Improved evaluation of minimum zone roundness by integrating bidirectional search of unequal probability and offset mechanisms

This paper reports an improved method that integrates a bidirectional search of unequal probability and an offset movement mechanism (BSOM) to evaluate the minimum zone roundness (MZR) with high speed and accuracy. The centre and roundness of a least-squares circle are first solved to construct an original search zone, and the initial candidate points of the minimum zone circle centre are configured. A bidirectional search of unequal probability that considers the subsequent points either toward or away from the current best candidate point is designed to enhance the global search ability. Considering the candidate points at different located positions have different effects on convergence characteristics, the search area is divided into two sections based on the average distance between the current best candidate point and the other candidate points, and different forward and backward search probabilities are configured. An adaptive offset movement mechanism is integrated to generate new candidate points for the next generation. The effectiveness of the proposed method is experimentally verified using datasets from previous studies. The configurations of BSOM parameters and influence of the distribution and number of data points on evaluation accuracy and efficiency are analyzed. The experimental examples and comparison results demonstrate the excellent convergence performance of the proposed method, which reaches the global optimum faster than previous methods. Across six different datasets, only 0.0095 s-0.0282 s is required when the average distance D 1.0 × 10^-7 mm as the iteration convergence condition, and the standard deviation of the MZR is less than 5.3777 × 10^-9 mm, while the search parameters are set as P ₁ = 0.6, P ₂ = 0.95, and b = 0.6. The proposed approach is expected to be suitable for on-line evaluation of roundness error.