Bayesian inference in probabilistic risk assessment—The current state of the art

Markov chain Monte Carlo (MCMC) approaches to sampling directly from the joint posterior distribution of aleatory model parameters have led to tremendous advances in Bayesian inference capability in a wide variety of fields, including probabilistic risk analysis. The advent of freely available software coupled with inexpensive computing power has catalyzed this advance. This paper examines where the risk assessment community is with respect to implementing modern computational-based Bayesian approaches to inference. Through a series of examples in different topical areas, it introduces salient concepts and illustrates the practical application of Bayesian inference via MCMC sampling to a variety of important problems.     

Risk based maintenance optimization: foundational issues

Lately there has been an increasing focus on risk based maintenance optimization in the offshore industry prompted by new functional regulations on risk. In this paper we present alternative probabilistic frameworks for this optimization, using a Bayesian approach. Some key features of the frameworks are discussed, including uncertainty treatment and type of performance measures to be used.     

Bayesian network approach to change propagation analysis

The prediction of change propagation is one of the important issues in engineering change management. The aim of this article is to explore the capability of Bayesian network (BN), which is an emerging tool for a wide range of risk management, in modeling and analysis of change propagation. To this end, we compare the BN with change prediction method (CPM), which is the most established probabilistic methods for predicting change propagation. This paper shows that a CPM-based model can be converted into an equivalent BN, and the probabilistic inference technique on the latter results in the same change prediction result obtained from the former. Then, this paper shows that several improvements can be obtained at various levels using the BN. At the modeling level, complex relationship between components such as combined effect of simultaneous changes or multistate relationship can be naturally represented with the BN. At the analysis level, various change propagation scenarios can be analyzed using probabilistic inference on the BN. Finally, BN provides a robust framework for learning change propagation probabilities from empirical data. The case study is conducted to show the feasibility of the model.     

Prediction of road accidents: A Bayesian hierarchical approach

In this paper a novel methodology for the prediction of the occurrence of road accidents is presented. The methodology utilizes a combination of three statistical methods: (1) gamma-updating of the occurrence rates of injury accidents and injured road users, (2) hierarchical multivariate Poisson-lognormal regression analysis taking into account correlations amongst multiple dependent model response variables and effects of discrete accident count data e.g. over-dispersion, and (3) Bayesian inference algorithms, which are applied by means of data mining techniques supported by Bayesian Probabilistic Networks in order to represent non-linearity between risk indicating and model response variables, as well as different types of uncertainties which might be present in the development of the specific models.     

Improving the analysis of dependable systems by mapping fault trees into Bayesian networks

Bayesian Networks (BN) provide a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of real-world tasks but they have received little attention in the area of dependability. The present paper is aimed at exploring the capabilities of the BN formalism in the analysis of dependable systems. To this end, the paper compares BN with one of the most popular techniques for dependability analysis of large, safety critical systems, namely Fault Trees (FT). The paper shows that any FT can be directly mapped into a BN and that basic inference techniques on the latter may be used to obtain classical parameters computed from the former (i.e. reliability of the Top Event or of any sub-system, criticality of components, etc). Moreover, by using BN, some additional power can be obtained, both at the modeling and at the analysis level. At the modeling level, several restrictive assumptions implicit in the FT methodology can be removed and various kinds of dependencies among components can be accommodated. At the analysis level, a general diagnostic analysis can be performed. The comparison of the two methodologies is carried out by means of a running example, taken from the literature, that consists of a redundant multiprocessor system.     

Modeling the effectiveness of oil combating from an ecological perspective--a Bayesian network for the Gulf of Finland; the Baltic Sea

Maritime traffic poses a major threat to marine ecosystems in the form of oil spills. The Gulf of Finland, the easternmost part of the Baltic Sea, has witnessed a rapid increase in oil transportation during the last 15 years. Should a spill occur, the negative ecological impacts may be reduced by oil combating, the effectiveness of which is, however, strongly dependent on prevailing environmental conditions and available technical resources. This poses increased uncertainty related to ecological consequences of future spills. We developed a probabilistic Bayesian network model that can be used to assess the effectiveness of different oil combating strategies in minimizing the negative effects of oil on six species living in the Gulf of Finland. The model can be used for creating different accident scenarios and assessing the performance of various oil combating actions under uncertainty, which enables its use as a supportive tool in decision-making. While the model is confined to the western Gulf of Finland, the methodology is adaptable to other marine areas facing similar risks and challenges related to oil spills.     

Assessing the reliability and the expected performance of a network under disaster risk

In a disaster situation, functionality of an infrastructure network is critical for effective emergency response. We evaluate several probabilistic measures of connectivity and expected travel time/distance between critical origin–destination pairs to assess the functionality of a given transportation network in case of a disaster. The input data include the most likely disaster scenarios as well as the probability that each link of the network fails under each scenario. Unlike most studies that assume independent link failures, we model dependency among link failures and propose a novel dependency model that incorporates the impact of the disaster on the network and at the same time yields tractable cases for the computation of the probabilistic measures. We develop algorithms for the computation of the measures and utilize a Monte Carlo simulation algorithm for the intractable cases. We present a case study of the Istanbul highway system under earthquake risk, and compare different dependency structures computationally.     

A new uncertainty importance measure

Uncertainty in parameters is present in many risk assessment problems and leads to uncertainty in model predictions. In this work, we introduce a global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations among the parameters. We discuss its mathematical properties and highlight the differences between the present indicator, variance-based uncertainty importance measures and a moment independent sensitivity indicator previously introduced in the literature. Numerical results are discussed with application to the probabilistic risk assessment model on which Iman [A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Anal 1987;7(1):22–33] first introduced uncertainty importance measures.     

A probabilistic approach for determining the control mode in CREAM

The control mode is the core concept for the prediction of human performance in CREAM. In this paper, we propose a probabilistic method for determining the control mode which is a substitute for the existing deterministic method. The new method is based on a probabilistic model, a Bayesian network. This paper describes the mathematical procedure for developing the Bayesian network for determining the control mode. The Bayesian network developed in this paper is an extension of the existing deterministic method. Using the Bayesian network, we expect that we can get the best estimate of the control mode given the available data and information about the context. The mathematical background and procedure for developing equivalent Bayesian networks for given discrete functions provided in this paper can be applied to other discrete functions to develop probabilistic models.     

Graph spectral analysis of protein interaction network evolution

We present an analysis of protein interaction network data via the comparison of models of network evolution to the observed data. We take a Bayesian approach and perform posterior density estimation using an approximate Bayesian computation with sequential Monte Carlo method. Our approach allows us to perform model selection over a selection of potential network growth models. The methodology we apply uses a distance defined in terms of graph spectra which captures the network data more naturally than previously used summary statistics such as the degree distribution. Furthermore, we include the effects of sampling into the analysis, to properly correct for the incompleteness of existing datasets, and have analysed the performance of our method under various degrees of sampling. We consider a number of models focusing not only on the biologically relevant class of duplication models, but also including models of scale-free network growth that have previously been claimed to describe such data. We find a preference for a duplication-divergence with linear preferential attachment model in the majority of the interaction datasets considered. We also illustrate how our method can be used to perform multi-model inference of network parameters to estimate properties of the full network from sampled data.     

Probabilistic reliability assessment of a heritage structure under horizontal loads

This paper proposes a methodology for the probabilistic reliability assessment of heritage buildings. The procedure addresses investigation and tests on the structure and it considers the implementation of Bayesian updating techniques for a rational use of the collected information. After having described the peculiarities of ancient buildings, it is shown how probabilistic methods can be adapted to evaluate their safety. A practical application of the methodology to a relevant case study is presented, namely a historic aqueduct in Italy. The main goal is to demonstrate the effectiveness of a probabilistic approach to the reliability assessment of heritage structures.     

基于代数决策图的贝叶斯网络参数简化技术

贝叶斯网络是一种进行不确定性知识表达和推理的有效工具,推理算法是贝叶斯网络研究的主要内容之一.目前,贝叶斯网络推理算法采用条件概率表(CPT)来存储贝叶斯网络中各节点的条件概率分布(CPD).CPT中的概率参数随父节点数目的增加呈指数增长,使得网络中概率参数急剧增加,降低了网络推理效率.为提高网络推理效率,本文提出采用代数逻辑图(ADD)取代CPT存储网络中各节点CPD的方法.结合有序二分决策图理论,分析并验证了ADD通过捕捉贝叶斯网络中父子节点之间的环境独立性来减少网络中的概率参数的原理,进而推导出了CPT到等价ADD转化的算法.最后,通过实例验证了ADD存储方式的有效性.结果表明,对于具有环境独立特性的贝叶斯网络,相对于CPT的存储方式,等价ADD存储方式可有效减少网络中的概率参数,为贝叶斯网络推理效率的提高提供一种有效手段.     

Multilevel approach to lifetime assessment of steam turbines

This paper presents a multilevel methodology for a steam turbine lifetime assessment based on the damage calculation, probabilistic analysis and fracture mechanics considerations. Creep-fatigue damage calculations serve as a basis for evaluating the current lifetime expenditure and for defining additional steps of analysis. The need for the use of probabilistic analysis results from the inherent uncertainty in estimating the lifetime expenditure primarily caused by scatter in material properties. Fracture mechanics considerations are helpful in determining additional safety margins for components containing cracks. This methodology has been illustrated using an example of the lifetime calculations of a high-temperature steam turbine rotor. The calculations were based on the results of 2D numerical simulations performed for steady state and transient operating conditions.     

Application of Bayesian Methods for Age‐Dependent Reliability Analysis

In this article, the authors present a general methodology for age‐dependent reliability analysis of degrading or ageing components, structures and systems. The methodology is based on Bayesian methods and inference—its ability to incorporate prior information and on ideas that ageing can be thought of as age‐dependent change of beliefs about reliability parameters (mainly failure rate), when change of belief occurs not only because new failure data or other information becomes available with time but also because it continuously changes due to the flow of time and the evolution of beliefs. The main objective of this article is to present a clear way of how practitioners can apply Bayesian methods to deal with risk and reliability analysis considering ageing phenomena. The methodology describes step‐by‐step failure rate analysis of ageing components: from the Bayesian model building to its verification and generalization with Bayesian model averaging, which as the authors suggest in this article, could serve as an alternative for various goodness‐of‐fit assessment tools and as a universal tool to cope with various sources of uncertainty. The proposed methodology is able to deal with sparse and rare failure events, as is the case in electrical components, piping systems and various other systems with high reliability. In a case study of electrical instrumentation and control components, the proposed methodology was applied to analyse age‐dependent failure rates together with the treatment of uncertainty due to age‐dependent model selection. Copyright © 2013 John Wiley & Sons, Ltd.     

Accounting for Parameter Uncertainty in Simulation Input Modeling

We formulate and evaluate a Bayesian approach to probabilistic input modeling for simulation experiments that accounts for the parameter and stochastic uncertainties inherent in most simulations and that yields valid predictive inferences about outputs of interest. We use prior information to construct prior distributions on the parameters of the input processes driving the simulation. Using Bayes' rule, we combine this prior information with the likelihood function of sample data observed on the input processes to compute the posterior parameter distributions. In our Bayesian simulation replication algorithm, we estimate parameter uncertainty by independently sampling new values of the input-model parameters from their posterior distributions on selected simulation runs; and we estimate stochastic uncertainty by performing multiple (conditionally) independent runs with each set of parameter values. We formulate performance measures relevant to both Bayesian and frequentist input-modeling techniques, and we summarize an experimental performance evaluation demonstrating the advantages of the Bayesian approach.     

Fuzzy belief propagation in constrained Bayesian networks with application to maintenance decisions

Bayesian networks have been widely applied to domains such as medical diagnosis, fault analysis, and preventative maintenance. In some applications, because of insufficient data and the complexity of the system, fuzzy parameters and additional constraints derived from expert knowledge can be used to enhance the Bayesian reasoning process. However, very few methods are capable of handling the belief propagation in constrained fuzzy Bayesian networks (CFBNs). This paper therefore develops an improved approach which addresses the inference problem through a max-min programming model. The proposed approach yields more reasonable inference results and with less computational effort. By integrating the probabilistic inference drawn from diverse sources of information with decision analysis considering a decision-maker's risk preference, a CFBN-based decision framework is presented for seeking optimal maintenance decisions in a risk-based environment. The effectiveness of the proposed framework is validated based on an application to a gas compressor maintenance decision problem.     

Assessment of the mineral industry NORM/TENORM disposal in hazardous landfills

The main objective of this paper is to describe the assessment methodology utilised in Brazil, to foresee the performance of industrial landfills to disposal solid wastes containing natural radionuclides arising from milling and metallurgical installations that process ores containing NORM. An integrated methodology is utilized and issues as risk, exposure pathways and the plausible scenarios in which the contaminant can migrate and reach the environment and human beings are addressed. A specific example of the procedure is described and results are presented for actual situations. The model consists of an engineered depository constructed of earthen materials which minimise costs and maintain integrity over long-term. In order to define the landfill characteristics and the potential consequences to the environment, an impact analysis is carried out, considering the engineering aspects of the waste deposit and the exposure pathways by which the contaminant can migrate and reach the environment and human beings. Analytical solutions are used in the computer program in order to obtain fast results.