Structural Health Monitoring Using Smart Sensors - ideals ...

measurement or mass perturbation can be greatly simplified with the SDLV method. The
SDLV method is briefly reviewed in this section.
Bernal (2006) stated that the null space of the change in the flexibility matrix will be
contained in the null of Q T . The matrix Q T is the transpose of the change in Q which
is defined as follows:
Q = – CA – p
+
H † p L
(6.33)
H
CA – p
p
=
CA – p
(6.34)
L
=
I
(6.35)
where I denotes identity matrix, denotes a zero matrix. p = 0, 1, or 2, depending on
whether the measured outputs are displacement, velocity, or acceleration. The system
matrix A and observation matrix C are determined through modal analysis such as ERA.
The null vectors of Q T are treated as DLVs.
Bernal (2006) also proposed a way to determine the number of DLVs and to combine
information from multiple DLVs. When there are q DLVs and the stress corresponding to
each vector is j
, a normalized stress index (nsi) is defined as follows:
j
nsi j
=
--------------
j max
(6.36)
Weighting can be incorporated to yield a weighted stress index (WSI) as
WSI =
q
j=1
j
nsi j
(6.37)
where is a weighting parameter. Potentially damaged elements ( PD ) are chosen as
j
PD = elements|WSI
tol
(6.38)
Bernal (2006) took j = and tol = 0.1 WSI max
. The number of DLVs, q , can be
estimated as
q = # of values
=
s i
------------
s j max
(6.39)
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