A regularization method for inverse heat transfer problems using dynamic Bayesian networks with variable structure

In this paper, dynamic Bayesian networks (DBNs) were employed to solve one-dimensional inverse heat transfer problems (IHTPs) with temperature history data. Temperature-dependent conductivities and surface heat flux histories were discretized into a finite number of parameters and used as parent nodes in the DBN. Parameter sensitivity analyses were adopted to identify the dominant parameters at each time step. Non-dominant parameters were removed from the corresponding frames for the sparsification of the DBN, which reduces the number of parameters to be identified simultaneously. Thus, the structure of the DBN was dynamically optimized for the regularization of inverse problems. Numerical and experimental tests for IHTPs were conducted to validate the proposed method. Both thermal conductivities and surface heat flux were identified with relatively small error, even if considering the measurement error. Sensitivities of the remaining parameters increased significantly with the parameter identification process, and insensitive parameters in the initial DBN frames were also effectively identified in the subsequent frames. The accuracy of parameter identification can be improved, and the cost of the parameter sampling combination can be reduced. The proposed method is not subject to heat transfer problems and can be used for a wide range of applications.