3.7 Practical implementation studies
3.7.2 Case study of the UCLA Factor building
change in global RREs for the experimental trial are shown in Table 3.4. It is worth noting from the table that the percentage change in RRE decreases (from 57.39% to 33.33%) with the decrease in the number of sensor data available as input to the algorithm. However, it should be noted that the algorithm is able to detect global damage in real time with a reasonable degree of accuracy even when the number of sensors is reduced down to 2 (which corresponds to a 33.33% change, as reported in Table 3.4) from the original set of sensor data input. The case studies validate that the proposed algorithm is well equipped to handle an underdetermined practical scenario where the number of sensors instrumented in the system are less than the actual number of DOF of the structure.
Table 3.4: Global RREs for experimental case
Damage cases Pre-damage RRE Post-damage RRE % change
Case 1 0.04 0.09 57.39
Case 2 0.07 0.13 46.71
Case 3 0.11 0.17 33.33
It is important to note that a lot of experimental setups have been devised in recent times to demonstrate damage detection strategies. In the present work, an effort has been made to create damage as a manifestation of nonlinear change in state that happens in real time amenable towards demonstration of online damage detection strategies.
modal identification and the results are reported in some published works [63]. To test the efficiency and damage detection capability of the proposed algorithm, a combination of floor accelerations due to ambient data and data recorded during the event that occurred on September 28, 2004, 10:15 AM PDT, due to ground shaking originating (with M= 6.0 on the moment magnitude scale) from Parkfield, CA, are considered.
0 300 600
−1 0
Roof acceleration data (EW component)
0 100 200 300 400 500 600
−0.5 0 0.5
Time (s)
Acceleration (in g)
5th floor acceleration data (EW )
Figure 3.20: Roof and 5th floor acceleration responses for UCLAFB in EW direction
The acceleration data at roof and fifth floor in EW direction is shown in Fig. 3.20. As seen from the figure, there is a considerable incidence of nonstationary activity in the vicinity of t=380s which indicates the onset of the Parkfield earthquake (magnitude of Mw=6.0). The data prior to the occurrence of the earthquake corresponds to ambient vibration regime which is evident from Fig.
3.20. The instant of shaking as well as the instant of maximal structural change can be estimated from the temporal RRE (χRR −2) plots for the N −S and E−W components responses. Upon a close analysis of the data, it could be easily inferred that the system response deviates from the ambient level at around t=380s, while the pronounced damage occurs at around t=410s. It is normal to expect these two instants to be different from each other because it takes a finite time for the structure to undergo significant changes (i.e. alteration of stiffness).
Previous modal identification studies on UCLAFB [63] show 14.31%, 13.95%, 15.61%, 8.49%, TH-1989_156104031
0 100 200 300 400 500 600 0
0.05 0.1 0.15 0.2
Time(s) χ RR2(t)
0 100 200 300 400 500 600
0 0.05 0.1 0.15
Start of shaking RRE EW
RRE NS
Major Damage
Figure 3.21: Residual error plots for UCLA in EW and NS directions
7.24%, 4.95%, 4.95%,30%, 6.5%, 4.75% percentage reduction in the values of identified frequencies between ambient vibration and earthquake data, which indicates significant global reduction in stiffness values. In the present context, global damage is expressed through percentage change in the average spatial RRE values (i.e. ∆hεRR−Yii using Eqn. 3.18) between the ambient and earthquake regimes corresponding to pre and post damage scenarios. Fig. 4.15 shows the plot εRR −Yi for a few representative floors. It can be observed from the figure that εRR −Yi deviates from the ambient regime at around t=380s and significantly in the vicinity of t=410s indicating the occurrence of damage. The percentage change in post damage RRE and pre damage RRE (i.e.
∆hεRR−Yii) for each floor as shown in Table 3.5 which indicates the appearance of damage not only at a single floor but the system as a whole which corroborates to the previously mentioned results on modal identification [63].
As mentioned in the previous sections, the proposed algorithm is well equipped to solve an underdetermined system which illustrates its ability to handle practical scenarios as well. In this context, responses from only the odd numbered dof are made available as input to the algorithm, closely emulating a practical underdetermined system where it is not feasible to instrument all the dof. Fig. 3.23 shows that χRR−2 clearly indicates the instant of damage even without processing the data from all the DOF, compared to Fig. 4.15 where the response from all the dof were made available to the algorithm.
TH-1989_156104031
310 340 370 400 430 460 490 Time(s)
0 1 2 3
RR-Y i
RR-Y
3 RR-Y
6 RR-Y
8 RR-Y
12 RR-Y
15
Figure 3.22: Residual error plots for floors of UCLA
Based on the results of application of the proposed RPCA based online damage detection method to practical scenarios, it can be safely concluded that the proposed framework is quite robust in de- tecting the instant of damage online. However, on the downside, the method still requires improve- ment as far as simultaneous spatio-temporal damage detection is concerned especially for practical nonstationary excitations. Although the present algorithm achieved significant success in detecting spatial and temporal damage simultaneously in simulation scenarios, the combined presence of am- plitude and frequency domain nonstationarities in excitation still poses challenges in simultaneous spatial and temporal detection of damage especially in field implementations, which is kept as a future work to be addressed by the author.