Realistic numerical modelling of ground penetrating radar for landmine detection
Ground-Penetrating Radar (GPR) is a popular non-destructive geophysical technique with a wide range of diverse applications. Civil engineering, hydrogeophysics, forensic, glacier geology, human detection and borehole geology are some of the fields in which GPR has been applied with successful or promising results. One of the most mainstream applications of GPR is landmine detection. A lot of methods have been suggested over the years to assist the landmine detection issue. Metal detectors, trained rats or dogs, chemical methods and electrical resistivity tomography are –amongst others– some of the suggested techniques. The non-destructive nature of GPR makes it an attractive choice for a problem such as demining in which contact to the ground is not allowed. The main advantage of GPR is its ability to detect both metallic and non-metallic targets. Furthermore, GPR can provide an insight regarding the nature of the target (e.g. size, burial depth, type). From the above, it is evident that GPR can potentially reduce the false alarms emerging from small metallic objects (e.g. bullets, wires, etc.) usually encountered in battle-fields and industrialised areas. Combining the robustness of the metal detector with the resolution of GPR results in a reliable and efficient detection framework which has been successfully applied in Cambodia and Afghanistan. Despite the promising, and in some cases impressive results, aspects of GPR can be further improved in an effort to optimise GPR’s performance and decrease its limitations. The validation of a GPR system is usually achieved through the so called Receiver Operation Characteristics (ROC) which depicts the probability of detection with respect to the false alarm rate. ROC is a highly nonlinear function which is sensitive to the environment as well as to the antenna unit. Landmines are typically small objects, often less than 10 cm diameter, which are shallow buried, usually in less than 10 cm depth, and sometimes almost exposed. In order for the landmines to be resolved, high frequency antennas are essential. The latter are sensitive to soil’s inhomogeneities, rough surface, water puddles, vegetation and so on. Apart from that, the near field nature of the problem makes the antenna unit part of the medium which contributes to the unwanted clutter. The above, outlines the multi-parametric nature of the problem for which no straightforward approach has yet to be proposed. Numerical modelling is a practical and solid approach to understand the physical behaviour of a system. In the case of GPR for landmine detection, numerical modelling can be a practical tool for designing and optimising antennas in synthetic but nonetheless realistic conditions. Apart from that, evaluation of a processing method only to a specific environment is not a robust approach and does not provide any evidence for its wider inclusivity and limitations. However, evaluation in different conditions can become costly and unpractical. Numerical modelling can tackle this problem by providing data for a wide range of scenarios. An extensive database of simulated responses, apart from being a practical testbed, can be also employed as a training set for machine learning. A multi-variable problem like demining, in order to be addressed using machine learning, requires a large amount of data. These must equally include all possible different scenarios i.e. different landmines, in different media with stochastically varied properties and topography. Additionally, different heights of the antenna and different depths of the landmines must also be examined. Numerical modelling seems to be a practical approach to achieve an equally distributed and coherent dataset like the one briefly described above. Numerical modelling of GPR for landmine detection has been applied in the past using generic antennas in simplified and clinical scenarios. This approach can be used in an educational context just to provide a rough estimation of GPR’s performance. In the present thesis a realistic numerical scheme is suggested in which, simplifications are kept to a minimum. The numerical solver, employed in the suggested numerical scheme, is the Finite- Difference Time-Domain (FDTD) method. Both the dispersive properties and the Absorbing Boundary Condition (ABC) are implemented through novel and accurate techniques. In particular, a novel method which implements an inclusive susceptibility function is suggested and it is shown that surpasses the performance of the previous approaches while retaining their computational efficiency. Furthermore, Perfectly Matched Layer (PML) and more specifically Convolutional Perfectly Matched Layer (CPML) is implemented through a novel time-synchronised scheme which it is proven to be more accurate compared to the traditional CPML with no additional computational requirements. An accurate numerical solver, although essential, is not the only requirement for a realistic numerical framework. Accurate implementation of the geometry and the dielectric properties of the simulated model is highly important, especially when it comes to high-frequency near-field scenarios such as GPR for landmine detection. In the suggested numerical scheme, both the soil’s properties as well as the rough surface are simulated using fractal correlated noise. It is shown, that fractals can sufficiently represent Earth’s topography and give rise to semi-variograms often encountered in real soils. Regarding the dielectric properties of the soils, a semi-analytic function is employed which relates soil’s dielectric properties to its sand fraction, clay fraction, sand density, bulk density and water volumetric fraction. Subsequently, the semi-analytic function is approximated using a Debye function that can be easily implemented to FDTD. Vegetation is also implemented to the model using a novel method which simulates the geometry of vegetation through a stochastic process. The experimentally-derived dielectric properties of vegetation are approximated –similarly to soil’s dielectric properties– with a Debye expansion. The antenna units tested in the numerical scheme are two bow-tie antennas based on commercially available transducers. Regarding the targets, three landmines are chosen, namely, PMN, PMA-1 and TS-50. Dummy landmines are used in order to obtain their geometrical characteristics and comparison between measured and numerically evaluated traces are used to tune the dielectric properties of the modelled landmines. Lastly, water puddles are realistically implemented in the model in an effort to realistically simulate high-saturated scenarios. The proposed numerical scheme has been employed in order to test and evaluate widely used post-processing methods. The results clearly illustrate that post-processing methods are sensitive to the antenna unit as well as the medium. This highlights the importance of an accurate numerical scheme as a testbed for evaluating different GPR systems and post-processing approaches in wide range of scenarios. Using an equivalent 2D numerical scheme –restricted to 2D due to computational constrains– preliminary results are given regarding the effectiveness of Artificial Neural Network (ANN) subject to an adequate and equally distributed database. The results are promising, showing that ANN can be successfully employed for detection as well as classification using only a single trace as input. A basic requirement to do so is a representative training set. This can be synthetically generated using a realistic numerical framework. The above, provide solid arguments for further expanding the proposed machine learning scheme to the more computationally demanding 3D case.
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