118 W. Locke et al. Fig. 7 Cumulative sums from(a) FDD and (b) ST-FDD analyses of direct bridge data during uncoupled bridge testing; plotted in 0.25Hz wide bins. Demonstrates narrower frequency bin distributions than base PP method shown in Figs. 5 and 6 bridge frequencies are noticeably influenced by the system’s time variant nature while other frequencies do not appear to be influenced at all. A partial explanation for the time variant nature of the bridge is that traffic excited breathing in existing cracks, which introduced variations in the bridge’s spectral response. Furthermore, tractor-trailers for logging and shipping regularly travel on US-221, meaning trucks similar in size to the HL-93 truck were continuously present during testing and could have caused cracks to completely open. Additionally, the mass of tractor-trailers would have also caused noticeable shifts in certain bridge frequencies, as vehicle-to-bridge mass ratios, assuming HL-93 loads, are estimated to be on the order of 20% [30]. A final explanation for observed frequency variations is that vehicle frequencies were potentially being captured in the bridge response [14]. As vehicles have been shown to introduce higher energy loads in the range of their sprung and unsprung mass frequencies (i.e. 1 Hz–2 Hz and 10 Hz–15 Hz, respectively), it is plausible that these higher energy loads drove the dynamics of the coupled system and caused the bridge to capture vehicle frequencies [14, 36–38]. This explanation is supported by the identification of frequencies at 1.5 Hz–2 Hz and the fact the 11.5 Hz–16.5 Hz distribution is wider than any other observed distribution. It can be noted that the variation in damping in the 11.5 Hz–16.5 Hz region supports all of the above mentioned explanations. Figure 7 provides the histograms for total peaks identified across all records for the FDD and ST-FDD analyses. To remain consistent with the PP analyses, bin widths were set equal to 0.25 Hz and frequencies detected less than four total times were excluded. As can be seen, the FDD and ST-FDD analyses produce similar results to the averaged and short-time PP analyses; however, the bin distributions between 11.5 Hz–16.5 Hz and 29 Hz–31 Hz in Figs. 5b and 6b are narrower in Fig. 7. The narrower frequency distributions suggests that the FDD technique is more robust against time variant properties when analyzing direct bridge data. The reasoning for this is that by taking the SVD of the CPSD between signals, frequencies continuously detected across all sensors are more pronounced and easily identified as resonant modes, while frequencies introduced by noise or time variant properties not necessarily captured by all sensors are less pronounced and less likely to be identified as peaks. Figure 7 also demonstrates that the damping ratios calculated using the NExT procedure are similar to those calculated using the half-power bandwidth method; however, there is a noticeable difference when considering the frequency bins around 1.5 Hz–2 Hz in Fig. 7a. This difference is believed to be caused by higher mean square errors introduced by initial coefficient estimates when fitting exponential curves to the envelope of impulse response functions for the NExT procedure. During the FDD analyses, average damping estimates were significantly influenced by the choice of initial coefficient estimates, suggesting that the subject NExT procedure is not as robust for identifying damping at certain frequencies and/or excitation levels [1]. 6.3 RAM Truck Uncoupled OMA Analysis When analyzing data from the RAM truck road test, emphasis was placed on unsprung data since sensors were only installed on the unsprung masses during DBHM testing. Figure 8 provides an example of a spectrogram plot obtained from road test data collected at 32.19 kph (20 mph). Initially, it can be seen that resonant peaks appear to occur in intervals of approximately
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