Structural Health Monitoring Using Smart Sensors - ideals ...

10 0
10 -2
10 -4
0 500 1000 1500 2000
10 -12
10 -14
10 -16
0 500 1000 1500 2000
discrete sample point
Figure 7.1. FFT accuracy check (Number of FFT data points: 4,096).
Fourier amplitude |F|
Fourier amplitude
error ratio |F-F0|/|F0|
give numerically identical FFT results, considering that double precision data has about 15
effective significant digits.
The FFT on double precision data needs n B memory space to store the data to be
analyzed; the data is then replaced with the FFT result. The Imote2’s 256 kB of on-board
memory can hold about 32,000 double data points. If FFT is applied to a longer record,
larger RAM or virtual memory is necessary. Note that the Imote2 has 32 MB of RAM,
which can hold a large amount of data. At the time of this research, however, only 256 kB
of memory is accessible.
7.1.2 Singular value decomposition
Singular Value Decomposition (SVD) is a part of both the ERA and DLV methods.
While SVD in the ERA and mass perturbation DLV method are applied to real valued
matrices, the SDLV method may involve SVD of a complex matrix, depending on how
the observation matrix, C, is reconstructed through modal analysis. A double precision
SVD function for real matrices, as well as one for complex matrices needs to be available.
The source code for SVD of a real matrix is found in Numerical Recipes in C and
CLAPACK, while CLAPACK also provides source codes for SVD of a complex matrix.
First, the matrix is transformed to a bi-diagonal form using the Householder reduction.
The bidiagonal matrix is then diagonalized to obtain the singular values. The source code
from Numerical Recipes in C and CLAPACK are modified for implementation on the
Imote2.
The accuracy of the implementation is examined. The singular values of the matrix
are chosen as accuracy indicators; singular values of various magnitudes are inspected. An
arbitrary matrix is first constructed and decomposed by SVD on MATLAB. The singular
values are then replaced with a decreasing geometric series; singular values of this matrix
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