A modified Levenberg–Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems. (June 2016)

• Record Type: Journal Article
• Authors: Cui, Miao; Yang, Kai; Xu, Xiao-liang; Wang, Sheng-dong; Gao, Xiao-wei
• Is Part Of: International journal of heat and mass transfer. Volume 97(2016:Jun.)
• Page Start: 908
• Page End: 916
• Publication Date: 2016-06
• Subjects: Inverse heat conduction problem -- Levenberg–Marquardt algorithm -- Complex-variable-differentiation method; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2016.02.085
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: It is the first study to present a general method for accurately calculating sensitivity coefficients for a LM algorithm. A modified LM algorithm is presented by introducing the complex-variable-differentiation method for sensitivity analysis. The modified LM algorithm has the advantages of the conventional LM algorithm, that are effective, accurate and robust. The efficiency and the convergence stability of the modified LM algorithm are improved. Abstract: Despite numerous studies of Levenberg–Marquardt (LM) algorithms for solving inverse heat conduction problems, sensitivity coefficients are mainly evaluated by numerical differentiation methods. However, sensitivity coefficients are difficult to be precisely calculated by numerical differentiation methods, if multi-dimensions, transient states and nonlinearities are involved. To the best knowledge of the authors, there has not been a general method for accurately calculating sensitivity coefficients for a LM algorithm, except numerical differentiation methods. In this study, a modified LM algorithm is presented by introducing the complex-variable-differentiation method for sensitivity analysis, and multi-parameters of boundary heat flux are simultaneously recovered by solving transient nonlinear inverse heat conduction problems. The results show that the modified LM algorithm has the advantages of the conventional LM algorithm, that are effective, accurate and robust for simultaneous estimation of multi-parameters of boundary heat flux. Meanwhile, the efficiency and the convergence stability of the modified LM algorithm are improved, which are attributed to accurate evaluation of sensitivity coefficients, compared with the conventional LM algorithm.