刚性目标形状反演的一种非线性最优化方法

尤云祥; 缪国平

刚性目标形状反演的一种非线性最优化方法

上海交通大学, 船舶与海洋工程学院, 上海, 200030

基金项目: 高等学校全国优秀博士论文作者专项基金资助项目;上海市教委曙光学者计划基金资助项目

详细信息

作者简介:
尤云祥(1963- ),男,江苏人,教授,博士,博士生导师(E-mail:gpmiao@mail.sjtu.edu.cn).

中图分类号: O175
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- 被引次数: 0
出版历程
- 收稿日期: 2001-11-27
- 修回日期: 2003-05-09
- 刊出日期: 2003-10-15

Numerical Method for the Shape Reconstruction of a Hard Target

School of Naval Architecture and Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, P.R.China

摘要

摘要: 发展了从声散射场的远场分布的信息来再现声刚性目标形状反问题的一种非线性最优化方法,它是通过独立地求解一个不适定的线性系统和一个适定的非线性最小化问题来实现的。对反问题的非线性和不适定性的这种分离式数值处理,使所建立方法的数值实现是非常容易和快速的,因为在确定声刚性障碍物形状的非线性最优化步中,只需求解一个只有一个未知函数的小规模的最小平方问题。该方法的另一个特别的性质是,只需要远场分布的一个Fourier系数,即可对未知的刚性目标作物形设别。进而提出了数值实现该方法的一种两步调整迭代算法。对具有各种形状的二维刚性障碍物的数值试验保证了本算法是有效和实用的。
- 声散射 /
- 反问题 /
- 远场分布
Abstract: A nonlinear optimization method was developed to solve the inverse problem of determining the shape of a hard target from the knowlegde of the far-field pattern of the acoustic scattering wave, it was achieved by solving independently an ill-posed linear system and a well-posed minimization problem.Such a separate numerical treatment for the ill-posedness and nonlinearity of the inverse problem makes the numerical implementation of the proposed method very easy and fast since there only involves the solution of a small scale minimization problem with one unknown function in the nonlinear optimization step for determining the shape of the sound-hard obstacle.Another particular feature of the method is that it can reproduce the shape of an unknown hard target efficiently from the knowledge of only one Fourier coefficient of the far-field pattern.Moreover,a two-step adaptive iteration algorithm was presented to implement numerically the nonlinear optimization scheme.Numerical experiments for several two dimensional sound-hard scatterers having a variety of shapes provide an independent verification of the effectiveness and practicality of the inversion scheme.
- acoustic scattering /
- inverse problem /
- far-field pattern

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参考文献(22)

[1]	Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory [M]. Berlin: Springer,1992.
[2]	Colton D, Monk P. A novel method for solving inverse scattering problem for time-harmonic acoustic waves in the resonance region Ⅱ [J]. SLAM Appl Math, 1986,46 (3): 506-523.
[3]	Colton D, Monk P. The numerical solution of the three-dimensional inverse scattering problem for time harmonic acoustic waves[J].SIAM J Sci Comput, 1987,8(3):278-291.
[4]	Kress R, Zinn A. On the numerical solution of the three-dimensional inverse obstacle scattering problem[J]. J Comput Appl Math, 1992,42:49-61.
[5]	Angell T S, Kleinman R E, Kok B, et al. A constructive method for identification of an impenetrable scatterer[J]. Wave Motion, 1989,11:185-200.
[6]	Jones D S, Mao X Q. Inverse problems in hard acoustic scattering [J]. Inverse Problems, 1989,5:731-748.
[7]	Murch R D, Tan D C H, Wall D J N. Newton-Kantorovich method applied to two-dimensional inverse scattering for an exterior Helmholtz problem[J]. Inverse Problems, 1988,4:1117-1128.
[8]	Kirsch A. The domain derivative and two applications in inverse scattering theory[J]. Inverse Problems, 1993,9:81-96.
[9]	Monch L A. A Newton method for solving the inverse scattering problem for a sound-hard obstacle [J]. Inverse Problems, 1996,12:309-323.
[10]	Hohag T.Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and inverse scattering problem[J]. Inverse Problems, 1997,13:1279-1299.
[11]	Oches J R. The limited aperture problem of inverse acoustic scattering: Dirichlet boundary conditions [J]. SIAM J Appl Math, 1987,47(6): 1320-1341.
[12]	Zinn A. On an optimization method for the full-and limited-aperture problem in inverse acoustic scattering for a sound-soft obstacle[J]. Inverse Problems, 1989,5:239-253.
[13]	Couchman L S.Inverse Neumann obstacle problem[J].J Acoust Soc Am,1998,104(5):2615-2621.
[14]	Kress R, Rundell W. Inverse obstacle scattering using reduced data[J]. SIAM J Appl Math, 1999,59(2): 442-454.
[15]	You Y X, Miao G P, Liu Y Z. A fast method for acoustic imaging of multiple three-dimensional objects [J]. J Acoust Soc Am,2000,108(1) :31-37.
[16]	You Y X, Miao G P, Liu Y Z. A simple method for visualizing multiple three-dimensional objects from near-field data with point source excitation[J]. Acta Acustica, 2001,87 (1): 1-10.
[17]	You Y X, Miao G P, Liu Y Z. A numerical method for solving the limited aperture problem in three-dimensional inverse obstacle scattering[J]. International of Nonlinear Science and Numerical Simulation,2001,2:29-42.
[18]	Miao G P, You Y X, Liu Y Z. A numerical method for the shape reconstruction problem in acoustic scattering[J]. Inverse Problems in Engineering,2000,8(3) :229-249.
[19]	You Y X, Miao G P,Liu Y Z.A nonlinear optimization method for an inverse transmission problem [J]. Inverse Problems, 2001,17: 421-435.
[20]	Colton D, Monk P. On a class of integral equations of the first kind in inverse scattering theory[J].SIAM J Appl Math, 1993,53(3) :847-860.
[21]	Reginska T. A regularization parameter in discrete ill-posed problems[J]. SIAM J Sci Comput, 1996,17 (3): 740-749.
[22]	赵风治.数值优化中的二次逼近法[M].北京:科学出版社,1994.