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“Epoch Maximum Number B Revised Eliminated
vertical of parameter model parameters
deflection Targets RMS RMS
(mm) (mm) (mm)
1 2.1 12 1:1 +1.3 C30
2 4.1 12 +0.9 +0.9
3 6.0 12 x37 137
4 8.0 12 t1 $1.7 C30
5 10.0 12 +2.4 +2.4
6 12.9 12 +23 x C30. Aj
7 0.9 11 252.1 +21
8 4.1 12 +12 +12
9 8.3 12 +2.0 +21 C30
10 13.2 B x32 +2.8 C30s A10
[1 28.8 12 127 +28 C30
12 48.3 11 £3.3 +35
Total RMS +2.4 +2.4
Table 2. Differences of vertical deflections between the LMS-
7210 and photogrammetry.
Most of the commercially available TLSs have a sufficiently
large vertical field of view permitting them to be positioned
high above the test structure or whatever the case may be.
Potentially, the TLS does not need to be levelled.
Measurements would be benefited by tilting the TLS towards
the structure. The critical factor is to maintain a stable
placement so that the TLS remains stationary for the duration of
testing. Despite the necessity of a thoughtful set up, both
experiments showed that it was still possible to successfully
measure deformation even though the imaging geometry was
suboptimal and scan data were scarce.
7. CONCLUSIONS
An analytical modelling approach was developed to detect and
measure vertical deformation. It involved representing the beam
with a compound polynomial containing parameters that have a
sound physical origin derived from first principles of beam
deflection mechanics. The solutions were found to suffer from
high parameter correlations.
Statistical testing of the significance of the estimated parameters
in the polynomial models proved an effective method of
removing insignificant parameters. All timber beam solutions
passed the F-tests. Testing of the parameters in the concrete
beam example revealed parameters that were not a significant
influence in the model. A revised model was created for those
cases and was compared to the photogrammetric benchmark
data. It was shown that the statistical testing of parameters could
be successfully used to remove redundant parameters without
compromising the accuracy of the model. These tests were
conducted, however, in relatively controlled conditions.
This modelling avoids the arbitrary nature inherent in some
other methods, such as gridding (Gordon et al., 2003b). The
sub-millimetre results for the Cyra Cyrax 2500 place it in the
Same accuracy league as close-range photogrammetry (at least,
for non-metric cameras). The perceived main advantage of
Photogrammetry over TLS is its high precision. The additional
advantages of TLS. however, include full surface representation
959
(as opposed to a few targets) and also a single set up geometry
that does not have an inherently weak dimension (as
photogrammetry has in depth). Furthermore, the reflectorless
nature of TLS does not require targets except for validation.
8. REFERENCES
Beer, F.P. and Johnston, E.R., 1992. Mechanics of Materials.
McGraw-Hill Book Company, Berkshire, England, 738 pages.
Fraser, C.S. and Edmundson, K.L. 2000. Design and
Implementation of a Computational Processing System for Off-
Line Digital Close-Range Photogrammetry. /SPRS Journal of
Photogrammetry and Remote Sensing, 55(2), pp. 94 - 104.
Gordon, S.J. and Lichti, D.D., 2004. Terrestrial Laser Scanners
with a Narrow Field of View: The Effect on 3D Resection
Solutions. Survey Review, 37(292), In press.
Gordon, S.J, Lichti, D.D., Chandler, L, Stewart, M.P. and
Franke, J., 2003a. Precision Measurement of Structural
Deformation using Terrestrial ‘Laser Scanners. In: Optical 3D
Methods, Zurich, Switzerland, 22 - 25 September, 8 pages.
Gordon, S.J., Lichti, D.D. and Stewart, M.P., 2003b. Structural
Deformation Measurement using Terrestrial Laser Scanners. In:
IHth International FIG Symposium on Deformation
Measurements, Santorini Island, Greece, 25 - 28 May, 8 pages.
Jacobsen, K., 1982. Attempt at Obtaining the Best Possible
Accuracy in Bundle Block Adjustments. Photogrammetria,
37(6), pp. 219 - 235.
Leica Geosystems, 2004. HDS2500 Specifications.
http://www.cyra.com/products/hds2500. specs.html — (accessed
23 April, 2004).
Lichti, D.D., 2004. A Resolution Measure for Terrestrial Laser
Scanners. In: /SPRS XX Congress, Istanbul, Turkey, 12 - 23
July, 6 pages.
Riegl, 2004. 3D Imaging Sensor LMS-Z2101.
http://www.riegl.com/Ims-z210i/e Ims-z210i.htm (accessed 23
April, 2004).
Stanton, J.F., Eberhard, M.O. and Barr, P.J., 2003. A Weight-
Stretched-Wire System for Monitoring
Engineering Structures, 25(3), pp. 347 - 357.
Deflections.
Zhong, D., 1997. Robust Estimation and Optimal Selection of
Polynomial Parameters for the Interpolation of GPS Geoid
Heights. Journal of Geodesy, 71(9), pp. 552 - 561.
9. ACKNOWLEDGEMENTS
The authors wish to thank Dale Keighley and Gerry Nolan from
McMullen Nolan and Partners Surveyors Pty. Ltd. (Perth,
Australia) for the use of their Cyra Cyrax 2500 and Dr lan
Chandler from the Department of Civil Engineering at Curtin
University of Technology, for organising the load tests.
