On combining chaos search and levenberg-marquardt algorithm for non-linear substituted geometric fitting problems

Product quality is becoming a main concern in today manufacturing. As such, dimensional metrology is strictly necessary. High accuracy result while reducing speed in measuring a product has to catch up with the improvement of metrology instrument which can capture many points in less time. Fitting algorithm of point clouds plays a critical role for the measurement accuracy and speed. In this study, non-linear least-square fitting of circle, sphere and cylinder without any prior knowledge of their nominal is addressed. These geometries have common use in practice, such as sphere for calibration and hole-shaft features in mechanical assembly application. The improvement of initial point guess for Levenberg-Marquardt (LM) algorithm by employing Chaos Optimization (CO) method is presented. The results show that, with this combination, higher quality of fitting results in term of smaller norm of the residuals can be obtained while preserving the computational cost.