A geometric‐identification–free mathematical model for recreating nonsymmetric horizontal railway alignments

The constant passage of trains on the railways tracks causes, in the course of time, deviations that must be corrected periodically by means of a track calibration process. It consists of designing a new layout, called recreated horizontal alignment (RHA), as close as possible to the deformed center track fulfilling also the technical constraints according to the operational requirements of the railway. In recent years, different models have been proposed to address this task. This paper proposes, first, a new geometrical model that works with continuous variables for the definition of horizontal alignments (HAs) to deal with nonsymmetric transition curves at both sides of a circular curve and second, an optimization algorithm to compute the recreated alignment suitable in sinuous railway sections. This new mathematical model frees the optimization process from the need to previously identify the geometric elements (tangents, circular curves, and transition curves) of the HA. The usefulness of this model is tested with two academic examples showing its good behavior and in a real case study, where this algorithm is compared with the solution adopted by the engineers in a section of the railway line Ourense–Monforte in the NW of Spain.