Structural Health Monitoring Using Smart Sensors - ideals ...

utilized in SHM applications followed by modal analysis. Nagayama et al. (2007) has
discussed the effects of synchronization errors on these estimates. Time synchronization
accuracy realized on the Imote2, the smart sensor platform employed in this research, is
then estimated and evaluated for the SHM applications. Because time synchronization
among smart sensors does not necessarily offer synchronized measurement signals, issues
critical to synchronized sensing are then investigated. Finally, synchronized sensing is
realized utilizing resampling (Nagayama et al., 2006a; Spencer & Nagayama, 2006).
5.3.1 Time synchronization effect on SHM applications
Consider the signal xt from a smart sensor in the local clock coordinate t . This
signal can be written in terms of the reference (or global) clock t as
xt =
x + t – t
(5.4)
where t is the initial time synchronization error and is the clock drift rate. In the frequency
domain, this relationship is expressed as
X
------------ –
(5.5)
+
i ------------
t
= X ------------
+
+
where X and X are the Fourier transform of xt and xt , respectively. In the
following derivation, is assumed to be zero.
The effect of time synchronization errors on modal parameters, such as the natural
frequency, damping ratio, and mode shape, are examined. Though only output
measurements can be obtained during most of the civil infrastructure monitoring, for
completeness, the effect of time synchronization error is investigated both for the inputoutput
measurement case and the output-only measurement case.
When both input force and output structural responses are measured, transfer
functions from input to output signals are first estimated and then modal analysis follows.
Therefore, the effect of time synchronization error on transfer function estimates is
studied.
Consider a structure for which the equation of motion is written as
Mx·· t
+ Cx· t + Kx
t = f
t
(5.6)
where M, C, and K are mass, damping, and stiffness matrices, respectively. x
t , x· x·· t ,
t , and f
t are the displacement, velocity, acceleration, and input force vectors,
respectively. By taking the Fourier transform of Eq. (5.6), the displacement vector can be
written as
X = – M + Ci + K – F
=
T FX
F
(5.7)
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