基桩抗力系数的贝叶斯优化估计

针对岩土工程中由于数据较少导致无法精确研究模型不确定性这一问题,基于数理统计理论和贝叶斯统计方法,提出了岩土工程数据处理的贝叶斯优化方法。收集了南非地区29根无黏性土中和59根黏性土中桩的承载力资料,并将承载力实测值和理论计算值的比定义为承载力的模型因子。利用本文提出的方法将收集的数据分为“好数据”、“一般数据”和“坏数据”,剔除了对计算结果造成较大误差的“坏数据”,并对“一般数据”进行贝叶斯优化。利用中心点法、验算点法和蒙特卡洛模拟法计算出桩的承载力的可靠度。计算结果表明：数据的分类和优化对可靠度指标和抗力系数计算结果有显著的影响,其中利用“好数据”和“更新后的数据”的计算结果大于利用其他类型数据的计算结果。最后,根据计算结果和美国的桥梁荷载抗力设计规范给出了打入桩抗力系数的建议值。本文的研究成果可为相关的研究人员以及相关规范的编制提供参考。     

Bayesian analysis of uncertainty for structural engineering applications

There has been recent interest in differentiating aleatory and epistemic uncertainties within the structural engineering context. Aleatory uncertainty, which is related to the inherent physical randomness of a system, has substantially different effects on the analysis and design of structures as compared with epistemic uncertainty, which is knowledge based. Bayesian techniques provide powerful tools for integrating, in a rigorous manner, the two types of uncertainties. In a purely probabilistic viewpoint, the uncertainties merge, resulting in widened probability densities. From the viewpoint of design or experimentation, however, the two types of uncertainties have widely different effects. The purpose of this paper is to develop insight into these effects, using Bayesian-based analytical expressions for the aleatory and epistemic uncertainties. The paper goes beyond standard Bayesian conjugate distributions by incorporating the effects of model uncertainty, where the applicability of two or more analytical models are used to describe the structure of interest. The influence of multiple model uncertainties is explored for two problems: the Bayesian updating process as data is acquired, and the design of simple parallel systems.     

Earthquake-related Natech risk assessment using a Bayesian belief network model

Natural hazard triggering technological disasters (Natech) events pose risks to industrial facilities and process plants. As these plants handle hazardous materials, they can endanger nearby residential areas and have financial consequences. Thus, proper Natech risk assessment is required for effective prevention, mitigation and emergency response planning at industrial plants and nearby residential areas. The parameters used to quantify Natech risk assessment are subject to uncertainties and their interactions are non-linear. In this study, a Bayesian belief network-based Natech risk assessment model is developed to assess the earthquake-related Natech risk considering different levels of uncertainties. The cause and effect relationships between different parameters are constructed based on published body of knowledge and expert knowledge. The capabilities of the proposed model are demonstrated for the earthquake-related Natech risk assessment of Kobe City, Higashinada Ward, Japan because of the Great Hanshin earthquake in 1995. The proposed model is also capable of performing both predictive analysis and diagnostic analysis.     

Performance‐based evaluation and strengthening of tall buildings in the Los Angeles region by using Bayesian structural reliability

This paper presents the motivation and the mathematics required for the introduction of Bayesian structural reliability theory into the process of evaluating and strengthening any tall building located in the Los Angeles region. Copyright © 2013 John Wiley & Sons, Ltd.     

基于Bayes方法的堤坝时变渗流风险率评估

随着工程的老化,影响堤坝防洪安全的各种不确定性因素将发生缓慢变化。定量评估各种随机量的时变特性,对确定时变的防洪风险率至关重要。Bayes方法提供了对随机量概率分布进行推断的框架,利用一切可以利用的先验信息,并通过不断的实时采样信息,修正和改进原有的概率分布规律假设,以减少所考察随机量的时变不确定性。本文以渗流随机量的时变特性分析为例,论证了采用Bayes方法对时变随机量进行定量评估的可行性和适用性,并建议以正态共轭分布模拟数据的采样过程并计算其后验分布。在此基础上,讨论了渗流风险率计算的实测法模型,分析了随机变量的时变特性对渗流风险率的影响。     

Bayesian networks for system reliability reassessment

This paper proposes a methodology to apply Bayesian networks to structural system reliability reassessment, with the incorporation of two important features of large structures: (1) multiple failure sequences, and (2) correlations between component-level limit states. The proposed method is validated by analytical comparison with the traditional reliability analysis methods for series and parallel systems. The Bayesian network approach is combined with the branch-and-bound method to improve its efficiency and to facilitate its application to large structures. A framed structure with multiple potential locations of plastic hinges and multiple failure sequences is analyzed to illustrate the proposed method.     

Limitations of some of the approximate structural analysis methods that are used in structural system reliability

Structural system reliability often involves structures with non-linear behavior. In the reliability analysis, simplified structural models and simplified analysis procedures are used to model and analyze these structures. These simplified analysis procedures, for both frames and trusses, have their limitations. These limitations are illustrated in this paper through deterministic examples. It is recommended that further research be done on understanding the limitations of these methods and their effect on structural reliability analysis.     

Structural fragility and principle of maximum entropy

The concept of structural fragility with application to seismic probabilistic risk assessment is considered. Different formats of structural fragility representation are discussed. The principle of maximum entropy for a fragility distribution is formulated. Using this principle, the appropriate analytical forms of the state-of-knowledge fragility distribution for several important cases are selected. In the case where few fragility data are available, the joint distribution of uncertainty of fragility parameters is developed using the likelihood density function method.     

Computational framework for risk-based planning of inspections,maintenance and condition monitoring using discrete Bayesian networks

This paper presents a computational framework for risk-based planning of inspections and repairs for deteriorating components. Two distinct types of decision rules are used to model decisions: simple decision rules that depend on constants or observed variables (e.g. inspection outcome), and advanced decision rules that depend on variables found using Bayesian updating (e.g. probability of failure). Two decision models are developed, both relying on dynamic Bayesian networks (dBNs) for deterioration modelling. For simple decision rules, dBNs are used directly for exact assessment of total expected life-cycle costs. For advanced decision rules, simulations are performed to estimate the expected costs, and dBNs are used within the simulations for decision-making. Information from inspections and condition monitoring are included if available. An example in the paper demonstrates the framework and the implemented strategies and decision rules, including various types of condition-based maintenance. The strategies using advanced decision rules lead to reduced costs compared to the simple decision rules when condition monitoring is applied, and the value of condition monitoring is estimated by comparing the lowest costs obtained with and without condition monitoring.     

Bayesian methods for regional-scale eutrophication models

We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amount of data available and (3) be flexible enough to permit updates and improvements. Tree-based methods are a flexible approach useful for variable subset selection and when the analyst suspects global nonlinearity and cannot (or does not want to) specify the functional form of possible interactions a priori. We use the US EPA National Eutrophication Survey data to fit three models demonstrating the methods and to highlight important differences arising from slightly different model specifications. The Bayesian approach offers many advantages, including the estimation of the value of new information and proper probability distributions on the variable of interest as an output, which can be directly used in risk assessment or decision-making.     

Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference

A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design. The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design. The posterior distributions are often complex, multidimensional functions whose analysis requires the use of Markov chain Monte Carlo (MCMC) methods. These procedures are used to draw representative samples of the parameters investigated, providing information on their best estimate values, variability and correlations. The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method (FORM). The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety (FS) is calculated with a surrogate model from the more likely values of the input parameters. The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure. In this case, the condition FS = 1 is treated as a data point that is compared with the model prediction of FS. The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters. The parameters are updated according to their uncertainty, which is determined by the amount of data supporting them. The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength. The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.     

A hierarchical Bayesian framework for calibrating micro-level models with macro-level data

Owners of housing stocks require reliable and flexible tools to assess the impact of retrofits technologies. Bottom-up engineering-based housing stock models can help to serve such a function. These models require calibrating, using micro-level energy measurements at the building level, to improve model accuracy; however, the only publicly available data for the UK housing stock is at the macro-level, at the district, urban, or national scale. This paper outlines a method for using macro-level data to calibrate micro-level models. A hierarchical framework is proposed, utilizing a combination of regression analysis and Bayesian inference. The result is a Bayesian regression method that generates estimates of the average energy use for different dwelling types whilst quantifying uncertainty in both the empirical data and the generated energy estimates. Finally, the Bayesian regression method is validated and the use of the hierarchical Bayesian calibration framework is demonstrated.     

Hierarchical infrastructure network representation methods for risk-based decision-making

Estimating the extent of hazard-induced damage to infrastructure networks is a complex task that goes beyond computing direct costs and requires considering the effect of network connection patterns and interactions. This article presents a new model that combines a systems approach with strategies for detecting the internal structure of networks, and providing flexibility and different levels of accuracy in estimating the extent of damage. The model describes networks as hierarchical structures obtained by successive clustering. Hierarchical analysis of networks provides unique insights about how damage affects performance throughout the whole infrastructure system. The model enables using information for decision-making more efficiently by generating different levels of resolution for different problems. This is illustrated using data from hurricane Ike, Texas, USA in 2008, where the primary transportation network is studied. Estimates of population affected and loss of productivity are discussed, emphasising the importance of multiple levels for assessment, and their application on fast decision-making for emergency situations.     

Structural analysis methods for system reliability

The appropriateness of the use of traditional methods of structural analysis in reliability analyses is examined using two examples: partially restrained steel beams and the stability of earth slopes. It is found that new and innovative methods of structural analysis may cause simplifications in the system reliability analysis.     

Quantifying and reducing uncertainty in life cycle assessment using the Bayesian Monte Carlo method

The traditional life cycle assessment (LCA) does not perform quantitative uncertainty analysis. However, without characterizing the associated uncertainty, the reliability of assessment results cannot be understood or ascertained. In this study, the Bayesian method, in combination with the Monte Carlo technique, is used to quantify and update the uncertainty in LCA results. A case study of applying the method to comparison of alternative waste treatment options in terms of global warming potential due to greenhouse gas emissions is presented. In the case study, the prior distributions of the parameters used for estimating emission inventory and environmental impact in LCA were based on the expert judgment from the intergovernmental panel on climate change (IPCC) guideline and were subsequently updated using the likelihood distributions resulting from both national statistic and site-specific data. The posterior uncertainty distribution of the LCA results was generated using Monte Carlo simulations with posterior parameter probability distributions. The results indicated that the incorporation of quantitative uncertainty analysis into LCA revealed more information than the deterministic LCA method, and the resulting decision may thus be different. In addition, in combination with the Monte Carlo simulation, calculations of correlation coefficients facilitated the identification of important parameters that had major influence to LCA results. Finally, by using national statistic data and site-specific information to update the prior uncertainty distribution, the resultant uncertainty associated with the LCA results could be reduced. A better informed decision can therefore be made based on the clearer and more complete comparison of options.     

A systematical Bayesian approach for outcome-oriented fire service data collection

Data collection is always related to costs and to investments of resources. Especially data collected by the fire services is often not collected in a systematic manner and often without a clear purpose. A more systematic approach is achieved by identifying the stakeholders or decision-makers who are intended to use or benefit from the data and bear the costs. Whether a survey is reasonable or not can be treated in the context of a decision-problem by performing a pre-posterior decision analysis in order to assess the value of information. Potential stakeholders are identified that can benefit from fire service data and an overview is provided on the type of information that can be obtained by a survey or information that results from engineering knowledge. Both information are associated with uncertainties and should be identified and quantified before the data is collected to limit the extent of the collection process. A hierarchical Bayesian probabilistic approach is proposed to combine both type of information by differentiate the uncertainties between aleatory and epistemic uncertainties. The data can be used to update epistemic uncertainties by applying Bayesian inference techniques. An example for the estimation of fire service intervention characteristics illustrates the approach and discusses how aleatory and epistemic uncertainties can be quantified.     

Improved Bayesian network configurations for probabilistic identification of degradation mechanisms: application to chloride ingress

Probabilistic modelling of deterioration processes is an important task to plan and quantify maintenance operations of structures. Relevant material and environmental model parameters could be determined from inspection data; but in practice, the number of measures required for uncertainty quantification is conditioned by time-consuming and expensive tests. The main objective of this study was to propose a method based on Bayesian networks for improving the identification of uncertainties related to material and environmental parameters of deterioration models when there is limited available information. The outputs of the study are inspection configurations (in space and time) that could provide an optimal balance between accuracy and cost. The proposed methodology was applied to the identification of random variables for a chloride ingress model. It was found that there is an optimal discretisation for identifying each model parameter and that the combination of these configurations minimises identification errors. An illustration to the assessment of the probability of corrosion initiation showed that the approach is useful even if inspection data are limited.     

基于贝叶斯网络的结构健康评估信息融合方法

为了充分利用大型结构健康监测系统中来自不同时间与空间的多传感器信息资源,获得被测对象的一致性决策和估计任务,进而提高确诊率,介绍了从多传感器数据融合的概念、基本原理出发,提出的一种基于贝叶斯网络数据融合技术的结构健康监测方法。重点叙述了用于结构健康检测的朴素贝叶斯网络和扩展的朴素贝叶斯网络结构构建,以及网络节点概率的确定方法,并在项目中进行了试验。基于贝叶斯网络的结构健康评估方法有效地利用了各信息源之间的互补性,提高了健康评估的准确率、可靠性和稳健性。