A simple method for stable identification of diffusion coefficients in the quasi-steady state of a post-discharge nitriding process

Abstract

This work presents a method for computing the diffusion coefficients during post-discharge nitriding through an inverse problem of coefficient identification in a model of the quasi-steady state. The related moving boundary diffusion problem is modeled by the authors taking into account the observed qualitative behaviour of the nitriding process in a laboratory. A constrained Goodman's type model is proposed to simulate the concentration profiles of the layers at the quasi-steady state. To develop an algorithm for the identification of the diffusion coefficients, using experimental data of the concentrations at different levels of depth, a least squares problem is solved. The solution method is reduced, with some algebraic manipulations, into a simple geometrical rule. Finally, the approach is applied when data errors are taken into account and a regularization algorithm is proposed.