Choosing the geodetic network for a system for tracking deformations of circular engineering structures

This paper examines and evaluates three possible versions of networks for circular structures (curvilinear structures in the general case), for which attention is focused on the accuracy of the positioning of reference points with respect to a specified production axis along the normal to the axis. A significant difference in the tolerances in two mutually perpendicular directions often obtains in setting up the production equipment of flow lines, accelerators and their storage rings, radiotelescope antennas, and others. Observance of one of the tolerances is ensured by the stability of the structure, while observance of the other, more stringent tolerance must be monitored through measurements. A comparison of the alternative networks was made on the basis of three main indices: (a) the rms errors in determining the position of points with respect to the production axis; (b) the correlation coefficients of the errors for the weakest point in the network and for all other points; (c) the rms amplitudes of the Fourier harmonics that characterize the smoothness of the curve obtained and the presence of hidden periodicities as a function of the residual errors