An Axle-Based, Uncertainty-Aware Safety-Envelope Model for Automatic Braking and Stopping of Runaway Rolling Stock at Railway Stations

This study presents an axle-based, uncertainty-aware safety-envelope framework for the Automatic Braking and Stopping System (ABSS), designed to arrest rolling stock before a hazard boundary after uncontrolled movement begins. The method combines free-rolling dynamics, response delay, active braking, deterministic force sizing, axle-capacity screening, and uncertainty-adjusted distance assessment. It separates gross mass, braking demand, and verified eligible axle positions. A browser-based tool performs these calculations and configuration checks. A predefined distance serves numerical verification; operational use requires the measured detection-to-boundary distance. For illustrative 94 t/4-axle, 188 t/8-axle, and 282 t/12-axle cases, the profile yields a detection speed of 7.973 km/h. With four 10-kN elements, deterministic stopping distances are 10.211, 16.553, and 23.277 m; uncertainty-adjusted upper distances are 10.698, 17.430, and 24.636 m. Deterministic sizing requires two elements in each case, while uncertainty-adjusted sizing requires three for 282 t. Restricting that case to two eligible positions raises the upper distance to 52.417 m and leaves no feasible configuration. Sensitivity is greatest to detection speed, followed by braking force and gross mass. Thus, distance adequacy alone is insufficient: uncertainty and physical installation capacity must also be checked. The framework supports traceable screening, software verification, and subsequent component, integration, and controlled-track validation.