Applying particle swarm optimization algorithm to roundness error evaluation based on minimum zone circle

Abstract

Minimum zone circle (MZC) method and least square circle (LSC) method are two most commonly used methods to evaluate roundness, but only the MZC method complies with the standard definition and can obtain the minimum roundness error value. The determination of the center of MZC is a nonlinear optimization problem which is suitable to be solved by particle swarm optimization (PSO) algorithms. In this paper, the standard PSO algorithm was introduced and theory analysis about the impact of value selection of some important parameters, such as inertia weight ω, on the algorithm’s stability and convergence was carried on so as to provide basis for giving these parameters better values. Furthermore, the superiority of making ω decrease linearly with iterations was verified through a computation experiment in terms of stability and accuracy, compared with the other three cases of ω=1, 0.5, 0. Based on the analysis, the novel PSO algorithm, with ω decreasing linearly from 0.9 to 0.4 and the LSC center as the initial positions of the particles, is implemented to obtain MZC-based roundness errors of sampling points collected from circular section profiles by a coordinate measuring machine (CMM). By comparing the novel PSO–MZC results with the LSC-based results, it is concluded that the former are a little smaller than the latter, which verifies that the novel PSO algorithm is feasible to calculate roundness error and the fact that a LSC-based one is generally larger than a MZC-based result; the values of the two roundness errors are both related to sample size and increase with an increase in the sample size with a decreasing increment.