Civil Engineering Reference
In-Depth Information
Table 14.3
Mean MAC rms error for the suitability of three different measurement locations with parametric uncertainty
and different noise levels
μ
(MAC rms error)
No noise
40 dB
30 dB
10 dB
11 sensors
0.0334
0.0377
0.0670
0.1422
14 sensors
0.0332
0.0363
0.0580
0.1131
25 sensors
0.0039
0.0064
0.0247
0.0659
a
b
Fig. 14.4
Probability density function of the MAC rms error for 25 sensors with (
a
) no noise and (
b
) 10 dB of noise
element models numerically to simulate their consequences. The signal-to-noise-ratio (SNR) is employed as a measure of
the noise level. The SNR is defined as the power ratio between a signal (meaningful information) and the background noise
(unwanted signal).
P
signal
P
noise
SNR
(14.6)
¼
In this case the noise is added to the meaningful information from the OSP objective, i.e. added to the target mode shapes.
Different SNR levels are considered, from a low noise case (SNR
10 dB). In the ideal
case of no-noise the evolution of the MAC rms error for different sensor configurations show how this value improves when
the number of sensors increase. For this example, the EFI method was selected as the sensor placement algorithm and was
implemented for different numbers of sensors. The MAC rms error for the best sensor locations for each number of sensor
decreases when the number of sensors increases. If noise is present then the MAC rms error increases. Table
14.3
presents
the mean value for the MAC rms error for different noise levels and also for different numbers of sensors. Figure
14.4
represents the MAC rms error histograms if all DOFs are measured at the same time and for different levels of SNR.
40 dB) to a high noise case (SNR
¼
¼
