The Inverse Heat Conduction Problem (IHCP) refers to the inversion of the internal characteristics or thermal boundary conditions of a heat transfer system by using other known conditions of the system and according to some information that the system can observe. It has been extensively applied in the fields of engineering related to heat-transfer measurement, such as the aerospace, atomic energy technology, mechanical engineering, and metallurgy. The paper adopts Finite Difference Method (FDM) and Model Predictive Control Method (MPCM) to study the inverse problem in the third-type boundary heat-transfer coefficient involved in the two-dimensional unsteady heat conduction system. The residual principle is introduced to estimate the optimized regularization parameter in the model prediction control method, thereby obtaining a more precise inversion result. Finite difference method (FDM) is adopted for direct problem to calculate the temperature value in various time quanta of needed discrete point as well as the temperature field verification by time quantum, while inverse problem discusses the impact of different measurement errors and measurement point positions on the inverse result. As demonstrated by empirical analysis, the proposed method remains highly precise despite the presence of measurement errors or the close distance of measurement point position from the boundary angular point angle.

An efficient method for estimating the range of forming force for an upsetting-extruding process was proposed, which may be useful to choose appropriate forming equipment. The accurate prediction of the forming force of an upsetting-extruding process is the key to form a work piece successfully. However, the forming force is variable in a certain range for the variation of material and process parameters. In general, the variation is dominated by some of the main effects and lower-order interactions due to the sparsity-of-effect principle. Therefore, the construction of polynomial chaos expansion with points of monomial cubature rules, which need fewer points than other kinds of integral, is particularly attractive in dealing with computational model for the forming simulation. An automobile threated plate is used to illustrate the validation of the method.