Bayesian belief networks for system fault diagnostics

Fault diagnostic methods aim to recognize when faults exist on a system and to identify the failures that have caused the fault. The symptoms of the fault are obtained from readings from sensors located on the system. When the observed readings do not match those expected then a fault can exist. Using the detailed information provided by the sensors, a list of the failures (singly or in combinations) that could cause the symptoms can be deduced. In the last two decades, fault diagnosis has received growing attention due to the complexity of modern systems and the consequent need for more sophisticated techniques to identify the failures when they occur. Detecting the causes of a fault quickly and efficiently means reducing the costs associated with the system unavailability and, in certain cases, avoiding the risks of unsafe operating conditions. Bayesian belief networks (BBNs) are probabilistic models that were developed in artificial intelligence applications but are now applied in many fields. They are ideal for modelling the causal relations between faults and symptoms used in the detection process. The probabilities of events within the BBN can be updated following observations (evidence) about the system state. In this paper we investigate how BBNs can be applied to diagnose faults on a system. Initially Fault trees (FTs) are constructed to indicate how the component failures can combine to cause unexpected deviations in the variables monitored by the sensors. Converting FTs into BNs enables the creation of a model that represents the system with a single network, which is constituted by sub‐networks. The posterior probabilities of the components' failures give a measure of those components that have caused the symptoms observed. The method gives a procedure that can be generalized for any system where the causality structure can be developed relating the system component states to the sensor readings. The technique is demonstrated with a simple example system. Copyright © 2008 John Wiley & Sons, Ltd.     

A Bayesian model for the joint optimization of quality and maintenance decisions

We develop a model for the economic design of a Bayesian control chart for monitoring a process mean. The process may randomly suffer failures that result in a non‐operating state, and thus call for an immediate corrective maintenance action, as well as assignable causes that shift the process mean to an undesirable level. Quality shifts, apart from poorer quality outcome and higher operational cost, also result in higher failure rate. Consequently, their removal, besides improving the outcome quality and reducing the quality‐related cost, is also a preventive maintenance action since it reduces the probability of a failure. The proposed Bayesian model allows the determination of the design parameters that minimize the total expected quality and maintenance cost per time unit. The effectiveness of the proposed model is evaluated through the comparison of its expected cost against the optimum expected cost of the simpler variable‐parameter Shewhart chart. Copyright © 2010 John Wiley & Sons, Ltd.     

Bayesian networks in reliability

Over the last decade, Bayesian networks (BNs) have become a popular tool for modelling many kinds of statistical problems. We have also seen a growing interest for using BNs in the reliability analysis community. In this paper we will discuss the properties of the modelling framework that make BNs particularly well suited for reliability applications, and point to ongoing research that is relevant for practitioners in reliability.     

Inference in hybrid Bayesian networks

Since the 1980s, Bayesian networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability techniques (like fault trees and reliability block diagrams). However, limitations in the BNs’ calculation engine have prevented BNs from becoming equally popular for domains containing mixtures of both discrete and continuous variables (the so-called hybrid domains). In this paper we focus on these difficulties, and summarize some of the last decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability.     

评价网络理论在电力公司反应堆建设决策中的应用

电力公司反应堆建设中的一个决策问题,是如何依据过去经验和试验结果来选取最优的建设方案。评价网络理论（valuation networks）是贝叶斯决策问题表示和求解的新方法。以某电力公司为例,应用评价网络理论,以反应堆建设的决策问题进行分析,给出了决策问题的具体表示和求解的详细过程。     

Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis

This paper deals with the use of Bayesian networks to compute system reliability. The reliability analysis problem is described and the usual methods for quantitative reliability analysis are presented within a case study. Some drawbacks that justify the use of Bayesian networks are identified. The basic concepts of the Bayesian networks application to reliability analysis are introduced and a model to compute the reliability for the case study is presented. Dempster Shafer theory to treat epistemic uncertainty in reliability analysis is then discussed and its basic concepts that can be applied thanks to the Bayesian network inference algorithm are introduced. Finally, it is shown, with a numerical example, how Bayesian networks’ inference algorithms compute complex system reliability and what the Dempster Shafer theory can provide to reliability analysis.     

Sensitivity analysis in Gaussian Bayesian networks using a symbolic-numerical technique

The paper discusses the problem of sensitivity analysis in Gaussian Bayesian networks. The algebraic structure of the conditional means and variances, as rational functions involving linear and quadratic functions of the parameters, are used to simplify the sensitivity analysis. In particular the probabilities of conditional variables exceeding given values and related probabilities are analyzed. Two examples of application are used to illustrate all the concepts and methods.     

Leakage detection in water pipe networks using a Bayesian probabilistic framework

A Bayesian system identification methodology is proposed for leakage detection in water pipe networks. The methodology properly handles the unavoidable uncertainties in measurement and modeling errors. Based on information from flow test data, it provides estimates of the most probable leakage events (magnitude and location of leakage) and the uncertainties in such estimates. The effectiveness of the proposed framework is illustrated by applying the leakage detection approach to a specific water pipe network. Several important issues are addressed, including the role of modeling error, measurement noise, leakage severity and sensor configuration (location and type of sensors) on the reliability of the leakage detection methodology. The present algorithm may be incorporated into an integrated maintenance network strategy plan based on computer-aided decision-making tools.     

Fuzzy uncertainty modelling for project planning: application to helicopter maintenance

Maintenance is an activity of growing interest, especially for critical systems. In particular, aircraft maintenance costs are becoming an important issue in the aeronautical industry. Managing an aircraft maintenance centre is a complex activity. One of the difficulties comes from the numerous uncertainties that affect the activity and disturb the plans in the short and medium term. Based on a helicopter maintenance planning and scheduling problem, we study in this paper the integration of uncertainties into tactical and operational multi-resource, multi-project planning (respectively Rough Cut Capacity Planning and the Resource Constraint Project Scheduling Problem). Our main contributions are in modelling the periodic workload on a tactical level considering uncertainties in macro-task work content, and modelling the continuous workload on the operational level considering uncertainties in task duration. We model uncertainties using a fuzzy/possibilistic approach instead of a stochastic approach since very limited data are available. We refer to the problems as the Fuzzy Rough Cut Capacity Problem (FRCCP) and the Fuzzy Resource Constraint Project Scheduling Problem (RCPSP). We apply our models to helicopter maintenance activity within the frame of the Helimaintenance project, an industrial project approved by the French Aerospace Valley cluster that aims at building a centre for civil helicopter maintenance.     

Analyzing the effect of introducing a kurtosis parameter in Gaussian Bayesian networks

Gaussian Bayesian networks are graphical models that represent the dependence structure of a multivariate normal random variable with a directed acyclic graph (DAG). In Gaussian Bayesian networks the output is usually the conditional distribution of some unknown variables of interest given a set of evidential nodes whose values are known. The problem of uncertainty about the assumption of normality is very common in applications. Thus a sensitivity analysis of the non-normality effect in our conclusions could be necessary. The aspect of non-normality to be considered is the tail behavior. In this line, the multivariate exponential power distribution is a family depending on a kurtosis parameter that goes from a leptokurtic to a platykurtic distribution with the normal as a mesokurtic distribution. Therefore a more general model can be considered using the multivariate exponential power distribution to describe the joint distribution of a Bayesian network, with a kurtosis parameter reflecting deviations from the normal distribution. The sensitivity of the conclusions to this perturbation is analyzed using the Kullback-Leibler divergence measure that provides an interesting formula to evaluate the effect.     

Fuzzy adaptive preventive maintenance in a manufacturing control system: a step towards self-maintenance

In this paper, a framework of integrating preventive maintenance (PM) and manufacturing control system is proposed. Fuzzy-logic control is used to enable an intelligent approach of integrating PM and a manufacturing control system. This will contribute to the novel development of an integrated and intelligent framework in those two fields that are sometimes difficult to achieve. This idea is based on combining work on an intelligent real-time controller for a failure-prone manufacturing system using a fuzzy-logic approach (Yuniarto, M.N. and Labib, A.W., Optimal control system of an unreliable machine using fuzzy logic control: from design to implementation. Int. J. Prod. Res. (in press a); Yuniarto, M.N. and Labib, A.W., Intelligent real time control of disturbances in manufacturing systems. Integr. Manuf. Syst.: Int. J. Manuf. Technol. Manage. (in press b) and the work on PM proposed by Labib et al. (Labib, A.W., Williams, G.B. and O’Connor, R.F., An intelligent maintenance model (system): an application of analytic hierarchy process and a fuzzy logic rule-based controller. J. Oper. Res. Soc., 1998, 49, 745–757)). The aim of the research is to control a failure-prone manufacturing system and at the same time propose which PM method is applicable to a specific failure-prone manufacturing system. The mean time to repair and mean time between failures of the system are used as integrator agents, by using them to couple the two areas to be integrated (i.e. a maintenance system and manufacturing system).     

基于贝叶斯网络的核电站应急电力系统安全评价

在故障树分析法(FTA)基础上提出了一种基于贝叶斯网络(BN)的核电站应急电力系统安全评价方法,比较了FTA和BN在建立安全评价模型和评价能力上的不同.该方法在应对众多影响因素上有很大优势,能进行更多有意义的分析:既能进行前向的预测推理,又能进行后向的诊断推理,可以找出影响故障的组合模式,从而能够找出系统的薄弱环节.同时采用基于Matlab的BNT软件包,大大简化了计算过程.通过对10MW高温气冷堆(HTR-10)应急电力系统的安全评价实例的分析,证明该方法是对传统的基于故障树分析的安全评价方法的有益改进.     

Uncertainty analyses in fault trees and Bayesian networks using FORM/SORM methods

Efficient computational methods based on first and second order approximations (FORM/SORM) of the tails of a random variable, which is defined as a function of a set of basic variables, are given. Interesting examples of these types of functions are the probabilities of occurrence of the root events of fault trees or nodes in a Bayesian network. The method allows estimation of extreme percentiles and high confidence one-sided probability intervals of the target variables. Several examples of applications to real cases are used to illustrate the whole process.     

Bayesian compressive sensing for approximately sparse signals and application to structural health monitoring signals for data loss recovery

The theory and application of compressive sensing (CS) have received a lot of interest in recent years. The basic idea in CS is to use a specially-designed sensor to sample signals that are sparse in some basis (e.g. wavelet basis) directly in a compressed form, and then to reconstruct (decompress) these signals accurately using some inversion algorithm after transmission to a central processing unit. However, many signals in reality are only approximately sparse, where only a relatively small number of the signal coefficients in some basis are significant and the remaining basis coefficients are relatively small but they are not all zero. In this case, perfect reconstruction from compressed measurements is not expected. In this paper, a Bayesian CS algorithm is proposed for the first time to reconstruct approximately sparse signals. A robust treatment of the uncertain parameters is explored, including integration over the prediction-error precision parameter to remove it as a “nuisance” parameter, and introduction of a successive relaxation procedure for the required optimization of the basis coefficient hyper-parameters. The performance of the algorithm is investigated using compressed data from synthetic signals and real signals from structural health monitoring systems installed on a space-frame structure and on a cable-stayed bridge. Compared with other state-of-the-art CS methods, including our previously-published Bayesian method, the new CS algorithm shows superior performance in reconstruction robustness and posterior uncertainty quantification, for approximately sparse signals. Furthermore, our method can be utilized for recovery of lost data during wireless transmission, even if the level of sparseness in the signal is low.     

A new modeling approach to the safety evaluation of N-modular redundant computer systems in presence of imperfect maintenance

A large number of safety-critical control systems are based on N-modular redundant architectures, using majority voters on the outputs of independent computation units. In order to assess the compliance of these architectures with international safety standards, the frequency of hazardous failures must be analyzed by developing and solving proper formal models. Furthermore, the impact of maintenance faults has to be considered, since imperfect maintenance may degrade the safety integrity level of the system. In this paper, we present both a failure model for voting architectures based on Bayesian networks and a maintenance model based on continuous time Markov chains, and we propose to combine them according to a compositional multiformalism modeling approach in order to analyze the impact of imperfect maintenance on the system safety. We also show how the proposed approach promotes the reuse and the interchange of models as well the interchange of solving tools.     

A comparative Full Bayesian before-and-after analysis and application to urban road safety countermeasures in New Jersey

This paper develops a step-by-step methodology for the application of Full Bayes (FB) approach for before-and-after analysis of road safety countermeasures. As part of this methodology, it studies the posterior prediction capability of Bayesian approaches and their use in crash reduction factor (CRF) estimation. A collection of candidate models are developed to investigate the impacts of different countermeasures on road safety when limited data are available. The candidate models include traditional, random effects, non-hierarchical and hierarchical Poisson-Gamma and Poisson-Lognormal (P-LN) distributions. The use of random effects and hierarchical model structures allows treatment of the data in a time-series cross-section panel, and deal with the spatial and temporal effects in the data. Next, the proposed FB estimation methodology is applied to urban roads in New Jersey to investigate the impacts of different treatment measures on the safety of “urban collectors and arterial roads” with speed limits less than 45 mph. The treatment types include (1) increase in lane width, (2) installation of median barriers, (3) vertical and horizontal improvements in the road alignment; and (4) installation of guide rails. The safety performance functions developed via different model structures show that random effects hierarchical P-LN models with informative hyper-priors perform better compared with other model structures for each treatment type. The individual CRF values are also found to be consistent across the road sections, with all showing a decrease in crash rates after the specific treatment except guide rail installation treatment. The highest decrease in the crash rate is observed after the improvement in vertical and horizontal alignment followed by increase in lane width and installation of median barriers. Overall statistical analyses of the results obtained from different candidate models show that when limited data are available, P-LN model structure combined with higher levels of hierarchy and informative priors may reduce the biases in model parameters resulting in more robust estimates.     

Multi‐system reliability trend analysis model using incomplete data with application to tank maintenance

This paper focuses on the estimation of power law type reliability trend analysis model given incomplete failure data from multiple homogeneous machines. In many real situations, we encounter data having missing parts especially in the initial recording stage, so‐called left censored data. We provide a method to estimate the failure intensity function of power law process using left censored data from multiple machines. The method consists of two folds: initially estimate parameters via the law of large numbers theory and revise the estimated parameters recursively through the EM algorithm. The validity of our method is confirmed by simulation experiments. We also apply our method to the real‐world case, Korean ARMY tank maintenance data, and show that our proposed method is applicable to practical maintenance planning.     

Activity-on-node networks with minimal and maximal time lags and their application to make-to-order production

Maximal time lags between activities of a project play an important role in practice in addition to minimal ones. However, maximal time lags have been discussed very rarely in literature thus far. This paper shows how to model projects with minimal and maximal time lags by cyclic activity-on-node networks. As an important application, the production process for make-to-order production with limited resources is studied, which can be represented by a multi-project network where the individual operations of the jobs correspond to the nodes of the network. For different product structures, careful consideration is given to the modelling of a nondelay performance of overlapping operations by appropriately establishing minimal and maximal time lags.     

RAMS+C informed decision-making with application to multi-objective optimization of technical specifications and maintenance using genetic algorithms

The role of technical specifications and maintenance (TSM) activities at nuclear power plants (NPP) aims to increase reliability, availability and maintainability (RAM) of Safety-Related Equipment, which, in turn, must yield to an improved level of plant safety. However, more resources (e.g. costs, task force, etc.) have to be assigned in above areas to achieve better scores in reliability, availability, maintainability and safety (RAMS). Current situation at NPP shows different programs implemented at the plant that aim to the improvement of particular TSM-related parameters where the decision-making process is based on the assessment of the impact of the change proposed on a subgroup of RAMS+C attributes.This paper briefly reviews the role of TSM and two main groups of improvement programs at NPP, which suggest the convenience of considering the approach proposed in this paper for the Integrated Multi-Criteria Decision-Making on changes to TSM-related parameters based on RAMS+C criteria as a whole, as it can be seem as a decision-making process more consistent with the role and synergic effects of TSM and the objectives and goals of current improvement programs at NPP. The case of application to the Emergency Diesel Generator system demonstrates the viability and significance of the proposed approach for the Multi-objective Optimization of TSM-related parameters using a Genetic Algorithm.     

利用贝叶斯推理估计二维含源对流扩散方程参数

为了克服观测数据的不确定性给参数反演带来的困难,利用贝叶斯推理建立了二维含源对流扩散方程参数估计的数学模型。通过贝叶斯定理,获得了模型参数的后验分布,从而获得反问题的解。对于多参数反演问题,基于数值解计算得到的参数后验分布很难直观地表现出来,采用马尔科夫链蒙特卡罗方法对参数的后验分布进行采样,获得了扩散系数和降解系数的估计值。研究了观测点位置对计算结果的影响;同时研究了似然函数的形式对估计结果的影响,结果表明在异常值可能出现时采用Laplace分布型的似然函数可以获得稳健估计。对不同观测点数目下的估计值进行了对比,认为对于二维稳态对流扩散方程的双参数估计问题,至少需要两个观测点才有可能得到合理的解。