Literature review for 3D Design Terrain Models for Construction Plans and GPS Control of Highway Construction Equipment

Transcription

1 Literature review for 3D Design Terrain Models for Construction Plans and GPS Control of Highway Construction Equipment Cassie Hintz Construction and Materials Support Center Department of Civil and Environmental Engineering University of Wisconsin Madison March, 2009 Cheng, J. (2005). Three-dimensional calculation of roadway earthwork volume. Journal of Southeast University.21(1), The article presents a 3-dimensional algorithm concept for computations of roadway earthwork volume to solve the inaccuracy dilemma that arises from use of the averageend-area method. The average-end-area method computations assume two adjacent sections change linearly along the center line of roadway, which is usually not the case. This new 3-dimensional concept utilizes geometric algorithms between the original terrain and design model (the roadway). Volumes are calculated by computing the change in triangle pairs sharing vertices in the horizontal plane where one is representative of the original terrain and on of the design surface. The difficult part of the method is organizing triangle pairs of a desired area. Steps to organize the area are outlined in the article. Comparison of the 3-dimensional model with average-end-area in earthwork computations revealed the 3-dimensional model is more accurate and is therefore applicable to roadway earthwork volume calculations. Easa, S. et. al. (2002). Three-dimensional transportation analysis: planning and design. Journal of Transportation Engineering. May/June 2002, With increasingly complex transportation systems, the need to generate three dimensional designs is a necessity. The article describes the concepts of one, two, three, and four dimensions and describes both visual and analytical uses of three dimensional designs in transportation applications. Three ways to apply the concept of 3D are presented: 1. X,Y,Attribute- The attribute dimension is a descriptive characteristic of the location X,Y. It can be physical such as elevation or conceptual such as population density. 2. X,Y, Time- The third dimension, time, is utilized to display data recorded at points X,Y in discrete time. 3. X,Y,Z- Z is used to display the location of an object. Data can be recorded at several points with same X,Y coordinates. This 3D model can be used to generate a DTM through triangulated irregular networks (TIN). The article also presents the ideal of four dimensions where either time or attribute dimension is added to three dimensional location X,Y,Z.

2 Many applications of using 3D are presented which apply to attributes and time. These include traffic volume, vehicle trajectory, interactive real time simulation in urban modeling, pollution concentrations at differing altitudes, etc. Applications of using the Z dimension as the third dimension are also discussed. Route planning can be enhanced through 3D modeling. Photogrammetry can be use to create stereoscopic visualization of terrain. GPS can also be used to produce digital maps and images. However, in GPS, vertical accuracy is lower than horizontal accuracy due to the geometry of satellites. Use of DTM analysis can be used extensively in geometric design to generate cross sections, profiles, drainage, and earthwork. Software (such as Microstation with Geopak) use either average-end-area or true finite elements between existing and finished ground wire frame to compute earthwork quantities. The software requires TIN generation, management, and inclusion of break lines. Once these are included contours and hence drainage lines can be generated from the DTM. Use of three dimensional modeling in geometric design has many applications. An analytical model of 3D geometric design using geometric elements to represent highways revealed 2D designs overestimate and underestimate required radii of horizontal curves and lengths of vertical curves. Vehicle stability was studied by looking at the overlap of horizontal and vertical curvature, which led to the conclusion the 2D formula of AASHTO currently (2002) used is adequate at constant speeds but insufficient when emergency maneuvers are performed. In bridge design, 3D parametric modeling improves automation in design and drafting. Using a 3D approach also aids in design of pavement drainage and highway aesthetics through coordination of horizontal and vertical alignments so revolving points approximately overlap. Structural design of pavements with respect to the selection of materials and thickness of individual pavement layers can also benefit from three dimensional design. In the past designs for both flexible and rigid pavements have been conducting using 2D models. With emerging technological advances in computers, it has become easier to model actual properties and behavior of pavement design. The most popular approach is to use the finite-element method (FEM). The finite-element method can be used to produce 2D or 3D solutions. At first, 2D solutions were more desirable because it took less time and memory to produce a 2D model. Eventually 3D models were improved and are now preferred in most cases. A 3D FEM can account for material characteristics, loading conditions, and environmental effects. To conclude, the article restates that there are many benefits to using 3D design in transportation applications. DTM analysis is becoming well developed for applications in geometric design. Visualization technology is likely to emerge as the future design environment for transportation engineering with increases in GPS technology and reduced computing costs, making the move to 3D design a necessity.

3 Hassanin, A. & Moshelhi, O. (2003). Data acquisition and analysis for highway construction using geographic information systems. Canada Journal of Civil Engineering. 30, The article puts forth a GIS model to enhance highway construction earth moving operations through automation of data acquisition process, estimation of cut and fill volumes, and generation of mass haul diagrams. The proposed model includes depiction of soil strata because of variations in swell and shrinkage of different soil types impact cut and fill quantities. Soil strata are determined through geotechnical bore hole data with linear interpolation between bore sites to create soil strata profiles. Ground water table and obstructions are also included which may influence mass haul diagrams. The model displays 3D visualization of ground elevations and underlying soil layers. The model accepts AutoCAD drawings into ArcView and places each layer separate 2D themes. To develop a DTM for earthwork calculations, TIN nodes are generated along contour lines. To determine the interval between TIN nodes along contours, an iterative process generates points irregularly spaced where the initial interval is equal to the horizontal distance to the nearest contour. From the TIN nodes, the DTM is created and volume is computed between terrain model of the DTM and the ground water table or the horizontal plane passing through the lowest point generated in the DTM. The process follows by generated new TIN nodes by cutting the interval between nodes in half and re-computing volume. The new volume is compared to the previous iteration and process repeats until the change in volume between iterations reaches a specified value. The accuracy of the model depends on the accuracy and detail of input data. Using GPS generally satisfy the precision requirements of the model. Hatake, K. (2006). Next-Generation Civil Design. Retrieved November 15, 2008 from In 2004 Yachiyo Engineering Company, Ltd. of Japan began adopting 3D design for a wider range of projects using Autodesk s Civil 3D. Yachiyo claims using 3D design allows for faster completion and more efficient designs, taking on tasks in house that would otherwise need to completed by outsources, and improve precision of route selection. Yachiyo s first project using 3D design was for a highway in a mountainous region, including three kilometers along a mountain ridge. With strict government regulations and cost limitations, Yachiyo faced a major challenge. Yachiyo started use of the 3D design by inputting 3D longitudinal data and used Civil 3D s cleanup function to automatically generate a polyline from existing drawings and to add elevation data. Designers continued by created horizontal alignment using a topographic model. It took

4 only 20 hours to produce final output of longitudinal and cross section diagrams for the new route. Thus, 3D design greatly expedited the design process for Yachiyo Engineering Company, Ltd. The head manager of Techology Division 1 at Yachiyo also stated, Civil 3D is great for other tasks, such as calculating soil volume. Hattori, S. (1989). Semi-automatic terrain measurement system for earthwork control. Photogrammetric engineering and remote sensing. 55(5), Stereo matching techniques are presented to speed photogrammetric processing for quick measurements of cut and fill terrain in construction applications. The method utilizes an image processing system for semi automatic production of DTMs from aerial photos. Hardware components include an AD Converter, optical disc unit, and a host computer. The AD converter generates a digitizing table used for the interactive system. The optical disc unit consists of two drives to handle stereo pairs. The processing the automatic measurement includes AD conversion of photographs, relative and absolute orientation, stereo matching, DTM production, and X- parallax corrector. The AD conversion designates areas to be digitized, and coordinates are measured on the graphic digitized table. Once digitized, images are stored on the optical disc. Two options are possible for choosing the coordinating orientation of points. One uses a stereo comparator where orientation parameters are entered manually. The second option finds pass points and control points in digitized images using least squares correlation. The stereo matching algorithm uses LOG filtering of patches, grid points allocation and correlation, median-filtering of X-parallaxes, and X-parallax elimination from the patch pair, and coarse to fine convergence with X-parallax output. The DTM is produced by interpolating terrain data to a regular grid using a weighted mean approach. X-parallex correction is conducted because in many cases matching errors of 2 to 3 meters can occur. The operator can correct these matching errors interactively on the computer screen. A test of the method was used on a 120 by 120 meter area. Results showed large errors in stereo matching in forested areas and at a building. However, for bare ground where earthwork measurements were made, results were highly reliable. Kari, G & Jha, M. (2007). A new method for 3-dimensional roadway design using visualization techniques. WIT Tracnsactions on The Built Environment. 96, Traditional two dimensional geometric design of roadways poses several problems. Critical information pertaining to geometric design may be missing when using planar projections of the roadway onto a Cartesian coordinate system. Designers may not be

5 able to see illusion effects where horizontal and vertical curvature overlap, which tends to lead drivers to believe they can drive faster on curves than they are safe to do so. Few 3D geometric highway design tools are available at the present time of the article (2007). The methodology presented in the article is based upon traditional 2D horizontal and vertical design methods. Traditional circular horizontal curve design and parabolic vertical curve design are maintained. The three dimensional design elements presented include 3D straight lines connected with spiral curves and 3D spline curves. The straight lines have a starting and ending point represented by Cartesian coordinates (x,y,z). The 3D spline curves consist of piecewise polynomials passing through a given set of control points. A designer must examine the given terrain and set control points along the path of the alignment. The designer then best fits 3D straight lines based on the position of the control points and proceeds by fitting a spline that passes through points between successive straight lines. Alterations can be made by adding additional control points or altering the location of existing control points. Microstation is used to generate control points, 3D straight lines, and alignment. The code to generate 3D spline elements was created in Matlab. The proposed method is advantageous because it allows a designer to view the vertical and horizontal alignment of a roadway simultaneously. The presented method does not assess driver comfort or check for design consistency. Katzil, Y. & Doytsher, Y. (2000). Height estimation methods for filling in gaps in gridded DTM. Journal of Surveying Engineering. November 2000, Since terrain relief is three dimensional and continuous in nature, and most data collected to generate digital terrain models are discrete in nature, the digital model of the terrain is represented by mathematical models of the discrete data. This article presents methods for filling in the gaps in gridded digital terrain models. Two common procedures for generation of a DTM in mapping applications are described. The first is a regular elevation grid, which is an ordered network of elevations at corners of a regular grid. The second is an irregular elevation grid where a triangulated irregular network is used to connect elevation points. Gridded models are generally used for large areas, which are the primary focus of the article. Gaps in DTM databases are caused by a variety of reasons. Using photographs to generate DTMs can result in problems where there are clouds preventing elevation samples at points and when there are gaps between photogrammetric models, there may be unmeasured areas in the DTM. These gaps can be filled by solving additional photogrammetric models to cover the area of the hole but this generally adds errors due to the use of independent models that measure elevations completed by different

6 operators. It is also costly to generate additional photogrammetric models. Hence, it is only useful to fill gaps with additional photogrammetric models in very large areas. Small holes, can be filled in using a computational process, where the holes are automatically filled in using mathematical relations based on the existing elevation points near the gap. The mathematical model produces error because it is a model and not the true elevation. Methods also have been developed to define areas of gross error, potentially from the discontinuity of adjacent photogrammetric strips. Height estimation methods consist of two main groups, local and global. Global height estimation methods are for large areas and utilize 2D polynomials or trigonometric functions. Errors are minimized using least squares adjustments. Local height estimations are for small areas and usually use a 1D polynomial or lower order fit where methods vary in both cost and complexity of the computation. In polynomial estimations, the height at a desired point is estimated based on a polynomial surface generated near the point of interest. Polynomial estimations preserve the continuity of the terrain. Several polynomial estimation models were studied in this article including linear estimation, 1D polynomial of third order, improved cubic spline, and 2D polynomial of third order. Linear estimation estimates the height of a point by calculating the average of the height of the two or four closest points to it. The 1D polynomial of third order consists of a polynomial passing through the point whose height is to be estimated in one main direction (North-South or East-West) and through four neighboring points in that main direction. The four points are used to generate the four coefficients of a third order polynomial. The improved cubic spline method uses a 1D polynomial of third order based on four adjoining points of the elevation grid. Slopes of the end points are measured and used for improved cubic spline, which maintains the continuity of the function in passing between points. The 2D third order polynomial method requires use of at least 10 points surrounding the point whose height is to be measured, (although 15 are preferred). The points are used to generate the ten coefficients of the polynomial based on a least square adjustment. Two methods not using polynomial estimations are also examined. The first is pyramid structure where points close to a point whose height is to be measured are used to generate a 3D structure with the center at the point whose height is to be measured. The circumference of the base of the pyramid is defined by connecting all points contributing to height determination of the unknown point. The height estimation is chosen by minimizing area of the structure. The other method presented is kriging, which uses a statistical method to estimate the value of the occurrence. The height of the desired point is calculated by this statistical method based on the surface being constructed passing through measured points. To evaluate the effect of the nature of relief on accuracy, three surface types were used, (mountainous, hilly, and planar). Results revealed there is a significant decrease in accuracy as relief becomes more mountainous with standard deviation ratios of 1:2:4 going from planar, to hilly, to mountainous. The effect of using different surface models

7 was also analyzed using the improved cubic spline, kriging, and linear estimation. There was no significant difference in accuracy between the three methods in any relief type. Analyses of the effect of grid density on DTM accuracy were conducted by using two gridded databases that cover the same area where one had a point density of one point every 50 meters and the other used a point density of one point every 10 meters. As expected, using the lower point density resulted in smoother contours than the high point density, especially in more mountainous regions. Kriging, linear estimation, and improved cubic spline were all used to determine if the surface model estimations differ in their height estimation accuracies. No significant differences were found between different estimation techniques. A gridded database covering a broad area with different relief types was performed on a gridded DTM database with two million points, having a density of 50 meters to evaluate the accuracy of height estimation accuracy in a broad area. All five estimation techniques were examined. Accuracies among the different methods were very similar but the processing times differed significantly. Linear estimation was the fastest and the improved cubic spline method was next, taking 1.84 times the linear estimation time. The rest were much slower with pyramidal estimation (four neighbors) taking 8.18 times the linear estimation, kriging taking times the linear estimation, and 2D polynomial of third order taking times the linear estimation. Filling in holes in DTM data due to gaps between coverage area of photogrammetric models and strips was also analyzed using linear estimation and improved cubic spline. Comparisons between the two methods revealed no significant difference between standard deviations and maximum errors. To conclude, there are various methods for filling in gaps in DTMs. Automatic completion of a DTM to fill in gaps adds to the integrity and continuity of the model without decreasing accuracy. Linear estimation is the simplest technique and works well with dense grids. Improved cubic spline is the fastest technique when dealing with sparse grids. Meneses, et al. (2005). Quality Control in Digital Terrain Models. Journal of Surveying Engineering. November The article presents a method to determine the quality of digital terrain models in civil engineering applications. The quality of a DTM is defined by the degree the representative surface generated by the DTM resembles the actual surface. To characterize the accuracy of volume characteristics of a DTM, analysis of the relation between point density sampled and volumetric accuracy of the DTM were conducted. The research was based on topographic surveys used to represent the actual conditions where structural features in the area were signified as breaklines and a closed contour line surrounded the area of study. Within this area, the DTM was generated. DTMs were generated using point densities ranging from 5% to 100% of the original survey and compared based on volumetric characteristics of the terrain. Comparisons using different

8 point densities revealed that using point densities above 60% of sampled points achieve minimal increases in accuracy of volume. Comparison of surveyed heights to interpolated heights in the DTM were used to evaluate accuracy of terrain height measurements using mean error and absolute mean error statistics. As with the volumetric analysis, DTMs were generated ranging from 5% to 100% to evaluated height errors. Results revealed that there is high stability in height errors relative to sampling density. Thus, it was determined height errors are less sensitive than volumetric errors when evaluating the quality of a DTM. The article concludes combined use of volumetric and height curves form an acceptable method of accessing DTM quality where high levels are accuracy are needed.