| Author: | Xie, Fei |
| Title: | Unified uncertainty models for depth estimation of objects in ground penetrating radar survey |
| Advisors: | Lai, Wallace (LSGI) Shi, John (LSGI) |
| Degree: | Ph.D. |
| Year: | 2021 |
| Subject: | Ground penetrating radar Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Land Surveying and Geo-Informatics |
| Pages: | xvii, 165 pages : color illustrations |
| Language: | English |
| Abstract: | The advanced development of electronics, signal processing and computation power has raised the expectation of ground penetrating radar (GPR) from an initially prospecting tool to an accurate surveying, mapping and imaging instrument in 3D. In any GPR 3D imaging, depth measurement of objects like utilities is always required though it is not a direct measurement and is never straightforward. Instead, it requires a series of indirect measurements represented by GPR wave velocity (v) and two-way travel time (t) affected by a number of individual uncertainties. PAS 128 (ICE, 2014) is the first specification classifying the overall uncertainty of depth measurement by GPR in different quality levels. It suggests that this uncertainty should be depth-dependent in a ratio 40% or 15% of the detected depth. But this rationale and the associated values have not yet been validated, neither through simulation nor experiments. It is in fact a compromise between the complexity in the real world and expectation perceived by the clients/engineers. This study aims to build unified models to correct, minimize and evaluate the uncertainty of depth estimation by GPR. The uncertainty in the estimated depth is firstly categorized into four sources: depolarization effect of electric field, host material, geometry of ray path, and instrumentation & signal processing. This study evaluates these errors through (1) the physics expressed in rigorous form of mathematical computations efficiently processed with robust programming, and (2) evaluated uncertainty through validation experiments in air and controlled underground environment. These two aspects are the major contributions in this thesis to the GPR research community and practitioners; and are expressed as the following. - Physics expressed in rigorous form of mathematics: The errors in the estimated depth of underground utilities by GPR were recognized and categorized into four sources: depolarization effect, host material, geometry of ray path, and instrumentation & signal processing (Chapter 3). The first source of error, depolarization effect is due to mismatch between the GPR trajectory/traverse and utility's linear alignment, and was modelled and corrected by introducing a trigonometric sin0 on the distance measurement 'xi' of the GPR traverse (Chapter 4). This correction became a prerequisite of the derivation of mathematical forms of the single trilateration model (ASTM, 2009) and the refined multi-trilateration model (Sham and Lai, 2015) in Chapter 5 and 6, respectively. The single trilateration model was found to over-simplify the actual wave path, leading to the need of developing a comprehensive multi-trilateration model taking antenna separation and radius of the cylindrical utility into account. The refined models were then used to solve the equations based on non-linear least square Levenberg-Marquardt and constrained least-square algorithms (Chapters 6 and 7). The confined least square algorithm was proven computationally efficient and robust to provide two sets of solutions simultaneously, namely (1) GPR wave velocity in the host materials and time of flight to and from the utilities, and then (2) depth of utilities and its combined uncertainty. - Evaluated uncertainty through validation experiments: Uncertainties of the two sets of solutions, based on the single- and multi-trilateration model respectively, were evaluated through a series of validation experiments in Hong Kong and IFSTTAR, France. Three main conclusions were drawn based on the experimental results. Firstly, it was found that the percentage error of estimated depth is significantly reduced from an average 10.0% (single trilateration) to an average 2.4% (multi-trilateration) while the corresponding error between estimated depth and actual depth is reduced from the order of tens of centimeters (single trilateration) to the order of several centimeters (Chapter 6). Secondly, error from time-zero dominates the evaluation of the combined uncertainty, whereas the scattering noise and the resolution of digitization in the radargram do not present explicit effects on the uncertainty evaluation. Lastly, with Gaussian-type distribution of estimated depth based on the measured pairs of hyperbolic reflection (xi, ti), 95% confidence interval or +/-2 standard deviation can be reasonably defined as the acceptable statistical criteria for concluding the combined uncertainty of the estimated depth. This work advocates unified models and comprehensive solution for the velocity and depth estimation of underground utility by GPR by providing a linear analytic solution based on the constrained least-square algorithm. This unified model and the solution cover all aspects of uncertainty evaluation by modelling, correcting, and minimizing errors of the four sources. Besides, not only depth of utilities but also velocity is obtained to evaluate soil wetness of host environment and water leakage due to pressurized water mains, though the latter part is not covered in this thesis. In conclusion, this work is believed to pave the way for enhancing the level of confidence in any GPR survey and expand its scope from geophysical prospecting to serious measurements involving rigorous evaluation of uncertainties. |
| Rights: | All rights reserved |
| Access: | open access |
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