Issue 48

J. Prawin et alii, Frattura ed Integrità Strutturale, 48 (2019) 513-522; DOI: 10.3221/IGF-ESIS.48.49 518 closing crack in the structure. The nonlinear components are isolated using SSA and damage index is then computed for closing crack localization . Closing Crack Localization – two different test cases The simply supported beam is simulated with closing crack at two different spatial locations in order to illustrate the robustness of the proposed technique in localizing the closing crack present anywhere in the structure. The first test case considers the breathing crack located at element no, 4, while the second test case considers the breathing crack at element no.7. Both the test cases have the same crack depth equal to 7% of the total depth. The results of the damage index evaluated for these two varied crack locations is shown in Fig. 5 using the noise-free and noisy time history response (i.e. actual response polluted with 10% noise before processing) measured at varied locations spatially across the structure. It can be concluded from Fig. 5 that the maximum value of the damage index in both the test cases considered is at the damaged element of the beam even with noisy measurements. Figure 5 : Damage index based on SSA – 9 sensors. Figure 6 : Damage index based on SSA – 4 sensors. Closing Crack Localization with Limited instrumentation In order to investigate the effectiveness of the proposed closing crack localization approach with limited sensors, we have used the measurements obtained at 4 selective locations (i.e. at nodes 2, 4, 6, 9), identified using the popular Effective Independence optimal sensor placement technique [10]. The results of the damage index, obtained with limited measurements for the above damage cases of Fig. 5 is presented in Fig. 6. It can be observed from Fig. 6 that the maximum value of the damage index is at node no.4 for the case of damage simulated in element no.4. The maximum value of the damage index for the case of damage simulated in element no. 7 is at node no.6, which is close to the nodes 7-8 (i.e. element no. 7). Therefore, with limited instrumentation, the closest possible spatial location of damage can be identified, while with more sensors, the maximum value of damage will be occurring exactly between the two closely spaced nodes corresponding to damaged element (i.e. peak at nodes 7-8 in the case of damage at element no. 7, as evident from Fig. 5). This investigation clearly concludes that the proposed algorithm has the ability to localize the closing crack even with limited measurements. Comparison with Previous work In order to demonstrate the effectiveness of the proposed algorithm in identifying smaller and subtle cracks, the results of the proposed damage index are compared with the previous vibration based breathing crack identification techniques based on only first few super harmonics [6-8]. The various damage indices given in the reported relevant research work in the literature are summarized as follows 1 1 2 2 1 1 1 1 1 2 1 1 2 i=1,2,3,...N; 2 i=2,3,...N-1; X X n i jω j i i ω i i i i i i A ( DI ) ; A ( DI ) ( DI ) ( DI ) ( DI ) d (( DI ) ); d (( DI ) ) h          (3)