Comparison of chaos optimization functions for performance improvement of fitting of non-linear geometries

• Proper seeding can improve geometric fitting algorithms convergence.
• Seeding by chaos optimization helps avoiding local minima.
• Different one-dimensional maps effectiveness is shown on different geometries.
• The logistic map is shown to be the best map for seeding Levenberg–Marquardt algorithm.

Fitting algorithms play an important role in the whole measuring cycle in order to derive a measurement result. They involve associating substitute geometry to a point cloud obtained by an instrument. This situation is more difficult in the case of non-linear geometry fitting since iterative method should be used. This article addresses this problem. Three geometries are selected as relevant case studies: circle, sphere and cylinder. This selection is based on their frequent use in real applications; for example, cylinder is a relevant geometry of an assembly feature such as pin-hole relationship, and spherical geometry is often found as reference geometry in high precision artifacts and mechanisms.In this article, the use of Chaos optimization (CO) to improve the initial solution to feed the iterative Levenberg–Marquardt (LM) algorithm to fit non-linear geometries is considered. A previous paper has shown the performance of this combination in improving the fitting of both complete and incomplete geometries. This article focuses on the comparison of the efficiency of different one-dimensional maps of CO. This study shows that, in general, logistic-map function provides the best solution compared to other types of one-dimensional functions. Finally, case studies on hemispheres and industrial cylinders fitting are presented.