A multimodal inverse problem for GPR pavement parameter estimation

Abstract

This thesis proposes a different approach to determine the permittivity and thickness of highways modeled as overlapping layers using the subsoil profile generated by the GPR. In this way, it was developed and analyzed an optimization algorithm based on evolutionary computation that could be applied to solve the inverse problem. By means of the proposed methodology, we intend to estimate the highway properties providing some advantages that wasnt alluded in previous studies in the area. The pavement parameter estimation using ground penetrating radar is approached from three different methodologies. These methodologies were tested on a flexible pavement structure attempting to perform a comparative analysis that allowed to highlight the advantages and disadvantages of their use. First, a time domain approach was treated and results showed that the method provides a closed form to evaluate the pavement parameters using single equations. However, it was demonstrated that the accuracy of this method is highly dependent on the evaluation of the reflection instants and the peak amplitudes. The presence of multiple reflections worsens the method performance, since it is difficult to associate the reflected pulse to its respective interface where the reflection originates. Moreover, very thin layers generate overlapped pulses that are not easily detected. Secondly, a frequency domain approach was performed minimizing an error function. In this case, the characteristics of the multiple layers could not be obtained in a closed form. The problem of pavement characterization is usually treated as an electromagnetic inverse problem, which is usually solved using some optimization method. Results for this method guaranteed that the problem was well-posed by means of the definition of a maximum frequency which also results in a unimodal optimization problem in the optimum point vicinity. This unimodal characteristic gives the advantage of using deterministic optimization tools, resulting in fast convergence methods. However, the main drawback concerning the existence of a maximal frequency is the size of the antenna. Setting a maximal frequency limits the minimal size of the antenna. Finally, a third approach was suggested by the author of this thesis to take advantages of both methods already defined. The inverse problem was also based on minimizing the error function, similarly to what was described on the previous approach. Nevertheless, the used signal was expanded to include multiple frequency components. Results showed that using this method it is guaranteed: the well-posedness of the problem without the maximal frequency restriction and that the pavement parameters were properly obtained. However, a strong multimodal characteristic is presented in the objective function which cancel any possibility of using deterministic optimization tools. This leads to the use stochastic algorithms that adds computational complexity