Inverse Geometry Problem Of Estimating The Location Of The 1150◦C Isotherm In A Blast Furnace Hearth.

Abstract

The hearth life is the key factor for the campaign length of a blast furnace and, in
order to understand the wear mechanisms, it’s useful to be able to estimate the location of the
1150◦C isotherm because it represents a potential limit on the penetration of the liquid iron into
the hearth wall.
The location of the 1150◦C isotherm can be estimated solving a nonlinear inverse heat transfer
problem, based on the thermocouples located inside the hearth. As the domain of the heat
transfer problem is unknown, a set of parameters is defined in order to describe it. These parameters
are the inverse geometry heat transfer problem unknowns. In previous publications
(M. Gonzalez et al., 4th IAS Ironmaking Conference, Nov. 2003, 381-386) the authors have
presented this inverse geometry model applied to a unidimensional geometry.
In this work we reformulate the model for a bidimensional geometry, where the iteratively regularized
Gauss-Newton method is used to solve the nonlinear inverse problem, Radial Basis
Functions (RBF) are used to describe the geometry from a set of parameters, and remeshing
techniques are used to discretize the domain. We describe the developed bidimensional inverse
model and validate the solution against simulated measurements with different levels of noise.