Structural Health Monitoring Using Smart Sensors - ideals ...

structural damage, the analysis to quantitatively relate the mode shape information to
structural damage is yet to be completed.
The dynamically measured flexibility matrix, calculated from the mass-normalized
mode shapes and modal frequencies, has been employed to determine structural damage.
By interpreting the physical meaning of the flexibility matrix, Toksoy and Aktan (1994)
observed that anomalies in the flexibility matrix can indicate damage even without a
baseline data set. Gao et al. (2005) reported that the flexibility matrix is estimated with
moderate accuracy using only a few lower modes, as opposed to the stiffness matrix (the
inverse of the flexibility matrix), which needs almost all of the modes. Though some
researchers insist that higher modes better indicate the damage due to their insensitivity to
support conditions and high sensitivity to local damage (Alampalli et al., 1992; Biswas et
al., 1990; Chowdhury, 1990; Lieven & Waters, 1994), estimation accuracy of these modes
is arguable. If adequate for the purpose, lower modes with more accurate estimation
would better suit SHM. The ability of the flexibility matrix to be estimated with only a few
lower modes is, therefore, advantageous. He and Ewins (1986), Lin (1990), and Zhang
and Aktan (1995) further studied flexibility-based SHM strategies. Deficient points of
these techniques include that the error due to the unmeasured modes and flexibility change
due to damage cannot be clearly separated, and that structural constraints such as
symmetry and connectivity have not been fully incorporated, though Doebling (1995)
conducted research to tackle this problem.
Matrix update methods offer another class of SHM methods. Structural characteristics
such as mass, stiffness, and damping are represented in matrix form and updated to be
consistent with the observation of the structure under consideration. As Doebling et al.
(1996) described, the objective function is numerically optimized to update the matrices
under constraints such as matrix sparsity, connectivity, symmetry, and matrix positivity.
Doebling et al. (1996) categorized matrix update methods as closed-form optimal matrix
update, sensitivity-based update, eigenstructure assignment, and hybrid matrix update.
Zimmerman and Kaouk (1994) introduced minimum rank perturbation theory (MRPT) to
the optimal matrix update problem; this approach has been published extensively (Kaouk
& Zimmerman, 1994, 1995; Zimmerman & Simmermacher, 1995; Zimmerman et al.,
1995). The limitation of these methods is that the rank of the perturbation is always equal
to the number of modes used in the computation of the modal force error. Also, the
number of degrees-of-freedom (DOFs) and type of FEM models can affect the final
results.
Wavelet transforms and analytical signals have been among popular data analysis
tools. Wavelet transforms are often used to extract features from complicated data.
Staszewski (1998) summarized the application of wavelet analysis for SHM. While
wavelet transforms provide flexible and powerful data analysis tools that can be used in
combination with other methods, the transforms do not possess a clear physical meaning,
as opposed to the Fourier transform. Feldman and Braun (1995) used an analytical signal,
which is a combination of the actual signal and its Hilbert transform, to get an
instantaneous estimate of the modal parameters. The analytical signal may not work when
more than one modal component exists in the signal. Features of nonstationary processes
are often analyzed with these tools.
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