexpected differences. Conventional fragilities are then combined in a Bayesian framework, in which also probability values are treated as random variables, characterized by their probability density functions. The results show that BCM efficiently projects the whole variability of input models into risk/loss estimations. This demonstrates that BCM is a suitable framework to treat IMV in vulnerability assessments, in a straightforward and explicit manner.     

Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations

ABSTRACT

Field data is commonly used to determine soil parameters for geotechnical analysis. Bayesian analysis allows combining field data with other information on soil parameters in a consistent manner. We show that the spatial variability of the soil properties and the associated measurements can be captured through two different modelling approaches. In the first approach, a single random variable (RV) represents the soil property within the area of interest, while the second approach models the spatial variability explicitly with a random field (RF). We apply the Bayesian concept exemplarily to the reliability assessment of a shallow foundation in a silty soil with spatially variable data. We show that the simpler RV approach is applicable in cases where the measurements do not influence the correlation structure of the soil property at the vicinity of the foundation. In other cases, it is expected to underestimate the reliability, and a RF model is required to obtain accurate results.     

Comparison of Mathematical Methods of Potential Modeling

Various attempts are known to turn the “catalogue” of mineral deposit models compiled by Cox and Singer (1986) operational, and have initiated activities called “potential mapping”, “potential modeling”, or “targeting”. The common ultimate objective is to estimate the probability for a given location that a mineralization of a given type occurred. The mathematics range from “weights of evidence” and others featuring a Bayesian approach to logistic regression by maximum likelihood, and include other realizations by means of fuzzy methods, genetic programming, and artificial neural nets. Once developed and coded, applications are not restricted to mineral prospection and exploration but include any kind of occurrences and their estimated probabilities, e.g., risk assessment of land slides and many others.     

Hydraulic routing of extreme floods in a large ungauged river and the estimation of associated uncertainties: a case study of the Damodar River, India

Many developing countries are very vulnerable to flood risk since they are located in climatic zones characterised by extreme precipitation events, such as cyclones and heavy monsoon rainfall. Adequate flood mitigation requires a routing mechanism that can predict the dynamics of flood waves as they travel from source to flood-prone areas, and thus allow for early warning and adequate flood defences. A number of cutting edge hydrodynamic models have been developed in industrialised countries that can predict the advance of flood waves efficiently. These models are not readily applicable to flood prediction in developing countries in Asia, Africa and Latin America, however, due to lack of data, particularly terrain and hydrological data. This paper explores the adaptations and adjustments that are essential to employ hydrodynamic models like LISFLOOD-FP to route very high-magnitude floods by utilising freely available Shuttle Radar Topographic Mission digital elevation model, available topographical maps and sparse network of river gauging stations. A 110 km reach of the lower Damodar River in eastern India was taken as the study area since it suffers from chronic floods caused by water release from upstream dams during intense monsoon storm events. The uncertainty in model outputs, which is likely to increase with coarse data inputs, was quantified in a generalised likelihood uncertainty estimation framework to demonstrate the level of confidence that one can have on such flood routing approaches. Validation results with an extreme flood event of 2009 reveal an encouraging index of agreement of 0.77 with observed records, while most of the observed time series records of a 2007 major flood were found to be within 95 % upper and lower uncertainty bounds of the modelled outcomes.     

拓扑克里格法与普通克里格法在区域洪水频率分析中的比较研究

依据北江(珠江流域支流)流域6个水文测站年最大洪峰流量资料,分别用Top-kriging(拓扑克里格法)和普通克里格法进行区域洪水频率估计。采用均方根误差作为频率分布线型拟合优度指标。运用线性矩法进行单站洪水频率分析,确定10、50、100、1000年一遇设计洪水值。在此基础上,从Topkriging和普通克里格法设计洪水估计不确定性和相对线性矩法单站洪水频率的估计误差两个方面比较Top-kriging和普通克里格法。结果表明:(1)Top-kriging法是更好的线性无偏估计,相比普通克里格法更适合于区域洪水频率估计;(2)Top-kriging法设计洪水估计不确定性明显小于普通克里格法;(3)Top-kriging法设计洪水估计结果更接近线性矩法单站洪水频率分析结果。     

考虑降水预报的三峡入库洪水集合概率预报方法比较

为了考虑预见期内降水预报的不确定性对洪水预报的影响,采用中国气象局、美国环境预测中心和欧洲中期天气预报中心的TIGGE(THORPEX Interactive Grand Global Ensemble)降水预报数据驱动GR4J水文模型,开展三峡入库洪水集合概率预报,分析比较BMA、Copula-BMA、EMOS、M-BMA 4种统计后处理方法的有效性。结果表明:4种统计后处理方法均能提供一个合理可靠的预报置信区间;其期望值预报精度相较于确定性预报有所提高,尤其是水量误差显著减小;M-BMA方法概率预报效果最佳,它能够考虑预报分布的异方差性,不需要进行正态变换,结构简单,应用灵活。     

Bayesian model selection for complex geological structures using polynomial chaos proxy

Different interpretation of sedimentary environments lead to “scenario uncertainty” where the prior reservoir model has a high level of discrete uncertainty. In a real field application, the scenario uncertainty has a considerable effect on flow response uncertainty and makes the uncertainty quantification problem highly nonlinear. We use clustering methods to address the scenario uncertainty. Our approach to cluster analysis is based on the posterior probabilities of models, known as “Bayesian model selection.” Accordingly, we integrate overall possible parameters in each scenario with respect to their corresponding priors to give the measure of how well a model is supported by observations. We propose a cluster-based reduced terms polynomial chaos proxy to efficiently estimate the posterior probability density function under each cluster and calculate the posterior probability of each model. We demonstrate that the convergence rate of the reduced terms polynomial chaos proxy is significantly improved under each cluster comparing to the non-clustered case. We apply the proposed cluster-based polynomial chaos proxy framework to study the plausibility of three training images based on different geological interpretation of the second layer of synthetic Stanford VI reservoir. We demonstrate that the proposed workflow can be efficiently used to calculate the posterior probability of each scenario and also sample from the posterior facies models within each scenario.     

Uncertainty as the overlap of alternate conditional distributions

An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator is the overlap of alternate conditional distributions.     

Effect of uncertainty in land use, damage models and inundation depth on flood damage estimates

With the recent transition to a more risk-based approach in flood management, flood risk models—being a key component in flood risk management—are becoming increasingly important. Such models combine information from four components: (1) the flood hazard (mostly inundation depth), (2) the exposure (e.g. land use), (3) the value of elements at risk and (4) the susceptibility of the elements at risk to hydrologic conditions (e.g. depth–damage curves). All these components contain, however, a certain degree of uncertainty which propagates through the calculation and accumulates in the final damage estimate. In this study, an effort has been made to assess the influence of uncertainty in these four components on the final damage estimate. Different land-use data sets and damage models have been used to represent the uncertainties in the exposure, value and susceptibility components. For the flood hazard component, inundation depth has been varied systematically to estimate the sensitivity of flood damage estimations to this component. The results indicate that, assuming the uncertainty in inundation depth is about 25 cm (about 15% of the mean inundation depth), the total uncertainty surrounding the final damage estimate in the case study area can amount to a factor 5–6. The value of elements at risk and depth–damage curves are the most important sources of uncertainty in flood damage estimates and can both introduce about a factor 2 of uncertainty in the final damage estimates. Very large uncertainties in inundation depth would be necessary to have a similar effect on the uncertainty of the final damage estimate, which seem highly unrealistic. Hence, in order to reduce the uncertainties surrounding potential flood damage estimates, these components deserve prioritisation in future flood damage research. While absolute estimates of flood damage exhibit considerable uncertainty (the above-mentioned factor 5–6), estimates for proportional changes in flood damages (defined as the change in flood damages as a percentage of a base situation) are much more robust.     

水文水资源系统贝叶斯分析现状与前景

简介了贝叶斯分析的基本原理,综述了它在水文水资源系统中考虑不确定性和风险的特点及其在径流预报、洪水分析与地区综合、水资源规划与管理等问题中的应用,并分析了其发展前景,着重指出将灰色先验分布、模糊似然函数在贝叶斯定理框架中耦合的综合途径.     

黄河源区雨季降水与汛期径流量重建及其千年尺度下的演变特征

黄河源区年内降水集中, 洪水风险大, 重建源区雨季降水和汛期径流量对于提高径流预报预测精度及防洪防灾具有重要科学意义和应用价值。本文利用黄河源区及周边筛选的16个树轮年表, 采用嵌套主成分层次贝叶斯回归模型, 估算参数后验分布替代固定值以考虑不确定性, 重建了黄河源区过去1 160 a的雨季降水; 提出了基于年径流的分类占比回归模型, 以考虑汛期径流量与年径流量的一致性, 将黄河源区汛期径流量展延至公元159年。结果表明: ①嵌套主成分层次贝叶斯回归模型的误差缩减值(E_R)和有效系数(E_C)评价指标值均显著高于0, 分类占比回归模型的E_R和E_C值最高分别达0.90和0.88, 重建结果可靠性较高; ②即使在千年尺度下, 1979—1985年亦是较为不寻常的汛期高径流量时期。     

Ensemble level upscaling for compositional flow simulation

Uncertainty quantification is typically accomplished by simulating multiple geological realizations, which can be very expensive computationally if the flow process is complicated and the models are highly resolved. Upscaling procedures can be applied to reduce computational demands, though it is essential that the resulting coarse-model predictions correspond to reference fine-scale solutions. In this work, we develop an ensemble level upscaling (EnLU) procedure for compositional systems, which enables the efficient generation of multiple coarse models for use in uncertainty quantification. We apply a newly developed global compositional upscaling method to provide coarse-scale parameters and functions for selected realizations. This global upscaling entails transmissibility and relative permeability upscaling, along with the computation of a-factors to capture component fluxes. Additional features include near-well upscaling for all coarse parameters and functions, and iteration on the a-factors, which is shown to improve accuracy. In the EnLU framework, this global upscaling is applied for only a few selected realizations. For 90 % or more of the realizations, upscaled functions are assigned statistically based on quickly computed flow and permeability attributes. A sequential Gaussian co-simulation procedure is incorporated to provide coarse models that honor the spatial correlation structure of the upscaled properties. The resulting EnLU procedure is applied for multiple realizations of two-dimensional models, for both Gaussian and channelized permeability fields. Results demonstrate that EnLU provides P10, P50, and P90 results for phase and component production rates that are in close agreement with reference fine-scale results. Less accuracy is observed in realization-by-realization comparisons, though the models are still much more accurate than those generated using standard coarsening procedures.