Abstract
A railway track gradually deviates from the originally designed vertical alignment in the operation. To ensure the safety and comfort, railway maintenance department must periodically recreate vertical alignment and calibrate existing track to it. The recreated alignment should be as close as possible to the measured points along the existing railway track, while satisfying multiple constraints. A vertical alignment consists of tangents and curves. Identifying the geometric element attribution of the measured points accurately and recreating the vertical alignment efficiently and accurately with all the constraints satisfied are the key problems. Existing methods need manual assistance and few constraints are considered. This paper proposes an automatic global iterations method considering multiple constraints. Firstly, geometric elements are identified based on the change rate of gradient and are set as initial values for the iterations. Then, the geometric elements are fitted iteratively. In each iteration, all the tangents are fitted simultaneously followed by the fitting of all vertical curves and the constraints are handled while the geometric elements are fitted. The attributions of all points are adjusted after each iteration. If the attributions of all the points are consistent with the ranges of fitted geometric elements, the iteration terminates. A software is developed based on this method, and applications demonstrate this method can identify all geometric elements automatically and recreate an optimized vertical alignment while satisfying all the constraints.
Highlights
Continuity and smoothness of an existing railway vertical alignment are critical to the safety and comfort of railway operations [1]
(1) Design variables A vertical alignment can be defined by a set of vertical points of intersections (VPIs)
Vertical curve should not overlap with the transition curve, which means that the distance between the vertical point intersection (VPI) and boundary points (the starting point (ZY) and end point (YZ) of ith vertical curve) should satisfy the following relation: Si − xmp > Ri tan β ⇒ Ri = Rc ≤ Si − xmp /tan β (30)
Summary
Continuity and smoothness of an existing railway vertical alignment are critical to the safety and comfort of railway operations [1]. H. Pu et al.: Global Iterations Method for Recreating Railway Vertical Alignment Considering Multiple Constraints. The latter is used to obtain the global optimal parameters for tangents and vertical curves considering a few of constraints This method can recreate the whole alignment. Li et al [28] proposed a swing iterations method based on the idea of points-alignments consistency, which is effective and automatic in the railway horizontal recreation. D. the method proposed by Li et al [28] has achieved good effect for horizontal alignment recreation, it cannot be directly used for vertical alignment because that the geometric elements composition is different and the characteristic of the measured points of vertical alignment is not obvious enough. This paper proposes an efficient and automatic recreation method for vertical alignment, while satisfying multiple constraints.
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