Inference in hybrid Bayesian networks (original) (raw)

Bayesian networks in reliability

Reliability Engineering & System Safety, 2007

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.

Bayesian networks in reliability: The good, the bad, and the ugly

Advances in mathematical modeling for reliability, 2008

Bayesian network (BN) models gain more and more popularity as a tool in reliability analysis. In this paper we consider some of the properties of BNs that have made them popular, consider some of the recent developments, and also point to the most important remaining challenges when using BNs in reliability.

Applications of Bayesian Networks in Reliability Analysis

2006

Over the last decade, Bayesian Networks (BNs) have become a popular tool for modelling many kinds of statistical problems. In this chapter we will discuss the properties of the modelling framework that make BNs particularly well suited for reliability applications. This discussion is closely linked to the analysis of a real-world example.

Hybrid Bayesian Networks for the Reliability Analysis of Systems with Continuous Variables

The International FLAIRS Conference Proceedings

The standard way of dealing with continuous variablesinto reliability models is to discretize (or even binarise)them, resulting in discrete state models. The presentpaper proposes an approach where continuous systemvariables can be directly exploited by resorting to HybridBayesian Networks (HBN), where both continuousand discrete variables can be mixed in a general way.This allows one to: model the inter-dependencies betweendiscrete state components or subsystems, modelthe inter-dependencies between continuous system variables,model the influence of contextual information onsystem variables and components, model the definitionof specific system events or conditions given specificvalues of the system variables. We will show how theabove issues can be captured in a principled way bythe HBN formalism, by making the final analyses moregrounded on the actual values of every system variable.We finally present a case study where the model of agranule storage tank system of a petrochemical ...

Modelling dependable systems using hybrid Bayesian networks

Reliability Engineering & System Safety, 2008

A hybrid Bayesian Network (BN) is one that incorporates both discrete and continuous nodes. In our extensive applications of BNs for system dependability assessment the models are invariably hybrid and the need for efficient and accurate computation is paramount. We apply a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction tree structures to perform inference in hybrid BNs. We illustrate its use on two example dependability problems: reliability estimation and diagnosis of a faulty sensor in a temporal system. Dynamic discretisation can be used as an alternative to analytical or Monte Carlo methods with high precision and can be applied to a wide range of dependability problems.

Modeling Dependable Systems using Hybrid Bayesian Networks

2006

A hybrid Bayesian Network (BN) is one that incorporates both discrete and continuous nodes. In our extensive applications of BNs for system dependability assessment the models are invariably hybrid and the need for efficient and accurate computation is paramount. We apply a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction tree structures to perform inference in hybrid BNs. We illustrate its use on two example dependability problems: reliability estimation and diagnosis of a faulty sensor in a temporal system. Dynamic discretisation can be used as an alternative to analytical or Monte Carlo methods with high precision and can be applied to a wide range of dependability problems.

Bayesian Belief Networks in Reliability

Over the last decade, Bayesian networks (BNs) have become a popular tool for modeling many kinds of statistical problems. In particular, we assisted to a growing interest for using BNs in the reliability analysis community [14]. As the quantities in reliability studies are uncertain, the end result should be a mathematically sound statistical model describing a set of random variables.

A new Bayesian Network approach to Reliability modelling

We present a new, effective and flexible event-based hybrid BN modelling method for reliability assessment that scales up to large, complex dynamic systems. By incorporating a recent powerful approximate inference algorithm for hybrid BNs, involving dynamically discretising the domain of all continuous variables, approximated solutions for both static and dynamic constructs are obtained simultaneously rendering unnecessary the use of modularisation techniques. Continuous and discrete nodes can be included in the model to represent the continuous failure times of system components and discrete reliabilities of the system (or any subsystem) for a given target requirement, respectively. Unlike other approaches (which tend to be restricted to using exponential distributions), our new approach is able to solve any configuration of static and dynamic gates with general parametric or emp irical time-to-failure distributions, without recourse to numerical integration techniques or simulation methods. Furthermore, the diagnostic analysis capabilities of the BN combined with the dynamic discretisation algorithm allow also to obtain estimates of the parameterised marginal failure distribution (for the root nodes), either using available raw failure data or as prior information according to expert knowledge. No exact expression for the marginal is needed and no conditional probability tables need to be completed. Our BN framework allows a compact representation of the eventdependent failure behaviours characteristic of fault-tolerant systems, avoiding the state space explosion problem of the Markov Chain based approaches. Our BN framework is mathematically sound and at the same time simple enough to allow the interaction with domain experts and decision makers. Sensitivity, uncertainty, diagnosis, common cause failures, and warranty analysis can also be easily performed within this framework.

Dynamic Bayesian Networks in System Reliability Analysis

Fault Detection, Supervision and Safety of Technical Processes 2006, 2007

Today industrial systems are characterized by a set of dependencies among the components and the environment of the system. To address these difficulties, this paper presents a method for modelling and analyzing the reliability of a complex system based on Dynamic Bayesian Networks (DBN). This method allows to take into account the influence of time or exogenous variables on the failure (degradation) modes of the system. The DBN graphical structure provides an easy way to specify the dependencies and, hence, to provide a compact representation of the model. In addition, the DBN formalism is associated to simulation tools that enable an efficient processing for the models.