APPLYING THE LINE FOLLOWING ALGORITHM IN THE CALCULATION OF THE
TENSION STRENGTH OF STAY-ROPES OF TOWERS
Janusz Cieslar
Department. Photogrammetry and Teledetection, AGH-University of Science and Technology, al. Mickiewicza 30,
Kraköw wislan@agh.edu.pl
Commission V, WG V/1
KEY WORDS: Algorithms, Semi automation, Non-metric, Real time, Digital, Computer, Close range, Orientation
ABSTRACT:
A computer system for the determination of the tension strength of a stay-rope has been elaborated. The tension strength in stay-
ropes of towers needs to be calculated to approve its verticality and to verify the safety of its exploitation. Traditionally, this was
done by means of time consuming methods such as an analog close-range photogrammetry or by means of the theodolite. I present a
new approach to this task. The presented technology uses digital images and the computer in order to speed up the elaboration time.
It uses the Kodak DCS 760 camera and a laptop as tools. As pictures are taken by a free-orientated, non-metric camera, an
appropriate approach to camera orientation should be adopted. 1 suggest doing this by means of a projective planar transformation,
which requires at least four control points. The shape of a freely dangling rope is determined by its tension strength. The catenary
equation is used for modeling the shape of the rope. The line following algorithms have been developed for semiautomatic line
measurement with sub-pixel accuracy (three points should be placed on the screen by the operator before algorithms can start). As a
result, the positions of thousands of points are determined. It gives a more reliable shape of the rope and allows more reliable
statistical estimation and evaluation of the results. Catenary parameters are calculated by means of the Least Square Method. As an
example, the system was tested on a test field and the results were compared to traditional methods. The obtained results seem to be
promising. A fully operable system is now ready to be used. Similar systems, based on line following algorithms but designed for
different tasks, such as the determination of fabric chimney rectilinearity, may also be claborated.
l. INTRODUCTION
At present, there is a widespread use of digital images in
close-range photogrammetry.
There exist a number of advantages of a digital sensor, some of
which are a high dynamic range (the ratio of the maximal signal
coming from a sensor to the noise) and radiometric
resolution[1]. À digital image is an ordered collection (a two-
dimension matrix) of small, square-shaped elements. One of the
important features of digital images, crucial for the realisation
of this project, is the possibility to carry out automatic analyses.
Automatic analyses are carried out for the purpose of extracting
useful information from the image. Extracting geometrical
information from an imaged object is extremely common in
modern digital photogrammetry. | Many automation
measurement processes used for DEM determination [2], aero
triangulation, and interior orientation are based on digital
images. In the project I have developed, automatic
measurement has also been introduced. Semi-automatic line
following algorithms for measuring the image of stay-ropes of
towers have been developed. An integrated computer system for
the semi-automatic calculation of the tension strength of stay
ropes of towers has been elaborated.
The main disadvantage of using digital images is that the
geometric resolution of the sensor is still not sufficiently
developed. To improve the precision of automatic measurement
and the quality of the final product, sub pixel measurement is
usually applied. Sub pixel precision for the line following
algorithms elaborated for this project has been introduced.
2. CONCEPTUAL ASPECTS
2.1 Theory
A drilling tower needs stay ropes to maintain its stability
and verticality. The ropes are set in at least three directions with
a 120° angle between them. Every stay rope has to be pulled out
with proper tension strength. The conditions are as follows:
tension strengths have to be equal to each other and their value
should be kept at a proper level.
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Figure 1: Definition of a catenary parameters, X, Z — a rope
plane coordinate system, x, z — a catenary coordinate system.
Strength should be checked every some period of time to
ensure the safety of the exploitation of the tower. There are
three methods which are used most often. The dynamometric
method based on the geodetic survey method, and the
photogrammetric method [6]; however, only the last two are
uscful in practice. The photogrammetric method’s significant
advantage over the geodetic survey method is its short
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