A novel non-iterative method for estimating boundary conditions and geometry of furnace inner wall made of FGMs

Highlights: • A novel non-iterative inverse method based on PIFEM is proposed. • Boundary conditions and geometry of the furnace inner wall are estimated. • Expansion coefficient scheme is adopted to improve the inversed accuracy. • LS and TR methods are used, that is very accurate and high-efficiency. -- Abstract: A non-iterative inverse method based on the precise integration finite element method (PIFEM) is established for estimating the transient boundary conditions and the geometry of furnace inner wall made of functional gradient materials. For estimating boundary conditions, a two-step scheme is presented. First of all, after obtaining the temperatures at measurement points, a matrix system of equations of transient heat conduction problem is formed by a series of matrix operations based on the PIFEM. After that, the transient temperature or heat flux at inner boundary nodes can be obtained by the least-square method, in which basis functions approximation and Tikhonov regularization method are used to reduce the ill-posed level of inverse problem. For identification of geometry of inner boundary, a three-step scheme based on the PIFEM is proposed. After obtaining the temperature at measurement points, a virtual boundary is introduced to form the new computing domain. Estimation the temperature of the virtual boundary is a primary task in this step. Finally, the geometry of the furnace inner wall is identified by searching the isotherm in the new domain. Numerical results show that the present method can obtain the great performance on both the accuracy and the efficiency.