Structural Health Monitoring Using Smart Sensors - ideals ...

REALIZATION OF DCS FOR SHM
Chapter 7
The Distributed Computing Strategy (DCS) for SHM reviewed in Chapter 6 is
developed for the Imote2 sensor platform in this chapter. First, a number of requisite
functions, such as FFT and SVD, are developed and their accuracy limitations are
evaluated. DCS is then implemented and validated on a component by component basis.
7.1 Functions
DCS involves numerical operations that are not provided by a standard math library.
NExT estimates correlation functions using FFT and the inverse FFT. ERA applies SVD
to a matrix of real numbers, as in Eq. (6.9). Eq. (6.11) needs a complex eigensolver. If the
initial modal amplitudes need to be estimated to distinguish system and noise modes, the
inverse of a complex matrix is essential, as shown in Eq. (6.12). Sorting is also needed in
ERA, as modes are usually sorted by their natural frequencies. DLV methods involve
SVD and sorting. Furthermore, the SDLV method may require SVD on a complex matrix,
depending on formulation of an observation matrix, C . These functions need to be
implemented on the Imote2 to realize structural health monitoring applications.
Numerical Recipes in C (Press et al., 1992) and the CLAPACK User’s Guide
(Anderson et al., 1999) explain a variety of numerical functions. Necessary functions are
coded based on these references. Because the code and libraries need to be cross-compiled
for the Xscale processor on the Imote2, instead of the x86 processor on a PC, the codes in
Numerical Recipes in C or in CLAPACK cannot be directly used. Relevant files are
extracted and modified for use with Imote2 applications.
7.1.1 Fast Fourier Transform
Fast Fourier Transform (FFT) is essential for implementation of the NExT
algorithms. NExT uses the auto- and cross-correlation functions for the measured systems
as input. First, time histories are converted to the frequency domain using the FFT and
averaged to produce the power- and cross-spectral densities. The auto- and crosscorrelation
functions are then obtained by applying the inverse FFT. The Cooley and
Turkey (1965) algorithm, using the Danielson and Lanczos Lemma (Danielson &
Lanczos, 1942), enables FFT in ON
N
operations. Double-precision FFT available
as a part of Numerical Recipes in C (Press et al., 1992), is modified to be used on the
Imote2.
The numerical accuracy of the FFT implementation on Imote2 is examined by
comparing FFT results from the Imote2 with those calculated by MATLAB on a PC. A
band-limited white noise is generated as a signal to be analyzed, and the FFT is applied to
this signal. As seen in Figure 7.1, the FFT implementation on the Imote2 and on the PC
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