Civil Engineering Reference
In-Depth Information
Fig. 9.6
Displacements
measured from point 03 to
point 07 in test 5 applying
pattern matching algorithm
03
04
05
06
07
8
6
4
2
0
8
10
12
14
16
time [s]
Fig. 9.7
Moduli of the
spectra of the bridge sag
computed at point 7: test 5
0.14
Edge
Pattern
Laser
0.12
0.1
0.08
0.06
0.04
0.02
0
2
4
6
8
10
12
freq [Hz]
It can be qualitatively noticed a higher noise level in the single point measure, as a consequence of the lower px to mm
scaling factor. The same conclusions can be derived by the comparison of the signal spectra estimated by the camera with
respect to the one measured by the interferometer at point #7 (Fig.
9.7
): as in the previous example, the camera based
approaches are correctly able to identify the peak frequencies but a higher noise level can be notice as a consequence of an
increased framed area.
Bringing attention to the measurement qualification, the Fig.
9.8
summarizes the results obtained from the tests, for the
position of #7; in the figure the RMS value of the discrepancy between the reference signal and the displacement estimation
is shown. The evaluation has been performed only for the time record corresponding to the train transit. The values are
plotted as a function of the image resolution in terms of the mm/px ratio. The data quantify the trend of the measuring
uncertainty with respect to the scaling factor. The results, as expected, show an increasing trend.
Figure
9.9
shows the RMS dynamic component (the standard deviation) and the RMS static component (the mean value)
which are related to the RMS value by the formula:
r
1
q
ðμðΔÞ
N
X
2
2
2
RMS
¼
Δ
¼
þ σðΔÞ
Þ
:
where
) are respectively the mean and the standard deviation of the discrepancies between camera and
reference signal in correspondence of a fixed target.
The analysis of the mean and standard deviation trends help to understand the RMS behaviour in Fig.
9.8
. The standard
deviation shows a clear linear increasing trend up to about 5 mm/px resolution value, whereas the mean takes random values
between
μ
(
Δ
) and
σ
(
Δ
0.20 and 0.20 mm. This means that the uncertainty linked to the dynamic component of the bridge vibrations is
strongly affected by the image resolution, whereas the uncertainty of the static measure of displacement due to the train mass
depends on the uncontrolled biased errors (mainly uncertainty in the mm/px ratio).
Finally, in Fig.
9.10
the mean and the standard deviations of the discrepancies between the interferometer and vision data
are shown in the case of no train on the bridge. The goal of this analysis is to analyse the uncertainty in this condition and
compare it with the measuring uncertainty obtained during the train transit. As it can be seen in Fig.
9.10
, the values and the
trend of the data match well with those of the previous figures. The conclusion is that the measurement uncertainty does not
