Solution of inverse geometry problems using bezier splines and sensitivity coefficients

Abstract

This chapter discusses an algorithm for phase change front identification in continuous casting. Nowadays, this process is frequently utilized for producing metals, alloys, and semiconductor crystals. By using this approach, a significant reduction in the number of identified values and, consequently, in the number of measurements has been achieved. Some modifications to the solution algorithm providing convergence of the iteration process have also been discussed. These modifications consist of guessing the initial phase change front position employing a lumping procedure.An accurate determination of the location of the interface between the liquid and solid phases is very important if the quality of the casting material is taken into account. The problem is formulated as an inverse geometry problem, and the solution procedure requires building up a series of direct solutions that gradually produce accurate results. The proposed algorithms make use of sensitivity analysis and the boundary element method. Cubic boundary elements are used in this work for modeling the interface between solid and liquid phases by cubic Bezier segments. A case study of continuous casting of copper is solved to demonstrate the main features of the developed algorithms.