smart technologies for safety engineering

VDM-Based Health Monitoring 49
μ A i
1
0.8
0.6
0.4
0.2
0
true defect
identified (with noise)
identified (without noise)
1 3 5 7 9 11 13 15 17 19 21 23 25
element no.
Figure 3.8 Identification of parameters μ A i
for pure and noisy data
A = 0.660 cm 2 and two lengths L1 = 0.5 m and L2 = 0.71 m. To join the structural elements
26 nodes have been used. Four nodes serve as supports – two of them cannot move in the
horizontal plane (out-of-plane rotations are allowed) while the other two can freely slide along
(rotations are also allowed). The overall dimensions of the truss are 4 m length, 0.5 m width,
0.35 m height.
Harmonic excitation is realized by a piezo-actuator in the middle of the structure (see the
lower left corner in Figure 3.10(a)). A piezo-patch sensor (see Figure 3.10(b)), supposed to
measure axial strain, is glued to each element. As some problems occurred with the strain
sensors due to inappropriate adhesion, 22 accelerometers in every node of the truss structures
have also been mounted. The identification problem was reformulated to handle vertical
acceleration measurements; i.e. the objective function was expressed in terms of accelerations.
First, the stage of tuning the numerical model to the experiment was completed. This was
achieved for the frequency of excitation ω = 35 Hz, just below the first natural frequency of
the structure. The material data adopted for the numerical model are Young’s modulus E =
205 GPa and density ρ = 7850 kg/m 3 . Figure 3.11(a) shows vertical acceleration amplitudes
in all 22 nodes measured in the experiment and modeled numerically for the intact structure. The
biggest deviation is around 20 %, so in order to have good correspondence with experiment, just
eight measurements were preserved. In this way, the deviation of the model from experiment
is reduced to less than 3 % (see Figure 3.11(b)).
From a purely mathematical point of view, if just one excitation frequency is dealt with,
a sensor in every element suspected of damage is needed. Otherwise the quasi-static inverse
μ J i
1
0.8
0.6
0.4
0.2
0
true defect
identified (with noise)
identified (without noise)
1 3 5 7 9 11 13 15 17 19 21 23 25
element no.
Figure 3.9 Identification of parameters μ J i
for pure and noisy data