Determining The Geometrical Parameters Of Exploited Rail Track Using Approximating Spline Functions

Abstract

The process of railway track adjustment is a task which includes bringing, in geometrical terms, the actual track axis to the position ensuring safe and effi cient traffi c of rail vehicles. The initial calculation stage of this process is to determine approximately the limits of sections of different geometry, i.e. straight lines, arcs and transition curves. This allows to draw up a draft alignment design, which is subject to control the position relative to the current state. In practice, this type of a project rarely meets the requirements associated with the values of corrective alignments. Therefore, it becomes necessary to apply iterated correction of a solution in order to determine the fi nal project, allowing to introduce minor corrections while maintaining the assumed parameters of the route. The degree of complexity of this process is defi ned by the quality of determining a preliminary draft alignment design. Delimitation of the sections for creation of creating such a design, is usually done by using the curvature diagram (InRail v8.7 Reference Guide [1], Jamka et al [2], Strach [3]), which is, however, sensitive to the misalignment of the track and measurement errors. In their paper Lenda and Strach [4] proposed a new method for creating curvature diagram, based on approximating spline function, theoretically allowing, inter alia, to reduce vulnerability to interference factors. In this study, the method to determine a preliminary draft alignment design for the track with severe overexploitation was used, and thus in the conditions adversely affecting the accuracy of the conducted readings. The results were compared to the ones obtained using classical curvature diagram. The obtained results indicate that the method allows to increase the readability of a curvature graph, which at considerable deregulation of a track takes an irregular shape, diffi cult to interpret. The method also favourably affects the accuracy of determining the initial parameters of the project, reducing the entire process of calculation.

A Method for Determining the Directional Angle of a Railway Route Based on Field Measurements

“…Many works attempt to automate this process. There are two variants of this procedure: geometric identification [ 17 , 18 , 19 , 20 ] and alignment optimization [ 21 , 22 , 23 , 24 , 25 , 26 ]. In the works [ 27 , 28 , 29 ], several methods were proposed to combine these variants into an iterative process of reconstructing the track axis.…”

A smoothness optimization method for horizontal alignment considering ballasted track maintenance

“…Han et al (2018) and Tong et al (2010) performed least-squares fitting based on point cloud data and calculated the curvature to identify alignment elements. Ben-Arieh et al (2004), Castro et al (2006), and Lenda (2014) identify alignment elements through the curvature of the spline curves, such as B-splines and cubic splines. Othman et al (2012) and Song et al (2021) identified different alignment elements by calculating the heading direction of measurement data and setting the threshold.…”

“…(2004), Castro et al. (2006), and Lenda (2014) identify alignment elements through the curvature of the spline curves, such as B‐splines and cubic splines. Othman et al.…”

Evaluation of the Possibility of Identifying a Complex Polygonal Tram Track Layout Using Multiple Satellite Measurements

“…The signal achieved is the so-called point cloud, which without further interpretation does not contribute valuable information. Hence, the signals should be interpreted in such a way that the data set can be converted into the model representation of geometric systems of the track, mainly in the horizontal plane (straight sections, transition curves and circular arcs), and also in the vertical alignment (sections of a constant slope and sections in vertical arcs) [ 10 , 11 , 12 ]. Because of the large number of collected coordinates, the effective analysis must include methods of automatic selection of particular sections of geometric systems [ 13 , 14 , 15 , 16 ].…”