Verification of the Theoretical Basis for Determining the Curvature of the Track Axis Using the Moving Chord Method
DOI:
https://doi.org/10.14738/aivp.113.14933Keywords:
Railway track, Curvature of the track axis, The moving chord method, Verification of theoretical foundationsAbstract
The paper indicates the possibility of a new approach to the problem of identifying the measured railway route. The currently used methods of identifying the track axis have been characterized, which consist in generating an optimized geometrical layout in the tested area by minimizing the occurring deviations of this layout from the measurement points. The proposed new approach uses the obtained measurement data to determine the existing curvature of the geometric layout. This paper presents a short review of the current activities related to the determination of the curvature of model geometrical layouts and the operated railway track using a new method of determining the curvature, known as the moving chord method. The demonstrated high efficiency of this method should not, however, obscure the fact that the assumptions adopted in it apply – generally speaking – only to a certain, limited range of geometric parameters. The presented analysis showed that the adopted assumptions could be applied to the railway track, because it uses large radii of circular arcs (of the order of several hundred or several thousand meters) and transition curves with a very mild change in curvature. However, the condition must be met that in the calculation procedure appropriate lengths of the moving chord will be used, increasing as the radius of the circular arc increases. Using the test geometric layout, it was clearly demonstrated that the discretization of data used in the moving chord method does not affect the accuracy of the obtained curvature values at individual measurement points.
References
Regulation of the Council of Ministers of 15 October 2012 on the national spatial reference system [in Polish]. 2012, Warszawa: Journal of Laws (Poland). 1247.
Moritz, H., Geodetic Reference System 1980. Journal of Geodesy, 2000. 74(1): p. 128-133.
Turiño, C.-E., Gauss Krüger projection for areas of wide longitudinal extent. International Journal of Geographical Information Science, 2008. 22(6): p. 703-719.
British railway track design, construction and maintenance. 6th edition, 1993, London: The Permanent Way Institution (United Kongdom).
883.2000 DB_REF-Festpunktfeld [in German]. 2016, Berlin: Deutsche Bahn Netz AG.
Railway applications—Track—Track alignment design parameters—Track gauges 1435 mm and wider. Part 1: Plain line. EN 13803-1. 2010, Brussels: European committee for standardization (CEN) (Belgium).
Code of federal regulations title 49 transportation. 2008, Washington, DC: Federal Railroad Administration, US Government Printing Office (USA).
NR/L3/TRK/0030 NR_Reinstatement of Absolute Track Geometry (WCRL Routes). Iss. 1, 2008. London: Network Rail (United Kingdom).
Standard: Railway Surveying, Version 1.0. T HR TR 13000 ST. 2016, Sydney: Government (Transport for New South Wales) (Australia).
Linienführung von Gleisen, B 50 – Oberbau – Technische Grundsätze [in German]. Teil 2, 2004, Wien: Österreichische Bundesbahnen, GB Fahrweg Technik (Austria).
Technical Standards – detailed technical conditions for the modernization or construction of railway lines for speed ≤ 200 km/h (for conventional rolling stock) / 250 km/h (for rolling stock with a tilting box). Volume I – Attachment ST-T1-A6: Geometrical layouts of tracks [in Polish]. 2018, Warszawa: Polish State Railways – Polish Railway Lines (Poland).
Ausführungsbestimmungen zur Eisenbahnver-ordnung. SR 742.141.11 [in German]. 2016, Bern: Schweizerische Bundesbahnen, Ministerium für Verkehr (Switzerland).
Li, W., et al., A method for automatically recreating the horizontal alignment geometry of existing railways. Computer–Aided Civil and Infrastructure Engineering, 2019. 34(1): p. 71–94.
Pu, H., et al., A global iterations method for recreating railway vertical alignment considering multiple constraints. IEEE Access, 2019. 7(1): p. 121199-121211.
Szwilski, A.B., et al., Employing HADGPS to survey track and monitor movement at curves. In Railway Engineering–2005; Forde, M.C., Ed.; The University of Edinburgh (United Kingdom).
A guide to using IMU (accelerometer and gyroscope devices) in embedded applications. Starlino electronics, 2009. Available online: http://www.starlino.com/imu_guide.html (accessed on 26th May 2023).
Guimarães-Steinicke, C., et al., Chapter Four – Terrestrial laser scanning reveals temporal changes in biodiversity mechanisms driving grassland productivity. Advances in Ecological Research, 2019. 61: p. 133-161.
Specht, C., and W. Koc, Mobile satellite measurements in designing and exploitation of rail roads. Transportation Research Procedia, 2016. 14: p. 625-634.
Alkan, R.M., Cm-level high accurate point positioning with satellite-based GNSS correction service in dynamic applications. Journal of Spatial Science, 2019. 66(2): p. 351-359.
Chang, L., et al., Railway infrastructure classification and instability identification using Sentinel-1 SAR and Laser Scanning data. Sensors, 2020. 20(24): 7108.
Quan, Y., and L. Lau, Development of a trajectory constrained rotating arm rig for testing GNSS kinematic positioning. Measurement, 2019. 140: p. 479–485.
Wang, L., et al., Validation and assessment of multi-GNSS real-time precise point positioning in simulated kinematic mode using IGS real-time service. Remote Sensing, 2018. 10(2): 337. Koc, W. (2023). Verification of the Theoretical Basis for Determining the Curvature of the Track Axis Using the Moving Chord Method. European
Wu, S., et al., Improving ambiguity resolution success rate in the joint solution of GNSS-based attitude determination and relative positioning with multivariate constraints. GPS Solutions, 2020. 24(1): 31.
Lai, X., and P. Schonfeld, Concurrent optimization of rail transit alignments and station locations. Urban Rail Transit, 2016. 2(!): p. 1-15.
Wei, X., et al., Railway track fastener defect detection based on image processing and deep learning techniques: A comparative study. Engineering Applications of Artificial Intelligence, 2019. 80: p. 66-81.
Song, T., et al., Mountain railway alignment optimization considering geological impacts: A cost-hazard biobjective model. Computer–Aided Civil and Infrastructure Engineering, 2020. 35(12): p.1365-1386.
Zhang, H., et al., multi-objective railway alignment optimization considering costs and environmental impacts. Applied Soft Computing, 2020. 89: 106105.
Pu, H., et al., Optimization of grade-separated road and railway crossings based on a distance transform algorithm. Engineering Optimization, 2021. 54(2): p. 232-251.
Ben-Arieh, D., et al., Geometric modeling of highways using Global Positioning System data and B-spline approximation. Journal of Transportation Engineering, 2004. 130(5): p. 632-636.
Castro, M., et al., Geometric modeling of highways using Global Positioning System (GPS) data and spline approximation. Transportation Research, Part C: Emerging Technologies, 2006. 14(4): p. 233-243.
Lenda, G., Determining the geometrical parameters of exploited rail track using approximating spline functions. Archives of Civil Engineering, 2014. 60(3): p. 295-305.
Imran, M., Y. Hassan, and D. Patterson, GPS-GIS-based procedure for tracking vehicle path on horizontal alignments. Computer–Aided Civil and Infrastructure Engineering, 2006. 21(5): p. 383-394.
Gikas, V., and J. Stratakos, A novel geodetic engineering method for accurate and automated road/railway centerline geometry extraction based on the bearing diagram and fractal behawior. IEEE Transactions on Intelligent Transportation Systems, 2012. 13(1): p. 115-126.
Li, Z., et al., Automated identification and extraction of horizontal curve information from Geographic Information System Roadway Maps. Transportation Research Record, 2012. 2291(1): p. 80-92.
Othman, S., R. Thomson, and G. Lanner, using naturalistic field operational test data to identify horizontal curves. Journal of Transportation Engineering, 2012. 138(9): p. 1151-1160.
Camacho-Torregrosa, F.J., et al., Use of heading direction for recreating the horizontal alignment of an existing road. Computer–Aided Civil and Infrastructure Engineering, 2015. 30(4): p. 282-299.
Banihashemi, M., Using quasi-horizontal alignment in the absence of the actual alignment. Accident Analysis and Prevention, 2016. 95(Part A): p. 33-41.
Luo, W., L. Li, and K. Wang, Automatic horizontal curve identification and measurement using Mobile Mapping System. Journal of Surveying Engineering, 2018. 144(4): 04018007.
Song, Z., et al., Integrating segmentation and parameter estimation for recreating vertical alignments. Computer–Aided Civil and Infrastructure Engineering, 2021. 36(4): p. 472-488.
Skala-Szymanska, M., S. Cellmer, and J. Rapinski, Use of Nelder-Mead simplex method to arc fitting for railway track realignment. In Selected Papers of The 9th International Conference ”ENVIRONMENTAL ENGINEERING” 2014, Vilnius, Lithuania, 22–23 May 2014. 595
Cellmer, S., et al., new approach to arc fitting for railway track realignment. Journal of Surveying Engineering, 2016. 142(2): 06015005.
Song, Z., et al., Circular curve-fitting method for field surveying data with correlated noise. Journal of Surveying Engineering, 2018. 144(4): 04018010.
Song, Z., et al., Heuristic strategies of modified Levenberg-Marquardt algorithm for fitting transition curves. Journal of Surveying Engineering, 2020. 146(2): 04020001.
Li, F., et al., Methodology for existing railway reconstruction with constrained optimization based on point cloud data. Applied Sciences–Basel, 2018. 8(10): 1782.
Easa, S.M., H. Dong, and J. Li, Use of satellite imagery for establishing road horizontal alignments. Journal of Surveying Engineering, 2007. 133(1): p. 29-35.
Dong, H., S.M. Easa, and J. Li, Approximate extraction of spiraled horizontal curves from satellite imagery. Journal of Surveying Engineering, 2007. 133(1): p. 36-40.
Easa, S.M., and A. Mehmood, Optimizing design of highway horizontal alignments: new substantive safety approach. Computer–Aided Civil and Infrastructure Engineering, 2008. 23(7): p. 560-573.
Easa, S.M., and F. Wang, fitting composite horizontal curves using the total least-squares method. Survey Review, 2011. 43(319): p. 67-79.
Chen, F., et al. Reconstruction method of existing speed rail based on precision measurement. Applied Mechanics and Materials, 2012. 256-259: p. 1761- 1764.
Han, F., X. Duan, and Y. Zhang, Research of coordinate extraction and curve realignment algorithm based on continuous point cloud data. In Proceedings of First International Conference on Rail Transportation, Chengdu, China, 10–12 July 2017.
Song, Z., et al., Effect of point configurations on parameter estimation analysis of circles. Journal of Surveying Engineering, 2021. 147(3): 04021010.
Um, J.H., et al., Optimization of alignment considering ride comfort for superimposition of vertical and horizontal curves. Proceedings of the. Institution of Mechanical Engineers, Part F – Journal of Rail and Rapid Transit, 2011. 225(6): p. 649-662.
Li, W., et al., Recreating existing railway horizontal alignments automatically using overall swing iteration. Journal of Transportation Engineering: Part A – Systems, 2022. 148(8): 04022046.
Koc, W., The method of determining horizontal curvature in geometrical layouts of railway track with the use of moving chord. Archives of Civil Engineering, 2020. 66(4): p. 579-591.
Koc, W., Analysis of the effectiveness of determining the horizontal curvature of a track axis using a moving chord. Problemy Kolejnictwa – Railway Reports, 2021. 65(190): p. 77-86.
Koc, W., Analysis of moving chord inclination angles when determining curvature of track axis. Current Journal of Applied Science and Technology, 2021. 40(10): p. 92-103.
Koc, W., Estimation of the horizontal curvature of the railway track axis with the use of a moving chord based on geodetic measurements. Journal of Surveying Engineering, 2022. 148(4): 04022007.
Koc, W., Identification of geometrical parameters of an operated railway route on the basis of the determined curvature of the track axis. European Journal of Applied Sciences, 2022. 10(5): p. 129-148. Koc, W. (2023). Verification of the Theoretical Basis for Determining the Curvature of the Track Axis Using the Moving Chord Method. European
Koc, W., Determination of moving chord length for determine the curvature of in-service railway track. Problemy Kolejnictwa – Railway Report, 2022. 66(197): 147-160.
Koc, W., The procedure of identifying the geometrical layout of an exploited railway route based on the determined curvature of the track axis. Sensors, 2023. 23(1): 274.
Fu, B.T., A chord curvature model for silhouette curvature calculations. In Electronics, Communications and Networks V, Hussain, A., Ed. 2016, Singapore: Springer, p. 11-17.
Guo, J., and B. Zhong, U-chord curvature: a computational method of discrete curvature. International Journal of Pattern Recognition Artificial Intelligence, 2014. 27(8): p. 683-691.
Zhong, B., On the stability of refined L-curvature under rotation transformations. Applied Mechanics and Materials, 2010. 20–23: p. 401-406.
Koc, W., New transition curve adapted to railway operational requirements. Journal of Surveying Engineering, 2019. 145(3): 04019009.
Koc, W., Designing the railway line direction changing area in linear and Cartesian coordinate systems. European Journal of Applied Sciences, 2022. 10(4): p. 277-296.
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Copyright (c) 2023 Wladyslaw Koc
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