Development of a frequency‐geometry‐temperature unified correlation equation for existing PRC bridges

In continuous Structural Health Monitoring (SHM), environmental and operational conditions significantly influence damage detection strategies. To accurately identify damage and avoid false alarms, statistical patterns must be calibrated under healthy structural conditions to distinguish changes in dynamic response caused by damage. Typically, SHM systems require thermocouples to measure temperature for such calibration. This study proposes an experimental approach to estimate the first natural frequency of structures based solely on the air temperature. Using a dataset of 13 Prestressed Reinforced Concrete (PRC) bridges, a bilinear regression model is developed to relate natural frequency to temperature, distinguishing behaviours above and below the freezing point. Additionally, a nonlinear regression model is derived linking natural frequency to span length. Ultimately, a unified equation that incorporates both span length and temperature is presented, with prediction intervals. The model's reliability is validated using data from an independent bridge.