10 Indirect Bridge Health Monitoring Using Time-Frequency Analysis: Analytical and Experimental Studies 95 Fig. 10.2 Proposed methodology was experimentally verified by [23]. To identify the beginning and growth of micro-damage in concrete, the energy change rate of the wavelet packet was calculated and defined as a criterion for micro-damage initiation. The results revealed that a larger wavelet packet energy change rate corresponded to a larger distribution area of micro-damage. 10.3 Methodology In this section, the proposed methodology and the steps involved in analyzing the data are discussed. The proposed method includes indirect monitoring, acquisition of vehicle measurement, and post-processing of the measured data. In Fig. 10.2, the data is collected from the vehicle containing the contributions of the vehicle and the bridge. After the data acquisition step, WPT is used for signal processing and to decompose the signal into its simpler components. The output of this step includes driving frequencies, bridge frequencies, and vehicle frequencies. In the next two sections, the proposed approach is verified using experimental data. 10.4 Numerical Investigation A coupled VBI system is simulated using Eq. 10.2 and the model shown in Fig. 10.1. Consider a simply supported beam subjected to a vehicle moving at speedυ. The mass and stiffness of the vehicle are 1200 kg and 500 kN/m, respectively. The simply supported beam has a length of 25 m and a mass density of 4800 kg/m. Young’s modulus of elasticity, E, for the beam is 2.75 ×1010N/m2, and moment of inertia, I, for the beam is 0.12 m4. Figure 10.3 shows the Fast Fourier Transform (FFT) of the vehicle acceleration response traveling at a speed of 40 km/h. The first frequency peak in this figure corresponds to the driving frequency, and the second and third frequency peaks represent the bridge frequency terms. The fourth frequency peak in Fig. 10.3 represents vehicle frequency, and the last two frequency peaks represent the second pair of bridge frequencies. As the dynamic response of the bridge is measured through the vehicle, the resultant is a pair of bridge frequencies, and the bridge frequency can be calculated by averaging the two values. The signal is processed through the WPT, which decomposes it into wavelet coefficients, shown in Fig. 10.4. It can be seen that the WPT algorithm can efficiently decompose the signal into its components. Driving frequencies, bridge frequencies, and vehicle frequencies are well separated using WPT. Figures 10.5 and 10.6 show the FFT and WPT results, respectively, for a vehicle traveling at a speed of 60 km/h over the bridge. It can be noted that WPT can decompose the frequency peaks from Fig. 10.5 into distinct individual peaks, which can be further classified into bridge frequencies, vehicle frequencies, and driving frequencies. 10.5 Laboratory Experiment A scaled vehicle bridge interaction model is built to investigate the viability of the indirect bridge monitoring approach. The bridge model used in the experiment is a 2.4 m simply supported wooden beam shown in Fig. 10.7. The bridge is instrumented with accelerometer sensors at the mid-span to collect the bridge response during the vehicle crossings shown in Fig. 10.8. The parameters for the bridge are shown in Table 10.1. A two-axle vehicle, shown in Figs. 10.7 and 10.8, is selected to travel across the bridge at a speed of 2 m/s. The vehicle is remotely controlled using a smartphone during its multiple passages over the bridge. An accelerometer sensor is mounted under the vehicle between the two axles to collect the vibration response of the vehicle shown in Fig. 10.8. A sampling frequency of 200 Hz is used for both sensors used in this
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