Research On Forward Modeling And Inversion Of GPR Detection Of Layered Structure Based On Symplectic Methods

Ground penetrating radar (GPR), as a kind of fast, effective and non-destructive tools, has been widely applied to non-destructive testing of road quality. The thickness, dielectric properties of structural layers and the void existing in pavement structure can be known according to back-analysis of real GPR signals. Construction of forward model of GPR wave propagation in layered structure and the choice of high efficient optimization algorithm are keys for the inverse-analysis. Therefore, the research on forward modeling and inversion of GPR detection of layered structure has significant meaning to application of GPR non-destructive testing. In this paper, aiming at some deficiencies in the forward and inverse algorithms of ground penetrating radar, the forward model based on symplectic methods and the inverse-analysis based on particle swarm optimization (PSO) are presented. The accuracy and efficiency of the forward and inverse algorithm have been improved and it will promote the development of GPR basic theory and applied technology. The main achievements and conclusions of this paper are summarized below:(1) The model of GPR electromagnetic wave propagating in lossy layered media has been constructed based on precise integration method (PIM). The Maxwell equations are formulated in the frequency-wavenumber domain as a set of first-order ordinary differential equations containing variables being only the horizontal components of the electric and magnetic fields. Then these equations are solved by PIM with specified two-point boundary value conditions. Numerical results of the reflection and transmission coefficients are calculated by PIM and then compared with the results obtained by the analytical means and transfer matrix method (TMM), the comparison results showed that the PIM can achieve high accuracy and unconditional stability, and also can avoid the exponent overflow which may occur in TMM. In addition, the simulated signals reflected from homogeneous and inhomogeneous layered structure are obtained by PIM, and then compared with that obtained by FDTD method and measured signal, The comparison results indicate that the forward model is accurate and adaptive for simulation of GPR wave propagation in pavement structure.(2) The model of GPR electromagnetic wave propagating in2-dimensional (2D) lossy media has been developed based on symplectic partitioned Runge-Kutta (SPRK) method. The first-order, second-order and fourth-order iterative schemes are derivated, and the numerical stability of the symplectic algorithm in the2D case is verified. The absorbing boundary condition (ABC) and total-field/scatter-field (TF/SF) technology which are suitable for SPRK method are also presented. Compared with the traditional FDTD method, the SPRK schemes require only two functions for the complete description of the electromagnetic field, hence, the SPRK schemes can save computer memory usage and CPU time significantly. The wiggle trace profiles of complicated models in which cracking, void, no dense region, etc exist are simulated by SPRK method. It is useful to interpretation of real GPR data.(3) The inverse-analysis of dielectric properties of layered structure is developed by PSO and a king of improved PSO. The performance of PSO is evaluated by different control parameters making use of three stardand test functions. The back-calculation of permittivity of theory model is used to evaluate the efficiency and precision of PSO and improved PSO. The results show that the accuracy and efficiency of improved PSO are better than PSO. In addition, the surface thickness of pavement is predicted based on inversion of the measured GPR signal by improved PSO and the detection precision is verified by core boring sampling, the results indicate that the errors are less than3%and can satisfy the precision requirement of the project. These will creat condition for application of back-analysis to road quality control.