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

Abstract

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.