Discrete Bayesian Networks Research Articles

Health Risk Prediction of Operational Subsea Tunnel Structure Based on Bayesian Network

Recently, subsea tunnel construction has developed rapidly in China. The traffic volume of subsea metro tunnels is large. Once a safety accident occurs, economic losses and social impacts will be extremely serious. To eliminate accidents in operational subsea metro tunnel structures, a health risk prediction method is proposed based on a discrete Bayesian network. Detecting and monitoring data of the tunnel structures in operation were used to evaluate the health risk by employing the proposed method. This method establishes a Bayesian network model for the health risk prediction of the shield tunnel structure through the dependency relationship between the health risk of the operational tunnel structure and 13 risk factors in five aspects: the mechanical condition, material performance, integrity state, environmental state, and deformation state. By utilizing actual detection and monitoring data of various risk factors for the health risk of the operational subsea metro shield tunnel structure, this method reflects the actual state of the tunnel structure and improves the accuracy of health risk predictions. The validity of the proposed method is verified through expert knowledge and the subsea shield tunnel structure of the Dalian Subway Line 5. The results demonstrate that the health risk prediction outcomes effectively reflect the actual service state of the shield tunnel structure, thus providing decision support for the control of health risks in the subsea metro shield tunnel.

Learning bayesian network parameters from limited data by integrating entropy and monotonicity

High-accuracy parameter learning in Bayesian Networks (BNs) is a key challenge in real-time decision support applications, particularly when the available data are limited. Prior/Expert knowledge was introduced to eliminate the drawbacks of insufficient information; however, this method is subjective. In this study, we explored the use of monotonicity constraints to control the causal relationships between the nodes and their parents-nodes in BNs and proposed a new learning algorithm called global domain monotonicity based on maximum information entropy (GDM-MIE), which was designed for parameter learning in uncertain discrete BNs with nonlinear equality constraints when only finite data are available. In the proposed algorithm, a class of monotonicity is encoded as a constraint on information entropy and the parameter learning problem is transformed into constraints among the node parameters based on a known network. Furthermore, we considered the parameters as uncertain entropy information and discussed the monotonicity among parameters in the global spatial domain, proving the accuracy of the logical relationships of the model, system reliability, and time complexity. Finally, the proposed method was validated using standard BNs, and its performance was analyzed by comparing the proposed method with the existing learning algorithms. The results showed that the proposed method is more accurate and has better Kullback–Leibler divergence. To revalidate the rationality of the proposed method, the Alarm and Asia networks were employed as special cases. The GDM-MIE was found to achieve the intended goal of observing the estimated parameters by closely approximating the original real parameters with a small sample size, indicating that the proposed algorithm can served as an efficient and feasible method for learning Bayesian parameter.

A Discrete Bayesian Network for Analyzing Hospital Discharge Data

A Discrete Bayesian Network for Analyzing Hospital Discharge Data

A discrete Bayesian network for analysing hospital discharge data

A discrete Bayesian network for analysing hospital discharge data

A probabilistic reasoning approach to analyze the severity of single-vehicle crashes at mid-ramp locations

Freeway ramps are one of the roadway elements that are considered as crash-prone sites with relatively more crashes per mile than other freeway segments. Among other crash types that occurred on freeway ramps, single-vehicle crashes have been found to be more severe. Thus, understanding the factors influencing the severity of single-vehicle crashes on freeway ramps is essential in improving the safety of our limited-access facilities. This study adopted a discrete Bayesian network (BN) approach to explore the probabilistic relationship among the potential factors associated with the severity of single-vehicle crashes at mid-ramp locations. The analysis was based on 6 041 single-vehicle crashes that occurred at the mid-ramp locations in California from 2009 to 2017. The findings indicated that ramp type, ramp traffic volume, road surface condition, and time of day were directly associated with the severity of single-vehicle crashes at the mid-ramp locations. The interdependency of off-ramps, ramp AADT of less than 13 000 vehicles per day, dry road surface condition, and off-peak hours were associated with the highest risk of fatal/severe injury crashes involving a single-vehicle. The study findings could potentially be used by transportation agencies in planning and implementing several strategies to improve the safety of freeway ramps.

Probabilistic robotic logic programming with hybrid Boolean and Bayesian inference

AbstractBayesian inference provides a probabilistic reasoning process for drawing conclusions based on imprecise and uncertain data that has been successful in many applications within robotics and information processing, but is most often considered in terms of data analysis rather than synthesis of behaviours. This paper presents the use of Bayesian inference as a means by which to perform Boolean operations in a logic programme while incorporating and propagating uncertainty information through logic operations by inference. Boolean logic operations are implemented in a Bayesian network of Bernoulli random variables with tensor-based discrete distributions to enable probabilistic hybrid logic programming of a robot. This enables Bayesian inference operations to coexist with Boolean logic in a unified system while retaining the ability to capture uncertainty by means of discrete probability distributions. Using a discrete Bayesian network with both Boolean and Bayesian elements, the proposed methodology is applied to navigate a mobile robot using hybrid Bayesian and Boolean operations to illustrate how this new approach improves robotic performance by inclusion of uncertainty without increasing the number of logic elements required. As any logical system could be programmed in this manner to integrate uncertainty into decision-making, this methodology can benefit a wide range of applications that use discrete or probabilistic logic.

Integrating non-intrusive load monitoring based on graph-to-point learning into a self-adaptive home energy management system

Non-intrusive load monitoring (NILM) can extract the detailed consumption of target appliances from mains reading of a building, which is of great significance for consumers to optimize their electricity consumption and participate in demand response programs. Due to the fact that appliances with multiple states and complex working patterns often bring the most challenging obstacles in energy disaggregation, conventional deep learning methods tend to lead to unsatisfactory disaggregation results. Hence, a novel graph-to-point learning is proposed, in which residual graph convolutional network (ResGCN) and dual attention bidirectional long short-term memory (DABiLSTM) are combined to inherently capture the characteristics of time dependency. Then, accurate NILM results are integrated into a user-centric and self-adaptive home energy management system (HEMS), where a discrete Bayesian network for each appliance is adopted to automatically describe the end-users’ consumption behaviors. Lastly, the proposed algorithm is compared with state-of-the-art methods based on REFIT and REDD datasets for performance validation. Experiments results show that compared with traditional HEMS, NILM-based HEMS can markedly reduce operation cost by 53% and improve the overall consumer comfort by 31%.

Interval-based reasoning over continuous variables using independent component analysis and Bayesian networks

Bayesian networks (BNs) can be used for probabilistic reasoning over discrete variables. Their extension to the continuous domain, however, remains an open research issue. In this work, we address the Bayesian inference problem for continuous variables when negative evidence is available. This situation is faced when, because of unreliable or imperfect sensors, some variables are observed to be at specific intervals. We propose two solutions to this issue. The first one, dubbed dynamic discrete BN (DD-BN), is simply an adaptation of the dynamic discretization method; the second, referred to as SICA, is based on spline functions and the independent component analysis (ICA) method. SICA can represent a wide range of general multivariate distributions and possesses some integration characteristics that facilitate the inference process. Empirical trials on public datasets and simulated data yielded promising results regarding inference time and accuracy. Indeed, SICA achieved the highest accuracy at the expense of increased inference time with increasing dimensions.

A continuous Bayesian network regression model for estimating seismic liquefaction‐induced settlement of the free‐field ground

AbstractThe Bayesian network (BN) method has been successfully applied to evaluate earthquake liquefaction‐induced settlement of free‐field ground in recent years due to several specific advantages. However, the existing BN models need to discretize all continuous variables, and therefore, they can only predict the range value of the settlement (i.e., classification). Thus, information loss is inevitable in the process of discretization, which will largely reduce the prediction accuracy of the model. To realize the application of the BN method in the regression prediction of seismic liquefaction‐induced settlement, this study proposes a hybrid modelling method combining a hill‐climbing algorithm and domain knowledge to construct the structure of a continuous BN regression model based on historical liquefaction‐induced settlement data, and then the conditional linear Gaussian approach is used to learn the conditional probability distributions of parameters. A five‐fold cross‐validation test is used to demonstrate better generalization performance and advantages (such as considering model uncertainty and prior knowledge) of the continuous BN regression model compared with a discrete BN classification model, simplified methods such as the Tokimatsu & Seed and Ishihara & Yoshimine methods, and an artificial neural network model. Their advantages and disadvantages are discussed. In addition, the other two continuous BN models using the Arias intensity and cumulative absolute velocity instead of the peak ground acceleration perform slightly worse than the proposed continuous BN model, and the reason for this difference is discussed.

Using discrete Bayesian networks for diagnosing and isolating cross-level faults in HVAC systems

Fault detection and diagnosis (FDD) technologies are critical to ensure satisfactory building performance, such as reducing energy wastes and negative impacts on occupant comfort and productivity. Existing FDD technologies mainly focus on component-level FDD solutions, which could lead to mis-diagnosis of cross-level faults in heating, ventilating, and air-conditioning (HVAC) systems. Cross-level faults are those faults that occur in one component or subsystem, but cause operational abnormalities in other components or subsystems, and result in a building level performance degradation. How to effectively diagnose the root cause of a cross-level fault is the focus of this study. This paper presents a novel discrete Bayesian Network (DisBN)-based method for diagnosing cross-level faults in an HVAC system commonly used in commercial buildings. A two-level DisBN structure model is developed in this study. The parameters used in the DisBN model are obtained either from expert knowledge or through machine-learning strategies from normal system operation data. Meanwhile, the probability parameters are discretized to incorporate the uncertainties associated with typical expert knowledge. Thus, the developed DisBN method addresses the challenges many other BN based FDD methods face, i.e., the lack of fault data for BN parameter training. The developed DisBN represents causal relationships between a fault and its cross-level system impacts (i.e., fault symptoms or fault indicators) by considering how fault impacts propagate across different levels in an HVAC system. A weather and schedule information-based Pattern Matching (WPM) method is employed to automatically create WPM baseline data sets for each incoming real time snapshot data from the building systems. Consequently, BN inference and real-time diagnostics are achieved by comparing incoming snapshot data and the WPM baseline data set. The proposed method is evaluated using experimental fault data collected in a campus building. Fault diagnosis results demonstrate that the WPM-DisBN method is effective at locating the root causes of cross-level faults in an HVAC system.

A stochastic variance-reduced coordinate descent algorithm for learning sparse Bayesian network from discrete high-dimensional data

This paper addresses the problem of learning a sparse structure Bayesian network from high-dimensional discrete data. Compared to continuous Bayesian networks, learning a discrete Bayesian network is a challenging problem due to the large parameter space. Although many approaches have been developed for learning continuous Bayesian networks, few approaches have been proposed for the discrete ones. In this paper, we address learning Bayesian networks as an optimization problem and propose a score function which guarantees the learnt structure to be a sparse directed acyclic graph. Besides, we implement a block-wised stochastic coordinate descent algorithm to optimize the score function. Specifically, we use a variance reducing method in our optimization algorithm to make the algorithm work efficiently for high-dimensional data. The proposed approach is applied to synthetic data from well-known benchmark networks. The quality, scalability, and robustness of the constructed network are measured. Compared to some competitive approaches, the results reveal that our algorithm outperforms some of the well-known proposed methods.

Disaster Mitigation Efforts Using K-Medoids Algorithm and Bayesian Network

Disaster mitigation is a series of efforts to reduce disaster risk. One of the disaster mitigation efforts is the supervision of the implementation of spatial planning. Knowing the level of damage to buildings in a region in the event of a disaster can supervise the implementation of spatial planning. To predict the level of damage to buildings in an area, we can use the Bayesian network (BN). There are several types of BN based on the variable type; discrete, continuous, and hybrid BN. A discrete BN is a model in which all the variables involved are discrete. Therefore, if there is a continuous variable, it is necessary to discretize the variable. In this paper, modifications are made to the algorithm commonly used in the clustering process to be used in the discretization process. The algorithm used is the K-Medoids algorithm, where this algorithm uses existing data as a representative of the cluster center. Then, the BN model and the K-Medoids algorithm were used to determine the level of damage to buildings due to the earthquake that occurred in West Sumatra in 2009. From 25,000 house damage data used in this study, we obtain an accuracy rate is 95.17%.

Continuous-discrete hybrid Bayesian network models for predicting earthquake-induced liquefaction based on the Vs database

The Bayesian network (BN) method has been increasingly applied in predicting earthquake-induced liquefaction. Nonetheless, the existing BN models treat all factors of liquefaction, including discrete and continuous variables, as discrete variables using different discretization approaches in the prediction of earthquake-induced liquefaction. Information loss may occur in the discretization process of the continuous variables, which reduces the predictive accuracy of the BN model. To tackle this issue, a shear wave velocity (Vs) database is taken as an example in this study for developing mixed continuous-discrete BN models to improve the predictive accuracy of earthquake-induced liquefaction. First, the discrete and continuous variables are distinguished and the continuous variables are tested whether they approximately obey the Gaussian distribution. Second, discrete variables (e.g., liquefaction potential as binary variables) and continuous variables are simultaneously considered in structural modeling. Then, the conditional linear Gaussian distribution and Markov chain Monte Carlo approaches are used to construct two hybrid BN models. A 10-fold cross-validation test is used to demonstrate that the performance of the hybrid BN models is better than those of the discrete BN models or other methods such as logistic regression, artificial neural network, support vector machine, and naïve Bayes. The hybrid BN models are applied to the 2010–2011 Canterbury earthquake sequence to demonstrate their generalizability. This study finally discusses the difference in information loss and computational cost between the discrete and hybrid BN models.

Region‐based estimation of the partition functions for hybrid Bayesian network models

The partition function Ƶ ${\boldsymbol{Ƶ}}$ is a normalization constant for normalizing all the distributions in probabilistic inference. Ƶ ${\boldsymbol{Ƶ}}$ is closely related to the log probability of evidence ( log p ( e ) $\mathrm{log}\unicode{x0200A}p(e)$ ) for Bayesian networks (BNs), which plays an important role in many applications, such as parameter learning, classification, and clustering. However, evaluating Ƶ ${\boldsymbol{Ƶ}}$ and log p ( e ) $\mathrm{log}\unicode{x0200A}p(e)$ for BNs containing both discrete and continuous variables (known as hybrid Bayesian networks [HBNs]) is generally difficult for analytical and simulation-based solutions. This paper describes the work addressing the problem of estimating the partition function for HBNs when exact methods become inefficient or numerically unstable. We use dynamic discretization to provide a discretized version of the model and then perform region-based free energy optimization to obtain the log p ( e ) $\mathrm{log}\unicode{x0200A}p(e)$ for the HBN efficiently, which is called the DDJT-region partition function (RPR) algorithm. It is novel since the region-based methods have previously only been applied to discrete BNs. We show that the log p ( e ) $\mathrm{log}\unicode{x0200A}p(e)$ obtained by DDJT-RPR is exact for discretized models and with space complexity equal to that in marginal inference, thus generally applicable to a wide range of applications. To demonstrate these properties, we combine the DDJT-RPR algorithm with an improved expectation-maximization algorithm to learn Gaussian mixture models (GMMs), for applications requiring data only and with prior knowledge, which performed more robustly than conventional GMM learning algorithms.

Practical application of a Bayesian network approach to poultry epigenetics and stress

BackgroundRelationships among genetic or epigenetic features can be explored by learning probabilistic networks and unravelling the dependencies among a set of given genetic/epigenetic features. Bayesian networks (BNs) consist of nodes that represent the variables and arcs that represent the probabilistic relationships between the variables. However, practical guidance on how to make choices among the wide array of possibilities in Bayesian network analysis is limited. Our study aimed to apply a BN approach, while clearly laying out our analysis choices as an example for future researchers, in order to provide further insights into the relationships among epigenetic features and a stressful condition in chickens (Gallus gallus).ResultsChickens raised under control conditions (n = 22) and chickens exposed to a social isolation protocol (n = 24) were used to identify differentially methylated regions (DMRs). A total of 60 DMRs were selected by a threshold, after bioinformatic pre-processing and analysis. The treatment was included as a binary variable (control = 0; stress = 1). Thereafter, a BN approach was applied: initially, a pre-filtering test was used for identifying pairs of features that must not be included in the process of learning the structure of the network; then, the average probability values for each arc of being part of the network were calculated; and finally, the arcs that were part of the consensus network were selected. The structure of the BN consisted of 47 out of 61 features (60 DMRs and the stressful condition), displaying 43 functional relationships. The stress condition was connected to two DMRs, one of them playing a role in tight and adhesive intracellular junctions in organs such as ovary, intestine, and brain.ConclusionsWe clearly explain our steps in making each analysis choice, from discrete BN models to final generation of a consensus network from multiple model averaging searches. The epigenetic BN unravelled functional relationships among the DMRs, as well as epigenetic features in close association with the stressful condition the chickens were exposed to. The DMRs interacting with the stress condition could be further explored in future studies as possible biomarkers of stress in poultry species.

Seasonal forecasting of lake water quality and algal bloom risk using a continuous Gaussian Bayesian network

Abstract. Freshwater management is challenging, and advance warning that poor water quality was likely, a season ahead, could allow for preventative measures to be put in place. To this end, we developed a Bayesian network (BN) for seasonal lake water quality prediction. BNs have become popular in recent years, but the vast majority are discrete. Here, we developed a Gaussian Bayesian network (GBN), a simple class of continuous BN. The aim was to forecast, in spring, mean total phosphorus (TP) and chlorophyll a (chl a) concentration, mean water colour, and maximum cyanobacteria biovolume for the upcoming growing season (May–October) in Vansjø, a shallow nutrient-rich lake in southeastern Norway. To develop the model, we first identified controls on interannual variability in seasonally aggregated water quality. These variables were then included in a GBN, and conditional probability densities were fit using observations (≤39 years). GBN predictions had R2 values of 0.37 (chl a) to 0.75 (colour) and classification errors of 32 % (TP) to 17 % (cyanobacteria). For all but lake colour, including weather variables did not improve the predictive performance (assessed through cross-validation). Overall, we found the GBN approach to be well suited to seasonal water quality forecasting. It was straightforward to produce probabilistic predictions, including the probability of exceeding management-relevant thresholds. The GBN could be sensibly parameterised using only the observed data, despite the small dataset. Developing a comparable discrete BN was much more subjective and time-consuming. Although low interannual variability and high temporal autocorrelation in the study lake meant the GBN performed only slightly better than a seasonal naïve forecast (where the forecasted value is simply the value observed the previous growing season), we believe that the forecasting approach presented here could be particularly useful in areas with higher sensitivity to catchment nutrient delivery and seasonal climate and for forecasting at shorter (daily or monthly) timescales. Despite the parametric constraints of GBNs, their simplicity, together with the relative accessibility of BN software with GBN handling, means they are a good first choice for BN development with continuous variables.

A cloud Bayesian network approach to situation assessment of scouting underwater targets with fixed‐wing patrol aircraft

AbstractThe battlefield situation changes rapidly because underwater targets' are concealment and the sea environment is uncertain. So, a great number of situation information greatly increase, which need to be dealt with in the course of scouting underwater targets. Situation assessment in sea battlefield with a lot of uncertain information is studied, and a new situation assessment method of scouting underwater targets with fixed‐wing patrol aircraft is proposed based on the cloud Bayesian network, which overcomes the deficiency of the single cloud model in reasoning ability and the defect of Bayesian network in knowledge representation. Moreover, in the method, the cloud model knowledge deal with the input data of Bayesian network reasoning, and the advantages in knowledge representation of cloud theory and reasoning of Bayesian network are applied; also, the fuzziness and stochasticity of cloud theory in knowledge expression, the reasoning ability of Bayesian network, are combined. Then, the situation assessment model of scouting underwater targets with fixed‐wing patrol aircraft is established. Hence, the directed acyclic graph of Bayesian network structure is constructed and the assessment index is determined. Next, the cloud model is used to deal with Bayesian network, and the discrete Bayesian network is obtained. Moreover, after CPT of each node and the transformation between certainty degree and probability are accomplished; the final situation level is obtained through a probability synthesis formula. Therefore, the target type and the operational intention of the other side are deduced to form the battlefield situation. Finally, simulations are carried out, and the rationality and validity of the proposed method are testified by simulation results. By this method, the battlefield situation can be gained. And this method has a wider application range, especially for large sample data processing, and it has better practicability.

Tractable Inference for Hybrid Bayesian Networks with NAT-Modeled Dynamic Discretization

Hybrid BNs (HBNs) extend Bayesian networks (BNs) to both discrete and continuous variables.Among inference methods for HBNs, we focus on dynamic discretization (DD) that converts HBN to discrete BN for inference.Complexity of BN inference is exponential on treewidth, which extends to DD for HBNs.We presents a novel framework where HBN is transformed into NAT-modeled BN (NAT: Non-impeding noisy-AND Tree) for tractable inference.A case-study under the framework is presented on sum of continuous variables.We report significant efficiency gain of approximate inference by NAT-modeled DD over alternative methods.

Hybrid Network Structures and Their Use in Diagnosing Complex Technical Systems

An approach to the technical diagnostics of complex technical systems based on the results of telemetry information processing by an external monitoring and diagnostics system using hybrid network structures is proposed. The principle of constructing diagnostic complexes of complex technical systems is considered, which ensures the automation of the technical diagnostics process and is based on the use of models in the form of hybrid network structures for processing telemetric information, including multilayer neural networks and discrete Bayesian networks with stochastic learning. A model of changes in the parameters of complex technical systems technical state based on multilayer neural networks has been developed, which makes it possible to form a probabilistic assessment of attributing the current situation of complex technical system functioning to the set of functions considered situations according to individual telemetry parameters, and multilevel hierarchical model of complex technical systems technical diagnostics based on a discrete Bayesian network with stochastic learning, which allows aggregating the information received from neural network models and recognizing the current situation of complex technical system functioning. In the conditions of functioning emergencies of the complex technical system, according to the results of processing telemetric information, faulty functional units are localized and an explanation of the cause of the emergency is formed. The stages of complex technical systems technical diagnostics implementation using the proposed hybrid network structures in the processing of telemetric information are detailed. An example of using the developed approach to solving problems of spacecraft onboard system technical diagnostics is presented. The advantages of the proposed approach to the technical diagnostics of complex technical systems in comparison with the traditional approach based on analysis of telemetry parameters values belonging to the given tolerances are shown.

Reliability Analysis of Special Vehicle Critical System Using Discrete-Time Bayesian Network

The reliability assessment of special vehicles has become very important. However, due to the special structure of special vehicles, it is difficult to collect a large amount of experimental data. The use of traditional fault tree analysis cannot accurately assess product reliability. In this paper, dynamic fault trees are used to model the critical systems of special vehicles, and discrete Bayesian networks are used to evaluate the reliability of critical systems of special vehicles, which solved the problems of difficulty in accurately describing complex systems in the process of system reliability analysis and difficulty in obtaining accurate data in the process of analysis. Finally, through the combination of expert experience and the evaluation of the calculation results, the rationality of the method used in this paper in the reliability evaluation of special vehicles is verified.