Abstract:

As the intelligent evaluation results of form error are of poor stability,it is necessary to investigate the probability distribution characteristics of the evaluation results and the corresponding fitting method to improve the reliability of the intelligent evaluation method. In this paper,by taking the flatness error evaluation based on the particle swarm optimization ( PSO) algorithm as an example,the probability distribution characteristics of the intelligent evaluation results was analyzed,and a β-distribution uniform expression was proposed to fit the intelligent evaluation results,followed by a fitting performance test via the K-S method. Then,the three-coordinate data of a plate were measured,the plate flatness was evaluated for 100 times by using the PSO algorithm,and the intelligent evaluation results were fitted by employing the β-distribution uniform expression method. It is demonstrated that,when the intercept percentile Q_p is in the interval of [20%,70%],the β-distribution uniform expression method is of high fitting performance for the intelligent evaluation results,the fitted shape parameters are both more than 1,and the fitted probability distribution deviates to the right,which is consistent with the probability distribution characteristics of the intelligent evaluation results.

Key words: flatness error, particle swarm optimization, probability distribution fitting, β-distribution