二阶非定常热传导反问题的多宗量辨识
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摘要
引入Bregman距离构造同伦函数,建立了二阶非定常多宗量热传导反问题的一种求解模式,可对导热系数和边界条件等宗量进行识别。时域上采用精细算法,建立了便于敏度分析的有限元正/反演模型,对各宗量进行有效的组合识别。对信息测量误差和初值选取作了初步探讨,数值验证取得了满意的结果。
This paper presents a general numerical model to identify multi-variables of twoorder transient heat conduction problems and the homotopic method is employed to solve inverse problems based on Bregman D-Function.A time stepping scheme is used for transient analysis and the finite element model is given,facilitating to sensitivity analysis for direct and inverse problems.Combined identifications can be carried out for thermal parameters and boundary conditions etc.Satisfactory numerical validation is given including a preliminary investigation of effect of noise data and initial value on the results.
This paper presents a general numerical model to identify multi-variables of twoorder transient heat conduction problems and the homotopic method is employed to solve inverse problems based on Bregman D-Function.A time stepping scheme is used for transient analysis and the finite element model is given,facilitating to sensitivity analysis for direct and inverse problems.Combined identifications can be carried out for thermal parameters and boundary conditions etc.Satisfactory numerical validation is given including a preliminary investigation of effect of noise data and initial value on the results.
引文
[1]BECK J V,BLACKWELL B,HAJI-SHEIKH A.Comparison of inverse heat conduction methods u-sing experimental data[J].Int J Heat Mass Trans-fer,1996,39(17):3649-3657.
[2]CHEN H T,LIN S Y.Estimation of two-sidedboundary conditions for two-dimensional inverse con-duction problems[J].International Journal of Heatand Mass Transfer,2002,45:15-23.
[3]CHEN H T,PENG S Y,YANG P C.Numericalmethod for hyperbolic inverse heat conduction prob-lems[J].Int.Comm.Heat Mass Transfer,2001,28,(6):847-856.
[4]杨海天,薛齐文.两级敏度分析求解非线性稳态多宗量热传导反问题[J].工程热物理学报,2003,24(3):463-465.(YANG Hai-tian,XUE Qi-wen.Solvingnon-linear inverse heat conduction problems in steadystate via 2-level sensitivity analysis[J].Journal ofEngineering Thermophysics,2003,24(3):463-465.(in Chinese))
[5]刘舒考,刘雯林.同伦神经优化理论及其在地震反演中的应用[J].石油地球物理勘探,1998,33(6):758-765.(LIU Shu-kao,LIU Wen-lin.Hompopic neural opti-mization theory and its application to seismic inver-sion[J].Oil Geophysical Prospecting,1998,33(6):758-765.(in Chinese))
[6]杨海天,薛齐文.同伦优化算法求解稳态传热反演问题[J].应用基础与工程科学学报,2004,12:93-100.(YANG Hai-tian,XUE Qi-wen.Solving inverse heatconduction problems in steady state via homotopicoptimization method[J].Journal of Basic Scienceand Engineering,2004,12:93-100.(in Chinese))
[7]CIDADE G A G,ANTENEODO C,ROBERTY NC,et al.A generalized approach for atomic force mi-croscopy image restoration with Bregman distancesas Tikhonov regularization terms[J].Inverse ProblEng,2000,8:457-472.
[8]杨海天,高强.粘弹性动力问题中的一种新的时域递推算法[J].应用数学和力学,2001,6:579-586.(HANG Hai-tian,GAO Qiang.A new algorithm oftime stepping in dynamic viscoelastic problems[J].Applied Mathematics and Mechanics,2001,6:579-586.(in Chinese))
[9]LEW R W,MORGAN K,THOMAS H R.The Fi-nite Element Method in Heat Transfer Analysis[M].UK:JOHN WILEY&SONS,1996.11-29.
[10]崔凯.非饱和土中污染物传输参数反演问题研究[D].大连:大连理工大学,2003.(CUI Kai.MethodsDevelopment for parameters inversion of contaminanttransport through unsaturate soils[D].Dalian:DalianUniversity of Technology,2003.(in Chinese))
[11]LI H Y.Inverse source problem in radiative transferfor spherical media[J].Numerical Heat Transfer,Part B,1997,31:251-260.
[2]CHEN H T,LIN S Y.Estimation of two-sidedboundary conditions for two-dimensional inverse con-duction problems[J].International Journal of Heatand Mass Transfer,2002,45:15-23.
[3]CHEN H T,PENG S Y,YANG P C.Numericalmethod for hyperbolic inverse heat conduction prob-lems[J].Int.Comm.Heat Mass Transfer,2001,28,(6):847-856.
[4]杨海天,薛齐文.两级敏度分析求解非线性稳态多宗量热传导反问题[J].工程热物理学报,2003,24(3):463-465.(YANG Hai-tian,XUE Qi-wen.Solvingnon-linear inverse heat conduction problems in steadystate via 2-level sensitivity analysis[J].Journal ofEngineering Thermophysics,2003,24(3):463-465.(in Chinese))
[5]刘舒考,刘雯林.同伦神经优化理论及其在地震反演中的应用[J].石油地球物理勘探,1998,33(6):758-765.(LIU Shu-kao,LIU Wen-lin.Hompopic neural opti-mization theory and its application to seismic inver-sion[J].Oil Geophysical Prospecting,1998,33(6):758-765.(in Chinese))
[6]杨海天,薛齐文.同伦优化算法求解稳态传热反演问题[J].应用基础与工程科学学报,2004,12:93-100.(YANG Hai-tian,XUE Qi-wen.Solving inverse heatconduction problems in steady state via homotopicoptimization method[J].Journal of Basic Scienceand Engineering,2004,12:93-100.(in Chinese))
[7]CIDADE G A G,ANTENEODO C,ROBERTY NC,et al.A generalized approach for atomic force mi-croscopy image restoration with Bregman distancesas Tikhonov regularization terms[J].Inverse ProblEng,2000,8:457-472.
[8]杨海天,高强.粘弹性动力问题中的一种新的时域递推算法[J].应用数学和力学,2001,6:579-586.(HANG Hai-tian,GAO Qiang.A new algorithm oftime stepping in dynamic viscoelastic problems[J].Applied Mathematics and Mechanics,2001,6:579-586.(in Chinese))
[9]LEW R W,MORGAN K,THOMAS H R.The Fi-nite Element Method in Heat Transfer Analysis[M].UK:JOHN WILEY&SONS,1996.11-29.
[10]崔凯.非饱和土中污染物传输参数反演问题研究[D].大连:大连理工大学,2003.(CUI Kai.MethodsDevelopment for parameters inversion of contaminanttransport through unsaturate soils[D].Dalian:DalianUniversity of Technology,2003.(in Chinese))
[11]LI H Y.Inverse source problem in radiative transferfor spherical media[J].Numerical Heat Transfer,Part B,1997,31:251-260.
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