Analysis of the influence of range and angle of incidence of terrestrial laser scanning measurements on tunnel inspection

https://doi.org/10.1016/j.tust.2014.04.011Get rights and content

Highlights

  • We propose a methodology to build an error model of the TLS measurements.

  • The angle of incidence has great influence on the point cloud quality.

  • TLS position influences the quality of the point cloud.

  • A high density of points compensates for errors produced by the scanner position.

Abstract

Terrestrial Laser Scanner (TLS) measurements are subject to errors which influence the quality of the 3D models built from the point clouds. In this paper, a methodology to build an error model of the TLS measurements is proposed. Measurement errors are estimated based on two of the factors that mostly affect their magnitude: distance to the object and angle of incidence.

The error model is used to analyze, by means of Monte Carlo simulation, the spatial distribution of the errors in a point cloud of a circular tunnel section and also to simulate the effect of the measurement error in tunnel inspection works.

The results obtained indicate that although the angle of incidence influences the point cloud quality when the laser is located near the tunnel gable, its effect is counteracted by the point density when a surface is fitted to the point cloud.

Introduction

In the last few years, Terrestrial Laser Scanners (TLS) have become systems frequently used in inverse engineering and in the quality control of facilities and infrastructures (Armesto et al., 2008, Armesto et al., 2009, Gordon and Lichti, 2007, Tang et al., 2010, Teza and Pesci, 2012, Von Der Haar et al., 2013).

Regarding tunnels, the use of TLS has become popular in recent years with various applications such as geotechnical studies (Fekete and Diederichs, 2013, Fekete et al., 2009, Fekete et al., 2010), deformation analysis (Gosliga et al., 2006, Lam, 2006, Qiu et al., 2009, Wang et al., 2009) and inspection (Pejić, 2013, Sandrone and Wissler, 2012).

The accuracy of the point cloud obtained with these systems depends on different factors: distance to the object, angle of incidence, material of the measured object, environmental conditions, etc. (Kaasalainen et al., 2011, Lee et al., 2010, Pesci et al., 2011, Yang et al., 2011, Zhu et al., 2008). For properly calibrated equipment, working on suitable environmental conditions and measuring on homogeneous material, the distance to the object, and especially the angle of incidence of the laser beam with the object surface, determine the spatial distribution of the errors in the point cloud (Argüelles-Fraga et al., 2013, Pejić, 2013, Soudarissanane et al., 2011). These errors increase with range and angle of incidence. However, when performing quality control works aimed at establishing whether the surface of an object (bridge, tunnel, industrial part, etc.) matches the theoretical surface (Golparvar-Fard et al., 2011, Guarnieri et al., 2013, Monserrat and Crosetto, 2008), we tend to consider that the point cloud obtained with TLS systems is error free or, to a lesser extent, that errors correspond to their nominal value given by the manufacturer. This assumption may lead to erroneous conclusions about the quality of the measured objects, which may have, in turn, a negative economic impact.

Since there is no standardized procedure such as the DIN 18723 or the ISO 17123, which apply to total stations, it is necessary to develop models for TLS measurement errors if we aim to have an estimation of the quality of the 3D models built from the point clouds.

In this paper, we propose the development of an error model based on empirical results in order to study the distribution of the errors through the scanned surface. Then, this model is used to establish conclusions about the effect of the angle of incidence, the distance to the object and the position of the scanner, in tunnel inspection.

Section snippets

Error model

In this work, an error model based on experimental data was constructed. First, we assume that each laser point Pi=(Xi,Yi,Zi) of the point cloud, for i = 1, …, n, is a measure of the theoretical point on the scanned object plus a term of error ɛi:(Xi,Yi,Zi)=(Xi,Yi,Zi)+εi

As we have no information concerning the spatial distribution of εi=(εXi,εYi,εZi), and assuming that its components are independent, it was considered, for simplicity, that the error is spatially distributed on a spherical

Spatial distribution of points measured with a TLS along a circular tunnel

In the previous section, an experiment was carried out to estimate functions f(r, α) and g(r, α) that provide an estimation of the error distribution of the point cloud, depending on the scanning distance and the angle of incidence, respectively. Now we are interested in using these functions to estimate the spatial distribution of the observed laser points for a hypothetical known surface of an object.

Given Ps, the origin of the scanner centered coordinate system, the procedure to simulate a

Application of the error model to tunnel inspection

Tunnel inspection is frequently devoted to comparing a surface adjusted to the TLS point cloud with the theoretical surface of the tunnel. Using our error model and by means of Monte Carlo simulation, it is possible to study the effect of the distance to the object, the angle of incidence and the position of the scanner on the results of the inspection.

Let (X, Y, Z) be the spatial coordinates of each point on the object surface and let us assume that coordinate Z can be obtained from (X, Y) by

Results and discussion

In previous sections, an error model for TLS point clouds has been developed and also a methodology to study its effects on tunnel inspection (that can be applied to other objects) has been proposed. In this section, we use this previous analysis to study the effect of the scanner distance to the object, the angle of incidence and the position of the scanner on tunnel inspection.

In Fig. 8, an estimation of the mean error along the tunnel is represented (calculated according to the error model

Conclusions

Terrestrial laser scanning is frequently used for tunnel inspection, given its capacity to measure millions of points in just a few minutes. Inspection is carried out comparing the theoretical surface of the tunnel to a surface fitted to the point cloud.

Simulating errors on the point cloud measured with a TLS system is possible to analyze the effect of the errors due to the distance to the object and the angle of incidence on tunnel inspection. For the maximum distances recommended for tunnel

Acknowledgments

This paper was funded by projects BIA2011-26915 and MTM2011-23204 of the Spanish Ministry of Science and Innovation, and project 10PXIB300068PR of the Xunta de Galicia Government (Spain).

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