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

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.