Structural Health Monitoring Using Smart Sensors - ideals ...

8.3 ERA
ERA results during monitoring are summarized in Table 8.1. ERA on a PC using the
same data gives the same results numerically. Note that the structure has undergone some
structural changes since the data injected to Imote2 networks in Chapter 7 was acquired;
some of connections were tightened and some of elements were adjusted. The identified
natural frequencies in Table 8.1 are not necessarily same as those in Table 7.3. By
comparing the identified natural frequencies with the cross-spectral density plots in Figure
8.6, the identified natural frequencies are considered to well capture the dynamic
characteristics of the signals.
Table 8.1. Identification of Natural Frequencies and Damping Ratios
Natural Frequency (Hz) Damping Ratio (%)
20.7229 2.9321
32.8985 0.2127
41.2990 0.4846
64.3174 0.2422
69.1086 0.3718
94.9259 0.2810
8.4 DLV methods
The DLV method based on the mass perturbation and SDLV methods are applied to
the modal parameters identified before and after damage. The mass perturbation DLV
method, involving initialization to determine the mass normalization constants is first
examined. Subsequently, the SDLV method is investigated.
The mass normalization constants to be used in the mass perturbation DLV method
are first estimated. Imote2s are installed at nodes 7, 9, 11, 13, 15, 17, 19, 21, 23, and 25.
Measurements are taken before and after additional mass is attached to node 11. The mass
is 1.253 kg. All the nodes measure vertical acceleration. The node at the location of the
additional mass measures acceleration in the longitudinal and transverse directions as
well, because the denominator of Eq. (6.21) requires mode shapes at the degrees-offreedom
corresponding to the mass perturbation, i.e., acceleration in all three directions is
needed. Thus, acceleration is measured in 12 channels. The mass normalization constants
are estimated and listed in Table 8.2, as well as natural frequencies of the structure with
and without the mass perturbation.
The identified mass normalization constants are utilized to reconstruct the flexibility
matrix as shown in Eqs. (6.19) and (6.32). Imote2s monitoring sensor communities 1, 2,
and 3 reconstruct the flexibility matrices before and after element 8 is replaced with an
element of reduced cross-section. The Imote2s then perform an SVD on the difference in
the flexibility matrices to estimate the DLVs. The DLVs are then multiplied by a matrix to
convert nodal force to element stresses. Elements with small stresses are identified as
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