Zacarías Grande

A Markovian-Bayesian Network for Risk Analysis of High Speed and Conventional Railway Lines Integrating Human Errors

The article provides a new Markovian-Bayesian network model to evaluate the probability of accident associated with the circulation of trains along a given high speed or conventional railway line with special consideration to human error. This probability increases as trains pass throughout the different elements encountered along the line. A Bayesian network, made up of a sequence of several connected Bayesian subnetworks, is used. A subnetwork is associated with each element in the line that implies a concentrated risk of accident or produces a change in the drivers attention, such as signals, tunnel, or viaduct entries or exits, etc. Bayesian subnetworks are also used to reproduce segments without signals where some elements add continuous risks, such as rolling stock failures, falling materials, slope slides in cuttings and embankments, etc. All subnetworks are connected with the previous one and some of them are multi-connected because some consequences are dependent on previous errors. Because drivers attention plays a crucial role, its degradation with driving time and the changes due to seeing light signals or receiving acoustic signals is taken into consideration. The model updates the drivers attention level and accumulates the probability of accident associated with the different elements encountered along the line. This permits us to generate a continuously increasing risk graph that includes continuous and sudden changes indicating where the main risks appear and whether or not an action must be taken by the infrastructure manager. Sensitivity analysis allows the relevant and irrelevant parameters to be identified avoiding wastes of time and money by concentrating safety improvement actions only on the relevant ones. Finally, some examples are used to illustrate the model. In particular, the case of the Orense-Santiago de Compostela line, where a terrible accident took place in 2013.

Bayesian Networks-Based Probabilistic Safety Analysis for Railway Lines

A Bayesian network model is developed, in which all the items or elements encountered when travelling a railway line, such as terrain, infrastructure, light signals, speed limit signs, curves, switches, tunnels, viaducts, rolling stock, and any other element related to its safety are reproduced. Due to the importance of human error in safety, especial attention is given to modeling the driver behavior variables and their time evolution. The sets of conditional probabilities of variables given their parents, which permits quantifying the Bayesian network joint probability, are given by means of closed formulas, which allow us to identify the particular contribution of each variable and facilitate a sensitivity analysis. The probabilities of incidents affecting safety are calculated so that a probabilistic safety assessment of the line can be done and its most critical elements can be identified and sorted by importance. This permits improving the line safety and saving time and money in the maintenance program by concentrating on the most critical elements. To reduce the complexity of the problem, an original method is given that permits dividing the Bayesian network in to small parts such that the complexity of the problem becomes linear in the number of items and subnetworks. This is crucial to deal with real lines in which the number of variables can be measured in thousands. In addition, when an accident occurs the Bayesian network allows us to identify its causes by means of a backward inference process. The case of the real Palencia-Santander line is commented on and some examples of how the model works are discussed.

A State-of-the-Art Review of the Sensor Location, Flow Observability, Estimation, and Prediction Problems in Traffic Networks

A state-of-the-art review of flow observability, estimation, and prediction problems in traffic networks is performed. Since mathematical optimization provides a general framework for all of them, an integrated approach is used to perform the analysis of these problems and consider them as different optimization problems whose data, variables, constraints, and objective functions are the main elements that characterize the problems proposed by different authors. For example, counted, scanned or “a priori” data are the most common data sources; conservation laws, flow nonnegativity, link capacity, flow definition, observation, flow propagation, and specific model requirements form the most common constraints; and least squares, likelihood, possible relative error, mean absolute relative error, and so forth constitute the bases for the objective functions or metrics. The high number of possible combinations of these elements justifies the existence of a wide collection of methods for analyzing static and dynamic situations.

An Alternate Double–Single Track Proposal for High‐Speed Peripheral Railway Lines

Alternate double-single track (ADST) lines are presented as an alternative to double-track lines in this article. The Palencia–Santander line is used to explain the proposal and some suggestions for using the ADST lines in several countries are presented. A linear programming program is given that is used to decide the optimal sequence of single and double tracks and also to optimize the timetables for the best or other alternative sequence. The idea consists of using single track where the infrastructure is very expensive (tunnels and viaducts) and double track where it is cheaper (smooth orography). This, combined with other small changes in departure times so that trains may cross in the double-track segments will normally result in no travel time reductions. The solution is shown to be very efficient for traffic demands between 30 and 40 trains per day and costs are reduced by about 40%.

A Time Partitioning Technique for Railway Line Design and Timetable Optimization

Existing computer models used to optimize railway timetables lead to a high complexity when the number of analyzed services exceeds a given threshold. A time partitioning technique is proposed which allows line design and timetable optimization and a reduction in the complexity of the problem by considering small time windows of the same or different durations in which the timetables of a small equal or not number of running trains are optimized in sequence. Though the optimal solution is not expected to be attained with this method, the analyzed examples demonstrate that the resulting solution is close to the global optimum and practically satisfactory. This technique can be used at the planning and implementation stages. Examples of two real lines are analyzed to show the goodness of the proposed methods. One is the network Madrid-Sevilla-Toledo-Malaga-Valencia-Albacete with a dense traffic of 170 trains per day. The second is the Palencia-Santander line with 70 trains in which as an alternative to a double-track proposal with a cost of Mi¾? 3,200 an alternate double-single-track ADST solution, with a cost of Mi¾? 330 one tenth is proposed.

Highway and Road Probabilistic Safety Assessment Based on Bayesian Network Models

A Bayesian network model is developed, in which all the items or safety related elements encountered when traveling along a highway or road, such as terrain, infrastructure, light signals, speed limit signs, intersections, roundabouts, curves, tunnels, viaducts, and any other safety relevant elements are reproduced. Since human error is the main cause of accidents, special attention is given to modeling the driver behavior variables (drivers tiredness and attention) and to how they evolve with time or travel length. The sets of conditional probabilities of variables given their parents, which permit to quantify the Bayesian network joint probability, are obtained and written as closed formulas, which allow us to identify the particular contribution of each variable to safety and facilitate the computer implementation of the proposed method. In particular, the probabilities of incidents affecting safety are calculated so that a probabilistic safety assessment of the road can be done and its most critical elements can be identified and sorted by importance. This permits the improvement of road safety making adequate corrections to save time and money in the maintenance program by concentrating on the most critical elements and effective investments. Some real examples of a Spanish highway and a conventional road are provided to illustrate the proposed methodology and show its advantages and performance.

Proactive, Backward Analysis and Learning in Road Probabilistic Bayesian Network Models

Some probabilistic safety assessment models based on Bayesian networks have been recommended recently for safety analysis of highways and roads. These methods provide a very natural and powerful alternative to traditional approaches, such as fault and event tree based methods. In this article, we present several new and original contributions to complement the inference engine tools of these models to provide new and relevant information about safety and backward analysis on one hand, and to learn the complex multidimensional joint probabilities of all variables, on the other hand. More precisely, we show how standard tools combined with the partitioning technique can be used in new ways to solve three relevant problems (1) to prognosticate the most probable combinations of variables leading to incidents, (2) to perform a backward analysis to identify the causes of accidents, and (3) to learn the model parameters using Bayesian conjugate methods (categorical and Dirichlet families). Finally, some real examples of applications are used to illustrate the proposed methods.

Complexity Reduction and Sensitivity Analysis in Road Probabilistic Safety Assessment Bayesian Network Models

This article is concerned with improving some existing methods for probabilistic safety analysis of roads and highways. After a quick review of a Bayesian network model, in which special attention is devoted to human error and all safety related items or elements existing along the road are considered, important problems are dealt with and some solutions provided. This includes: (1) a new and general method for a detailed description of the conditional probabilities of variables given their parents leading to closed-form formulas, (2) a partitioning technique that allows us to reduce drastically the CPU time required for the calculations, based on dividing the Bayesian network into very small subnetworks using the conditional independence property and leading to a reduced complexity, which is linear in the number of variables or road length instead of the nonlinear character of alternative methods, and (3) a range sensitivity analysis method, which takes advantage of the partitioning technique and is superior to a local sensitivity analysis. Finally, some real examples are provided to show the usefulness of the proposed methodologies to assess the safety of highways or conventional roads.

A Bayesian Network Model for the Probabilistic Safety Assessment of Roads

A Bayesian network model for probabilistic safety analysis of roads and highways is introduced. After indicating how the list of variables and the conditional probability tables of the Bayesian network model are built, based on a video of the road, a short discussion about how maximum likelihood and Bayesian network methods can be applied to estimate the model parameters using standard methods. Next, a partitioning technique is suggested to convert the non-linear problem of computing marginal and conditional probabilities after evidence into a problem whose complexity becomes linear in the number of variables. Finally an example of application is used to illustrate the proposed methodology and some conclusions are drawn.

Bayesian Networks Probabilistic Safety Analysis of Highways and Roads

A probabilistic safety analysis methodology based on Bayesian networks models for the probabilistic safety assessment (PSA) of highways and roads is presented. The main idea consists of (a) identifying all the elements encountered when travelling the road, (b) reproducing these elements by sets of variables, (c) identifying the direct dependencies among variables, (d) building a directed acyclic graph to reproduce the qualitative structure of the Bayesian network, and (e) building the conditional probability tables for each variable conditioned on its parent nodes. Since human error is the most important cause of accidents, driver’s tiredness and attention are used to model how the driver’s behaviour evolves with driving and how it is affected by the environment, signs and other factors. A computer program developed in Matlab implements the Bayesian network model from the list of road items and a set of parameter values given by a group of experts. In this way, the most critical elements can be identified and sorted by importance, thus, an improvement of the global safety of the road can be done savings time and money. The proposed methodology is illustrated in real examples of a Spanish highway and a conventional road.