Assessment of Various Methods in Solving Inverse Heat Conduction Problems

In an inverse heat conduction problem (IHCP), the boundary conditions, initial conditions, or thermo-physical properties of material are not fully specified, and they are determined from measured internal temperature profiles. The challenge is that the effect of changes in boundary conditions are normally damped or lagged, i.e. the varying magnitude of the interior temperature profile lags behind the changes in boundary conditions and is generally of lesser magnitude. Therefore, such a problem would be a typically ill-posed and would normally be sensitive to the measurement errors. Also, in the uniqueness and stability of the solution are not generally guaranteed (Beck et al., 1985; Alifanov, 1995; Ozisik, 2000). Inverse heat conduction problems, like most of the inverse problems encountered in science and engineering may be reformulated as an optimization problem. Therefore, many available techniques of solving the optimization problems are available as methods of solving the IHCPs. However, the corresponding objective function of the inverse problems can be highly nonlinear or non-monotonic, may have a very complex form, or in many practical applications, its analytical expression may be unknown. The objective function usually involves the squared difference between measured and estimated unknown variables. If Y and T are the vectors of the measured and estimated temperatures, then the objective function will be in the form of