现代非线性优化算法在大地测量反演中的应用
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摘要
本文探讨了目前现代非线性优化算法(禁忌搜索，模拟退火算法，遗传算法，人工神经网络，蚁群算法等)在大地测量数据反演中的应用，比较了它们在大地测量反演中的优缺点。针对非线性优化算法收敛速度较慢的缺点，做了几种相应的改进措施。同时基于当今最流行的面向对象编程技术编写了这几种算法的大地测量反演程序。
通过分析可以看出，现代非线性优化算法本身的全局搜索，非线性计算和可并行计算等显著的优点决定了它在大地测量反演中必定会越来越受到重视。同时也应当看到这些算法虽然是通用算法，但并不是对每一种情况都是最佳的，而且在算法理论研究上还待于进一步地加强。因此只要在可接受的时间消耗内获得满意的结果，就认为此算法是可取的。对于目前的几种非线性优化算法，本文利用代码清晰便于理解，易维护和调试，代码重用性高的面向对象编程技术编写了相应的计算程序。
本文最后将非线性优化算法用于反演断层运动中，利用GPS观测资料和本文编制的大地测量非线性反演程序对印度板块向欧亚大陆的俯冲速率进行了反演。结果表明，现代非线性优化算法在大地测量反演中稳定性较好，几种非线性优化算法都能给出基本一致的结果。反演结果给出了现今印度板块以约8.4°的倾角，20.4mm/y的速率向欧亚大陆俯冲。这与从地质推断的过去2～3百万年期间内，印度板块向欧亚大陆俯冲平均为18mm/y的速率大致相同，表明在较长时间范围内，印度板块向欧亚大陆俯冲的速率是稳定的。
The study of this dissertation mainly discusses several popular modern nonlinear optimization algorithms ( Tabu Search,Simulated Annealing,Genetic Algorithms,Artificial Neural Networks,Ant Colony Optimization etc.),and the comparative advantages and disadvantages among them on geodetic inversion. Some improved methods
are given to prevent the drawback of these algorithms---slow convergence in actual
uses. Then,based on Object Oriented Programming,author gives a geodetic inversion computer programme using modern nonlinear optimization algorithms.
Modern nonlinear optimization algorithms have many outstanding advantages:global search,nonlinear calculate and parallel calculate etc,so they will be paid more attention on geodetic inversion. Meanwhile,they are not fitted in every situation and needed to strengthen their theoretic study,although they are general algorithms. So,we say they' re applicable if only we can get satisfying result. Gives a computer programme based on Object Oriented technology,which can make your programme clear,understandable,handled,easy-to-debug and having highly recycle rate,etc.
Finally,the convergence rate of India to Eurasia subdirection is given using nonlinear optimization algorithms and GPS data. The results calculated by several algorithms are almost consistent,which indicates good stabi I i ty oT modern nonlinear optimization algorithms used on geodetic inversion. The result of geodetic inversion shows that India block moves at rates of 20.4 millimeters per year with respect to the stable Eurasia,consistent with the result comes from geology. This indicates that the rate India block moves towards Eurasia is stable.
通过分析可以看出，现代非线性优化算法本身的全局搜索，非线性计算和可并行计算等显著的优点决定了它在大地测量反演中必定会越来越受到重视。同时也应当看到这些算法虽然是通用算法，但并不是对每一种情况都是最佳的，而且在算法理论研究上还待于进一步地加强。因此只要在可接受的时间消耗内获得满意的结果，就认为此算法是可取的。对于目前的几种非线性优化算法，本文利用代码清晰便于理解，易维护和调试，代码重用性高的面向对象编程技术编写了相应的计算程序。
本文最后将非线性优化算法用于反演断层运动中，利用GPS观测资料和本文编制的大地测量非线性反演程序对印度板块向欧亚大陆的俯冲速率进行了反演。结果表明，现代非线性优化算法在大地测量反演中稳定性较好，几种非线性优化算法都能给出基本一致的结果。反演结果给出了现今印度板块以约8.4°的倾角，20.4mm/y的速率向欧亚大陆俯冲。这与从地质推断的过去2～3百万年期间内，印度板块向欧亚大陆俯冲平均为18mm/y的速率大致相同，表明在较长时间范围内，印度板块向欧亚大陆俯冲的速率是稳定的。
The study of this dissertation mainly discusses several popular modern nonlinear optimization algorithms ( Tabu Search,Simulated Annealing,Genetic Algorithms,Artificial Neural Networks,Ant Colony Optimization etc.),and the comparative advantages and disadvantages among them on geodetic inversion. Some improved methods
are given to prevent the drawback of these algorithms---slow convergence in actual
uses. Then,based on Object Oriented Programming,author gives a geodetic inversion computer programme using modern nonlinear optimization algorithms.
Modern nonlinear optimization algorithms have many outstanding advantages:global search,nonlinear calculate and parallel calculate etc,so they will be paid more attention on geodetic inversion. Meanwhile,they are not fitted in every situation and needed to strengthen their theoretic study,although they are general algorithms. So,we say they' re applicable if only we can get satisfying result. Gives a computer programme based on Object Oriented technology,which can make your programme clear,understandable,handled,easy-to-debug and having highly recycle rate,etc.
Finally,the convergence rate of India to Eurasia subdirection is given using nonlinear optimization algorithms and GPS data. The results calculated by several algorithms are almost consistent,which indicates good stabi I i ty oT modern nonlinear optimization algorithms used on geodetic inversion. The result of geodetic inversion shows that India block moves at rates of 20.4 millimeters per year with respect to the stable Eurasia,consistent with the result comes from geology. This indicates that the rate India block moves towards Eurasia is stable.
引文
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[2] Bean, J., Genetic algorithms and random keys for sequencing and optimfzation, ORSA Journal on Computing, vol. 6, no. 2, pp. 154-160. 1994.
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[4] Borland Software Corporation, Delphi6. Developer's Guide, Software Corporation 100 Enterprise
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[46] 王勇，许厚泽，成层自重弹性—粘弹性半空间膨胀引起的地表形变和重力变化，地震学报，1997，19(4)：408～412
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[2] Bean, J., Genetic algorithms and random keys for sequencing and optimfzation, ORSA Journal on Computing, vol. 6, no. 2, pp. 154-160. 1994.
[3] Bilharm R, Larson k, Freymueller J, et al. GPS measurements of present day convergence rates in the Nepal Himalava. Nature, 1997, 336 61～64
[4] Borland Software Corporation, Delphi6. Developer's Guide, Software Corporation 100 Enterprise
[5] Douglas W. Oldenburg, 1974, The Inversion and Interpretation of Gravity Anomalies, Geophysics, VOL. 39, NO. 4(1974), P. 526-536
[6] England P C, Molnar P. The field of curstal velocity ia Asia calculated from Quaternary rates of slip on faults. Geophys J Int, 1997, 130:551～582
[7] Englland P C, Molnal P. The field of curstal velocity in Asia calculated from Quaternary rates of slip on faults. Geophys J Int, 1997, 130:551～582
[8] Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides, Design Patterns, Elements of Reusable Object-Oriented Software, Addison-Weley, 1995
[9] Erwin Groten, TU Darmstadt, Determination of global parameters for modern reference frames. C/Chris/Hawaii. doc 22.02. 01
[10] Grady Booch, Object-Oriented Analysis and Design with Applications, 2nd Ed., Addison-Wesley, 1994
[11] Jackson M, Bilharm R. Constraints of Himalayan deformation inferred from vertical velocity fields in Nepal and Tibet. J Geophys Res, 1994, 99:13897～13912
[12] Larson K, Burgmann R, Bilham R, et al. Kinematics of the India-Eurasia collision zone from GPS measurements. J Geophys Res, 1999, 104:1077～1093
[13] M. Dorigo, E. Bonabeau, and G. Theraulaz. Ant algorithms and stigmergy. Future Generagtion Computer Systems, 16(8): 851-871, 2000.
[14] M. Miki. Object-oriented optimization of discrete structures[J]. AIAA Journal, 1995, 33(10): 1940
[15] Marco Cant(?), Mastering Delphi6, published by WWW.sybex.com
[16] Molar P, Deng Q. Faulting associated with large earthquakes and the average rate of deformation in central and eastern Asia. J Geophys Res. 1984,89:6293～6228
[17] Molnar P, Burchfiel, B C, Kuangyi Let al. Geomorphic evidence for active faulting in the Altyn Tagh and northern Tibet and qualitative estimates of its contribution to the convergence of India and Eurasia. Geology, 1987,15:249～253
[18] Molnar P, Lyon-Caen H. Fault plane solutions of earthquakes and active tectonics of the Tibetan Plateau and its margins. Geophys J Int, 1989,99:123～153
[19] Okada Y. Surface deformation due to shear and tensile faults in a half space. Bull Seism Sec America, 1985,75(4):1135～1154
[20] P.C. Sabatier, Positivity constraints in linear inverse problems--Ⅰ. General theory. Geophys. J.R. astr. Soc. (1977) 48,415--441
[21] P.C. Sabatier, Positivity constraints in linear inverse problems--Ⅱ. Appliactions. Geophys. J.R. astr. Soc.(1977) 48,443--459
[22] R. Guerraoui, et al. Strategic Directions in object-oriented programming[J]. ACM Computing Surverys, 1996, 28(4): 691-700
[23] R. L. Parker, 1972, The Rapid Calculation of Polintiai Anomalies, Geophys. J. R. astr. Soc. (1972)31,447-455
[24] R.S. Solanki, J. K. Gorni. Implementation of an integer optimization platform using object oriented programming[J].Computers and Operations Research, 1997,24(6):549-557
[25] Robert L. Parker, Best bounds of density and depth from gravity data. Geophysics, Vol.39, No. 5(1974)P. 644-649
[26] Robert L. Parker, The theory of ideal bodies of gravity interpretation. Geophys, J.R. astr. Soc. (1975) 42,315-334.
[27] Rundle J B. Static elastic-gravitational deformation of a layered half-space by point couple sources. J Geophys Res, 1980,85:5355～5363
[28] Shuhei okubo, 1991, Potential and Grarity Changes Raised by Point Dislocations, Geophys, J. int. (1991) 105,573-586, Japan
[29] Shuhei okubo, 1992, Gravity and Potential Changes Due To Shear and Tensile Faults in A Half-Space, Journal of Geophysical Research, Vol. 97, Ne. B5, Pages 7137-7144
[30] Teng J.W. Wei S.Y. Sun K.Z. et al. The characteristics of the seismic activity in the Qinghai-Xizang(Tibet) Plateau of China. Tectonophysics, 1987. 134, 129～144
[31] Wang Yong, Theoretical modeling of local gravity changes and deformation caused by dilatancy with magma intrusion. In Segawa Y et al eds. Gravity, Geoid and Marine Geodesy, gerlin Heidelberg:Springer-Verlag, 1997. 289～296
[32] Ward F.K. The Himalaya east of the Tsangpo. Geographical Journal, 1934.84,369～397
[33] Yoshimitsu okada, 1985, Surface DeFormation Due To Shear and Tensile Faults in A Half-Space, Bulletin of the Seismological Society of America, Vol. 75, No..4, pp. 1135-1154, August 1985
[34] Zhao W, Nelson K D,INDEPTH Project Team. Deep seismic refleetion evidence for continental underthrusting beneath southern Tibet. Nature, 1993, 366:557～559
[35] 党亚民 基于反演理论的大地测量形变分析与解释的理论和方法 武汉测绘科技大学博土论文，1998
[36] 党亚民，陈俊勇，晁定波，大地测量非线性随机反演算法，测绘通报，第3期1999
[37] 林丹，李敏强，寇纪凇，基于实数编码的遗传算法的收敛性研究，计算机研究与发展，第37卷第11期2000．11
[38] 林锦，朱文兴，凸整数规划问题的混合蚁群算法，福州大学学报，1999．12 第27卷 第6期
[39] 刘经南，许才军，宋成骅等，精密全球卫星定位系统多期复测研究青藏高原现今地壳运动与应变，科学通报．2000，45(27)：2658～2663
[40] 刘勇，康立山，陈毓屏 非数值并行算法(第二册)遗传算法 北京科学出版社，1995
[41] 佘春峰。十进制遗传算法的理论分析及其应用。清华大学硕士论文，1998
[42] 施光燕，董加礼 最优化方法 北京高等教育出版社，1999
[43] 滕古文，王绍舟，姚振兴，青藏高原及其邻近地区的地球物理场特征与大陆板块构造，地球物理学报，1980．23，254～268
[44] 汪泓，韩文秀，面向对象退火，青岛大学学报，第12卷第4期 1999．12
[45] 王琪，游新兆，王文颖，等。跨喜马拉雅的GPS观测与现代地壳运动。地壳形变和地震，1998，18(3)：43～5
[46] 王勇，许厚泽，成层自重弹性—粘弹性半空间膨胀引起的地表形变和重力变化，地震学报，1997，19(4)：408～412
[47] 王勇，许厚泽，中国大陆及邻区岩石圈挠曲强度变化和均衡补偿机制，95大地测量综合性学术年会论文集，p1～11
[48] 吴庆洪，张纪会，徐心和，具有变异特征的蚁群算法，计算机研究与发展，第九卷第10期 1999．10
[49] 杨文采 地球物理反演的理论与方法 北京地质出版社，1997
[50] 杨行峻，郑君里，人工神经网络。高等教育出版社，1992
[51] 曾融生，丁志峰，吴庆举等，喜马拉雅及南藏的地壳俯冲带—地震学证据，地球物理学报，2000，43(6)：780～797
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