46 S.A. Ravanfar et al. Table 6.1 GA variables Variable name Range Optimized value in tested beam Daubechies order DB1–DB31 DB2 Decomposition level 2–7 5 3 30 66 0 2 4 6 8 10 12 14 1 3 5 7 9 11 13 15 Depth of damages (mm) RWPE Locations Fig. 6.2 Histograms of damage indictors in beam 3 with DB2 6.4.2 Results and Discussion To validate the proposed damage detection method, the simulated simply-supported beams with damage elements were considered. Fig. 6.2 shows the values of damage indicators calculated according to Eq. (6.7). By running the GA, DB2 and level 5 were selected as the best values for the Daubechies order and decomposition level, respectively. Results have illustrated that the damage locations can be accurately determined from the measured time history acceleration responses through variation of damage indicators. In addition, the respective amplitude levels of the histograms can be used as a criterion to identify severity of damage, although not quantitatively. 6.5 Experimental Verification Most modal-based damage features such as natural frequencies, mode shapes, modal strain energy and modal flexibility are sensitive to noise and measurement errors, which results in difficulties for practical applications. Therefore, the proposed damage detection method should be verified with real measurement data from dynamic tests on structures where noise and measurement errors are present. To illustrate the proposed algorithm, the vibration tests were performed on the steel beam with a span length and different damage scenarios, as shown in Fig. 6.3. Sixteen accelerometers were mounted on the top flange along the beam to measure the acceleration response with a sampling frequency of 2000 Hz for all signals. 6.5.1 Experimental Results From the results, the following observations can be made based on the structural response signal of damaged beam. By running the GA, Daubechies order 2 and decomposition level 6 were chosen as the best parameters for the adjustment of the algorithm for differentiating the damages, as shown in Fig. 6.4. The damage location at position 5 could be precisely identified with the significant change in values of damage indicators. The results have demonstrated that for different wavelet-based methods, the choice of the mother wavelet function is of paramount importance to improve the performance of the algorithm.
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