应力盘面形变化量与驱动器策动力间的多元统计模型

Multivariate Statistical Model Between Stressed-Lap Surface Displacements and Driving Forces

为了保证应力盘与非球面光学元件在不同位置上实时吻合研磨,将回归分析法应用于应力盘盘面面形变化量与驱动器策动力间变化规律的分析,建立磨盘面形变化量关于驱动器策动力的多元回归分析模型。该模型将分别以面形变化、策动力为因变量和自变量建立多元回归分析模型,并根据最小二乘原理求得回归方程系数,从而对于任意的驱动器策动力可以快速地求得与其对应的磨盘面形变化量。此外,还建立了驱动器策动力关于磨盘面形变化量的多元回归分析模型,对任意目标曲面可以快速求得与其对应的各驱动器策动力大小。这两个模型互逆,建模过程类似,能实时地为能动磨盘控制系统提供合理的输入。针对有效变形口径为420 mm,包含12个驱动器和60个微位移阵列传感器的能动磨盘,建立的应力盘面形变化量与驱动器策动力间的多元回归分析模型计算结果与试验值极为接近,验证了模型的精确性和可行性。

In order to ensure the fitting of stressed-lap and optical elements with aspheric surface with different local position in real time, regression analysis is used to analyze the changing rule between stressed-lap surface displacements and driving forces. The relationship between stressed-lap surface displacements and driving forces was formulated as a multivariate regression model. The surface displacements of a stressed-lap are modeled as a function of driving forces. The regression coefficients of the model are determined by using the least-squares method. The surface displacements can therefore be calculated quickly based on arbitrary given driving forces. At the same time, the multivariate regression model between driving forces and stressed-lap surface displacements is also proposed in this paper. The solution method is similar to the former model. The driving forces are also quickly calculated based on arbitrary given surface displacements. The proposed models are used to a 420 mm diameter stressed-lap with 12 motors and 60 macro-movement sensors. The case studies show that the results are very close to testing values, and indicate that the proposed models have the accuracy and feasibility.