Statistical Models of the Lambert Road Bridge: Changes in Natural Frequencies Due to Temperature

Structural health monitoring (SHM) using ambient vibration has become a tool in evaluating and assessing the condition of civil structures. For bridge structures, a vibration-based SHM system uses the dynamic response of a bridge to measure modal parameters. A change in a structure’s modal parameters can indicate a physical change in the system, such as damage or a boundary condition change. These same modal parameters are sensitive to environmental factors, mainly temperature. Statistical models have been utilized to filter out modal parameter changes influenced by temperature and those caused by physical changes. Statistical models also help describe the relationship between modal parameters and environmental conditions. The Lambert Road Bridge is a concrete integral abutment bridge located south of Sacramento, California, and is studied through this paper. A SHM system has been installed and has been recorded for 3 years. Three months of SHM records will be used to understand how the bridge’s natural frequencies typically change due to temperature. First, temperature was observed to be the driving force behind many of the SHM records. A linear relationship was found between the structure’s natural frequency and temperature. Collinearities between potential predictor variables were noticed. Initial linear regression analyses were completed with a bridge average temperature. Certain strain gauge regression models were used as “base” models to eliminate other regression models that potentially were altered by aliasing. These base models, and the other seven corresponding models, showed a direct linear relationship between temperature and natural frequency. It was concluded that changes in boundary conditions due to bridge expansion have a greater effect on global dynamic properties than material property changes due to temperature. Stepwise linear regression followed the initial regression modeling. Eight thermocouple readings were consistently being selected in the stepwise process and were chosen to be the main predictor variables. Due to collinearities among the predictor variables, ridge regression was completed to eliminate any unstable variables. The final six sensors’ locations indicate that longitudinal, transverse, and depth gradients are all important factors in the linear regression models of this relationship. Comparing the multiple linear regression models to single-variable regression models with the highest averaged adjusted R2 values, a minimum percent difference of 21% and 19% was seen for the first and second natural frequencies, respectively. It was also concluded that these multiple linear regression models explained more of the variability in the natural frequencies and would be a better model to use to filter out temperature effects