Mathematical Foundations for Form Inspection and Adaptive Sampling

Nonlinear forms such as the cone, sphere, cylinder, and torus present significant problems in representation and verification. In this paper we examine linear and nonlinear forms using a heavily modified support vector machine (SVM) technique. The SVM approach applied to regression problems is used to derive quadratic programming problems that allow for generalized symbolic solutions to nonlinear regression. We have tested our approach to several geometries and achieved excellent results even with small data sets, making this method robust and efficient. More importantly, we identify process or inspection tendencies that could help in better designing the processes. Adaptive feature verification can be achieved through effective identification of the manufacturing pattern.