Redundant data and future times in the inverse heat conduction problem

Abstract

This paper considers a case study focusing on the use of redundant data and the trade between data density and number of future time steps used in Beck's Sequential Function Specification Method (SFSM) [1] for solving the Inverse Heat Conduction Problem (IHCP). The effect of the number of future time steps (r) and size of data time difference (Δt) have been observed and are presented in this paper. The results indicate that use of redundant sensors can improve heat flux estimates in the one-dimensional IHCP. Furthermore, it is demonstrated that the number of future time steps used r and the size of the time step in the data Δt should be combined into a new parameter, the “look-ahead” time period, p = rΔt. Different applications of the method with the same value of p are seen to give correspondingly similar results. A subsequent numerical experiment is used to give guidelines on the selection of the parameter “p” for the method.