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Inverse analysis of thermal conductivities in transient non-homogeneous and non-linear heat conductions using BEM based on complex variable differentiation method

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Science China(Physics,Mechanics & Astronomy) 2013年第5期56卷 966-973页

作者： YU XiaoChun BAI YuGuang CUI Miao GAO XiaoWei State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology

This paper presents a new inverse analysis approach to sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element method (BEM) analysis based on complex variable differentiation method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.

关键词： parameter identification boundary element method complex-variable-differentiation method inverse heat conduction

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A novel method for simultaneous determination of thermophysical properties and boundary conditions of phase change problems based on element differential method

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2023年第1期157卷 1-11页

作者： Zhang, Chunyun Li, Yuxuan Cui, Miao Sun, Chengbao Gao, Xiao-wei Dalian Univ Technol State Key Lab Struct Anal Optimizat Dalian 116024 Peoples R China Dalian Univ Technol Key Lab Adv Technol Aerosp Vehicles Liaoning Prov CAE Software Ind Equipment Dalian 116024 Peoples R China

Thermophysical properties and boundary conditions for phase change thermal management systems are challenging to be accurately determined, due to the phase change heat transfer phenomenon and complex working conditions. In this work, the element differential method (EDM) and a gradient-based method are combined to simultaneously predict thermal conductivity, mass specific heat, and boundary heat flux in two-dimensional (2D) and three-dimensional (3D) inverse phase change problems, for the first time. The multi-parameter identification for the 3D physical model with phase change is more general than the previous attempts. Moreover, the effective heat capacity method is employed to deal with phase change problems, to improve efficiency. The sensitivity coefficient is accurately determined by the complex-variable-differentiation method (CVDM) in the multiparameter prediction. Finally, the effect of measurement points, measurement errors, and initial guessed values on the multi-parameter identification are investigated. This study demonstrates that the present method has good accuracy, efficiency, stability, and robustness in dealing with transient nonlinear inverse problems during phase change process.

关键词： Element differential method Phase change problems Inverse analysis complex-variable-differentiation method

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Simultaneous identification of multi-parameter for power hardening elastoplastic problems in three-dimensional geometries

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ENGINEERING COMPUTATIONS 2022年第8期39卷 2990-3011页

作者： Zhang, Chunyun Mei, Jie Bai, Yushuai Cui, Miao Peng, Haifeng Gao, X. W. Dalian Univ Technol Key Lab Adv Technol Aerosp Vehicles Liaoning Prov State Key Lab Struct Anal Ind Equipment Dalian Peoples R China China Acad Launch Vehicle Technol Sci & Technol Space Phys Lab Beijing Peoples R China

Purpose The purpose of this study is to simultaneously determine the constitutive parameters and boundary conditions by solving inverse mechanical problems of power hardening elastoplastic materials in three-dimensional geometries. Design/methodology/approach The power hardening elastoplastic problem is solved by the complex variable finite element method in software ABAQUS, based on a three-dimensional complex stress element using user-defined element subroutine. The complex-variable-differentiation method is introduced and used to accurately calculate the sensitivity coefficients in the multiple parameters identification method, and the Levenberg-Marquardt algorithm is applied to carry out the inversion. Findings Numerical results indicate that the complex variable finite element method has good performance for solving elastoplastic problems of three-dimensional geometries. The inversion method is effective and accurate for simultaneously identifying multi-parameters of power hardening elastoplastic problems in three-dimensional geometries, which could be employed for solving inverse elastoplastic problems in engineering applications. Originality/value The constitutive parameters and boundary conditions are simultaneously identified for power hardening elastoplastic problems in three-dimensional geometries, which is much challenging in practical applications. The numerical results show that the inversion method has high accuracy, good stability, and fast convergence speed.

关键词： Inverse analysis Multiple parameters identification Elastoplastic problem complex-variable-differentiation method User-defined element

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Inverse analysis of radiative properties of internal medium and surface for cylindrical system using CSM-CGM approach

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2023年第1期190卷

作者： Zhang, Chao Li, Ben-Wen Zhou, Rui-Rui Li, Pan-Xin Huang, Ling-Yun Dalian Univ Technol Sch Energy & Power Engn Key Lab Ocean Energy Utilizat & Energy Conservat Minist Educ Dalian 116024 Peoples R China Univ Shanghai Sci & Technol Sch Energy & Power Engn Shanghai Key Lab Multiphase Flow & Heat Transfer P Shanghai 200093 Peoples R China Kunming Univ Sci & Technol Fac Land Resource Engn State Key Lab Complex Nonferrous Met Resources Cle Kunming 650093 Peoples R China

An inverse analysis is conducted to simultaneously estimate the radiative properties in a 2D cylindrical system including the extinction coefficient, scattering albedo, and the wall emissivity from the knowledge of the radi-ative heat flux over different boundaries. In which the collocation spectral method (CSM) is developed to solve the forward problem, the conjugate gradient method (CGM) is employed to solve the inverse problem, and the complex-variable-differentiation method is used to treat the sensitivity problem, separately. Meanwhile, the effects of measurement errors, initial values, and imaginary values of complex variables on the precision of the inverse analysis are investigated. Results show that the proposed inverse analysis can successfully retrieve the unknown radiative physical properties of 2D cylindrical system. Under the same physical properties, good inversion results can be obtained by using different wall (end walls and side wall) radiative heat fluxes, but the inversion efficiency from sidewall radiative heat flux is higher. Besides, it is found that, the inversion for the scattered participating medium is more efficient than that for the non-scattered participating medium;the true values and iterative convergence values have little effect on the inversion result;the influence of the initial values and the imaginary values of the complex variable on the inversion cannot be ignored.

关键词： Inverse analysis Radiative physical properties Collocation spectral method Conjugate gradient method complex-variable-differentiation method 2D cylindrical system

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A new inverse approach for the equivalent gray radiative property of a non-gray medium using a modified zonal method and the complex-variable-differentiation method

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JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2011年第8期112卷 1336-1342页

作者： Cui, Miao Gao, Xiaowei Chen, Haigeng Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Northeastern Univ Sch Met & Mat Shenyang 110004 Peoples R China

Non-gray radiative properties of an absorbing, emitting, non-gray participating medium significantly increase the difficulty of solving the radiative transfer equation. This paper presents a new inverse approach for the equivalent gray radiative property of a non-gray medium. In this approach, the unknown equivalent gray radiative properties are treated as the optimization variables, and the errors to be minimized are the differences between the calculated temperatures and the measured ones. The measured data are simulated by solving the direct problem, in which a modified zonal method together with the Edwards exponential wide-band model is employed. In the inverse problem, the sensitivity coefficients are first calculated by the complex-variable-differentiation method, and then the least-square method and the Newton-Raphson iterative method are employed to minimize the target function. The effectiveness and efficiency of the inverse problem are demonstrated in an example, and another case is given to show the accuracy and potential of the proposed algorithm. The effects of the measurement error and the number of measurement points on the accuracy of the inverse analysis are also investigated in detail. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Inverse radiation Non-gray medium Zonal method complex-variable-differentiation method

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A modified optimization algorithm for back analysis of properties for coupled stress-seepage field problems

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TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY 2019年 94卷 103040-000页

作者： Wu, Chuangzhou Hong, Yi Chen, Qingsheng Karekal, Shivakumar Zhejiang Univ Coll Civil Engn & Architecture Hangzhou 310058 Zhejiang Peoples R China Kangwon Natl Univ Dept Geophys Chunchon 200701 Gangwon Do South Korea Natl Univ Singapore Dept Civil & Environm Engn 21 Lower Kent Ridge Rd Singapore 119077 Singapore Univ Wollongong Sch Civil Min & Environm Engn Wollongong NSW 2522 Australia

The study is aimed at developing a new algorithm for back analysis of rock mass parameters based on the observed displacements of tunnel excavations under coupled stress-seepage field problems which are generally encountered in hydraulic tunnel projects. The back-analysis algorithm is developed by incorporating the Levenberg-Marquardt optimization technique with complex-variable differentiation method. Additional auxiliary technique is also incorporated to enhance the convergence and stability of the proposed algorithm during the back-estimation of multiple rock mass parameters. A hypothetical hydraulic tunnel case was used for testing and validating the proposed algorithm by incorporating the method in a finite element code in which multiple rock mass parameters (such as modulus, permeability, and in situ stress) were treated as target parameters. Results show that the multiple rock mass parameters can be accurately and efficiently estimated by back analysis using a newly developed algorithm for coupled stress and seepage fields encountered in tunneling. The proposed algorithm can be used for predicting excavation behavior, particularly, the stress-induced deformations at subsequent stages of tunnel excavation under coupled multiple fields (e.g. stress and seepage fields).

关键词： Back analysis Coupled stress and seepage fields Levenberg-Marquardt optimization complex-variable-differentiation method Parameters estimation

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A modified Levenberg-Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2016年第0期97卷 908-916页

作者： Cui, Miao Yang, Kai Xu, Xiao-liang Wang, Sheng-dong Gao, Xiao-wei Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Beijing Inst Nearspace Vehicles Syst Engn Beijing 100076 Peoples R China

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. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Inverse heat conduction problem Levenberg-Marquardt algorithm complex-variable-differentiation method

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An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation

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OPTICS AND LASERS IN ENGINEERING 2016年第Mar.期78卷 155-164页

作者： Qiao, Yaobin Qi, Hong Chen, Qin Ruan, Liming Tan, Heping Harbin Inst Technol Sch Energy Sci & Engn Harbin 150001 Peoples R China

An efficient and robust method based on the complex-variable-differentiation method (CVDM) is proposed to reconstruct the distribution of optical parameters in two-dimensional participating media. An upwind-difference discrete-ordinate formulation of the time-domain radiative transfer equation is well established and used as forward model. The regularization term using generalized Gaussian Markov random field model is added in the objective function to overcome the ill-posed nature of the radiative inverse problem. The multi-start conjugate gradient method was utilized to accelerate the convergence speed of the inverse procedure. To obtain an accurate result and avoid the cumbersome formula of adjoint differentiation model, the CVDM was employed to calculate the gradient of objective function with respect to the optical parameters. All the simulation results show that the CVDM is efficient and robust for the reconstruction of optical parameters. (c) 2015 Elsevier Ltd. All rights reserved.

关键词： complex-variable-differentiation method Optical tomography Time-domain equation of radiative transfer Multi-start iterative technique

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A new inverse analysis method based on a relaxation factor optimization technique for solving transient nonlinear inverse heat conduction problems

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2015年 90卷 491-498页

作者： Cui, Miao Duan, Wei-wei Gao, Xiao-wei Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

The relaxation factor is a key parameter in gradient-based inversion and optimization methods, as well as in solving nonlinear equations using iterative techniques. In gradient-based inversion methods, the relaxation factor directly affects the inversion efficiency and the convergence stability. In general, the bigger the relaxation factor is, the faster the inversion process is. However, divergences may occur if the relaxation factor is too big. Therefore, there should be an optimal value of the relaxation factor at each iteration, guaranteeing a high inversion efficiency and a good convergence stability. In the present work, an optimization technique is proposed, using which the relaxation factor is adaptively updated at each iteration, rather than a constant during the whole iteration process. Based on this, a new inverse analysis method is developed for solving multi-dimensional transient nonlinear inverse heat conduction problems. One- and two-dimensional transient nonlinear inverse heat conduction problems are involved, and the instability issues occurred in the previous works are reconsidered. The results show that the new inverse analysis method in the present work has the same high accuracy, the same good robustness, and a higher inversion efficiency, compared with the previous least-squares method. Most importantly, the new method is more stable by innovatively optimizing and adaptively updating the relaxation factor at each iteration. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Inverse heat conduction problem Least-squares method Newton-Raphson method complex-variable-differentiation method

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A Modified Conjugate Gradient method for Transient Nonlinear Inverse Heat Conduction Problems: A Case Study for Identifying Temperature-Dependent Thermal Conductivities

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JOURNAL OF HEAT TRANSFER-TRANSACTIONS OF THE ASME 2014年第9期136卷 091301-1-091301-7页

作者： Cui, Miao Zhu, Qianghua Gao, Xiaowei Dalian Univ Technol Sch Aeronaut & Astronaut Fac Vehicle Engn & Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

Despite numerous studies of conjugate gradient methods (CGMs), the "sensitivity problem" and the "adjoint problem" are inevitable for nonlinear inverse heat conduction problems (IHCPs), which are accompanied by some assumptions and complicated differentiating processes. In this paper, a modified CGM (MCGM) is presented for the solution of a specified transient nonlinear IHCP, to recover temperature-dependent thermal conductivities for a case study. By introducing the complex-variable-differentiation method (CVDM) for sensitivity analysis, the sensitivity problem and the adjoint problem are circumvented. Five test examples are given to validate and assess the performance of the MCGM.

关键词： modified conjugate gradient method inverse problem transient nonlinear heat conduction complex-variable-differentiation method

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