Abstract
The establishment of the terrestrial laser scanner changed the analysis strategies in engineering geodesy from point-wise approaches to areal ones. During recent years, a multitude of developments regarding a laser scanner-based geometric state description were made. However, the areal deformation analysis still represents a challenge. In this paper, a spatio-temporal deformation model is developed, combining the estimation of B-spline surfaces with the stochastic modelling of deformations. The approach’s main idea is to model the acquired measuring object by means of three parts, similar to a least squares collocation: a deterministic trend, representing the undistorted object, a stochastic signal, describing a locally homogeneous deformation process, and the measuring noise, accounting for uncertainties caused by the measuring process. Due to the stochastic modelling of the deformations in the form of distance-depending variograms, the challenge of defining identical points within two measuring epochs is overcome. Based on the geodetic datum defined by the initial trend surface, a point-to-surface- and a point-to-point-comparison of the acquired data sets is possible, resulting in interpretable and meaningful deformation metrics. Furthermore, following the basic ideas of a least squares collocation, the deformation model allows a time-related space-continuous description as well as a space- and time-continuous prediction of the deformation. The developed approach is validated using simulated data sets, and the respective results are analysed and compared with respect to nominal surfaces.
Highlights
Deformation analysis has always been part of a large range of application fields: the monitoring of an object’s change over time is of high interest in gas and oil production, civil and mechanical engineering, hydrology or environmental sciences (Velsink 2015)
terrestrial laser scanner (TLS) provides the best conditions for an areal deformation analysis, overcoming the drawbacks of classical approaches
An approach to an areal deformation analysis is developed which allows a point-to-surface-based comparison of laser scanning point clouds with respect to an initial and undistorted reference surface as well as a pointto-point-based comparison between two distorted states of the measuring object
Summary
Deformation analysis has always been part of a large range of application fields: the monitoring of an object’s change over time is of high interest in gas and oil production, civil and mechanical engineering, hydrology or environmental sciences (Velsink 2015). Classical geodetic approaches like levelling, GNSS or total station measurements allow a point-based determination of deformations by repeatedly measuring representative points of an object. The evaluation of the resulting coordinate differences represents the object’s deformation (Wunderlich et al 2016). With the development of the terrestrial laser scanner (TLS), a measuring instrument which allows a fast, efficient and contactless data acquisition even of inaccessible measuring objects moved into focus of engineering geodesy. TLS provides the best conditions for an areal deformation analysis, overcoming the drawbacks of classical approaches. When performing a laser scanner-based deformation analysis, new challenges occur (cf Wunderlich et al 2016; Mukupa et al 2016; Holst and Kuhlmann 2016).
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