Integrating segmentation and parameter estimation for recreating vertical alignments

Abstract

A major problem of vertical alignment recreation is to automatically attribute the measured points to geometric elements (i.e., grades and vertical curves) and to efficiently recreate the vertical alignment with constraints. Most existing methods are nonoptimal in theory, semiautomatic, or inefficient in recreating an alignment. A new approach is proposed for automatically determining segmentation into geometric elements from measured points and efficiently optimizing a recreated alignment with constraints. First, independent parameters defining an alignment, are proposed to represent a vertical alignment. Then, a statistical deflection angle (SDA) method is proposed to determine segmentation by exploring statistical features of the geometric elements. Analysis shows that the SDA method outperforms the curvature method in distinguishing between grades and curves. Patterns of the segmentation process are found, and a segmentation algorithm is provided. Further, an optimization model is proposed to recreate the alignment with constraints. Experiment results demonstrate that this approach is highly efficient and effective compared with existing methods, reducing the number of searched alignments from tens of thousands to tens, while improving the value of the objective function.

Exploring and exploiting ant colony optimization algorithm for vertical highway alignment development

“…Some of the important optimization methods used in developing a computer‐aided optimization‐based vertical alignment are summarized in Table 1. Apart from developing a new vertical alignment, researchers also attempted to recreate a vertical alignment of as‐built roads (Song et al., 2021).…”

Modeling side slopes in vertical alignment resource road construction using convex optimization

“…Many efficient models have been proposed for vertical alignment optimization incorporating various interesting techniques: various heuristic approaches (e.g., Akay, 2003; Goktepe et al., 2009; Jong & Schonfeld, 2003; Lee & Cheng, 2001; Li et al., 2017; Song et al., 2021; Vázquez‐Méndez et al., 2021), deep learning techniques (e.g., Gao et al., 2022), dynamic programming (e.g., Fwa, 1989; Goh et al., 1988; Goktepe et al., 2005; Li et al., 2013), linear or mixed integer linear programming (MILP; e.g., Easa, 1988; Hare et al., 2011, 2015; Koch & Lucet, 2010; Moreb, 1996, 2009; Moreb & Aljohani, 2004), and other methods (e.g., Ozkan et al., 2021).…”

A smoothness optimization method for horizontal alignment considering ballasted track maintenance

“…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. Camacho-Torregrosa et al (2015) did not set a recognition threshold but instead selected a heuristic algorithm to optimize the theoretical heading direction of the measurement data and searched for the boundary points of the alignment element.…”

“…Easa and Wang (2010), Cellmer et al (2016), and Tong et al (2010) proposed an optimization model that can continuously estimate the parameters of each section of the curve by fitting the horizontal and vertical curve components with the least-squares method. Song et al (2020Song et al ( , 2021 selected the least-squares residual as the objective function, combined it with a heuristic strategy, and employed the Levenberg-Marquardt algorithm to fit the optimal alignment of the transition curve. Camacho-Torregrosa et al (2015) proposed using a heuristic algorithm to fit the geometric elements of different combined alignments.…”

“…(2012) and Song et al. (2021) identified different alignment elements by calculating the heading direction of measurement data and setting the threshold. Camacho‐Torregrosa et al.…”