Improved evaluation of minimum zone roundness using an optimal solution guidance algorithm

Abstract

This study proposes a high speed and accurate evaluation method for minimum zone roundness (MZR) using an optimal solution guidance algorithm (OSGA). The least-square center and roundness determine an original search zone, then the initial candidate points are configured as the centers of a minimum zone circle (MZC). To enhance the global search ability, subsequent candidate points follow the current optimal candidate points. The best three current candidate points jointly generate the new candidate points for the next iteration. In addition, a dynamic search zone updating strategy is proposed to achieve fast convergence of the optimal solution. The width of the search zone varies with the number of iterations required to achieve this rapid convergence. The effectiveness and performance of the proposed method are validated using datasets from previous studies. The proposed OSGA achieves excellent convergence performance, and reaches the global optimal solutions more quickly than previous methods. Across four different datasets, the termination condition is satisfied in only 0.0031–0.0058 s, the optimal solutions are obtained within 5–15 iterations, and the standard deviation of the MZR is less than 5.8276 × 10‒6 mm. The proposed method is also expected to extend to rapid and high-precision evaluation of cylindricity or straightness.