Abstract:

In the construction and maintenance of particle accelerators, all the accelerator elements should be installed in the same coordinate system, only in this way could the devices in the actual world be consistent with the design drawings. However, with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term, the control points upon the engineering structure will be displaced, and the fitness between the subnetwork and the global control network may be irresponsible. Therefore, it is necessary to evaluate the deformations of the 3D alignment control network. Different from the extant investigations, in this paper, to characterize the deformations of the control network, all of the congruent models between the points measured in different epochs have been identified, and the congruence model with the most control points is considered as the primary or fundamental model, the remaining models are recognized as the additional ones. Furthermore, the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models. Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network. Considering the actual work of the alignment, it is essential to identify the competitive models in the monitoring network, which can provide us a hint that, even the fitness between the subnetwork and the global control network is good, there are still deformations which may be ignored. The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.

Key words: similarity transformation; 3D alignment control network; deformation analysis; hypothesis testing; iterative global congruence test; iterative combinatorial theory