Structural Deflection Measurement with a Single Smartphone Using a New Scale Factor Calibration Method

This study proposes a novel structural deflection measurement method using a single smartphone with an innovative scale factor (SF) calibration technique, eliminating reliance on laser rangefinders and industrial cameras. Conventional off-axis digital image correlation (DIC) techniques require laser rangefinders to measure discrete points for SF calculation, suffering from high hardware costs and sunlight-induced ranging failures. The proposed approach replaces physical ranging by deriving SF through geometric relationships of known structural dimensions (e.g., bridge length/width) within the measured plane. A key innovation lies in developing a versatile SF calibration framework adaptable to varying numbers of reference dimensions: a non-optimized calculation integrates smartphone gyroscope-measured 3D angles when only one dimension is available; a local optimization model with angular parameters enhances accuracy for 2–3 known dimensions; and a global optimization model employing spatial constraints achieves precise SF resolution with ≥4 reference dimensions. Indoor experiments demonstrated sub-0.05 m ranging accuracy and deflection errors below 0.30 mm. Field validations on Beijing Subway Line 13′s bridge successfully captured dynamic load-induced deformations, confirming outdoor applicability. This smartphone-based method reduces costs compared to traditional setups while overcoming sunlight interference, establishing a hardware-adaptive solution for vision-based structural health monitoring.