An optimal solution to inverse heat conduction problems based on frequency-domain interpretation and observers

Observers are proposed as a solution algorithm for the inverse heat conduction problem (IHCP) of reconstructing a time-dependent surface heat flux at the boundary of a linear heat conductor. The derivation of optimal observer equations follows directly from a novel interpretation of the IHCP in the frequency domain: Solving the IHCP is viewed as a filter design problem in which the reconstructed heat flux is obtained by low-pass filtering of the true heat flux. It is demonstrated that observers are easier to tune, yield a better trade-off between the deterministic bias and the sensitivity to measurement errors, and lead to smaller-size computational problems than other solution approaches.