A new frequency-geometry-temperature equation tool for existing PRC bridges in structural health monitoring

Environmental and operational conditions have a significant impact on the dynamic response of structures under continuous Structural Health Monitoring (SHM), playing a critical role in damage detection strategies. To accurately identify damage and avoid false alarms, statistical models must be calibrated under healthy structural conditions, allowing changes due to damage to be distinguished from those induced by environmental variability. This study proposes an experimental approach to estimate the first natural frequency of bridge deck using span length and the total deck depth as the primary geometrical parameters, supplemented by a correction term to account for temperature effects. A dataset of 30 prestressed reinforced concrete (PRC) bridges was used to develop a bilinear regression model that captures the relationship between natural frequency and temperature, distinguishing the structural behaviors above and below the freezing point. Additionally, a non-linear correlation term is introduced to estimate the natural frequency at the reference temperature (0 degrees C) based on span-to-depth ratio. The result is a unified regression model that integrates both geometrical and environmental parameters, with associated prediction interval; however, its applicability below 0 degrees C remains limited due to the scarcity of available data in that range. The model's reliability is validated using data from an independent bridge, confirming its effectiveness as a tool for one-time system identification and as a statistical model in continuous SHM applications.