Sensitivity of the inverse problem solution related to detection of rebars buried in concrete by using GPR scanning

Abstract

Ground Penetrating Radar is a device which is nowadays largely used in civil engineering applications. Considering a rebar buried in a concrete medium, this work addresses sensitivity of the inverse problem solution associated to identification of the object radius and its depth from B-scan data acquired by the GPR. The approach uses a closed form parameterisation of the hyperbola trace emerging in the radargram as function of the hyperbola apex coordinate along the direction of B-scan, the cover depth, the radius of the object and the relative permittivity of the medium. Estimation of the wave velocity, the hyperbola apex coordinates and the rebar radius was performed through solution of an appropriate nonlinear least mean squares problem. Perturbation analysis was then conducted by assuming that the hyperbola points coordinates, extracted from raw data of radargram, are randomly distributed according to Gaussian densities of probabilities. The effect of the amount of data was also analyzed. The method was implemented in Matlab environment. The obtained results have shown that identification process is extremely sensitive to noise affecting the B-scan raw data, but not to the number of points used in identification.