Sequential estimation of the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters

In many thermal engineering problems involving high temperatures/high pressures, the boundary conditions are not fully known since there are technical difficulties in obtaining such data in hostile conditions. To perform the task of estimating the desired parameters, inverse problem formulations are required, which entail to performing some extra measurements of certain accessible and relevant quantities. In this paper, justified also by uniqueness of solution conditions, this extra information is represented by either local or non-local boundary temperature measurements. Also, the development of numerical methods for the study of coefficient identification thermal problems is an important topic of research. In addition, in order to decrease the computational burden, meshless methods are becoming popular. In this article, we combine, for the first time, the method of fundamental solutions (MFS) with a particle filter sequential importance resampling (SIR) algorithm for estimating the time-dependent heat transfer coefficient in inverse heat conduction problems. Two different types of measurements are used. Numerical results indicate that the combination of MFS and SIR shows high performance on several test cases, which include both linear and nonlinear Robin boundary conditions, in comparison with other available methods.