基于自适应带宽核密度估计的压气机叶片加工误差统计分析方法

Statistical analysis method of compressor blade machining error based on adaptive bandwidth kernel density estimation

针对压气机叶片的加工误差统计分析建模问题,本文提出了一种自适应带宽的非参数核密度估计方法,实现了压气机叶片加工误差的概率密度建模。首先,基于拇指法则求解固定带宽核密度估计中的固定最优带宽作为起始带宽。然后,在固定最优带宽的基础上引入灵敏因子构建了自适应带宽函数,并通过自适应带宽函数对核密度估计进行调控。在此基础上,以核密度估计的精度均方差(MSE)与灵敏度S为目标函数,采用精英策略遗传算法对灵敏因子进行优化获得最优灵敏因子。进而计算出不同数据样本点对应的最优带宽,使得带宽能够根据数据样本疏密程度进行自适应调整。最后,对134组机械加工叶片的叶型截面的6种叶型误差进行统计建模,并采用交叉检验法验证了自适应带宽核密度估计的泛化性能。实验结果表明该方法的适用性好精度高,且拟合优度均在0.9以上,同时避免了传统固定带宽核密度估计的局部适应性问题。本文所提出的统计分析方法能够准确获得现有工艺能力下压气机叶片加工误差的分布特性,为叶片气动设计优化改进提供了一种有效手段。

Aiming at the problem of statistical analysis and modeling of machining error of compressor blades,this paper proposes a nonparametric kernel density estimation method with adaptive bandwidth,and realizes the probability density modeling of machining error of compressor blades.Firstly,based on the thumb rule,the fixed optimal bandwidth in the fixed bandwidth kernel density estimation is solved as the initial bandwidth.Then,based on the fixed optimal bandwidth,the sensitivity factor is introduced to construct the adaptive bandwidth function,and the kernel density estimation is regulated by the adaptive bandwidth function.On this basis,the accuracy MSE and sensitivity S of kernel density estimation are defined as objective functions,and the elite strategy genetic algorithm is used to optimize the sensitivity factor to obtain the optimal sensitivity factor.Then the optimal bandwidth corresponding to different data sample points is calculated,so that the bandwidth can be adaptively adjusted according to the density of data samples.Finally,six kinds of blade profile errors of 134 groups of machined blades are statistically modeled,and the generalization performance of adaptive bandwidth kernel density estimation is verified by cross-test method.The experimental results show that the method has good applicability and high precision,and avoids the local adaptability problem of traditional fixed bandwidth kernel density estimation.The statistical analysis method proposed in this paper can accurately obtain the distribution characteristics of compressor blade machining error under the existing process capability.It provides an effective means for the optimization and improvement of blade aerodynamic design.