Application of the Simulated Annealing algorithm and robust weight functions for identification of constant reference points in 3D deformation analysis

Abstract

Identification of the reference base in deformation analysis is a key element in obtaining the correct deformations of the monitored object. As it cannot be assumed that all the reference points are stable, a stability check must be conducted as the initial stage of the deformation analysis. Most known methods used for the identification of stable reference points cover leveling or horizontal networks. This study presents an approach using a coordinate transformation for the comparison of coordinates corresponding to two measurement epochs in 3D deformation analysis. The proposed algorithm is aimed at selecting such coordinate transformation parameters that correspond to the acceptable transformation residuals for the points of the reference base. Three robust adjustment weight functions (Kadaj, Huber, and Danish) were selected as a basis for formulating the objective function. The six 3D transformation parameters create a 6D search space. The optimization algorithm (simulated annealing) was applied for the search through the search space for desirable transformation parameters. The simulated example 3D two-epoch network was used for testing the performance of particular objective functions. The necessary parameters of the objective functions and optimization procedure were selected empirically. The test results confirmed the correctness of the adopted solution and the ability of all objective functions to detect the groups of fitting points. The objective function based on the Danish weight function appeared to be most promising due to the wide possibilities of shaping its features, which enable tailoring the objective function to the specific need.