Extending the inverse sequential quasi-Newton method for on-line monitoring and controlling of process conditions in the solidification of alloys

This work introduces the sequential quasi-Newton method (SQNM) to solve the inverse design problem of estimating the transient boundary heat fluxes that produce desired evolutions of the solidus and liquidus isotherms in alloys' solidification processes. This is an unprecedented application for sequential gradient-based methods. The final goal is monitoring and controlling the evolution of the mushy zone in a near real-time fashion, which is of high technological interest to the foundry industry. We assess the performance of the SQNM in solving several inverse design problems in one- and two-dimensional domains. The method satisfactorily estimates the boundary heat fluxes using relatively few future measurements. However, some instabilities have been detected in the SQNM-predicted heat fluxes. To alleviate this issue, we proposed a modified version of SQNM, say mSQNM, that employs an inexact line search strategy to find the optimal step length during the iterative estimation procedure. We finally show how mSQNM improves the estimation of the boundary heat fluxes.