Two-epoch TLS deformation analysis of a double curved wooden structure using approximating B-spline surfaces and fully-populated synthetic covariance matrices

Abstract

This contribution presents a B-spline-based approach of area-wise deformation analysis applied on elements of a double curved wooden tower. The monitored object is the Urbach Tower with a height of 14 m. Terrestrial laser scans from two epochs acquired under real-world conditions are used for approximating two jointly parametrized B-spline surfaces of the tower’s outer shell. The stochastic model of the observations used within the surface approximation is based on elementary error theory and is defined by a synthetic variance-covariance matrix (SVCM). In addition to previous work on this topic, the object’s dimension is extended from a few dm to a few m and the measurement distance ranges from 20 to 60 m. Moreover, environment specific error sources are addressed in the SVCM, revealing the effect of the object’s dimension as well as of additional elementary errors on the estimated B-spline surfaces and the subsequent deformation analysis. Based on constructed points pairs using a grid of surface parameters, rigid body movements of the object under investigation are estimated while at the same time distorted regions of the wooden tower are detected. All results of the deformation analysis are statistically verified using hypothesis tests based on the elementary error model propagated through the processing algorithms of surface estimation and deformation analysis. The results demonstrate that during the modelling and deformation analysis, the measurement noise is reduced and therefore distorted regions are detectable in a statistically correct way.