New Approach to Arc Fitting for Railway Track Realignment

Vertical alignment reconstruction obtains alignment parameters by fitting geometric components to a set of measured points representing the profile of an existing road or railroad, which is essential in alignment consistency analysis and maintenance to ensure safety and comfort. The neural dynamics model of Adeli and Park is explored and improved for reconstructing vertical alignments with constraints. The structure of the dynamics model is modified to include three layers: parameter layer, intermediate layer, and energy layer. The number of nodes in the parameter or intermediate layers corresponds to the number of independent parameters defining a vertical alignment. The number of nodes in the energy layer is the sum of the number of deviations and the number of constraints in the alignment reconstruction problem. The coefficients connecting nodes between the parameter layer and the intermediate layer determine the integral operations, which define the Levenberg–Marquardt algorithm of the dynamics model (LMADM) and the steepest descent algorithm of the dynamics model (SDADM). Both the LMADM and SDADM methods satisfy the Lyapunov stability theorem, but the LMADM method outperforms the SDADM method in its objective function value and computation time. Experiment results demonstrate that there are multiple local optima for a vertical alignment reconstruction, and the solutions obtained by the LMADM method are the best obtained so far, compared with those reported in the literature, with 57.1% and 23.4% decreases of the mean squared error for the highway and the railroad examples, respectively.

Section: Introductionmentioning

confidence: 99%

Two algorithms for reconstructing vertical alignments exploring the neural dynamics model of Adeli and Park

Song,

Chen,

Schonfeld

et al. 2023

“…In the second stage of reconstructing the tamping target alignment, it is necessary to fit the tangent segments and curved segments according to the identified alignment elements and then to obtain the design parameters that correspond to the fitted alignment. 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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

A smoothness optimization method for horizontal alignment considering ballasted track maintenance

Jin

Zhang

Chen

et al. 2022

This paper proposes a smoothness optimization method of horizontal alignment based on orthogonal least squares and the theory of controlling the track smoothness. With this method, multiple curve types can be fitted simultaneously according to the maintenance requirements, and the residual deviation in the track is optimized according to the smoothness standard. The target alignment of the tamping operation is constructed, providing support for the maintenance of the ballasted track. The implementation results show that the proposed method fully adapts to operating railway maintenance conditions, and the optimized design parameters resemble the field observation results. The lateral profile track quality index is reduced from 0.78 to 0.39, the amplitudes of the 10 and 60 m mid‐chord offset decrease by 73% and 52%, respectively, and the 30‐m vector distance difference decreased by 53%, indicating effective improvement.

“…Song, Ding, Li, and Pu (2018) presented a circular curve fitting method considering correlated noise. Cellmer, Rapiński, Skala, and Palikowska (2016) proposed an arc fitting method with constraints of fixed straight lines for railway track realignment. Dong, Easa, and Li (2007) also presented an approximate method for extracting a compound horizontal curve consisting of a circular curve and a spiral curve.…”

Section: Introductionmentioning

confidence: 99%

Integrating segmentation and parameter estimation for recreating vertical alignments

Song

Yang

Schonfeld

et al. 2020

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.