International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
measurement technique. At each epoch, three repeat scans were
collected and averaged to produce one mean scan.
Figure 2. Concrete beam and the Riegl LMS-Z210.
5.3 Photogrammetric Results
Each photogrammetric epoch consisted of nine images from
around the front of the beam ensuring strong convergent
imaging angles. Photogrammetric adjustment was undertaken in
a similar fashion to the timber beam experiment. The stable
targets were used to define the datum in a free-network
adjustment. Several scale measurements were acquired using a
steel band. The RMS of the estimated coordinate precision of
the photogrammetric targets was +0. 2mm (160), +0.21mm (10)
and +0.09mm (16) for X, Y and Z respectively.
5.4 Derivation and Adoption of Beam Deflection Models
Unlike the timber beam, the two load points used for the
concrete beam experiment meant that it was divided into three
sections. Figure 3 is a schematic diagram of the concrete beam.
4
= yy + :
x (m)
support beam support
Figure 3. Schematic diagram for the concrete beam
The load points were situated 3m and 4m in from the left of the
beam. Eq. 5 is the model adopted for the concrete beam. A y-
term was included to cater for rotations about the x-axis in the
concrete beam. Results indicated that the beam carried
approximately 1.5? of rotation compared to the horizontal plane
of the reference frame.
7,(x) =a30x> +a gx +agy +391 9 0<x<3
2
z(x) 29(x)=bagx" +bj0*+boo *äo1Y 3<x<4 (5)
d<x <7
3 got d in
23(x)=C39x" +e20x" +E10* + Cop * 301"
5.5 Analysis of the Adjustment
The overall RMS of residuals was +2.5mm for the least-squares
estimation using a mean of 268 points. This is two times better
than the fit of the timber beam models using the LMS-Z210 and
most likely due to the extra terms. of the concrete beam
deflection functions making it more flexible when modelling the
data. The mean value estimated for the y-term from all 12 load
epochs was 0.027 +0.006 (unitless). The beam top tilt, revealing
itself as the gradient of the y-term, was more precisely
determined than in the timber beam experiment.
5.6 Statistical Testing of Estimated Parameters
The smallest critical value for all global tests was
F(0.01;11,188) = 2.39. The smallest computed global test
statistic (Eq. 3) is much greater than the critical value for all
cases suggesting that the models are adequate. However, there
are six instances where the individual test statistics for the cy
parameter are less than their respective critical value at a 1%
significance level. There is also one instance where the test
statistic for the a; term is less than its critical value (load case
6). For instances where the test statistic is less than the critical
value, the parameter does not have significant influence on the
model and it should be removed. Consequently, where required,
each model was revised and recomputed until all parameters
satisfied the individual parameter statistical test.
5.7 Vertical Deflections
Computation of vertical deflections was undertaken in a similar
fashion to the timber beam experiment. Planimetric coordinates
of 12 photogrammetric targets were passed through the
estimated models producing a height coordinate. The number of
targets varied depending on their visibility in the
photogrammetric images. Vertical deflections were computed
by differencing the height coordinates. Table 2 shows the
original differences for the entire | |-parameter model (Eq. 5).
The table also includes the RMS of differences for the revised
models and shows which parameters were eliminated.
The total RMS of differences has not changed despite using
models that have had terms removed. Load cases 6 and 10 have
actually (marginally) improved in accuracy. Load cases 1, 4, 9
and 11 are equivalent, or slightly worse, in accuracy compared
to the original | 1-parameter model.
6. DISCUSSION
It is unknown why the LMS-Z210 performed slightly better for
the second experiment (concrete beam). The imaging geometry
was similar in both instances whereby the TLS was 6.4m from
the (front, centre) of the timber beam with a zenith angle of
approximately 96°40’ and 7m from the front, centre of the
concrete beam with an zenith angle of approximately 96°17".
The only difference was that the concrete beam was outdoors
and the TLS was not set in front of the timber beam but offset to
one side. The mean size of the point clouds (of the beam tops)
were actually smaller for the concrete beam (mean of 268
points) compared to the timber beam (mean of 1099 points)
implying that the sample size was not the reason.
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