Model predictive inverse method for recovering boundary conditions of two-dimensional ablation

doi:10.1088/1674-1056/abc2b6

Abstract A model predictive inverse method (MPIM) is presented to estimate the time-and space-dependent heat flux on the ablated boundary and the ablation velocity of the two-dimensional ablation system. For the method, first of all, the relationship between the heat flux and the temperatures of the measurement points inside the ablation material is established by the predictive model based on an influence relationship matrix. Meanwhile, the estimation task is formulated as an inverse heat transfer problem (IHTP) with consideration of ablation, which is described by an objective function of the temperatures at the measurement point. Then, the rolling optimization is used to solve the IHTP to online estimate the unknown heat flux on the ablated boundary. Furthermore, the movement law of the ablated boundary is reconstructed according to the estimation of the boundary heat flux. The effects of the temperature measurement errors, the number of future time steps, and the arrangement of the measurement points on the estimation results are analyzed in numerical experiments. On the basis of the numerical results, the effectiveness of the presented method is clarified.

Keywords: ablation heat transfer model predictive inverse method (MPIM) boundary reconstruction

Received: 08 August 2020
Revised: 29 September 2020
Accepted manuscript online: 20 October 2020

PACS:	02.30.Zz	(Inverse problems)
	44.10.+i	(Heat conduction)
	43.20.Ye	(Measurement methods and instrumentation)
	64.70.-p	(Specific phase transitions)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 51876010 and 51676019).

Corresponding Authors: ^†Corresponding author. E-mail: chenh@cqu.edu.cn

Cite this article:

Guang-Jun Wang(王广军), Ze-Hong Chen(陈泽弘), Guang-Xiang Zhang(章广祥), and Hong Chen(陈红) Model predictive inverse method for recovering boundary conditions of two-dimensional ablation 2021 Chin. Phys. B 30 030203

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