The observation and analysis of movements of large structures, man-made as well as natural
ones, such as high-rise buildings, dams or rock slides and earthquake zones, is a highly
responsible task in engineering. Deformation monitoring is essential to public safety by
reducing the risk of structural failure. It is also an important aid in the understanding of
the behaviour of certain natural phenomena like glacial drift.
The procedure for a deformation analysis can be divided into three steps: a global congruency
test to determine in which epochs deformations occur, the localization of the deformed
points and the determination of deformations. The single-point analysis typically used in
the localization step, requires the two epochs under comparison to refer to the same datum.
If this is not the case an S-transformation to a common datum has to be carried out. This is
only possible however, if both epochs share the same reference frame, and particularly, the
same network scale.
In this dissertation a generalized model for a congruence analysis is proposed which allows
the coordinates to refer to di fferent reference frames. This model utilizes a combinatorial
search for the largest similar point group based on the angular di fferences between epochs.
This is combined with a 3D Helmert transformation that allows to derive deformations
directly from the adjusted coordinates of each epoch and their, typically singular, cofactor
matrices, independent of the coordinate system they are given in.
A set of computer-based simulations are carried out to evaluate the performance of the proposed
algorithm. The computer simulations reveal that the proposed algorithm can reliably
locate the largest similar point group between epochs. The transformation parameters as well
as the deformations are accurately recovered. Finally, a real-world application, the Frank
Slide /Turtle Mountain, is presented where the proposed methodology was applied.