A neural-fuzzy model with confidence measure for controlled stressed-lap surface shape presentation

In computer controlled large aspheric mirror polishing process, it is crucially important to build an accurate stressed-lap surface model for shape control. It is desirable to provide a practical measure of prediction confidence to access the reliability of the resulting models. To build a reliable prediction model for representing the surface shape of stressed lap polishing process in large aperture and highly aspheric optical surface, this paper proposed a predictive model with its own confidence interval estimate based on a fuzzy neural network. The calculation of confidence interval accounts for the training data distribution and accuracy of the trained model with the given input-output data. Simulation results show that the proposed confidence interval estimation reflects the data distribution and extrapolation correctly, and works well in high-dimensional sparse data set of the detected stressed lap surface shape changes. The original data from the micro-displacement sensor matrix were used to train the neural network model. The experiment results showed that the proposed model can represent the surface shape of the stressed-lap accurately and facilitate the computer controlled optical polishing process.