On a General Parameterization for Inverse Analysis of Heat Deposition Processes

Abstract

A general parameterization for inverse analysis of heat deposition processes using incomplete or minimal experimental data is presented. This parameterization is considered general in the sense that it can be applied, in principle, to the inverse analysis of a wide range of different types of heat deposition processes, including welding. The structure of this 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 corresponding optimal parametric representation lies in the model space and is determined by the characteristics of the available data sets spanning the data space and the nature of the data sampling for purposes of parameter determination via appropriate optimization techniques. The elements of the proof presented here provide an elucidation of certain aspects of inverse heat-deposition analysis that are important for practical application.