A sparse regularization approach to inverse heat source identification

•A new sparse regularization approach is proposed for both location and strength identification of the heat sources.•The key idea resides at that the heat sources are always spatially sparse.•Numerical examples show that the sparse regularization indeed improves the robustness of heat source identif...

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Bibliographic Details
Published in:International journal of heat and mass transfer Vol. 142; p. 118430
Main Authors: Lu, Zhong-Rong, Pan, Tiancheng, Wang, Li
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01.10.2019
Elsevier BV
Subjects:
Algorithms
Alternating minimization algorithm
Heat source identification
Heat sources
Identification
Regularization
Robustness (mathematics)
Sparse regularization
Sparsity
Steady state
Stormwater
Threshold setting method
Sparse regularization
Threshold setting method
Heat source identification
Alternating minimization algorithm
ISSN:0017-9310, 1879-2189
Online Access:Get full text
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Summary:•A new sparse regularization approach is proposed for both location and strength identification of the heat sources.•The key idea resides at that the heat sources are always spatially sparse.•Numerical examples show that the sparse regularization indeed improves the robustness of heat source identification.•The present approach is found to perform superior to the Tikhonov regularization and the conjugate gradient method.•The proposed approach can identify the transient heat sources using only boundary data. This paper proposes a new sparse regularization approach for both steady-state and transient heat source identification within the finite element (FE) framework. The whole work is mainly twofold. On the one hand, the sparse regularization is introduced to formulate heat source identification with the sparsity constraint that the heat sources are often spatially sparse and thereof, the FE heat source vector is a sparse vector. On the other hand, the alternating minimization algorithm is developed to get the solution. Particular attention is paid to the choice of the regularization parameter which controls the sparsity of the heat sources and to this end, an efficient threshold setting method is presented. Three numerical examples concerning one-dimensional steady-state, two- and three-dimensional transient heat source identification are studied to testify the feasibility, performance and robustness of the proposed approach for steady-state or transient, single or multiple heat source identification.
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ISSN:0017-9310
1879-2189
DOI:10.1016/j.ijheatmasstransfer.2019.07.080