Segmented Sampling Least Squares Algorithm for Green's Function of Arbitrary Layered Soil

Abstract

Accurate grounding parameters calculation ensures the safe and stable operation of the power equipment, and the Green's function calculation of layered soil is the basis of the grounding parameters calculation. The conventional complex image method for Green's function of layered soil mainly include the global equal interval sampling method and the Prony's fitting method, which often have 2 disadvantages: 1. The complex exponential terms of Prony's method are usually twice the number of soil layers, and the amount of calculation increases linearly with the number of soil layers; 2. The global equal interval sampling method cannot guarantee to accurately approximate the integral kernel function, causing the failure to solve Green's function of some complex layered soils. To accurately and efficiently solve the Green's function of arbitrary layered soil, this paper, taking Green's function of horizontally layered soil where the field points and source points are both on the soil surface as an example, summarizes 3 key features of the integral kernel function. Segmented sampling method based on the extreme points of the integral kernel function and the 3-order least squares method are combined to innovatively propose the segmented sampling least squares algorithm (SSLSA) for solving Green's function of layered soil. Only 6 sampling points are required for SSLSA in each sampling segment. The results show that the SSLSA can approximate the integral kernel function more accurately, solve some complicated cases that the conventional complex image method cannot, and has the advantages of good accuracy and efficiency.