Uncertainty Analysis in Dispersive and Lossy Media for Ground-Penetrating Radar Modeling

A Surrogate Model Based on Artificial Neural Networks for Wave Propagation in Uncertain Media

“…Submitting (5), (7) and (8) into the update equations of ADE-FDTD, we obtain the electric field E z and the magnetic fields H x and H y . In the iteration provided in (9), (10), (11), and (12), the three auxiliary variables are written as L k z (nx, ny, θ), D k z (nx, ny, θ) and R k p z (nx, ny, θ), where nx and ny are space steps along the x and y directions, respectively, and k is the time step.…”

“…The center of the solid metallic medium is (1.80m, 0.80m) and its size is 0.30 m × 0.30 m. The metallic medium is buried 2.05 m below ground level. The details of the model are given in [8]. Compared with the intrusive gPCE method proposed in [8], the number of uncertain parameters in this paper is increased from one to seven, and the variation in each parameter is increased from 5% to 10%.…”

“…In practice, the exact values of the inputs are always unknown, leading to the uncertainties in the output of the simulation [7]. Quantifying the uncertainty in the simulation result is an indispensable part in GPR calculation when the acceptability of the output is considered [8].…”

“…The traditional non-intrusive method is Monte Carlo simulation (MCS) which requires running the deterministic simulation code several thousand times to converge, resulting in a high computational cost [7]. In [8], the authors propose an intrusive method which implements generalized polynomial chaos expansion (gPCE) into the auxiliary differential equation (ADE) FDTD [6] to quantify uncertainty induced by uncertain parameters. A considerable computational advantage over MCS is achieved.…”

“…A considerable computational advantage over MCS is achieved. However, one of its limitations is that the computational complexity increases rapidly with the increasing number of uncertain input parameters [8]. To solve this problem, it is essential to identify important uncertain parameters from all inputs for some applications, which is not easy to achieve in practice.…”