Innovative Displacement Calculation Techniques: A Comparative Analysis of Velocity and Acceleration Data Integration for Structural Health Monitoring

Accurately calculating displacements from sensor data is crucial in structural engineering, yet it presents significant challenges due to inherent errors and noise in sensor data. This study presents a comparative analysis of two dis-placement derivation methods, one based on velocity data and the other on acceleration data. Deriving displacements from acceleration data involves in-herent errors due to double integration, while velocity-based calculations suf-fer from considerable background noise owing to instrument sensitivity. To assess and compare the performance of both approaches, a Python-based simulation was developed to model the free vibration response of a simply supported reinforced concrete (RC) beam. Two scenarios were considered: one using the analytical solution of the damped vibration equation, and anoth-er based on Newmark’s method for numerical time integration. Synthetic ac-celeration and velocity data generated from both scenarios were used as input to derive displacement via integration. These derived displacements were then compared to the original displacement values from the model. Results show that displacements obtained from velocity data closely match the original model values, while those derived from acceleration data exhibit larger deviations due to cumulative integration errors. Both methods, howev-er, can complement each other when used in combination, offering valuable cross-validation. These findings reflect the outcomes of the first phase of a two-stage research effort. In the next phase, the methodology will be validated through laboratory experiments using real sensor data obtained from a physical RC beam specimen instrumented with accelerometers and velocimeters.