3.7 Practical implementation studies
3.7.1 Experimental study
An experimental setup has been devised to emulate an online damage and the current algorithm has been utilized to identify the instant of damage in real time (Fig. 3.14). The setup consists of an TH-1989_156104031
0 10 20 Time (s) 30 40 50
-0.5 0 0.5
Acceleration(m/s2 ) 1st DOF Acceleration
5th DOF Acceleration
RR-1
Y-Transf 4
Y-Transf 3
5.01 s 13.01 s 26.01 s 31.01 s 44.01 s
34 = 0.99 34 = -0.85
34 = 0.92
34 = 0.99
Damage occurs here
34 = -0.76
Figure 3.13: Residual error and scatter plots for El Centro excitation
Figure 3.14: Details of the experimental setup, courtesy [157]
aluminium beam of dimension 120cm×3.5cm×0.5cm fixed on a base plate which is drilled on top of a shake table (model no. Bi-00-300). The base plate is a welded structure of two plates at right angle butt weld having dimensions 23cm×15cm×1cmeach. The shake table specifications include:
(i) table dimensions- 150cm×150cm. (ii) payload capacity- 5tons. (iii) peak velocity- 153cm/sec.
(iv) peak acceleration- ±2.0 g. (v) frequency range- 0− 20 Hz. The model is subjected to an earthquake excitation and the acceleration data are collected using QuantumX MX410 HBMT M Data Acquisition System (DAQ) at a sampling frequency of 75 Hz. The aluminium beam model is instrumented using Honeywell accelerometers T EDS byHBMT M at four positions. The positions of the four accelerometers from the free end are 1cm, 30cm, 47cmand 81cmrespectively. The output TH-1989_156104031
acceleration plot obtained from the sensors is shown in Fig. 3.15. The free end of the cantilever beam is attached with a thin rubber strip (Fig. 3.14) which has a taut length of 70 cm and the other end of which is clamped rigidly on a heavy steel platform. This rubber strip induces a nonlinearity to the experimental setup. This model can be readily used to validate the accuracy of the proposed method as explained in the following segment.
0 5 10 15 20 25 30
Time(s) -1
0
1 Sensor 1
0 5 10 15 20 25 30
-1 0 1
Acceleration (m/s2 )
Sensor 2
0 5 10 15 20 25 30
-1 0
1 Sensor 3
0 5 10 15 20 25 30
-2 0
2 Sensor 4
Figure 3.15: Output acceleration plot obtained from experiment
In order to simulate earthquake response of the structure, scaled ChiChi ground motion is used.
A realistic case of damage employed in this study involves a change in the nonlinear state of the system, induced by snapping the rubber strip suddenly at a particular time instant. The snapping of the rubber strip accounts for an overall reduction in the stiffness of the model and is interpreted as damage to the system. The measurement of the instant of the snap is accurately done using a stop watch. To ensure that the time instant of damage is recorded accurately, the entire experiment is recorded in the form of videos. The recorded time of damage is exactly 33s. However, caution should be exercised in interpreting the event itself. Damage ideally should be an instantaneous phenomenon, the action of snapping action as observed after repeated trials of experimentation takes at least 0.5 to 1s. This small lag should be considered while calculating the damage instant.
Hence, it is safe to assume that there is an error of 0.5 to 1s in recording the time of damage. The real time streaming of data is acquired by the DAQ and then the RPCA algorithm is applied.
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Interpretation of the damage
To investigate the effect of the rubber strip on the response of the structure, the cantilever beam model with the rubber strip attached at its free end was excited using ChiChi earthquake scaled to different intensities (1.0 and 1.1 respectively). Fig. 3.16 shows the fourier spectra of the measured responses which clearly indicates a shift in the dominant frequency of the response obtained from the higher intensity excitation. The increase in the first modal frequency (of the order 12%) with the increase in the amplitude of the excitation reveals that a stiffening type of nonlinearity is induced in the aluminium beam by the rubber strip. As previously mentioned, damage in this case is inflicted by a sudden cut of the rubber strip at a particular instant of time, thereby reducing the stiffness of the structure in real time. To further validate this reduction, the Fourier spectra of responses of pre and post damage conditions are shown in Fig. 3.17. It can be clearly observed from the figure that there is a significant reduction (of the order of about 30%) in the first modal frequency of the damaged system as compared to the undamaged one.
0 5 10 15 20
0 0.002 0.004 0.006 0.008 0.01
X: 1.664
Y: 0.009721 a.) ChiChi Earthquake (Intensity 1.0) Response FFT Plot
Frequency(hz)
0 5 10 15 20
0 0.002 0.004 0.006 0.008
0.01 X: 1.854
Y: 0.008574
b.) ChiChi Earthquake (Intensity 1.1) Response FFT Plot
Frequency(hz)
Shift in frequency representing the stiffening effect of the rubber
Figure 3.16: FFT plots for response obtained from scaled versions of ChiChi earthquake
Experimental Results
The real time streaming data from the sensors are processed by the online algorithm to identify the instant of damage by utilizing a set of recursive CIs. The proposed algorithm is tested to TH-1989_156104031
0 5 10 15 20 Frequency (Hz)
0 0.005 0.01
Fourier amplitude
(a)
0 5 10 15 20
Frequency (Hz) 0
0.005 0.01 0.015 0.02
Fourier amplitude
(b)
Shift in frequency representing damage X: 1.2
Y:0.019
X: 7.891 Y:0.004521 X: 1.66
Y:0.008
X: 7.676 Y:0.007117
Figure 3.17: (a) and (b) Respective FFT plots of damaged state and undamaged states detect damage for an underdetermined case study as well. As previously discussed in section 3.6.3, an underdetermined case assumes a subset of sensor measurements available for online damage detection. Studies are carried out for the following cases:
1. Case 1: All the sensors available
2. Case 2: 3 sensors are available (this case considers the output from the sensors 1, 3 and 4) 3. Case 3: 2 sensors are available (sensors 1 and 4)
0 1 2 3 4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Principal Components
Cumulative Contribution(in %)
Figure 3.18: Contribution factor for PCs
For the first case, real time streaming data from all the sensors are made available to the RPCA algorithm. However, for the subsequent cases, the proposed algorithm assumes a reduced order TH-1989_156104031
Y transformed 1
t=10s
Cluster Plots at various times (case 3: 2 sensors)
t=15s
Y transformed 4
t=30s t=45s t=60s
Time(s)
0 10 20 30 40 50 60
0 0.05 0.1
0 10 20 30 40 50 60
0 0.1 0.2
0 30 60
χ RR-1
0 0.1 0.2
ρ14=0.67 ρ14=0.71
Case 3 - RRE using 2 sensor data
ρ14=0.51
Time(s)
ρ14= - 0.49 ρ
14= - 0.67
Case 2 - RRE using 3 sensor data Case 1 - RRE using all 4 sensor data
Time of damage identified at 33 sec
Figure 3.19: Recursive CIs for experimental trial
system, corresponding to the streaming data available from the number of sensors taken under consideration. Hence, RPCA algorithm produces eigen spaces corresponding to the reduced DOF.
Fig. 3.18 shows the cumulative percentage contribution of the PCs, clearly indicating that 2 PCs are sufficient to capture the dynamics of the present experimental setup, thus facilitating utilization of lesser number of responses (2 out of 4 in this case). Recursive CIs applied on the reduced eigen space provide indications of damage in the system, as shown in Fig. 4.13, for all the aforementioned cases. It can be seen from the figure that plots of χRR−1 ascertain the instant of damage at 33s for all cases which indicates the efficacy of the proposed algorithm to detect damage for a practical case where the number of sensors instrumented are less than the number of dof. The plots in Fig.
4.13 clearly indicate the instant of damage by showing a change in the level of RRE at 33sand then hitting a plateau region which is continued for the rest of the duration.
Scatter plots are considered for the final case where data from 2 sensors are made available as inputs to the algorithm. The scatter plots corroborate with the damage instant, showing a change in orientation at 33s, with justifies the ground truth. Although plots of RRE reveal some fair amount of activity before the instant of damage is reached, these are primarily due to the nonstationary nature of the input excitation and the proposed algorithm further substantiates the instant of damage with a change in orientation of scatter plots only at 33s, as clearly seen from Fig. 4.13. The percentage TH-1989_156104031
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.