A Hybrid Procedure for the Sequential Estimation of Surface Heat Flux From Measurements of Surface Temperature

The sequential estimation of surface heat flux from discrete and noisy data of surface temperature is an ill-posed problem. From Duhamel's theorem and Fourier's law and using a stabilization technique based on the sequential application of the ordinary least squares (SOLS), we obtain a relatively simple but effective method. As the SOLS method uses a least squares fit over r-future and r-past temperatures, this method can be compared with the well-known function specification method (FSM). FSM is a more general method, but the numerical validations considered in this study reveal that the SOLS method gives better results. It is also shown that SOLS cannot be guided by the residual principle and consequently cannot be used in a practical scope. The ultimate goal of this study is to obtain a reliable estimation of heat flux history in an on-line industrial process where the tuneable parameter should be a time-variable r-value and it must be automatically updated from the experimental data. This requires that (i) the corresponding SOLS algorithm must be rewritten in recursive form, (ii) the classical definition of the residual principle is rewritten in recursive form, and (iii) the estimates are obtained from a hybrid procedure based on SOLS and FSM.