Geometrical deviation modeling and monitoring of 3D surface based on multi-output Gaussian process

Abstract

Geometrical deviation is an important factor in determining the quality of a three-dimensional (3D) Surface. For 3D surfaces with complex shapes, the high-definition measurement (HDM) technology can provide detailed information on surface topography, which inspired new challenges in characterizing, modeling, and monitoring geometrical deviations. This paper proposes a spherical multi-output Gaussian process (S-MOGP) method to model and monitor 3D surfaces. Firstly, the surface in the 3D coordinate system is mapped to the spherical 2D parameter domain. Secondly, a state equation based on the multi-output Gaussian process is established to model the 3D surface. Finally, statistics are calculated and control charts are presented to monitor the geometrical deviation. The results of simulations and a case study show that the proposed method can effectively model 3D surfaces and monitor the geometrical deviations.