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

PurposeThe development of adaptable and intelligent educational systems is widely considered one of the great challenges in scientific research. Among key elements for building advanced training systems, an important role is played by methodologies chosen for knowledge representation. In this scenario, the introduction of ontology formalism can improve the quality of formative process, allowing the introduction of new and effective services. Ontology can lead to important improvements in the definition of courses knowledge domain, in the generation of adapted learning path and in the assessment phase. The purpose of this paper is to provide an initial discussion of the role of ontology in the context of e‐learning. It seeks to discuss the improvements related to the introduction of ontology formalism in the e‐learning field and to show a novel algorithm for ontology building through the use of Bayesian networks. Finally, it aims to illustrate its application in the assessment process and some experimental results.Design/methodology/approachA novel method for learning ontology for e‐learning is illustrated, using an approach based on Bayesian networks. Thanks to their characteristics, these networks can be used to model and evaluate the conditional dependencies among the nodes of ontology on the basis of the data obtained from student tests. An experimental evaluation of the proposed method was performed using real student data.FindingsThe proposed method was integrated in a tool for the assessment of students during a learning process. This tool is based on the use of ontology and Bayesian network. In particular through the matching between ontology and Bayesian network, it was found that our tool allows an effective tutoring and a better adaptation of learning process to demands of students. The assessment based on Bayesian approach allows a deeper analysis of student's knowledge.Research limitations/implicationsThe proposed approach needs more experimentation with other domains and with more complex ontology.Originality/valueThis paper provides an initial discussion of the role of ontology in the context of e‐learning. The improvements related to the introduction of ontology formalism in the e‐learning field are discussed and a novel algorithm for ontology building through the use of Bayesian Networks is showed. Finally, its application in the assessment process and some experimental results are illustrated.

Based on system analysis of information security risk factors and evaluation process, aiming at the uncertainty information is difficult to quantify the evaluation process, Bayesian network inference algorithm, and combined with the inference rules of conditional probability matrix is given by expert knowledge of Bayesian network, the evaluation model of information security risk. Finally an instance of the risk assessment approach on the model is analyzed which demonstrates the rationality and feasibility of this method. So it provides a new method for information security assessment.

Travel time uncertainty can have a significant impact on the performance of Intelligent Transportation Systems. Various applications such as routing or pricing can benefit from accurate estimations of travel times. In this thesis, we propose an approach that can estimate travel time distributions for any path in the road network using GPS data. We focus on situations when only sparse data is available: we consider a dataset that contains GPS trajectories from probe vehicles sampled on average with 1-minute intervals. We propose employing a novel Bayesian network inference algorithm and combining it with the Gaussian copula model. This allows us to estimate the marginal distributions and the covariance structure separately.

Bayesian network (BN) inference is an important statistical tool with additive symmetry. However, BN inference cannot deal with the uncertain, fuzzy, random, and conflicting information from experts’ knowledge in the process of conducting a risk assessment. To tackle this issue, a new fuzzy BN inference approach for risk assessments was proposed based on cloud model (CM), interval type-2 fuzzy set (IT2 FS), interval type-2 fuzzy logic system (IT2 FLS), modified Dempster–Shafer (D-S) evidence theory (ET), and Latin hypercube sampling (LHS) methods along the following lines. Firstly, CM was integrated into IT2 FS, and CM-based IT2 FS (CM-IT2 FS) was defined in the IT2 FLS. Secondly, modified D-S ET was utilized to determine the CM-IT2 FS-based a priori probabilities, and the CM-IT2 FS-based BN model was established. Thirdly, the CM-IT2 FS-based a priori probabilities were reduced to the CM-IT1 FS-based ones using a type reducer in the IT2 FLS, LHS was applied to propose a new fuzzy BN inference algorithm, and then, the new algorithm was used in a typical case to perform the fuzzy BN positive inference for risk prediction and the fuzzy BN reverse inference for risk sensitivity analysis. Finally, the BN inference results were analyzed using the proposed algorithm and the two common BN inference algorithms, and the effectiveness of the proposed approach was validated. It can be concluded that the proposed approach was both accurate and promising.

Dynamic event tree (DET) is an important method in dynamic probabilistic risk assessment; however its real application is limited due to its heavy computation complexity and inconvenience to deal with dependent events. This paper aims at constructing Bayesian networks based on dynamic event tree, and solving the probability of each consequence by utilizing various exact and approximate inference algorithms in Bayesian networks. The dependencies between events, such as common cause failures, could be easily modeled in Bayesian networks. The comparison of the simulation results is carried out by an example in the end.

We present our generic neural network training algorithm, called Sky Net and the accelerated Bayesian inference algorithm, BAMBI. Sky Net combines multiple techniques already developed individually in the literature to create an efficient and robust machine-learning tool that is able to train large and deep feed-forward neural networks for use in a wide range of learning applications, such as regression, classification, density estimation, clustering and dimensionality reduction. Sky Net uses a powerful `pre-training' method, to obtain a set of network parameters close to the true global maximum of the training objective function, followed by further optimisation using an automatically-regularised variant of Newton's method that uses second-order derivative information to improve convergence, but without the need to evaluate or store the full Hessian matrix, by using a fast approximate method to calculate Hessian-vector products. This combination of methods allows for the training of complicated networks that are difficult to optimise using standard back propagation techniques. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest package for nested sampling as well as the training of an artificial neural network by Sky Net to learn the likelihood function. In the case of computationally expensive likelihoods, this allows the substitution of a much more rapid approximation in order to increase significantly the speed of the analysis. Astrophysical examples are provided for both Sky Net and BAMBI.

We consider the problem of reasoning with uncertain evidence in Bayesian networks (BN). There are two main cases: the first one, known as virtual evidence, is evidence with uncertainty, the second, called soft evidence, is evidence of uncertainty. The initial inference algorithms in BNs are designed to deal with one or several hard evidence or virtual evidence. Several recent propositions about BN deal with soft evidence, but also with ambiguity and vagueness of the evidence. One of the proposals so far advanced is based on the fuzzy theory and called fuzzy evidence. The original contribution of this paper is to describe the different types of uncertain evidence with the help of a simple example, to explain the difference between them and to clarify the appropriate context of use.

We suggest Darwinian networks (DNs) as a simplification of working with Bayesian networks (BNs). DNs adapt a handful of well-known concepts in biology into a single framework that is surprisingly simple, yet remarkably robust. With respect to modeling, on one hand, DNs not only represent BNs, but also faithfully represent the testing of independencies in a more straightforward fashion. On the other hand, with respect to two exact inference algorithms in BNs, DNs simplify each of them, while unifying both of them.

In recent years, there often exist multiple priors from experienced experts or historical experiments with the rapid development of system structure in engineering fields. Bayesian Melding Method is commonly used for integrating multiple priors, which is based on the deterministic system structure. However, if the system model cannot be described by an explicit expression, the traditional Bayesian Melding Method is not feasible for system reliability analysis anymore. In order to describe the structure relationship clearly, Bayesian Network is applied in this paper to construct the complex system structure model and the system reliability is calculated by node probability tables rather than explicit expressions. Combining the advantages of the Bayesian Melding Method and Bayesian Network, a multi-prior integration and updating algorithm is developed for the system reliability analysis of complex system structures. Finally, a satellite attitude control system is used to demonstrate the proposed method. The system is established by the Bayesian Network and the comparison between natural prior and updated prior is discussed at length.

There are many methods applied including Bayesian network and D-S evidence theory to cope with uncertainty involving aleatory uncertainty and epistemic uncertainty in reliability analysis of complex systems. This paper introduces theories of these two methods briefly, and then conversion rules that convert fault tree into Bayesian network under uncertainty are put forward, including AND node, OR node, XOR node, NOT node and Two-out-of-three vote node. Comparing to probability importance, structural importance and criticality importance, epistemic importance is given to measure the influence of root event to top event. At last, a type of engine is taken for example. Bayesian network model is established by referring to the fault tree of the engine, and D-S evidence theory is used to determine the belief functions and plausibility functions of uncertain nodes by data fusion. Weak nodes in reliability design and distribution are pointed out after reliability assessment, importance analysis, and backward reasoning. And corresponding measures can be taken to improve the reliability of the whole system.

Novel recursive inference algorithm for discrete dynamic Bayesian networks

Suya is a spicy meat skewer popular as a food item in the sub-Sahara regions. It is traditionally prepared by the Hausa people ofnorthern Cameroon, Nigeria, Niger, Ghana, and some parts of Sudan. Suya is generally made with skewered beef, ram, chickenand innards such as kidney, liver and tripe. Being a stable meat caviar for people of this region, prepared for consumption and inalmost all cases, very unhygienic and sanitary conditions, the beef regalement is exposed massively to microbiome especiallyEscherichia coli (E. coli). Though most E.coli strains are harmless, some can cause serious food poisoning and severe disease.This paper aims to adopt the generality of Bayesian networks to represent and solve decision problems under uncertainty usinginfluence diagrams from Bayesian taxonomies. It also investigates the application of Bayesian networks principles in makingreliable predictions about reoccurrence of microbe growths. Based on the analytical categorisation, the research work builds onextant historical trends which establish referential patterns for microbiome growth in suya meat using Bayesian Networks as aformal model for characterizing and reasoning with uncertain information. Bayesian network models have proven useful inDecision Support Systems (DSS) and in many fields of Artificial Intelligence (AI) including medical domain diagnosis andweather forecasting. This research extends the use of Bayesian networks and analysis in the interdisciplinary studies ofinformation system in microbiology

Bayesian networks (BNs) are being studied in recent years for system diagnosis, reliability analysis, and design of complex engineered systems. In several practical applications, BNs need to be learned from available data before being used for design or other purposes. Current BN learning algorithms are mainly developed for networks with only discrete variables. Engineering design problems often consist of both discrete and continuous variables. This paper develops a framework to handle continuous variables in BN learning by integrating learning algorithms of discrete BNs with Gaussian mixture models (GMMs). We first make the topology learning more robust by optimizing the number of Gaussian components in the univariate GMMs currently available in the literature. Based on the BN topology learning, a new multivariate Gaussian mixture (MGM) strategy is developed to improve the accuracy of conditional probability learning in the BN. A method is proposed to address this difficulty of MGM modeling with data of mixed discrete and continuous variables by mapping the data for discrete variables into data for a standard normal variable. The proposed framework is capable of learning BNs without discretizing the continuous variables or making assumptions about their conditional probability densities (CPDs). The applications of the learned BN to uncertainty quantification and model calibration are also investigated. The results of a mathematical example and an engineering application example demonstrate the effectiveness of the proposed framework.

Use of evidential reasoning for eliciting bayesian subjective probabilities in human reliability analysis: A maritime case

Bayesian belief networks as a meta-modelling tool in integrated river basin management — Pros and cons in evaluating nutrient abatement decisions under uncertainty in a Norwegian river basin