Equalization of free geodetic networks by search methods for geodetic monitoring of structures in arctic areas

Abstract

While carrying out work to ensure the technical safety of buildings and structures in the Arctic regions, one of the important stages is geodetic monitoring. Provided that the complexity of ensuring the stability of reference points in the Arctic zone when conducting geodetic monitoring of engineering facilities, geodetic networks should preferably be equated as free, i.e., to equate the reference points on a par with the defined ones. The present article provides variants how to to equalize geodetic networks to carry out a search method of non-linear programming, which is given a theoretical substantiation for the method and the order of estimating accuracy of the outcomes of the equalization of the generalized Makarov method. The procedure of pseudo transformation of a matrix of normal equations of unknowns with the application of an algorithm of a search method of nonlinear programming is given. The correctness of the application of the search method to the pseudo transformation of a matrix of normal equations of unknowns by the coincidence of outcomes of the pseudo transformation of the given matrix based on skeleton expansion done in M. Mashimov's work is proved. Equalization and estimation of accuracy of free leveling network with the application of search method and generalized Makarov's method are carried out. The conclusion about the correctness of the application of a search method of nonlinear programming for the processing of free geodetic networks at the performance of geodetic monitoring of buildings and constructions in the Arctic area is made.

Keywords

• geodesic monitoring
• search method
• free network
• matrix inversion
• pseudo-inversion