New Layer-Moduli Back-Calculation Method Based on the Constrained Extended Kalman Filter

In pavement engineering, good estimation of layer moduli from nondestructive methods is an important tool for scheduling and designing rehabilitation projects. The falling weight deflectometer test is perhaps the most commonly used nondestructive method for the evaluation of the structural performance of pavement systems. These measurements are then used to back-calculate the properties of the layered pavement materials. A new method based on constrained extended Kalman filter (EKF) is proposed for back-calculating layer moduli. The method uses a transformation to constrain the "searchable" domain for determining the optimal estimates of material parameters and a weighted iteration algorithm that enhances the speed and convergence of the iterative procedure. In numerical examples, the proposed method converges to the actual layer moduli with high accuracy for three-, four-, and five-layer pavement systems even though very different initial values are used. The paper also compares the performance of EKF with other methods published in the literatures. The proposed method shows excellent performance in terms of speed and stability while providing highly accurate estimates of material properties including cases in which nonlinear layers were considered. It is concluded that the constrained EKF is a fast, stable, and consistent algorithm used in back-calculation of layer moduli.