Application of Terrestrial Laser Scanning Methodology in Geometric Tolerances Analysis of Tunnel Structures Steve Y. W. Lam Department of Land Surveying and Geo-Informatics, Hong Kong Polytechnic University, Hong Kong SAR, China ABSTRACT With the point-clouds from a terrestrial laser scanner, surveying of all types of geometric tolerance has never been easier in controlling all aspects of tunnel shape and providing displacement vectors of the finished components in the construction. This paper describes how to select a suitable laser scanner, the calibration method, the procedures for acquiring survey data by the instrument in the field, and the computational algorithms of computer software needed for registration, fusion and error analysis of multimodality and range images so that the point clouds obtained by the instrument can be applied effectively in assessing the various geometric tolerances of tunnel structures in the as-built surveying. 1. INTRODUCTION Current advancement of terrestrial or ground-based laser scanning technologies has enabled surveyors to map complex surface and objects in digital format and create 3D electronic model for engineering applications in construction, shipbuilding and other production industries. The laser scanning methodology, an effective method of acquiring vast amount of precision 3-D data, has the advantages of high speed, high resolution, non-intrusive and non-contact sensing. It is particularly useful under the condition of hazardous environment where human intervention would be impossible. Different laser scanning systems are now available for tunnel surveying, for examples, Optech s LIRIS-3D long-range system and Callidus s medium-range system. These laser scanners are chosen by surveyors based on: (a) the system s ease of use; (b) laser range and accuracy; (c) adjustable scanning speed, scan density and field of view; (d) type and class of laser; (e) weight and size of the instrument, tripod and battery; and (f) special features such as internal camera/video, weather proofing, computer hardware and software. Unlike conventional total stations, it is not necessary to set up on a known control point. It can be mounted on a small vehicle or carriage on rails for rapid surveying of tunnel geometry. Some laser scanners also support standard surveying procedures like levelling and centring over a known point, height-of-scanner measurement, line-of-sight orientation, and setup with GPS receiver. A laser scanner for land surveying and mapping combines data from a non-contact distance meter, angle sensors and tilt sensors to measure 3D coordinates of points on an object surface. Nearly all surveying scanners are designed based on Light Detection and Ranging (LIDAR) technology and determine distance by measuring the time-of-flight (TOF) between an outgoing pulse and its return signal reflected by the object or reflector. The amplitude of the return signal is also recorded for computing the reflectivity of the object s surface and to expedite image registration. Accuracy of the range measurement is affected by: (a) precision of the instrument s mechatronic components, (b) reflectivity and material properties of the object, (c) target s perpendicularity or angle of repose, (d) temperature and temperature variations, (e) atmospheric pressure and humidity, (f) dust and vapour, and (g) background noise and radiation. 1
Among the survey operations and methodology for tunnel construction (e.g., Chrzanowski, 1981; Lam and Tang, 2001, 2003), 3D laser-scanning systems are often employed in: 1. Detail mapping of ground surface and underground features for subsequent operations of realignment design, structural analysis or construction simulation. 2. Acquisition of amorphous data (e.g., progress of tunnel excavation) for monitoring the project s status. 3. As-built surveying to determine the geometric tolerances of structural components (e.g., tunnel liners, portal beams and shafts) in accordance with the allowable tolerances, specifications and standards of the construction. 4. Monitoring of ground displacements and structural deformation under the combined geodetic, geotechnical and finite-element-analysis (FEA) model. Although the accuracy of laser scanning can not reach the accuracy of geodetic instruments, the scanning system and reflective targets have recently been improved so that high resolution of the scan data is now sufficient to detect millimetre displacement vectors in deformation monitoring surveys. This paper describes the survey methodology and computational algorithms for use with terrestrial laser scanners focussing as-built surveying of tunnel structures as well as analysing their geometric tolerances. Main advantages of using laser scanners in the as-built surveying are: 1. Laser scanner is able to capture data without the need to set up on any control point inside the confines of a tunnel. 2. Comparing with conventional tunnel profiler and reflector-less total station, point clouds on the object are captured by the instrument within a short period of time (e.g., over 2000 range points per second). 3. Validation of design model by the as-built geometry from the scanner. 4. Fast fit-up simulation for wriggle surveying or realignment of cross-sections, longitudinal profiles and tunnel alignments. 5. Incorporation of as-built data (e.g., existing structural components and installations) in new designs, reverse engineering and facilities management. 2. DATA ACQUISITION AND REGISTRATION OF 3D SHAPES Under the ISO 9001 in construction practice, all surveying instruments including laser scanners must be calibrated before using them in the field. One calibration method is to establish a calibration frame of say 9 survey targets on a flat reference surface which can be tilted vertically and horizontally. At different tilted positions, the 3D coordinates (x, y, z) of the target points are obtained by both the laser scanner and bearing-bearing intersections from two fixed geodetic-theodolite stations. The 3D coordinates measured by the scanner at different ranges are then transformed to the 3D-reference coordinates by applying Helmert s seven-parameter model from which the scale factor and the rootmean-square (RMS) value of the differences between the corresponding coordinates are found and checked against the manufacturer s specifications (Santala and Joala 2003; Rietdorf et al., 2004). As shown in Figure 1, the various stages of acquisition, post-processing and registration of 3-D shapes using the laser scanner are: Stage 1: Range images and camera (colour) images covering the surface of the entire object are captured by the scanner from different view points. Each range point comprising of a 3-D range (x, y, z), brightness and colour (red, green, blue) data is stored in an indexed element of the two-dimensional array of computer memory inside the scanner. The coordinates of (x, y) are represented by the row and column indices of the memory array while z-coordinate is the laser-range value. Thereafter, surface model of each scan is formed by Delaunay triangulation in post-processing. Stage 2: Images having overlapping area are aligned pair-wise to a common co-ordinate frame by applying iterative-closest-point (ICP) registration algorithms. Steps of a standard ICP algorithm (e.g., Besl and McKay, 1992) are to: (a) determine the nearest point in the second cloud of points with respect to a given point in the first cloud of points, (b) compute the 2
Euclidean motion (rotation and translation) by quaternions and eigenvector analysis minimising the least-squared distance between the corresponding points, and (c) apply the transformation to the first point-set. These three steps are iterated until the coupling error is smaller than a specified threshold or the maximum number of iterations is reached. Since minimum three identifiable points or survey targets are surveyed for the overlapping area, the ICP algorithm converges very fast and produces high accuracy result after a rough registration through the initial transformation matrices. Thereafter, unwanted images or data in the scene (e.g., construction workers and vehicles passing through the scanner s line of sight) are deleted. Measures of registration accuracy are presented in terms of ground-truth transformation error with respect to ground control points. Or, in terms of non-ground-truth measures by computing the normalised least-square error (LSE), root-mean-squared error (RMSE), average residual error (ARE) and maximum residual error (MRE) from individual residual distances between each range point and its corresponding closest model point. However, non-ground-truth measures do not guarantee good registration accuracy because they are more sensitive to noise in the data. Techniques to improve searching for closest point, outlier rejection and pose transformation are summarised in (e.g., Rodrigues and Liu, 2002, Table 1; Matabosch et al. 2004, Table 1). Among these techniques, colour and reflectance components (i.e., texture mapping) are utilised successfully by Sagawa et al. (2005), Beinat and Crosilla (2001), and Johnson and Kang (1997) to simultaneously register multiple images into the final geometric and photometric model. Stage 3: All image pairs are sequentially merged into a single geometric and photometric model and geo-referenced into real-world coordinates using minimum three known target points on the entire model or three known scanner stations. Automatic hole filling, edge and corner reconstruction, and surface smoothing are also incorporated in the merging process of the software system. Conversion from triangulated mesh to grid representation may be needed while maintaining the required level of accuracy and mapping details. The purpose is to reduce the number of data points to a size and format (e.g., DXF, DWG, DGN, IGES and STEP) acceptable and manageable by downstream engineering software and geographic information systems (GIS). The resulting model is then segmented into regions or structural components for construction assessment, computing actual quantities of earthwork and materials, geometric tolerances analysis by comparing the design with the as-built data, and other engineering applications. Multiple images of object captured by Terrestrial Laser Scanner Range points Colour pixels Registration of images pair-wise into common coordinate frame by geometric ICP algorithm Registration of colours and textures by colour ICP algorithm Merging of all image pairs into a single geometric, photometric and geo-referenced model Unified 3D model with object recognition Figure 1: Geometric and Photometric Modelling by Terrestrial Laser Scanner 3
3. ASSESSMENT OF GEOMETRIC TOLERANCES IN TUNNEL CONSTRUCTION There are three main categories of tolerance in modern construction practice, namely conventional tolerances, statistical tolerances and geometric tolerances. Conventional tolerances are dimensional or coordinate tolerances and specified as plus or minus deviation from the lengths, angles and coordinates. During the course of the construction, discrete points at changes of geometry on the object surface are surveyed with respect to one coordinate reference datum or the dimensions given in construction drawings. The surveyed coordinates or dimensions are then checked against their allowable tolerances. This is the traditional practice of checking the tolerances of finished structures. Statistical tolerances specify a statistical distribution of tolerances for a dimension together with the property of distribution and values of mean or variance, which allows one to determine the probability that certain dimension or size of the product is unacceptable. In modern construction practice, the checking of dimensional and coordinate tolerances has been replaced by the rigorous approach of analysing the geometric tolerances of the finished structures. Under ISO 1101 or its equivalent, the ANSI Y14.5M, all types of geometric tolerance, namely form tolerance, orientation tolerance, location tolerance, runout tolerance and profile tolerance (Table 1) can be found by using laser scanner and analysed geometrically. These standards are originally designed for the manufacturing industry but being adopted for assessing the geometric tolerances of both concrete and steel structures in tunnel construction. As shown in Figure 2, tolerances of tunnel structures are surveyed and analysed geometrically with respected to two or three local datum planes or axes which help to define the local orientation and/or location of the tolerance zone. The checking of tunnel profile, surface form and column eccentricity is shown in Figure 3 in which tolerances of positions or dimensions are extracted from the point-clouds and checked against the allowable tolerances given in (e.g., British Tunnelling Society, 1997, Table 4). Report on profile tolerance is illustrated in Figure 3(a). In Figure 3(b), two nominally parallel surfaces are designed to determine the form deviation of an as-built surface with respect to a tertiary datum or a median plane. In Figure 3(c), straightness tolerance of a column axis is defined by a cylindrical zone along the whole length of the column. The as-built axis of the column is computed by least-squares estimate so that the effect of eccentricity from its designed position can be assessed by the structural engineer. Depending on the requirements of the construction, lower tolerance (i.e., higher accuracy) may be required in the assessment. If the surveyed tolerance exceeds the allowable tolerance or exceeds the maximum displacement given by the FEA, remedial work and/or realignment design will be implemented. Table 1: Types and characteristics of geometric tolerances (ISO 1101, 1983) Feature Type Type of Tolerance Characteristic Individual features Form Straightness, flatness, cylindricity Related features Orientation Location Runout Angularity, perpendicularity, parallelism Position, concentricity Circular runout, total runout Undetermined features Profile Line profile, surface profile Tertiary Datum Axes for assessment of profiles in slicing Secondary Datum Axes for assessment of vertical alignment 4 Primary Datum Axes for assessment of horizontal alignment
Figure 2: Establishment of primary, secondary and tertiary datum axes for assessing geometric tolerances of tunnels Y Overcut Designed Profile/Envelope Undercut X (a) Profile Tolerance of Tunnel Cross-section Tertiary Datum Plane Tertiary Datum Form Tolerance As-built Surface Deviations from Median Designed position of the Column Axis (Tertiary Datum) Axis surveyed Column Axis computed by Least Squares Model to determine its eccentricity Tolerance Zone of Axis (b) Form Tolerance of Surface Figure 3: Assessment of Geometric Tolerances 4. CONCLUSIONS AND FUTURE DEVELOPMENTS (c) Straightness Tolerance of Column Axis 5
This paper has presented the surveying techniques and computational algorithms needed for applying terrestrial laser scanning system in determining the various geometric tolerances of tunnel construction. The evolution of laser scanning technologies has no doubt improved the capabilities of tunnel surveyors and other professionals. It is anticipated that, by applying the laser scanning system, new automated systems and construction methods will be developed to facilitate the construction surveying, computer-aided design and planning, and FEA of different kinds of tunnels and their associated structures. REFERENCES ASME, 1982. ANSI Standard Y14.5M Dimensioning and Tolerancing. American Society of Mechanical Engineers. Besl, P. and McKay, N., 1992. A Method for Registration of 3-D Shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 2, pp. 239-256. Beinat, A. and Crosilla, F., 2001. A Direct Method for the Simultaneous and Optimal Multidimensional Models Registration, Proceedings, IEEE/ISPRS Joint Workshop on Remote Sensing and Data Fusion over Urban Areas, 8-9 Nov., 2001, pp. 283-287. British Tunnelling Society of Institution of Civil Engineers, 1997. Model Specification for Tunnelling, London: Thomas Telford. Chrzanowski, A., 1981. Optimisation of breakthrough accuracy in tunnelling surveys, Canadian Surveyor, Vol. 35, pp. 5-16. ISO 1101, 1983. Geometrical Tolerances. Geneva: International Organization for Standardization. ISO 9001, 2000. Quality Management Systems Requirements. Geneva: International Organization for Standardization. Johnson, A. and Kang, S., 1997. Registration and Integration of Textured 3-D Data, Proceedings, International Conference on Recent Advances in 3-D Digital Imaging and Modeling, Ottawa. Lam, S. and Tang, C., 2001. An Overview of Surveying Techniques for the Construction of Highway Tunnels in Hong Kong, Geomatica, Vol. 55, No. 3, pp. 325-332. Lam, S. and Tang, C., 2003. Geometric Modeling Systems for Construction Surveying of Highway Tunnels, ASCE Journal of Surveying Engineering, Vol. 129, No. 4, pp. 146-150. Matabosch, C., Salvi, J., Pinsach, X. and Garcia, R., 2004. Surface Registration from Range Image Fusion, Proceedings, pp. 678-683, IEEE International Conference on Robotics and Automation, New Orleans, USA. Rietdorf, A., Gielsdorf, F. and Gruendig, L., 2004. A Concept for the Calibration of Terrestrial Laser Scanners, Proceedings, INGEO 2004 and FIG Regional Central and Eastern European Conference on Engineering Surveying, Slovakia, November 11-13, 2004. Rodrigues, M. and Liu, Y., 2002. On the Representation of Rigid Body Transformations for Accurate Registration of Free-form Shapes, Robotics and Autonomous Systems, Vol. 39, pp. 37-52. Sagawa, R., Nishino, K. and Ikeuchi, K., 2005. Adaptively merging Larger-Scale Range Data with Reflectance Properties, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 27, No. 3, pp. 392-405. 6