116 W. Locke et al. 5 Methodologies 5.1 Peak Picking In this study, the PSD for bridge and vehicle responses was estimated using the Welch’s periodogram method. A moving Hann window with a 66% overlap was employed to enable averaging to reduce spectral leakage within response spectra; the size of the moving window was selected such that a 0.25 Hz spectral resolution was achieved for all data. Resonant frequencies were identified within each response spectra by leveraging Liutkus A.’s PP algorithm based on scale-space theory [33]; a total of ten peaks were selected within each response spectrum. The damping associated with identified resonant frequencies was estimated using the half-power bandwidth method [34]. To identify if the dynamic properties of the bridge and vehicle vary with time, PP was also conducted on the short-time fast Fourier transform (ST-FFT) of response data. The ST-FFT was estimated by employing Matlab’s spectrogram function and utilizing the same windowing properties as the Welch periodogram analysis. During this analysis, the ten largest peaks across all windows of the subject spectrogram were identified and their damping was calculated using the half-power bandwidth method. 5.2 Frequency Domain Decomposition The automated FDD routine developed by Cheynet E. was employed for system identification in this study [35]. Under this methodology, the CPSD needed for SVD was calculated using the same windowing properties as the Welch’s periodogram method in Sect. 5.1. Additionally, Liutkus A.’s PP algorithm is pre-coded into the routine to automatically identify the most dominant peak frequencies within the response spectrum; the top ten peaks were selected for all FDD analyses in this study. The referenced methodology calculates the damping associated with each identified peak by fitting an exponential decay to the envelope of impulse response functions obtained via the Natural Excitation Technique (NExT); it can be seen by Fig. 2 that NExT is also classified as an OMA technique [1, 35]. Peak frequencies were also identified from the ST-FDD of response data. The ST-FDD was estimated by dividing time histories into overlapping Hann windows in the same manner as Matlab’s spectrogram function. During this analysis, the ten largest peaks across a subject time series were identified and their damping calculated using the NExT procedure as mentioned before. 6 Uncoupled System Identification 6.1 Preprocessing Preprocessing was performed prior to employing OMA techniques to remove any linear trends, aliasing, and high frequency noise effects. Matlab’s digital signal processing toolbox was employed for all signal processing in this study. Initially, detrending was performed to remove linear trends. Then, to decrease the computational cost of OMA procedures, downsampling was employed to reduce sample rates fs by half the initial values provided in Table 1. After the data was downsampled, aliasing and high frequency noise effects were removed by applying an eighth-order lowpass FIR filter with a passband up to 50 Hz. The 50 Hz cutoff was selected due to an initial analysis of direct bridge data identifying low levels of excitation at higher frequencies. Additionally, DBHM literature indicates that it is difficult to indirectly capture bridge frequencies higher than the second or third mode, which from a preliminary numerical model developed from the bridge plans, were believed to fall below 50 Hz [11]. 6.2 Bridge Uncoupled OMA Analysis The PP and FDD algorithms were used to analyze the averaged and short-time spectrums of the bridge response to ongoing traffic. Figure 5a demonstrates how the PP algorithm identifies obvious resonant frequencies as well as frequencies that have low levels of excitation within an averaged spectrum. To verify identified peak frequencies are associated with bridge modes and not noise, a cumulative sum of the peaks identified by PP in the averaged spectrum was obtained across all records and
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