Structural Health Monitoring Using Smart Sensors - ideals ...

used for SHM applications, transfer and processing of this large amount of data need to be
well-planned.
5.1.2 Model-based data aggregation
The amount of data involved in SHM applications normally exceeds practical
communication capabilities of smart sensor networks if all of the measurement data needs
to be collected centrally; data aggregation has been an important issue to be addressed
before an SHM system employing smart sensors is realized. One approach to overcome
this data aggregation problem has been an independent data processing strategy (i.e.,
without internode communication). This approach, however, cannot fully exploit
information available in the sensor network. Distribution of data processing and
coordination among smart sensors play a central role in addressing many smart sensor
implementation issues, including data aggregation. This section will demonstrate that
distribution and coordination can be well-planned so that the data aggregation problem is
addressed without sacrificing performance of the SHM algorithms.
The auto-correlation and cross-correlation functions are the inverse Fourier transform
of the PSD and CSD functions, respectively; their estimation is the beginning step of
many output-only SHM algorithms. CSD estimation requires data from two sensor nodes.
Measured data needs to be transmitted from one node to the other before data processing
takes place. Associated data communication can be prohibitively large without careful
consideration of the implementation. Distributed estimation of correlation functions is
proposed in this section.
Correlation functions are, in practice, estimated from finite length records. PSD and
CSD functions are estimated first through the following relation (Bendat & Piersol, 2000):
Ĝ xy
=
n d
-------- X
n d
T i
Y i
i =
(5.1)
where Ĝ xy is an estimate of CSD G xy
between two stationary Gaussian random
processes, xt and yt . X and Y are the Fourier transforms of xt and yt ; *
denotes the complex conjugate. T is time length of sample records, x i
t and y i
t . When
n d
= , the estimate has large random error. The random error is reduced by computing
an ensemble average from n d different or partially overlapped records. The normalized
RMS error
Ĝ xy
of the spectral density function estimation is given as
Ĝ xy
=
------------------
xy
n d
(5.2)
xy
=
G xy
-----------------------------------
G xx
G yy
(5.3)
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