Numerical simulation of a casting furnace

Industrial furnaces constitute a complex, nonlinear, distributed-parameter thermal system. The usual way to model them is to write the equations describing the physical phenomena. The analytic model thus obtained is often too complex to be useful for control and optimization purposes. The authors propose to build a linear model by running the analytic model to obtain the simulated data, then apply the least square approximation to those data to obtain the linearizing coefficients. This statistical approach is simple to implement and yields linear models with good representativity. The annoying aspect is that some of the coefficients thus obtained may not lend themselves to a direct interpretation of the physical process. But with proper consideration, this is no obstacle to the use of the model.