Calibration-light multi-point displacement measurement for railway bridge monitoring via a differential-form projection model

This study proposes a calibration-light framework for practical multi-point displacement monitoring of railway bridges using a single high-resolution video camera (and, when needed, two synchronized cameras for 3D reconstruction) with a wide-angle lens. The method enables synchronous displacement estimation during train passage without requiring full on-site calibration of external parameters. A differential-form projection model was developed to relate pixel movement to physical displacement increments in a bridge-fixed coordinate system, incorporating perspective-effect compensation via the pixel-to-displacement mapping (Eq. (15)), radial lens distortion correction, and camera-to-target distance estimation. Laboratory experiments demonstrated that the proposed method achieved accurate displacement estimation even under wide-angle imaging. Field applications to four railway bridges demonstrated the method’s practical applicability: Bridge A showed accurate vertical displacement consistent with velocimeter data; Bridge B revealed resonance and vibration modes across three spans; Bridge C demonstrated long-distance measurement (over 100 m) with span-specific modal characteristics; and Bridge D achieved 3D displacement estimation using two synchronized cameras consistent with laser Doppler velocimeter results at the same location. These results highlight the method’s practical applicability for bridge monitoring under diverse structural and environmental conditions.