## 4 Verification by Experiment
### Analysis of Experimental Results  
The loading types in this experiment include hammer excitation and vibration under sudden release of initial displacement. The typical strain time-history curves under the condition of single hammering and multiple hammering are shown in Figure 13. The deflection time-history at any position of the beams can be obtained using the aforementioned moment-area method. Furthermore, the deflection distribution along the beams at a certain time can also be achieved. The sampling frequency of FBG-based LGSSs (interrogator of SM130 from Micron Optics) and laser displacement meters is 100 Hz. Strain responses from each FBG sensor and displacement responses from each meter were simultaneously acquired. Taking 1/4 span, mid-span and 3/4 span of the beam as examples, deflection comparisons between the estimated results (Equation (7)) and directly measured results by laser displacement meters are shown in Figure 14. These figures show the time-varying deflection from \(t=0\) s to \(t=13\) s as well as the expanded one from \(t=1\) s to \(t=3\) s. From these expanded figures, it was found that the trend of the calculated deflection changing versus time was the same as the directly measured one. The errors between the calculated and measured deflection at the first peak (positive) and second peak (negative) were about 5.92% and 6.78% for 1/4 span of the beam. At mid-span, the errors between the calculated and the measured deflection were about 4.87% and 2.27% for the first and second peaks. At 3/4 span, the errors between the calculated and the measured deflection were about 5.30% and 7.76% for the first and second peaks. Generally, the relative errors of peak values can be controlled within about 10%. It is worth noting that \"prediction\" in Figure 14 means the results estimated using strain response, and \"test results\" means the results directly measured by laser displacement meters. Figure 12: Experimental details. Figure 13: Typical long-gauge strain time-history curves. The deflection distribution along the length of the beam at a certain time can also be calculated using Equation (7). Typical calculated deflection shapes of the beam at different times are demonstrated in Figure 15.  
Figure 14: Comparison results of the beam under single hammering. Figure 15: Calculated deflection shapes of the beam at different times. Excitation in terms of the sudden release of initial vertical displacement of about 60 mm was also exerted at mid-span. When the initial vertical displacement was removed suddenly, strain and deflection responses were obtained with the beam vibrating. Similarly, the deflection changing with time at any position on the beam can be calculated using strain responses. Take calculated deflection at 1/4 span, mid-span and 3/4 span as examples, the comparison results for the estimated and measured deflection are shown in Figure 16. The calculated time-varying deflection tallies with the test result from Figure 16. The relative errors for the maximum values of deflection at 1/4 span, mid-span and 3/4 span of the beam are below 5%. On the whole, the deflection accuracy under excitation of the sudden release of vertical displacement is slightly better than that under hammering. It can be explained that the beam under excitation of the sudden release of vertical displacement mainly vibrates at low-frequency, which results in the error between the measured average strain and actual strain being relatively smaller compared to the excitation of hammering. Figure 16: Comparison results of the beam under sudden release of initial displacement. Meanwhile, the beam was also excited by repeatedly hammering. Take the time-varying deflection at mid-span, for example; the comparison results between the calculated and measured deflection of the beam under multiple hammering are illustrated in Figure 14.0 It is clear that the beam was hammered nine times on the basis of peaks of the deflection time history.