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

Abstract:
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 lowpass-filtering of the true heat flux. The observer, comprising both a heat conductor reference model and suitable feedback of the prediction error, is designed to maximize the passband of the filter while minimizing amplification of measurement noise. It is demonstrated that observers are easier to tune, yield a better tradeoff between the deterministic bias and the sensitivity to measurement errors, and lead to smaller-size computational problems than all other classic solution approaches.

Keywords:
Heat transfer, inverse heat conduction problem, observer, lowpass filter

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