双曲型热传导方程双参数的同步反演
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摘要
为解决双曲型热传导方程双参数同步反演问题,基于由材料表面检测到的光热频谱信号,利用脉冲谱技术和正则化方法,对非均匀固体样品的热弛豫时间和热传导系数予以深度剖面同步重构.在数值实验中,分别模拟了单调和非单调分布2套参数进行形态重构,并考虑噪声对重构的影响.结果显示:重构数据与原始数据吻合度良好,所建立的算法具有较好的稳定性和抗噪性.
To solve the problem of simultaneous inversion of two-parameters from hyperbolic heating conduction, based on surface photo-thermal signals, the numerical simulations of reconstructing the depth profile of the thermal relaxation time and thermal conductivity for inhomogeneous solid sample have been performed using pulsed spectrum technique and regulariza-tion method. In the numerical experiments,the profiles of two sets of parameters have been simulated which one set is monotonous and the other is non-monotonous configuration are reconstructed,and the influence of noise on the reconstructed profiles has been also considered. The results show that the reconstructed profiles agree well with the original ones, and the established algorithm has good stability and anti-noise performance.
To solve the problem of simultaneous inversion of two-parameters from hyperbolic heating conduction, based on surface photo-thermal signals, the numerical simulations of reconstructing the depth profile of the thermal relaxation time and thermal conductivity for inhomogeneous solid sample have been performed using pulsed spectrum technique and regulariza-tion method. In the numerical experiments,the profiles of two sets of parameters have been simulated which one set is monotonous and the other is non-monotonous configuration are reconstructed,and the influence of noise on the reconstructed profiles has been also considered. The results show that the reconstructed profiles agree well with the original ones, and the established algorithm has good stability and anti-noise performance.
引文
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[7]唐中华,钱炜祺,刘永利.基于伴随方程法的材料热传导系数反演方法[J].计算物理,2010,27(4):561-566.
[8]唐中华,钱国红,钱炜祺.材料热传导系数随温度变化函数的反演方法[J].计算力学学报,2011,28(3):377-382.
[9]黄耀英,张东健,周建兵.基于施工期实测温度的大坝混凝土热扩散率反演[J].水利水电科技进展,2013,33(4):6-9.
[10]周宇,钱炜祺,何开锋,等.同时反演材料热传导系数和比热的算法[J].计算物理,2011,28(5):719-724.
[11]BERTERO M,MOL C D,PIKE E R.Linear inverse problems with discrete data:Ⅱ.Stability and regularization[J].Inverse Problems,1988,4(3):573-594.
[12]BARLETTA A.Hyperbolic propagation of an axisymmetric thermal signal in an infinite solid medium[J].International Journal of Heat and Mass Transfer,1996,39(15):3261-3271.
[13]KMINSKI W.Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure[J].Journal of Heat Transfer,1990,112(3):555-560.
[14]LYU Y K,ZHOU Q B,ZHANG S Y.Depth profiling of thermal relaxation time and thermal conductivity related to hyperbolic heating propagation[J].Applied Physics A,2001,73(2):193-198.
[15]XU M H,CHENG J C,ZHANG S Y.A new method of reconstruction of thermal conductivity:depth profiles from photoacoustic or photothermal measurements[J].Journal of Physics D:Applied Physics,1998,31(21):3154-3159.
[2]OZISIK M N,TZOU D Y.On the wave theory in heat conduction[J].ASME J Heat Transfer,1994,116(3):526-535.
[3]LYU Y K,ZHANG S Y,CHENG J C.Theoretical study of transient thermal conduction and temperature distribution generated by pulsed laser[J].Applied Physics B-Lasers and Optics,2000,70(1):85-90.
[4]VOTI R L,SIBILIA C,BERTOLOTTI M.Photothermal depth profiling by thermal wave backscattering and genetic algorithms[J].International Journal of Thermophysics,2005,26(6):1833-1848.
[5]MARZOUK Y M,NAJM H N,RAHN L A.Stochastic spectral methods for efficient Bayesian solution of inverse problems[J].J Comput Phys,2007,224(2):560-586.
[6]吕跃凯,张淑仪.双曲型热传导方程的热参数反演[J].南京大学学报:自然科学版,2002,38(2):260-265.
[7]唐中华,钱炜祺,刘永利.基于伴随方程法的材料热传导系数反演方法[J].计算物理,2010,27(4):561-566.
[8]唐中华,钱国红,钱炜祺.材料热传导系数随温度变化函数的反演方法[J].计算力学学报,2011,28(3):377-382.
[9]黄耀英,张东健,周建兵.基于施工期实测温度的大坝混凝土热扩散率反演[J].水利水电科技进展,2013,33(4):6-9.
[10]周宇,钱炜祺,何开锋,等.同时反演材料热传导系数和比热的算法[J].计算物理,2011,28(5):719-724.
[11]BERTERO M,MOL C D,PIKE E R.Linear inverse problems with discrete data:Ⅱ.Stability and regularization[J].Inverse Problems,1988,4(3):573-594.
[12]BARLETTA A.Hyperbolic propagation of an axisymmetric thermal signal in an infinite solid medium[J].International Journal of Heat and Mass Transfer,1996,39(15):3261-3271.
[13]KMINSKI W.Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure[J].Journal of Heat Transfer,1990,112(3):555-560.
[14]LYU Y K,ZHOU Q B,ZHANG S Y.Depth profiling of thermal relaxation time and thermal conductivity related to hyperbolic heating propagation[J].Applied Physics A,2001,73(2):193-198.
[15]XU M H,CHENG J C,ZHANG S Y.A new method of reconstruction of thermal conductivity:depth profiles from photoacoustic or photothermal measurements[J].Journal of Physics D:Applied Physics,1998,31(21):3154-3159.