Coordinate transformation uncertainty analysis and reduction using hybrid reference system for aircraft assembly

In aircraft assembly, standard reference points with nominal coordinates are commonly applied for coordinate transformation between multiple measurement stations and the assembly coordinate system. For several reasons in practical application, these points often fail to envelop the key assembly space, which leads to large transformation uncertainty. This paper aims to analyze and further reduce the coordinate transformation uncertainty by introducing a new hybrid reference system (HRS).

Several temporary extension points without known coordinates are added to enhance the tightness between different stations, especially at the weakness area in the network, thus constituting an HRS together with the existing standard reference points. The coordinate transformation model of the HRS-based measurement network is established based on an extend Gauss–Markov model. By using the geometrical differential property and variance-covariance propagation law, the covariance matrixes in the transformation model are calculated, and the analytical solution of the uncertainties of transformation parameters are ultimately derived. The transformation uncertainty of each check points is presented by Helmert error expression.

The proposed analytical solution of transformation uncertainty is verified using the state-of-the-art Monte Carlo simulation method, but the solution process is simpler and the computation expenses are much less.

The HRS with three temporary extension points is practically applied to a tail boom in-site measurement for assembly. The average transformation uncertainty has been reduced by 26 per cent to less than 0.05 mm.

The hybrid coordinate transformation model is proposed for the first time. The HRS method for transformation uncertainty reduction is more economical and practical than increasing the number of standard reference points.