Optimized Detection Algorithm for Vertical Irregularities in Vertical Curve Segments

The vertical curve is designed to smooth sudden gradient changes in the longitudinal profile, enhancing train operational safety and passenger comfort. However, dynamic detection in these segments has consistently encountered issues with long-wavelength vertical irregularities exceeding tolerance limits. To investigate the root causes of this phenomenon and develop a targeted solution, a comprehensive vehicle-track dynamics simulation model was first constructed, based on the design principles for intercity railway vertical curves. The inertial reference method was then applied to process the acceleration and relative displacement data between the detection beam and the track, yielding virtual irregularities. These were compared with excitation irregularities to identify key factors affecting detection accuracy in vertical curve segments. Through further analysis of abnormal exceedances in detection data, the reference cancellation method was proposed. By employing smoothing filters and orthogonal least squares fitting, this method effectively removes track alignment components from the acceleration integration results. Detection errors under various conditions were then compared between the two methods to evaluate the feasibility and effectiveness of the reference cancellation approach. Results indicate that regions with increased longitudinal profile detection errors are primarily located at and near gradient transition points. The vertical curve radius was found to be the primary factor influencing the accuracy of long-wavelength irregularity detection. The proposed reference cancellation method effectively reduces detection errors in areas near gradient transition points to levels comparable to other track sections. Compared to the inertial reference method, the reference cancellation method reduces the maximum detection error by up to 71.77% and the root mean square error by up to 86.61%, effectively mitigating the abnormal exceedances associated with vertical curves.