Spectral element technique for efficient parameter identification of layered media Part II: Inverse calculation

In Part I of this series of articles a forward model was presented for the simulation of wave propagation in a multi-layer system by means of the spectral element method. In the current article and, on the basis of the forward model, a procedure is presented for inverse calculation of the system parameters. The proposed procedure is based on iterative comparisons of measured versus theoritically determined system transfer functions. The performance of three minimization algorithms; factored Secant update, modified Levenberg-Marquardt and Powell hybrid for solving the resulting system of nonlinear equations is evaluated. For the problem under consideration, the Powell hybrid algorithm exhibits better stability and convergence characteristics. As an application, the inverse procedure is utilized for the determination of pavement layer moduli and thicknesses via the use of the falling weight deflectometer (FWD) test. The calculations show that the developed procedure is accurate and computationally efficient. As a result of these calculations, modifications to the standard practice of FWD measurements and instrumentation are suggested.