Online Estimation of Heat Flux Using Tikhonov Digital Filter Method and Mollified Measured Temperatures

In this paper presents a digital filter method for online estimation of heat flux on a one - dimensional plate. Two inverse problems are designed to investigate this method. In the first problem, the unknown heat flux and the boundary condition on the other side of the plate are not known and in the second problem, the heat flux on the sides of a two-layers plate is unknown. in both cases, two sensors have been used to measure the temperature history of the plate. In the proposed algorithm, one of the two sensors is used as a boundary condition. To evaluate the accuracy and capability of digital filter, several experiments were designed. The filter coefficients are calculated only once in the proposed method and used in all experiments. The results show that this algorithm is very successful in estimating different forms of heat flux with different noise intensity at measured temperatures and different thermocouple positions in the plate and the Tikhonov digital filter method has more precision compared to Beck’s method. Also, using the mollified data in the proposed algorithm increases the accuracy and efficiency of the proposed algorithm.