Intelligible Forecasting of Transportation Capacity Risk in Rail Transit Using Bayesian Networks

By Dr Silpaja Chandrasekar, PhDReviewed by Susha Cheriyedath, M.Sc.Aug 8 2023

In an article recently submitted to the arXiv* server, researchers address the challenge of predicting transportation capacity risk by introducing an intelligible forecasting method that employs a linear Gaussian Bayesian network. Through the utilization of a three-tier simulation model that encompasses the rail transit system's network, train flow, and passenger flow, the method acquires training data for prediction modeling. The Bayesian network structure is formulated based on the topology of the rail transit network, and parameter learning is executed through Maximum Likelihood Estimation (MLE). The effectiveness of the proposed approach is validated through simulation examples.

*Important notice: arXiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Related works

Research in rail transportation has extensively examined risk assessment, predominantly focusing on equipment failures and traditional risk factors. However, these studies often overlook the holistic evaluation of the global risk of carrying capacity risk and its interaction with local single-point risk. Similarly, existing research on rail transit transport capacity assessment primarily concentrates on the assessment of transport capacity or the reliability of network structure and topology without considering the dynamic matching of global transport capacity and passenger flow demand. 

In rail transit, the assessment of risk and transport capacity has encountered significant limitations. The interplay between single-point risk and network transport capacity is frequently overlooked, leading to a fragmented understanding of global risk and capacity. Additionally, existing research often emphasizes network structure and topology reliability, neglecting research on the overall dynamic capacity-related risk, which involves aligning global capacity with changing passenger flow. Furthermore, previous methods for rail transit risk of transportation capacity prediction lack interpretability and the ability to incorporate expert knowledge for refinement. Addressing these gaps, the present paper proposes a Bayesian network-based approach to predict the dynamic risk associated with transport capacity in rail transit, fostering a comprehensive understanding of risk and enabling informed decision-making.

Proposed method

The design principles for rail transit risk of carrying capacity indexes emphasize reasonability, completeness, and compatibility. The assessment system integrates the dynamic matching between passenger demand and network capacity while incorporating single-point risk and interactions between them. A static assessment system forms the basis, followed by a dynamic system that uses monitoring data to evaluate global risk regarding transportation capacity. The dynamic risk comprises risk probabilities and consequences for various risk points, such as station saturation and passenger detention. This approach enables the calculation of station, line, and global capacity-related risks for the rail transit network.

Bayesian networks, introduced by Judea Pearl, model causal uncertainty through directed acyclic graphs (DAGs) with nodes representing variables and edges indicating relationships. In rail transit risk assessment, continuous Bayesian networks, like Gaussian Bayesian networks (GBNs), are employed due to their capacity to maintain continuous variable information. A joint probability distribution of the GBN follows a multivariate normal distribution, aligning with the linear relationships often found in rail transit capacity risk scenarios. Based on rail transit topology, a Bayesian network construction approach is proposed. Nodes symbolize passenger flow saturation and evacuation time, forming a causal network reflecting the risk levels of stations, sections, lines, and the overall network. Bayesian network parameter learning utilizes the MLE method to establish conditional dependencies among risk nodes, enhancing risk prediction and localized sensitivity analysis.

Experimental results

This study evaluates and predicts capacity-related risk using Chongqing Rail Transit as a case study. For various rail lines, including Lines 1 to 10, Loop line, and International Expo line, simulation models are created for 168 stations and 362 sections. Utilizing Python programming and discrete event simulation, real line data, topology, and passenger flow information are considered. Passenger flow data is generated every 15 minutes for 30 days, and the dataset is divided into 1600 training data and 320 testing data sets for validation.

A relevant simulation model is constructed to assess the risk of carrying capacity for both rail transit networks and lines. Employing the Bayesian network structure, parameter learning is achieved through maximum likelihood estimation. To gauge its predictive effectiveness, it is contrasted with the autoregressive (AR) method, a benchmark scheme. The AR method solely utilizes present and past values of each risk associated with the transport capacity node (station, line, or network) as input, disregarding additional data and the inter-node correlations.

In the initial approach, a comprehensive Bayesian network, denoted as GBN1 is constructed based on the overall topology of the rail transit network. Inputs at time t0 are utilized to directly forecast the capacity-related risk for each line and the global risk of transportation capacity of the rail transit network at time t (t>t0). Expanding on GBN1, the second strategy, called GBN2, integrates time-series prediction data correlation and explores the influence of historical information. The evaluation metric employed is the Weighted Mean Absolute Percentage Error (WMAPE), which considers feature weights based on Mean Absolute Percentage Error (MAPE). WMAPE addresses large error results when predicting low-risk values. In terms of WMAPE, using GBN1 reduces the prediction error from 36.88% to 24.44% compared to AR, affirming the efficacy of the proposed prediction model. The addition of historical data notably enhances prediction effectiveness from 24.44% in GBN1 to 19.10% in GBN2. Incorporating historical passenger flow characteristic data improves the prediction of station and line capacity-related risk, ultimately refining the global risk prediction of transportation capacity.

Conclusion

This study proposes an interpretable rail transport capacity risk prediction method using a linear Gaussian Bayesian network. The approach constructs a network based on rail transit topology, employs simulation models for risk assessment, and utilizes maximum likelihood estimation for parameter learning. Validation of Chongqing rail transit data demonstrates its effectiveness and the impact of prior knowledge on predictions. Future steps involve considering more operational factors, expanding the structure of the model, and exploring dynamic Bayesian networks for time-dependent predictions.

*Important notice: arXiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.