A two-stage algorithm of adaptive model-based parameter estimation and its application in the fast calculation of Green's function in multi-layer soils *

Abstract

Abstract A two-stage algorithm is presented to determine an analytical model-based rational function by adaptively selecting sampling points. At the first stage, the rational interpolation function is created by using Stoer-Bulirsch algorithm and comparing the fitted model with the different ranks. At the second stage, the fitted model is validated by comparing with the first-principle model at a set of checking points. Some checking points will be added to the sampling series determined in the first stage to improve the fitted model. The new proposed algorithm is more accurate and effective than that using Stoer-Bulirsch interpolation only due to the fact that it appends the validation approach. When a highly oscillating curve is approximated, the validation ensures the fitting precision. With the two-stage MBPE algorithm, some time-consuming electromagnetic computations can be replaced by the interpolation from the fitting functions, which can increase the computational efficiency greatly. This method is used to calculate the samplings of the Green's functions in a multi-layer horizontal soil to demonstrate its effectiveness. The number of samples used to accurately model such Green's functions is less than 20 for the typical soil parameters. The computational time can be reduced by more than two orders of magnitude compared with that using the conventional uniform sampling technology.