Equivalent Bayesian Network Research Articles

Scalable k-out-of-n models for dependability analysis with Bayesian networks

Availability analysis is indispensable in evaluating the dependability of safety and business-critical systems, for which fault tree analysis (FTA) has proven very useful throughout research and industry. Fault trees (FT) can be analyzed by means of a rich set of mathematical models. One particular model are Bayesian networks (BNs) which have gained considerable popularity recently due to their powerful inference abilities. However, large-scale systems, as found in modern data centers for cloud computing, pose modeling challenges that require scalable availability models. An equivalent BN of a FT has no scalable representation for the k-out-of-n (k/n) voting gate because the conditional probability table that constitutes the k/n voting gate grows exponentially in n. Thus, the memory becomes the limiting factor.We propose a scalable k/n voting gate representation for BNs, based on the temporal noisy adder. The resulting model reduces the initial exponential to polynomial memory growth without a custom inference algorithm. Previous BN implementations of the k/n voting gate could only handle around 30 input events until memory limits make inference infeasible. However, our evaluation shows that our scalable model can handle more than 700 input events per gate, making it possible to evaluate large scale systems.

A Bayesian network based method for reliability analysis of subsea blowout preventer control system

Subsea drilling needs extremely complex equipment, but engineering challenges are posed by harsh offshore environments. A subsea blowout preventer (BOP) is a critical device used to seal, control and monitor oil wells to ensure safety during the drilling process. In this paper, a novel approach to construct an equivalent Bayesian network (BN) from a GO model is proposed and it is used for assessing reliability of the subsea BOP control system. The proposed method relaxes some limitations of GO models and enriches the ways of developing BNs. Probability updating and adaption of the presented BN is demonstrated by case studies. A three-axiom-based validation method is used for partial validation of the BN. The proposed method can be applied to other existing GO models.

System Analysis by Mapping a Fault-tree into a Bayesian-network

In view of the limitations of fault tree analysis in reliability assessment, Bayesian Network (BN) has been studied as an alternative technology. After a brief introduction to the method for mapping a Fault Tree (FT) into an equivalent BN, equations used to calculate the structure importance degree, the probability importance degree and the critical importance degree are presented. Furthermore, the correctness of these equations is proved mathematically. Combining with an aircraft landing gear’s FT, an equivalent BN is developed and analysed. The results show that richer and more accurate information have been achieved through the BN method than the FT, which demonstrates that the BN is a superior technique in both reliability assessment and fault diagnosis.

Risk analysis of subsea blowout preventer by mapping GO models into Bayesian networks

Bayesian network (BN) is commonly used in probabilistic risk quantification due to its powerful capacity in uncertain knowledge representation and uncertainty reasoning. For the formalization of BN models, this paper presents a novel approach on constructing a BN from GO model. The equivalent BNs of the seventeen basic operators in GO methodology are developed. Therefore, the existing GO model can be mapped into an equivalent BN on basis of these developed BNs of the operators. Subsea blowout preventer (BOP) system plays an important role in providing safety during the subsea drilling activities. A case of closing the subsea BOP in the presence of pump failures is used to illustrate the mapping process. First, its GO model is presented according to the flow chart of the case. Then, BN is obtained based on the presented GO model. The developed BN relaxes the limitations of GO model and is capable of probability updating and probability adapting. Sensitivity analysis is performed to find the key influencing factor. The three-axiom-based analysis method is used to validate the developed BN.

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.

Probabilistic Fault Diagnosis of Safety Instrumented Systems based on Fault Tree Analysis and Bayesian Network

Safety instrumented systems (SISs) are used in the oil and gas industry to detect the onset of hazardous events and/or to mitigate their consequences to humans, assets, and environment. A relevant problem concerning these systems is failure diagnosis. Diagnostic procedures are then required to determine the most probable source of undetected dangerous failures that prevent the system to perform its function. This paper presents a probabilistic fault diagnosis approach of SIS. This is a hybrid approach based on fault tree analysis (FTA) and Bayesian network (BN). Indeed, the minimal cut sets as the potential sources of SIS failure were generated via qualitative analysis of FTA, while diagnosis importance factor of components was calculated by converting the standard FTA in an equivalent BN. The final objective is using diagnosis data to generate a diagnosis map that will be useful to guide repair actions. A diagnosis aid system is developed and implemented under SWI-Prolog tool to facilitate testing and diagnosing of SIS.

Reliability evaluation of auxiliary feedwater system by mapping GO-FLOW models into Bayesian networks

Bayesian network (BN) is a widely used formalism for representing uncertainty in probabilistic systems and it has become a popular tool in reliability engineering. The GO-FLOW method is a success-oriented system analysis technique and capable of evaluating system reliability and risk. To overcome the limitations of GO-FLOW method and add new method for BN model development, this paper presents a novel approach on constructing a BN from GO-FLOW model. GO-FLOW model involves with several discrete time points and some signals change at different time points. But it is a static system at one time point, which can be described with BN. Therefore, the developed BN with the proposed method in this paper is equivalent to GO-FLOW model at one time point. The equivalent BNs of the fourteen basic operators in the GO-FLOW methodology are developed. Then, the existing GO-FLOW models can be mapped into equivalent BNs on basis of the developed BNs of operators. A case of auxiliary feedwater system of a pressurized water reactor is used to illustrate the method. The results demonstrate that the GO-FLOW chart can be successfully mapped into equivalent BNs.

Reliability assessment of complex electromechanical systems under epistemic uncertainty

The appearance of macro-engineering and mega-project have led to the increasing complexity of modern electromechanical systems (EMSs). The complexity of the system structure and failure mechanism makes it more difficult for reliability assessment of these systems. Uncertainty, dynamic and nonlinearity characteristics always exist in engineering systems due to the complexity introduced by the changing environments, lack of data and random interference. This paper presents a comprehensive study on the reliability assessment of complex systems. In view of the dynamic characteristics within the system, it makes use of the advantages of the dynamic fault tree (DFT) for characterizing system behaviors. The lifetime of system units can be expressed as bounded closed intervals by incorporating field failures, test data and design expertize. Then the coefficient of variation (COV) method is employed to estimate the parameters of life distributions. An extended probability-box (P-Box) is proposed to convey the present of epistemic uncertainty induced by the incomplete information about the data. By mapping the DFT into an equivalent Bayesian network (BN), relevant reliability parameters and indexes have been calculated. Furthermore, the Monte Carlo (MC) simulation method is utilized to compute the DFT model with consideration of system replacement policy. The results show that this integrated approach is more flexible and effective for assessing the reliability of complex dynamic systems.

Reliability Evaluation of Data Communication System Based on Dynamic Fault Tree under Epistemic Uncertainty

Fault tree analysis is a well-structured, precise, and powerful tool for system evaluation. However, the conventional approach has been found to be inadequate to deal with the absence of fault data, failure dependency, and uncertainty problems. This paper presents a comprehensive study on the evaluation of data communication system (DCS) using dynamic fault tree approach based on fuzzy set. It makes use of the advantages of the dynamic fault tree for modelling, fuzzy set theory for handling uncertainty, and Bayesian network (BN) for inference ability. Specifically, it adopts expert elicitation and fuzzy set theory to evaluate the failure rates of the basic events for DCS and uses a dynamic fault tree model to capture the dynamic failure mechanisms. Furthermore, some reliability parameters can be calculated by mapping a dynamic fault tree into an equivalent BN. The results show that the proposed method is more flexible and adaptive than conventional fault tree analysis for fault diagnosis and reliability estimation of DCS.

Expectation maximization over binary decision diagrams for probabilistic logic programs

Recently much work in Machine Learning has concentrated on using expressive representation languages that combine aspects of logic and probability. A whole field has emerged, called Statistical Relational Learning, rich of successful applications in a variety of domains. In this paper we present a Machine Learning technique targeted to Probabilistic Logic Programs, a family of formalisms where uncertainty is represented using Logic Programming tools. Among various proposals for Probabilistic Logic Programming, the one based on the distribution semantics is gaining popularity and is the basis for languages such as ICL, PRISM, ProbLog and Logic Programs with Annotated Disjunctions. This paper proposes a technique for learning parameters of these languages. Since their equivalent Bayesian networks contain hidden variables, an Expectation Maximization algorithm is adopted. In order to speed the computation up, expectations are computed directly on the Binary Decision Diagrams that are built for inference. The resulting system, called EMBLEM for EM over Bdds for probabilistic Logic programs Efficient Mining, has been applied to a number of datasets and showed good performances both in terms of speed and memory usage. In particular its speed allows the execution of a high number of restarts, resulting in good quality of the solutions.

A Novel Framework for Real-Time Fault Diagnosis Based on Dynamic Fault Tree Analysis

To meet the real-time diagnosis requirements of the complex system, this study proposes a novel framework for real-time fault diagnosis using dynamic fault tree analysis. It pays special attention to meeting two challenges: model development and real-time reasoning. In terms of the challenge of model development, we use a dynamic fault tree model to capture the dynamic behavior of system failure mechanisms and calculate some reliability results by mapping a dynamic fault tree into an equivalent Bayesian Network (BN) in order to avoid the infamous state space explosion problem. In terms of the real-time reasoning challenge, we adopt a logic compilation based inference algorithm, which compiles the BN into an arithmetic circuit and retrieves answers to probabilistic queries by evaluating and differentiating the arithmetic circuit. Furthermore, we incorporate sensors data into fault diagnosis, cope with the sensors reliability and propose the schemes on how to update the Diagnostic Importance Factor (DIF) and the minimal cut sets. Finally, a case study is given to validate the efficiency of this method.

A New Fault Diagnosis Method Based on Fault Tree and Bayesian Networks

This paper presents a novel method for diagnosing faults using fault tree analysis and Bayesian networks (BN) to optimize system diagnosis. All minimal cut sets were generated via qualitative analysis of fault tree using an efficient zero-suppressed binary decision diagram (ZBDD), while the diagnostic importance factor (DIF) of components and minimal cut sets were calculated by mapping fault tree into equivalent BN. Also, these analysis results such as minimal cut sets and DIF were updated after receiving the evidence data from sensors and used to develop an efficient diagnostic decision algorithm. Furthermore, a diagnostic decision tree (DDT) was generated to guide the maintenance personnel to repair the system. Finally, a real example is given to demonstrate the efficiency of this method.

Reliability block diagram with general gates and its application to system reliability analysis

For those systems that can be modeled with perfect nodes and unreliable arcs such as communication systems, a reliability graph with general gates (RGGG) was developed. Similarly, for more efficient system reliability analysis of those systems that can be modeled with unreliable nodes and perfect arcs, a reliability block diagram with general gates (RBDGG) was developed as an intuitive and easy-to-use method for system reliability analysis. One of the unique characteristics of RBDGG is to allow node connection relations of general gates such as the AND gate and the k-out-of- n gate other than the OR gate connection relation of the conventional reliability block diagram (RBD). Mathematical formulations for RBDGG and a method of mapping a RBDGG model into an equivalent Bayesian network model without losing the one-to-one matching characteristic of the RBDGG for quantitative analysis is also provided. With the application to two example systems, the usefulness of the proposed RBDGG is demonstrated.

Applying the information bottleneck to statistical relational learning

In this paper we propose to apply the Information Bottleneck (IB) approach to the sub-class of Statistical Relational Learning (SRL) languages that are reducible to Bayesian networks. When the resulting networks involve hidden variables, learning these languages requires the use of techniques for learning from incomplete data such as the Expectation Maximization (EM) algorithm. Recently, the IB approach was shown to be able to avoid some of the local maxima in which EM can get trapped when learning with hidden variables. Here we present the algorithm Relational Information Bottleneck (RIB) that learns the parameters of SRL languages reducible to Bayesian Networks. In particular, we present the specialization of RIB to a language belonging to the family of languages based on the distribution semantics, Logic Programs with Annotated Disjunction (LPADs). This language is prototypical for such a family and its equivalent Bayesian networks contain hidden variables. RIB is evaluated on the IMDB, Cora and artificial datasets and compared with LeProbLog, EM, Alchemy and PRISM. The experimental results show that RIB has good performances especially when some logical atoms are unobserved. Moreover, it is particularly suitable when learning from interpretations that share the same Herbrand base.

Design of scalable decoders for sensor networks via Bayesian network learning

Minimum mean square error (MMSE) decoding in a large-scale sensor network which employs distributed quantization is considered. Given that the computational complexity of the optimal decoder is exponential in the network size, we present a framework based on Bayesian networks for designing a near-optimal decoder whose complexity is only linear in network size (hence scalable). In this approach, a complexity-constrained factor graph, which approximately represents the prior joint distribution of the sensor outputs, is obtained by constructing an equivalent Bayesian network using the maximum likelihood (ML) criterion. The decoder executes the sum-product algorithm on the simplified factor graph. Our simulation results have shown that the scalable decoders constructed using the proposed approach perform close to optimal, with both Gaussian and non-Gaussian sensor data.

REVIEW OF VARIOUS DYNAMIC MODELING METHODS AND DEVELOPMENT OF AN INTUITIVE MODELING METHOD FOR DYNAMIC SYSTEMS

Conventional static reliability analysis methods are inadequate for modeling dynamic interactions between components of a system. Various techniques such as dynamic fault tree, dynamic Bayesian networks, and dynamic reliability block diagrams have been proposed for modeling dynamic systems based on improvement of the conventional modeling methods. In this paper, we review these methods briefly and introduce dynamic nodes to the existing reliability graph with general gates (RGGG) as an intuitive modeling method to model dynamic systems. For a quantitative analysis, we use a discrete-time method to convert an RGGG to an equivalent Bayesian network and develop a software tool for generation of probability tables.

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.

CHARACTERIZATION OF ESSENTIAL GRAPHS BY MEANS OF THE OPERATION OF LEGAL MERGING OF COMPONENTS

One of the most common ways of representing classes of equivalent Bayesian networks is the use of essential graphs which are also known in the literature as completed patterns or completed pdags. The name essential graph was proposed by Andersson, Madigan and Perlman who also gave a graphical characterization of essential graphs. In this paper an alternative characterization of essential graphs is presented. The main observation is that every essential graph is the largest chain graph within a special class of chain graphs. More precisely, every equivalence class of Bayesian networks is contained in an equivalence class of chain graphs without flags (= certain induced subgraphs). A special operation of legal merging of (connectivity) components for a chain graph without flags is introduced. This operation leads to an algorithm for finding the essential graph on the basis of any graph in that equivalence class of chain graphs without flags which contains the equivalence class of a Bayesian network. In particular, the algorithm may start with any Bayesian network.