Structural Health Monitoring Using Smart Sensors - ideals ...

1.5 x10-17 Time (sec)
Difference in correlation function (g 2 )
1
0.5
0
-0.5
-1
-1.5
0 0.5 1
Figure 7.21. Difference in correlation function estimates.
7.2.3 ERA
The ERA method is implemented on the Imote2 using the previously developed
eigensolver and SVD functions. To study the validity of the implementation, the outputs
from ERA on the Imote2 are compared with those calculated on the PC.
While the algorithm is well-established as described in section 6.2, the algorithm
implementation on Imote2 is subject to memory limitations, necessitating cautious
consideration. One of the numerical operations requiring a large amount of memory is the
SVD of the Hankel matrix as shown in Eq. (6.9) . The number of columns and rows is
often in the hundreds. A Hankel matrix with more than a thousand rows is not uncommon.
The Imote2’s 256 kB of on-board RAM, however, is filled to capacity by a double
precision matrix of size . SVD of a matrix outputs two unitary matrices and a
vector containing the singular values, further limiting the size of the matrix to be analyzed
with ERA. In practice, some of the memory is already used by other variables, other
programs, and the OS. Therefore, the size of the Hankel matrix on the Imote2 is limited by
the available memory.
A Hankel matrix, occupying about 19 kB of RAM, is employed for
implementation of ERA on the Imote2. In general, a small Hankel matrix results in the
inclusion of more noise modes in the modal identification. To avoid missing physical
modes in modal identification, the number of nonzero singular values in Eq. (6.9) is
assumed to be larger than the expected number of physical modes. Envisioning
identification of the truss vibration modes in the frequency range lower than 100 Hz, the
ERA implementation assumes 28 singular values as nonzero. Among 14 identified pairs of
modes, those with a small modal amplitude coherence (Juang & Pappa, 1985) or with a
large damping ratio are considered to be noise and are eliminated. Even after this noise
mode elimination, modes that do not show clear peaks on the cross-spectral density plots
may still be present in the identified sets of modes. The Imote2 first estimates the peaks of
the cross-spectral density amplitudes as local maximums, and picks the ERA output
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