Inverse modelling for estimation of average grain size and material constants - An optimization approach

The goal is to build up an inverse model capable of finding the average grain size history during an extrusion process and other material constants by using simulated strain and temperature values. This problem of finding the parameter values is based on linear and nonlinear least-squares regressions, coupled with microstructure control models and the solution of a finite element extrusion model. The problem is ill posed and we use the Tikhonov's regularisation to stabilise the solution process. Further some of the parameters in the model are linear and some are nonlinear. We determine the linear parameters using simple linear algebra and for the computation of non-linear parameters we use MATLAB's routine lsqnonlin.