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Erschienen in: Mathematics in Computer Science 3/2019

04.07.2019

An Algebraic Approach to DC Railway Electrification Verification

verfasst von: Eugenio Roanes-Lozano, Rubén González-Martín, Javier Montero

Erschienen in: Mathematics in Computer Science | Ausgabe 3/2019

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Abstract

Gröbner bases have been applied to a number of problems related to the verification of Knowledge-Based Systems (KBS) and other problems within graph theory. In particular, the authors have developed in previous papers algebraic approaches to decide whether a situation in a railway interlocking system is safe or not. These algebraic approaches stand out because of the briefness of the code (as they use implementations of well-known algorithms for solving linear or algebraic systems provided by computer algebra systems). The authors have also developed a matrix-based computer tool that helps an expert to check whether a proposed railway electrification scenario (given through the topology of the railway station and the position of the isolation devices and the position and state of the “electrical bypasses” and feeders) fulfills the mandatory requirements of the Spanish railway infrastructure administrator (ADIF) for 3000 V railway electrifications or not. The second author works in the field of railway electrifications and he compares the present-day methods for verification of railway electrifications with the way KBS were verified in the past (manually by experts). In this article we approach this latter problem using algebraic techniques. The new computer tool is based on an algebraic translation of the problem (instead of based on the use of matrices) and is really simple and fast. Determining which electrification sections are under electric tension is computed solving linear systems (because in this case the graph is undirected and no polynomials of degree \(>\,1\) arise in the algebraic translation, so it is not necessary to use Gröbner bases, unlike in the two problems mentioned in the beginning of the Abstract). Therefore far bigger railway facilities can be addressed than if non-linear systems were involved.

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Fußnoten
1
Maple is a trademark of Waterloo Maple Inc.
 
2
Three-phase AC electrifications were experimented by the military in Germany in the beginning of the XXth century (they set a railway speed world record) and some lines existed in South East Spain and North Italy that survived till the second half of the XXth century. Using three-phase electrifications has many advantages from the electrical point of view, but has great disadvantages from the practical point of view: either two overhead lines or three side lines have to be used.
 
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Metadaten
Titel
An Algebraic Approach to DC Railway Electrification Verification
verfasst von
Eugenio Roanes-Lozano
Rubén González-Martín
Javier Montero
Publikationsdatum
04.07.2019
Verlag
Springer International Publishing
Erschienen in
Mathematics in Computer Science / Ausgabe 3/2019
Print ISSN: 1661-8270
Elektronische ISSN: 1661-8289
DOI
https://doi.org/10.1007/s11786-019-00407-6

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