Estimation of the heat flux density during the induction heating process based on the parametric optimisation

The main goal of the paper is solving the problem of estimating the heat flux generated during induction heating process in the typical case of a complex heat transfer process under poorly defined boundary conditions. The problem is formulated in the extremal statement as an inverse heat conduction problem (IHCP) of optimal control. The induction heating process is considered as a distributed parameters system under control, the heat flux density is used as a control action. The experimentally measured temperature data are used as the input for the inverse heat transfer model. The set of control actions is limited to the class of continuous and continuously differentiable functions. On the basis of parameterisation of control actions, the problem is reduced to a problem of mathematical programming. The special optimisation method based on the alternance properties of the sought optimum solutions is applied to estimate the induction heat flux.