Integrated Time-Space Modelling of Deformations

When designing and conducting engineering geodetic core tasks like geometric quality assurance or deformation analysis, measurement methods allowing a space continuous geometric acquisition of artificial or natural measurement objects move currently into focus. Some examples are the terrestrial laser scanning (TLS), the ground based radar or the imaging tacheometry. The fundamental prerequisite for exploiting the added value of the resulting space continuous geometries is the development of appropriate models to integrate the measurement methods into engineering geodetic processes. Usually, in geodesy a distinction between measurement models and geodetic models is made. The former are used to correct the measurement result from an instrument-specific and a physical point of view as well as to describe its uncertainty. The latter is based on the measurement model and relates the respective results by means of physical and mathematical equations to parameters being of interest. The project Integrated time-space modelling based on correlated measurements for the determination of survey configurations and the description of deformation processes (IMKAD II) deals with those models development for the case of TLS point clouds, taking into account the results of the preceding project. The project aims to describe the measurements uncertainty of the acquired point clouds by means of extended variance covariance matrices, allowing a realistic space continuous modelling of the measurement objects geometry. These models form the basis for a statistically based identification and description of potential changes arising between the two measuring epochs. The point clouds mathematical modelling is based on freeform surfaces like B- splines. The developments of the preceding project already allow a modelling of single point clouds using these surfaces. However, a statistical comparison of the geometries is not yet possible. Thus, the determination of comparable B-spline surfaces using a joint estimation of control points and surface parameters while taking into account the stochastic information is one of the projects innovative core items. The projects key research hypothesis is the statistically based identification and description of space continuous deformations using the B-splines surface parameters which define the surfaces inner geometry. Firstly the approach to be developed is used to determine the objects overall translation or rotation (rigid body movement); secondly additional strains are localized and qualitatively described. The deformation types separation is realized using statistically based hypothesis tests. The developed methods for point cloud modelling and for deformation analysis are assessed in two ways. On the one hand, they are validated by means of nominal values; on the other hand an evaluation is performed using methods which represent the state of the art. Because of the integrated stochastic information, the developed method can be investigated regarding its attainable precision. A further evaluation happens by a nonlinear sensitivity analysis which is used to investigate the methods sensitivity to small deformations or changing acquisition configurations, allowing the determination of optimal acquisition configurations.

When designing and conducting engineering geodetic core tasks like geometric quality assurance or deformation analysis, measurement methods allowing a space continuous geometric acquisition of artificial or natural measurement objects move currently into focus. The fundamental prerequisite for exploiting the added value of the space continuous geometries is the development of appropriate models and their integration into engineering geodetic processes. This project aims at a realistic space continuous modelling of a measurement object's geometry. These models form the basis for an identification and description of potential changes arising between two measuring epochs. The point clouds' mathematical modelling is based on freeform surfaces like B-splines. This kind of approximating surfaces are very flexible and thus entail the parametric representation of various kinds of objects. As a drawback, this versatility requires setting a large amount of parameters. Within this project we developed an approach that allows setting two groups of these parameters - the control points and the surface parameters - in an optimal way via an estimation process. Compared to the classic approximation approach, that only estimates the control points the problem becomes highly non-linear and requires the introduction of inequalities in order to account for the definition domain of the surface parameters as well as for the measurement order of the points. We solved this estimation problem by transferring it to a Linear Complementarity Problem (LCP). Different tests performed on synthetic and real data showed that better approximation accuracy can be achieved with the developed approach and that the estimated values of the parameters are closer to the nominal ones compared to the classical approximation approach. The developed approximation approach was employed in a second part of the project to model the surface geometry measured at two different time epochs to estimate deformations that potentially occurred between these epochs. Points were calculated on the two approximating surfaces at locations corresponding to the same surface parameters. These points were treated as homologues points in order to estimate in a first step the rigid body motion and subsequently localised distortions. As these two components of a deformation process may occur simultaneously, an iterative procedure was developed to detect points, that are solely part of the rigid body motion. This allows an unbiased estimation of the translations and rotations characterising this motion. The distortion parameters were estimated based on a 3D-affine transformation subsequently to the application of the rigid body model. The developed approach was tested and validated at various measuring objects, covering different spatial scales ranging from 0,3 m (a B-spline test specimen) over 30 m (a wooden tower) to 100 m (a dam). The case studies proved the practical applicability of the developed approaches and the stability of the obtained results.