Structural Health Monitoring Using Smart Sensors - ideals ...

where s j
are the singular values of Q . Bernal (2006) demonstrated that the proposed
WSI successfully indicates damage in a numerical truss structure.
6.6 Extension of DCS for SHM with the SDLV method
The SDLV method simplifies DCS for SHM. The SDLV method does not require
normalization constant estimation, eliminating the need for initialization with input force
measurement or mass perturbation. The derivation does not assume response
measurement at locations distributed over the entire structures. Structural responses are
measured only within local sensor communities before and after damage, and the SDLV
method is applied subsequently.
There are several ways to construct the system matrix A and the observation matrix
C. The triple D – 1/2 P T H rs
QD – 1/2 D 1/2 Q T E E T PD 1/2 , determined in ERA is a
m p
minimum realization of the system; the first and third terms can be used as A and C.
However, in practice, the triple may contain noise modes. Another way to formulate A
and C matrices is to use modal parameters, i.e.,
A = diag
n
n
(6.40)
C
=
1
2
n
1
2
n
(6.41)
By selecting modes to be used in Eqs. (6.40) and (6.41), only specified modes contribute
to the matrices. C can also be formulated as
C
=
1 2 n
(6.42)
assuming the observed variables are the real part of the outputs. Following this
formulation, Q T becomes a complex matrix yielding complex DLVs and stress field.
The absolute value of the complex stress induced by complex DLVs is used as j .
Numerical simulation showed the C matrix formulation in Eq. (6.42) gives more accurate
damage detection results than that in Eq. (6.41). One explanation is that the imaginary
parts of the C matrix in Eq. (6.41) are cancelled out in Eq. (6.33), losing certain
information; the C matrix from the other formation maintains the information from the
imaginary part. In the subsequent chapters, the formulation in Eq. (6.42) is utilized.
6.7 Summary
Algorithms to be implemented on smart sensors are briefly reviewed in this section.
DCS for SHM is proposed as an algorithm enabling distributed SHM employing densely
deployed smart sensors. DCS is extended with the SDLV method to eliminate the need for
input force measurement or mass perturbation during the initialization. In the next chapter,
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