Structural Health Monitoring Using Smart Sensors - ideals ...

Figure 5.5. Effect of data loss and observation noise: acceleration power spectral density.
to simulate data loss. Data loss is assumed to take place only at this step, where the largest
amount of data is transferred among the sensor nodes.
Data is processed following each step of DCS. The impulse response functions
associated with each measurement points are estimated. Then the impulse response
functions are fed into the ERA routine for modal analysis. The natural frequency, damping
ratio, and mode shapes are among the major outputs. These modal parameters yield
flexibility matrix estimations. Then, one of the truss elements of the structure, element 9,
is replaced with a damaged element, which has a 40 percent cross-section reduction. Data
acquisition, impulse response estimation, modal analysis, and flexibility matrix estimation
are repeated on this data. From the estimated flexibility matrices for an undamaged and
damaged model, the DLVs are calculated. The accumulated stress, small values of which
indicate possible damaged elements, is then calculated. This simulation is conducted
assuming several data loss levels.
For the results of the data loss analysis to be better interpreted, the outcome is
compared to that of computer simulation including observation noise (but without data
loss). A band-limited white noise is superimposed onto each of observed signals. RMS
noise level is specified as a percentage of the RMS of physical responses.
The effect of data loss is first examined by comparing the PSD and coherence
functions of the measurement data. Figure 5.5 shows representative PSD functions
calculated with and without noise/data loss. The PSD’s peaks remain nearly unchanged
when the data loss or the noise is introduced; however, zeros are blurred. Although further
investigation is necessary for quantitative judgment, these results indicate that data loss of
0.5 percent and 5 percent observation noise have similar impact on PSD estimation.
Coherence functions indicate the degree of linearity between two variables. In this
computer simulation, the input excitation is applied only at node 11. Because the response
of the truss structure is linear, the coherence function between the two measurement
signals is expected to be unity over the entire frequency range. When no data loss and no
observation noise are considered, the coherence function is indeed close to one, as shown
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