15 Automated Modal Parameter Extraction and Statistical Analysis of the New Carquinez Bridge Response to Ambient Excitations 169 Fig. 15.5 Relationship of modal frequency and structural temperature for mode 1, 3 and 4 with colored density (a)mode1, (b)mode3, (c)mode4 (d) density plot of observed temperature 4 clearly have a linear relationship between modal frequency and structural temperature with a negative slope. Modal frequency of mode 1 also has a linear relationship with temperature, but with a positive slope and less steep. For all three modes, there are two high density regions observed (10–15 and 22–27 ıC), which matches with the distribution of observed temperature. The distribution of frequency for most of the temperature ranges (shown as one vertical strip in Fig. 15.5a–c) is symmetric (normal). 15.6 Conclusions Using 1-year worth of acceleration data collected from a wireless long-term structural monitoring system installed on the New Carquinez Bridge, automated modal parameter extraction methods are successfully implemented. Based on modes obtained using stochastic subspace identification, knowledge-based and triangulation-based extraction (TEMP) methods are shown able to extract modal parameters in an automated fashion. Fundamental modes (namely, modes 1, 3, 4, and 5) are identified consistently. The mean values for each mode (Mode 1, 0.194 Hz, Mode 3, 0.258 Hz, Mode 4, 0.35 Hz, Mode 5, 0.41 Hz) and distributions (normal distribution) of the results obtained using these two different methods agree. Higher modes are also detected, but the distribution exhibits greater scatter. Damping ratios obtained using SSI is very sensitive to the model order. Damping ratios obtained fall between 1 and 5 % using TEMP and between 0.5 and 3 % using the knowledge-based method. Relationships between modal frequency and temperature are also explored with linear trends illustrated. Acknowledgments The authors would like to gratefully acknowledge the generous support offered by the U.S. Department of Commerce, National Institute of Standards and Technology (NIST) Technology Innovation Program (TIP) under Cooperative Agreement Number 70NANB9H9008. Additional support was provided by the University of Michigan and the California Department of Transportation (Caltrans). On site assistance with sensor installation on the New Carquinez Bridge by Caltrans personnel, especially Mr. Edward Thometz, are also greatly appreciated.
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