Simultaneously regular inversion of unsteady heating boundary conditions based on dynamic matrix control

Based on the dynamic matrix control (DMC) idea, a method is established to simultaneously estimate boundary heat flux for unsteady heat conduction system in this paper. The measured temperature information at two measured points in the internal system is utilized to simultaneously determine transient heat flux q1(t) and q2(t) at two boundaries in the system. The algorithm adopts step response function to describe dynamic relationship of the system, without prior supposing the surface heat flux in the next period, and then the boundary heat flux at the present moment is inversed simultaneously through rolling optimization. In order to give attention to both the stability of inversion results, the inversing heat flux q1(t) and q2(t) are regularized respectively using different regularization parameters α1 and α2. A method of same temperature discrepancy curve (STDC) is designed to estimate the optimal values (α1)opt and (α2)opt of regularization parameters according to discrepancy principle. Numerical experiments are divided into two parts. First of all, compared with the sequential function specification method (SFSM), the effects of the future time steps as well as the measured temperature error on simultaneously inversion results of the boundary heat flux are investigated. Results show that the DMC inversion method established by this paper can use smaller future time steps r to simultaneously estimate transient boundary heat flux of the system, and obviously improve the anti-interference of measured noise. Second, the validity of the inversion results obtained by the proposed method is discussed respectively by cases with different sizes and changing rules of boundary heat fluxes as well as different measured locations. And by comparing with the traditional centralized regularization (CR), the necessity of respectively regularization for each inversing heat flux is confirmed by using different regularization parameters.