Abstract
Deformation monitoring of structures is a common application and one of the major tasks of engineering surveying. Terrestrial laser scanning (TLS) has become a popular method for detecting deformations due to high precision and spatial resolution in capturing a number of three-dimensional point clouds. Surface-based methodology plays a prominent role in rigorous deformation analysis. Consequently, it is of great importance to select an appropriate regression model that reflects the geometrical features of each state or epoch. This paper aims at providing the practitioner some guidance in this regard. Different from standard model selection procedures for surface models based on information criteria, we adopted the hypothesis tests from D.R. Cox and Q.H. Vuong to discriminate statistically between parametric models. The methodology was instantiated in two numerical examples by discriminating between widely used polynomial and B-spline surfaces as models of given TLS point clouds. According to the test decisions, the B-spline surface model showed a slight advantage when both surface types had few parameters in the first example, while it performed significantly better for larger numbers of parameters. Within B-spline surface models, the optimal one for the specific segment was fixed by Vuong’s test whose result was quite consistent with the judgment of widely used Bayesian information criterion. The numerical instabilities of B-spline models due to data gap were clearly reflected by the model selection tests, which rejected inadequate B-spline models in another numerical example.
Highlights
Deformation monitoring of engineering structures such as bridges, tunnels, dams, and tall buildings is a common application of engineering surveying [1]
According to the test decisions, the B-spline surface model showed a slight advantage when both surface types had few parameters in the first example, while it performed significantly better for larger numbers of parameters
In order to statistically discriminate between the aforementioned polynomial and B-spline surface models listed in Table 1, the result of Cox’s and Vuong’s test for the two segments are given in Tables 2 and 4, respectively
Summary
Deformation monitoring of engineering structures such as bridges, tunnels, dams, and tall buildings is a common application of engineering surveying [1]. The point-to-point-based analysis is a common approach to describe deformations that are captured by conventional point-wise surveying techniques. The procedure of a surface-to-surface-based deformation analysis, which is appropriate in certain situations, is to divide the point clouds into cells and to compare the parameters of fitted planes based on cell points in two epochs. This method is applied in Lindenbergh et al [14], where the different positions of the laser scanner and strong wind contribute to the change of the coordinate system. The authors of Girardeau-Montaut et al [15] presented three simple cloud-to-cloud comparison techniques for detecting changes in building sites or indoor facilities within a certain time
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