Structural Health Monitoring Using Smart Sensors - ideals ...

From Eq. (6.26), one obtains
F
V
=
(6.27)
Eqs. (6.23) and (6.27) indicate that L = V
, i.e., DLVs can be obtained from the
SVD of the difference matrix F
. In Eq. (6.24), because of noise and computational
errors, the singular values corresponding to V
are not exactly zero. To select DLVs from
SVD results of the matrix , Bernal (2002) proposed an index svn defined as
F
svn i
=
s i c
-------------------------- i
max s k c k
k
(6.28)
where s i
is the i-th singular value of the matrix F
; c i
is the constant that is used to
normalize the maximum stress in the structural element, which is induced by the state load
c i
V i
, to have a value of one; and V i
is the right singular vector of F
.
Each of the DLVs is then applied to an undamaged analytical model of the structure,
and the stress in each structural element is calculated. If an element has zero normalized
accumulative stress, this element is a candidate damaged element. The normalized
accumulative stress for the j-th element is defined as
j
=
j
k
----------------------
max
k
(6.29)
where
j
=
abs
n
i=
----------------------- ij
max i
k
k
(6.30)
In Eq. (6.30), ij
is the stress in the j-th element induced by the i-th DLV; j
is the
cumulative stress in the j-th element. In practice, the normalized accumulative stress
induced by DLVs in the damaged elements may not be exactly zero due to noise and
uncertainties. A reasonable threshold should be chosen to select damaged elements.
6.4 Distributed Computing Strategy for SHM
Gao (2005) proposed the Distributed Computing Strategy (DCS) for SHM employing
the algorithms reviewed in previous sections of this chapter. In this approach, a hierarchy
of local sensor communities is organized, so that the data does not need to be centrally
collected or analyzed. Because these algorithms are applicable to data only from nodes in
a local sensor community, the analysis can be performed within a local sensor community
independent of the other nodes; data from a given community is processed within the
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