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

机译：基于最小区域圆的粒子群优化算法在圆度误差评估中的应用

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摘要

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 resu 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.
机译：最小区域圆（MZC）方法和最小二乘圆（LSC）方法是评估圆度的两种最常用方法，但是只有MZC方法符合标准定义，才能获得最小圆度误差值。 MZC中心的确定是一个非线性优化问题，适合用粒子群算法（PSO）解决。本文介绍了标准的PSO算法，并对惯性权重ω等重要参数的取值对算法的稳定性和收敛性的影响进行了理论分析，为为这些参数提供更好的值提供了依据。 。此外，与其他三种情况ω= 1，0.5，0相比，通过计算实验在稳定性和准确性方面证明了使ω随着迭代线性降低的优越性。在分析的基础上，新颖的PSO算法具有通过将ω从0.9线性减小到0.4，并将LSC中心作为粒子的初始位置，来实现通过坐标测量机（CMM）获得基于MZC的从圆形截面轮廓收集的采样点的圆度误差。通过将新颖的PSO-MZC结果与基于LSC的结果进行比较，可以得出结论，前者比后者小一些，这证明了新颖的PSO算法可用于计算圆度误差，并且证明了基于LSC的事实。通常大于基于MZC的结果;两个圆度误差的值都与样本大小有关，并且随着样本大小的增加而增加，而减少的程度则增加。

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