Multi-layer Bayesian Network Research Articles

Bayesian Network Demand-Forecasting Model Based on Modified Particle Swarm Optimization

With the increasing variety of products, the increasing substitutability of products, and the trend of customized products, the volatility of market demand is increasing, which poses a challenge to make accurate demand forecasting. The Bayesian method is particularly promising and appealing when the data fluctuate greatly. This paper proposes a product-demand forecasting model based on multilayer Bayesian network, which introduces hidden layer variables and volatility factors to meet the time series connection and volatility of the demand data. However, most studies use sampling methods to estimate the parameters. We use Bayesian maximum a posteriori estimation to estimate the model parameters and introduce an improved particle swarm optimization algorithm (MPSO) to optimize the objective function. In order to increase the diversity of the particle population and accelerate the convergence, an adaptive particle velocity, position updating strategy, and nonlinear changing inertia weight are introduced in the algorithm. Finally, RMSE (Root Mean Square Error) and MAPE (Mean Absolute Percentage Error) are used as the evaluation criterion to conduct experiments on six different datasets, and the experimental results are compared with the results of the ARIMA (autoregressive integrated moving average model) method and PSO algorithm. The experimental results show that the method has a good prediction effect. It provides a new idea for demand forecasting in the supply chain.

A Multilayer Bayesian Network Approach-Based Predictive Probabilistic Risk Assessment for Overhead Contact Lines Under External Weather Conditions

Due to being completely exposed outdoors without backup, overhead contact lines (OCLs) are more vulnerable to external weather conditions. To perceive the weather-related failure risk and evaluate the associated potential risks, a multilayer Bayesian network (MLBN) approach is proposed for predictive probabilistic risk assessment for OCLs. More specifically, the weather-driven failure probabilities of OCLs are predicted using a first-layer Bayesian network (BN), including lightning strikes, windstorms, and fog-haze. Then, the weather-driven failure patterns of OCLs are investigated and captured, and furthermore, the second-layer BN is embedded to evaluate the risk propagation. Furthermore, the third-layer BN is implemented to calculate and quantify weather-driven risk consequences from perspectives of economic loss and social trust loss constrained by power outage time and train timetable. The three-layer BN models are built by connecting the nodes with causal relationships, avoiding complicated structure learning. The experiments on the actual OCL failure records and weather data demonstrate that the proposed MLBN approach can identify weather-involved risk activities and comprehensively analyze the weather-driven cumulative risks of OCLs from spatiotemporal perspectives. In addition, it is capable of giving reasonable guiding information for mitigating the operational risks of OCLs against external weather conditions.

Prediction Method of Short-Term Demand for e-Commerce Goods Based on Deep Neural Network

In order to improve the short-term demand prediction effect of e-commerce commodities, this paper combines the deep neural network algorithm to predict the short-term demand of e-commerce commodities and proposes a nonparametric supply chain demand prediction model based on multilayer Bayesian network. Moreover, this paper uses the hidden layer factor to describe the internal relationship of customer demand in time series and uses the bottom layer factor to represent the actual customer demand. In addition, this paper directly takes side information into consideration to improve the accuracy of customer demand prediction. Through simulation experiments, it can be seen that the prediction method of short-term demand for e-commerce goods based on deep neural network is close to the actual demand, and it can play a certain role in the demand prediction of e-commerce goods.

A multi-layer Bayesian network method for supply chain disruption modelling in the wake of the COVID-19 pandemic

ABSTRACT While the majority of companies anticipated the negative and severe impacts of the COVID-19 pandemic on the supply chains (SC), most of them lacked guidance on how to model disruptions and their performance impacts under pandemic conditions. Lack of such guidance resulted in delayed reactions, incomplete understanding of pandemic impacts, and late deployment of recovery actions. In this study, we offer a method of modelling and quantifying the SC disruption impacts in the wake of a pandemic. We develop a multi-layer Bayesian network (BN) model that can be used to identify SC disruption triggers and risk events amid the COVID-19 pandemic and quantify the consequences of pandemic disruptions. The unique features of BN, such as forward and backward propagation analysis, are utilised to simulate and measure the impact of different triggers on SC financial performance and business continuity. In this way, we combine resilience and viability SC perspectives and explicitly account for the pandemic settings. The outcomes of this research open a novel theoretical lens on application of BNs to SC disruption modelling in the pandemic setting. Our results can be used as a decision-support tool to predict and better understand the pandemic impacts on SC performance.

A Risk-Based Dynamic Decision-Making Approach for Cybersecurity Protection in Industrial Control Systems

Decision-making is a key component of industrial control system (ICS) security. However, due to the stability and real-time requirements of ICSs, current decision-making approaches typically designed for IT systems are not entirely suitable for ICSs. In this paper, with consideration of the characteristics of ICSs, a risk-based multistep dynamic decision-making approach for protecting ICSs is proposed. Following this proposal, multiple models, including multilayer Bayesian network, process model, and attack-defense strategy model are built first. On this basis, a state controller is designed to ensure the safe degradation/upgradation of ICSs. Finally, a game theory-based optimal defense strategy generation approach is presented. To verify the effectiveness of the proposed approach, a simulation on a simplified chemical reactor control system is conducted in MATLAB. The simulation results clearly demonstrate that the proposed dynamic decision-making approach has the ability to generate the optimal defense strategy to minimize system loss.

"Fault Prediction of Online Power Metering Equipment Based on Hierarchical Bayesian Network"

The failure rate assessment of online metering equipment is significan t for power metering. For traditional methods, the performance of the model is not satisfactory especially in the case of small samples. In this paper, a n online power measuring equipment fault evaluation method based on Weibull parameter hierarchical Bayesian model is proposed. Firstly, the z-score method is used to eliminate outliers in the raw failure data. Then, a generalized linear function with variable intercept is established according to the characteristics of failure data. The information of each region is merged using the characteristics of multi-layer Bayesian network uncertainty reasoning. The model parameters are updated based on the Markov chain Monte Carlo method. Thereafter, the trend of failure rate is provided with time-dependent. Finally, the proposed method is verified by the failure samples of the online measurement equipment in three typical environmental areas. The accuracy and validity of the hierarchical Bayesian model is verified by a series of experiments

Efficient approximate inference in Bayesian networks with continuous variables

Inference is one key objective in a Bayesian network (BN), and it aims to estimate the posterior distributions of state variables based on evidence (observations). While efficient analytical inference algorithms (either approximate or exact) for BN with discrete variables have been well-established in the literature, the inference in BN with continuous variables is still challenging if the BN is non-linear and/or non-Gaussian. In this case we can either discretize the continuous variable and utilize the inference approaches for discrete BN; or we have to use sampling-based methods such as MCMC for static BN and particle filter for dynamic BN. This paper proposes a network collapsing technique based on the concept of probability integral transform to convert a multi-layer BN to an equivalent simple two-layer BN, so that the unscented Kalman filter can be applied to the collapsed BN and the posterior distributions of state variables can be obtained analytically. For dynamic BN, the proposed method is also able to propagate the state variables to the next time step analytically using the unscented transform, based on the assumption that the posterior distributions of state variables are Gaussian. Thus the proposed method achieves a very fast approximate solution, making it particularly suitable for dynamic BN where inference and uncertainty propagation are required over many time steps.

Hierarchical Terrain Classification Based on Multilayer Bayesian Network and Conditional Random Field

This paper presents a hierarchical classification approach for Synthetic Aperture Radar (SAR) images. The Conditional Random Field (CRF) and Bayesian Network (BN) are employed to incorporate prior knowledge into this approach for facilitating SAR image classification. (1) A multilayer region pyramid is constructed based on multiscale oversegmentation, and then, CRF is used to model the spatial relationships among those extracted regions within each layer of the region pyramid; the boundary prior knowledge is exploited and integrated into the CRF model as a strengthened constraint to improve classification performance near the boundaries. (2) Multilayer BN is applied to establish the causal connections between adjacent layers of the constructed region pyramid, where the classification probabilities of those sub-regions in the lower layer, conditioned on their parents’ regions in the upper layer, are used as adjacent links. More contextual information is taken into account in this framework, which is a benefit to the performance improvement. Several experiments are conducted on real ESAR and TerraSAR data, and the results show that the proposed method achieves better classification accuracy.

Bayesian Network Based Fault Prognosis via Bond Graph Modeling of High-Speed Railway Traction Device

Reliability of the traction system is of critical importance to the safety of CRH (China Railway High-speed) high-speed train. To investigate fault propagation mechanism and predict the probabilities of component-level faults accurately for a high-speed railway traction system, a fault prognosis approach via Bayesian network and bond graph modeling techniques is proposed. The inherent structure of a railway traction system is represented by bond graph model, based on which a multilayer Bayesian network is developed for fault propagation analysis and fault prediction. For complete and incomplete data sets, two different parameter learning algorithms such as Bayesian estimation and expectation maximization (EM) algorithm are adopted to determine the conditional probability table of the Bayesian network. The proposed prognosis approach using Pearl’s polytree propagation algorithm for joint probability reasoning can predict the failure probabilities of leaf nodes based on the current status of root nodes. Verification results in a high-speed railway traction simulation system can demonstrate the effectiveness of the proposed approach.

A Bayesian Network Model for Automatic and Interactive Image Segmentation

We propose a new Bayesian network (BN) model for both automatic and interactive image segmentation. A multilayer BN is constructed from an oversegmentation to model the statistical dependencies among superpixel regions, edge segments, vertices, and their measurements. The BN also incorporates various local constraints to further restrain the relationships among these image entities. Given the BN model and various image measurements, belief propagation is performed to update the probability of each node. Image segmentation is generated by the most probable explanation inference of the true states of both region and edge nodes from the updated BN. Besides the automatic image segmentation, the proposed model can also be used for interactive image segmentation. While existing interactive segmentation (IS) approaches often passively depend on the user to provide exact intervention, we propose a new active input selection approach to provide suggestions for the user's intervention. Such intervention can be conveniently incorporated into the BN model to perform actively IS. We evaluate the proposed model on both the Weizmann dataset and VOC2006 cow images. The results demonstrate that the BN model can be used for automatic segmentation, and more importantly, for actively IS. The experiments also show that the IS with active input selection can improve both the overall segmentation accuracy and efficiency over the IS with passive intervention.

Image Segmentation with a Unified Graphical Model

We propose a unified graphical model that can represent both the causal and noncausal relationships among random variables and apply it to the image segmentation problem. Specifically, we first propose to employ Conditional Random Field (CRF) to model the spatial relationships among image superpixel regions and their measurements. We then introduce a multilayer Bayesian Network (BN) to model the causal dependencies that naturally exist among different image entities, including image regions, edges, and vertices. The CRF model and the BN model are then systematically and seamlessly combined through the theories of Factor Graph to form a unified probabilistic graphical model that captures the complex relationships among different image entities. Using the unified graphical model, image segmentation can be performed through a principled probabilistic inference. Experimental results on the Weizmann horse data set, on the VOC2006 cow data set, and on the MSRC2 multiclass data set demonstrate that our approach achieves favorable results compared to state-of-the-art approaches as well as those that use either the BN model or CRF model alone.