Spatial Modulation and Filtering of Diffusion Patterns for Inverse Analysis of Heat Deposition

Abstract

General parameterizations are constructed for spatial modulation and filtering of heat diffusion patterns according to general energy deposition characteristics occurring within a volume of material resulting from a volumetrically coupled energy source. These parameterizations include previously constructed models of energy deposition as special cases. The construction of a general parameterization of energy deposition processes is necessary for their inverse analysis. The structure of such a parameterization follows from the concepts of model and data spaces that imply the existence of an optimal parametric representation for a given class of inverse problems. Accordingly, the optimal parametric representation is determined by the characteristics of the available data, which in principle can contain both experimental measurements and numerical simulation data. Parameterizations for spatial modulation and filtering of heat diffusion follow from the observation that many different types of energy deposition processes can be represented by weighted sums of basis functions whose general forms are that of spatially modulated or filtered diffusion. A significant aspect of the parameterizations presented is that the definition of the inverse heat deposition problem, which is adopted for their construction, provides a rigorous foundation for a highly flexible and general parameterization of energy deposition processes, which is essential for their inverse analysis. A preliminary proof is presented that shows the significance of these parameterizations for the application of similarity transformations to the inverse analysis of energy deposition processes. The applicability of similarity transforms to the inverse analysis of heat deposition is another property that follows from the specific definition of the inverse heat deposition problem considered here.