Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

Abstract

The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)—the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances between two PC and are implemented in nearly all commercial software. Unfortunately, they are affected by measurement noise, particularly when correlations are present. In this contribution, we focus on terrestrial laser scanner (TLS) observations and assess the impact of neglecting correlations on the distance computation when a mathematical approximation is performed. The results of the simulations are extended to real observations from a bridge under load. Highly accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the HD and AHD between two raw PC or between their mathematical approximations regarding reference values. Based on these results, we determine which distance is better suited in the case of heteroscedastic and correlated TLS observations for local deformation analysis. Finally, we set up a novel bootstrap testing procedure for this distance when the PC are approximated with B-spline surfaces.

Monitoring of the Production Process of Graded Concrete Component Using Terrestrial Laser Scanning

“…There are many approximation approaches for surface modeling based on 3D scattered points, including a polygonal model (e.g., a mesh by interpolation) or a regression model (e.g., a polynomial or B-spline surface) [30][31][32]. The difference of the concrete level among the gaps is typically not too significant owing to uniform casting and the concrete's fluidity.…”

A Decade of Modern Bridge Monitoring Using Terrestrial Laser Scanning: Review and Future Directions

“…However, the available TLS devices on the market offer the possibility to collect high-accuracy data of less than a millimeter. More accurate TLS devices with lower deviations can be a valid alternative for electrical and mechanical measuring equipments generally used in the field of bridge engineering [167]. Table 8 summarizes different examples of using TLS for deflection measurement of bridges.…”

How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements

“…When the inverse of the VCM exists explicitly, the VCM can be replaced by a simple factor, which we call the Variance Inflation Factor (VIF), see Kermarrec et al (2020a) and "Appendix B." An explicit formulation of the inverse exists when the correlation structure can be modeled with a Matérn model corresponding to ν = 1 2 , which corresponds in one dimension to a so-called autoregressive model of first order AR(1), see (Rao and Toutenburg 1995) or (Rasmussen and Williams 2006).…”

“…As aforementioned in Sect. 3.3.3, the inverse of the VCM from an AR(1) model can be replaced by a scaled identity in the LS adjustment, see Kermarrec et al (2020a) for a detailed explanation. The authors recommend using the AR(1) model due to the potential numerical instability of the DCM for high smoothness and low α (see, e. g., Fig.…”

“…The point clouds obtained can be visualized in specific commercial software or approximated with parametric models, among which are the increasingly popular and flexible B-spline curves or surfaces (e.g., Bureick et al 2016;Koch 2010;Neitzel et al 2019). The main advantage of point cloud modelization strategies over visualization comes from the possibility of performing rigorous test statistics, for example, for deformation analysis purposes (Zhao et al 2019;Kermarrec et al 2020a). The mathematical model can be simplified for basic objects, such as ellipsoids, cylinders or planes (e.g., Ahn 2004;Fang et al 2015;Lehmann 2019).…”