Infinite-Dimensional Thermal Observability in Materials Processing

This article addresses the question of thermal observability as encountered in thermal manufacturing processes of solids. The Green-Galerkin method, previously developed to address the dual question of thermal controllability in infinite-dimensional heat conduction systems, is further explored and utilized to study various temperature profiles of variable complexity. It is proved that, despite the formulation complexities that arise from the spatial and temporal variation of the system variables, the developed method is able to observe the temperature field that exists within a solid body through surface temperature measurements alone