基于辛算法的层状结构探地雷达检测正反演研究
|
摘要
探地雷达作为一种快速,高效,无破损的探测工具,已经广泛应用于道路工程无损检测中。通过对实测探地雷达信号进行反演分析,可以对路面结构层厚度,介电参数以及是否存在脱空等结构病害作出判断。进行反演分析的关键就是构建探地雷达电磁波在层状有耗介质中传播的正演模型和寻找高效的反演优化算法。因此,开展层状体系探地雷达检测正反演研究对于推动探地雷达在道路无损检测中的应用具有重要意义。本文针对目前探地雷达正反演算法中存在的一些问题,提出了基于辛算法的正演模型以及基于粒子群优化算法的反演策略,提高了正反演算法的精度和效率,对探地雷达基础理论与应用技术的发展具有一定推动作用。取得的主要成果和结论如下：
(1)基于精细积分方法构建了探地雷达电磁波在层状有耗介质中的传播模型。将频率-波数域中Maxwell方程组化为仅含有电场和磁场水平分量的一阶常微分方程组形式,采用基于两点边值问题的精细积分方法求解层状有耗介质中电磁波的反射系数和透射系数。通过与解析解以及传递矩阵方法计算结果的对比可知,精细积分方法不仅精度高,而且数值稳定性好,可有效避免传递矩阵方法中可能出现的指数溢出现象。依据该模型模拟合成了均匀以及非均匀层状结构中探地雷达电磁波的反射信号,并将反射信号分别与FDTD方法模拟结果和实测信号进行对比,验证了模型的精确性以及对于实际工程的适应性。
(2)基于辛分块Runge-Kutta方法构建了探地雷达电磁波在二维有耗介质中传播的正演模型,推导了一阶,二阶以及四阶迭代格式,给出了适用于辛算法的吸收边界条件以及总场散射场技术,并证明了二维情况下辛算法的数值稳定性。相比于传统FDTD方法,辛算法仅需要两个方程就可以完整描述整个电磁场,而FDTD方法需要三个方程,这大大节省了计算机内存和计算时间。采用辛分块Runge-Kutta方法模拟了路面裂缝,路基脱空以及土基不密实等道路病害的探地雷达检测wiggle图,为解释实测雷达剖面提供了依据。
(3)基于标准粒子群优化算法和一类改进的粒子群优化算法,分别建立了层状结构介电特性反演分析方法。首先利用3种标准测试函数分析了不同控制参数对于粒子群算法性能的影响；然后通过理论模型对层状结构介电常数进行反演分析,对比标准粒子群算法和改进粒子群算法的精度和效率,结果表明,改进粒子群算法的精度和效率都优于标准粒子群算法;最后利用改进粒子群算法对实际路面结构层厚度进行反演分析,通过钻芯验证,反演结果误差控制在3%以内,能够满足工程精度需要,这为反演分析在道路质量控制中的实际应用创造了条件。
Ground penetrating radar (GPR), as a kind of fast, effective and non-destructive tools, has been widely applied to non-destructive testing of road quality. The thickness, dielectric properties of structural layers and the void existing in pavement structure can be known according to back-analysis of real GPR signals. Construction of forward model of GPR wave propagation in layered structure and the choice of high efficient optimization algorithm are keys for the inverse-analysis. Therefore, the research on forward modeling and inversion of GPR detection of layered structure has significant meaning to application of GPR non-destructive testing. In this paper, aiming at some deficiencies in the forward and inverse algorithms of ground penetrating radar, the forward model based on symplectic methods and the inverse-analysis based on particle swarm optimization (PSO) are presented. The accuracy and efficiency of the forward and inverse algorithm have been improved and it will promote the development of GPR basic theory and applied technology. The main achievements and conclusions of this paper are summarized below:
(1) The model of GPR electromagnetic wave propagating in lossy layered media has been constructed based on precise integration method (PIM). The Maxwell equations are formulated in the frequency-wavenumber domain as a set of first-order ordinary differential equations containing variables being only the horizontal components of the electric and magnetic fields. Then these equations are solved by PIM with specified two-point boundary value conditions. Numerical results of the reflection and transmission coefficients are calculated by PIM and then compared with the results obtained by the analytical means and transfer matrix method (TMM), the comparison results showed that the PIM can achieve high accuracy and unconditional stability, and also can avoid the exponent overflow which may occur in TMM. In addition, the simulated signals reflected from homogeneous and inhomogeneous layered structure are obtained by PIM, and then compared with that obtained by FDTD method and measured signal, The comparison results indicate that the forward model is accurate and adaptive for simulation of GPR wave propagation in pavement structure.
(2) The model of GPR electromagnetic wave propagating in2-dimensional (2D) lossy media has been developed based on symplectic partitioned Runge-Kutta (SPRK) method. The first-order, second-order and fourth-order iterative schemes are derivated, and the numerical stability of the symplectic algorithm in the2D case is verified. The absorbing boundary condition (ABC) and total-field/scatter-field (TF/SF) technology which are suitable for SPRK method are also presented. Compared with the traditional FDTD method, the SPRK schemes require only two functions for the complete description of the electromagnetic field, hence, the SPRK schemes can save computer memory usage and CPU time significantly. The wiggle trace profiles of complicated models in which cracking, void, no dense region, etc exist are simulated by SPRK method. It is useful to interpretation of real GPR data.
(3) The inverse-analysis of dielectric properties of layered structure is developed by PSO and a king of improved PSO. The performance of PSO is evaluated by different control parameters making use of three stardand test functions. The back-calculation of permittivity of theory model is used to evaluate the efficiency and precision of PSO and improved PSO. The results show that the accuracy and efficiency of improved PSO are better than PSO. In addition, the surface thickness of pavement is predicted based on inversion of the measured GPR signal by improved PSO and the detection precision is verified by core boring sampling, the results indicate that the errors are less than3%and can satisfy the precision requirement of the project. These will creat condition for application of back-analysis to road quality control.
(1)基于精细积分方法构建了探地雷达电磁波在层状有耗介质中的传播模型。将频率-波数域中Maxwell方程组化为仅含有电场和磁场水平分量的一阶常微分方程组形式,采用基于两点边值问题的精细积分方法求解层状有耗介质中电磁波的反射系数和透射系数。通过与解析解以及传递矩阵方法计算结果的对比可知,精细积分方法不仅精度高,而且数值稳定性好,可有效避免传递矩阵方法中可能出现的指数溢出现象。依据该模型模拟合成了均匀以及非均匀层状结构中探地雷达电磁波的反射信号,并将反射信号分别与FDTD方法模拟结果和实测信号进行对比,验证了模型的精确性以及对于实际工程的适应性。
(2)基于辛分块Runge-Kutta方法构建了探地雷达电磁波在二维有耗介质中传播的正演模型,推导了一阶,二阶以及四阶迭代格式,给出了适用于辛算法的吸收边界条件以及总场散射场技术,并证明了二维情况下辛算法的数值稳定性。相比于传统FDTD方法,辛算法仅需要两个方程就可以完整描述整个电磁场,而FDTD方法需要三个方程,这大大节省了计算机内存和计算时间。采用辛分块Runge-Kutta方法模拟了路面裂缝,路基脱空以及土基不密实等道路病害的探地雷达检测wiggle图,为解释实测雷达剖面提供了依据。
(3)基于标准粒子群优化算法和一类改进的粒子群优化算法,分别建立了层状结构介电特性反演分析方法。首先利用3种标准测试函数分析了不同控制参数对于粒子群算法性能的影响；然后通过理论模型对层状结构介电常数进行反演分析,对比标准粒子群算法和改进粒子群算法的精度和效率,结果表明,改进粒子群算法的精度和效率都优于标准粒子群算法;最后利用改进粒子群算法对实际路面结构层厚度进行反演分析,通过钻芯验证,反演结果误差控制在3%以内,能够满足工程精度需要,这为反演分析在道路质量控制中的实际应用创造了条件。
Ground penetrating radar (GPR), as a kind of fast, effective and non-destructive tools, has been widely applied to non-destructive testing of road quality. The thickness, dielectric properties of structural layers and the void existing in pavement structure can be known according to back-analysis of real GPR signals. Construction of forward model of GPR wave propagation in layered structure and the choice of high efficient optimization algorithm are keys for the inverse-analysis. Therefore, the research on forward modeling and inversion of GPR detection of layered structure has significant meaning to application of GPR non-destructive testing. In this paper, aiming at some deficiencies in the forward and inverse algorithms of ground penetrating radar, the forward model based on symplectic methods and the inverse-analysis based on particle swarm optimization (PSO) are presented. The accuracy and efficiency of the forward and inverse algorithm have been improved and it will promote the development of GPR basic theory and applied technology. The main achievements and conclusions of this paper are summarized below:
(1) The model of GPR electromagnetic wave propagating in lossy layered media has been constructed based on precise integration method (PIM). The Maxwell equations are formulated in the frequency-wavenumber domain as a set of first-order ordinary differential equations containing variables being only the horizontal components of the electric and magnetic fields. Then these equations are solved by PIM with specified two-point boundary value conditions. Numerical results of the reflection and transmission coefficients are calculated by PIM and then compared with the results obtained by the analytical means and transfer matrix method (TMM), the comparison results showed that the PIM can achieve high accuracy and unconditional stability, and also can avoid the exponent overflow which may occur in TMM. In addition, the simulated signals reflected from homogeneous and inhomogeneous layered structure are obtained by PIM, and then compared with that obtained by FDTD method and measured signal, The comparison results indicate that the forward model is accurate and adaptive for simulation of GPR wave propagation in pavement structure.
(2) The model of GPR electromagnetic wave propagating in2-dimensional (2D) lossy media has been developed based on symplectic partitioned Runge-Kutta (SPRK) method. The first-order, second-order and fourth-order iterative schemes are derivated, and the numerical stability of the symplectic algorithm in the2D case is verified. The absorbing boundary condition (ABC) and total-field/scatter-field (TF/SF) technology which are suitable for SPRK method are also presented. Compared with the traditional FDTD method, the SPRK schemes require only two functions for the complete description of the electromagnetic field, hence, the SPRK schemes can save computer memory usage and CPU time significantly. The wiggle trace profiles of complicated models in which cracking, void, no dense region, etc exist are simulated by SPRK method. It is useful to interpretation of real GPR data.
(3) The inverse-analysis of dielectric properties of layered structure is developed by PSO and a king of improved PSO. The performance of PSO is evaluated by different control parameters making use of three stardand test functions. The back-calculation of permittivity of theory model is used to evaluate the efficiency and precision of PSO and improved PSO. The results show that the accuracy and efficiency of improved PSO are better than PSO. In addition, the surface thickness of pavement is predicted based on inversion of the measured GPR signal by improved PSO and the detection precision is verified by core boring sampling, the results indicate that the errors are less than3%and can satisfy the precision requirement of the project. These will creat condition for application of back-analysis to road quality control.
引文
[1]中华人民共和国交通部.公路工程质量检验评定标准(JTJ.071-2004)[M].北京：人民交通出版社,2005.
[2]曾昭发,刘四新,王者江.探地雷达方法原理及应用[M].北京：科学出版社,2006.
[3]张蓓.路面结构层材料介电特性及其厚度反演分析的系统识别方法[D]：(博士学位论文).重庆：重庆大学,2003.
[4]Saarenketo T, Scullion T. Road evaluation with ground penetrating radar [J]. Journal of Applied Geophysics,2000,43(2-4):119-138.
[5]Saarenketo T, Hietala K, Salmi T. GPR application in geotechnical investigations of peat for road survey purposes [C]. Fourth International Conference on Ground Penetrating Radar, Rovaniemi, Finland,1992:293-305.
[6]Saarenketo T, Scullion T. Laboratory and GPR tests to evaluate electrical and mechanical properties of Texas and Finnish base course aggregates [C]. Proceeding of the Sixth International Conference on Ground Penetrating Radar, Sendai, Japan.1996:477-482.
[7]Saarenketo T. Using Ground Penetrating Radar and dielectric probe measurements in pavement density quality control [C].1997 Annual Meeting of the Transportation Research Board, Washington D C, USA,1997:34-41.
[8]Saarenketo T, Roimela P. Ground Penetrating Radar technique in asphalt pavement density quality control [C]. Proceeding of the Seventh International Conference on Ground Penetrating Radar, Lawrence KS,1998:461-466.
[9]Saarenketo T, Nikkinen T, Lotvonen S. The use of Ground Penetrating Radar for monitoring water movement in road structures [C]. Proceedings of Fifth International Conference on Ground Penetrating Radar, Ontario, Canada,1994:1181-1192.
[10]Lau C L, Scullion T, Chan P. Using Ground Penetrating Radar technology for pavement evaluations in Texas [C]. Proceedings 4th International Conference on Ground Penetrating Radar, Rovaniemi, Finland,1992:277-283.
[11]Scullion T, Saarenketo T. Application of Ground Penetrating Radar technology for network and project level pavement management systems [C]. Proceedings of the Fourth International Conference on Managing Pavements, Durban, South Africa,1998:254-268.
[12]Scullion T, Saarenketo T. Integrating Ground Penetrating Radar and falling weight deflectometer technology in pavement evaluation [C]. Proceedings of the Third ASTM Symposium of Nondestructive Testing of Pavements and Backcalculation of Moduli, Seattle,Washington, 2000:23-37.
[13]Rmeili E, Scullion T. Detecting stripping in asphalt concrete layers using Ground Penetrating Radar [C].1997 Annual Meeting of Transportation Research Board, Washington D C USA,1997:165-174.
[14]Saarenketo T, Scullion T. Moisture susceptibility and electrical properties of base course aggregates [C]. Proceedings of BCRA,Trondheim, Norway,1998:1401-1410.
[15]Lau C L.Scullion T, Chan P. Modeling of Ground Penetrating Radar wave propagation in pavement systems [C].72nd Annual Meeting, Washington D C,1992:99-107.
[16]Cuvillier M, Boaddard J F, Retour P. New methods developed in France for road network survey and maintenance [C]. Proc.6th Conf. Struct. Des. of Asphalt Pavements, Univ. of Michigan, Ann Arbor, MI,1987:562-573.
[17]Attoh-Okine B N. Time series analysis for ground penetrating radar (GPR) asphalt thickness profile [J]. Applied Stochastic Models and Data Analysis,1994,10(3):153-167.
[18]Fernando E, Liu W T, Dietrich B. Computer program for network level determination of pavement layer thicknesses[C], Proceedings of SPIE-The International Society for Optical Engineering, Gold Coast, Australia,2000:194-199.
[19]Loulizi A, Al-Qadi I L, Lahouar S. Optimization of ground-penetrating radar data to predict layer thicknesses in flexible pavements [J]. Journal of Transportation Engineering,2003,129(1):93-99.
[20]Huang C L, Su Y. A new GPR calibration method for high accuracy thickness and permittivity measurement of multi-layered pavement [C]. Proceedings of the Tenth International Conference on Ground Penetrating Radar, Delft, The Netherlands,2004:627-630.
[21]Willett D A., Mahbou K C, Rister B. Accuracy of ground-penetrating radar for pavement-layer thickness analysis [J].Journal of Transportation Engineering,2006,132(1):96-103.
[22]Maser K R, Holland T J, Roberts R. NDE methods for quality assurance of new pavement thickness [J].International Journal of Pavement Engineering,2006,7(1):1-10.
[23]Malva L J, Cline G D. Detecting voids under airfield pavements[C]. Proceedings of the Specialty Conference, Las Vegas, Nevada, United States,2003:366-377.
[24]Saarenketo T, Soderqvist M K. Ground penetrating radar applications for bridge deck evaluations in Finland [J]. Insight-Non-Destructive Testing and Condition Monitoring,1994,36(7):496-50.
[25]Chen Roger H L, Chen H U, Pei L F, et al. An experimental evaluation of concrete bridge decks and pavements using ground penetrating radar[C]. Structures Congress-Proceedings, Building to Last, Portland, Oregon,1997:1508-1512.
[26]Narayanan R M, Hudson S G, Kumke C J. Detection of rebar corrosion in bridge decks using statistical variance of radar reflected pulses[C]. GPR 98, Proc.7th Intl. Conf. on GPR, Lawrence, Kansas,1998:601-605.
[27]Du S, Rummel P. Reconnaissance studies of moisture in the subsurface with GPR[C].GPR 94, Proc. 5th Intl. Conf. on GPR, Kitchener, Ontario,1994:1241-1248.
[28]Greaves R J, Lesmes D P, Lee J M, et al. Velocity variations and water content estimated from multioffset ground penetrating radar [J]. Geophysics,1996(61):683-695.
[29]Hubbard S, Grote K, Rubin Y, Estimation of near subsurface water content using high frequency GPR ground wave [J]. Leading Edge of Exploration, Society of Exploration Geophysics,2002, 21(6):552-559.
[30]Maser Kenneth R. Condition assessment of transportation infrastructure using ground-penetrating radar [J]. Journal of Infrastructure Systems,1996,2(2):94-101.
[31]Maser K R, Sande I. Application of ground penetrating radar for evaluation of sub-surface airfield pavement conditions [J].Insight:Non-Destructive Testing and Condition Monitoring,2000, 42(7):451-453.
[32]李大心.探地雷达方法与应用[M].北京：地质出版社,1994.
[33]Cook J C. Radar exploration through rock in advance of mining [J], Transactions of AIME, Society of Mining Engineers,1973,254:140-146.
[34]Holser W T, Brown R J, Roberts F A, et al. Radar logging of a salt dome [J]. Geophycics, 37(5):889-906.
[35]Simmons G, Strangway D, Annan A P, et al. Surface electrical properties experiment [R] in Apollo 17:preliminary science report, scientific and technical office, NASA, Washington D C, 1973:15-1-15-14.
[36]Coon J B, Fowler J C, Schafers C J. Experimental uses of short pulse radar in coal seams [J]. Geophysics,1981,46(8):1163-1168.
[37]Davis J L, Annan A P. Ground penetrating radar for high-resolution mapping of soil and rock stratigraphy [J]. Geophysical prospecting,1989,37:531-551.
[38]Boniger U, Tronicke J. Integrated data analysis at an archaeological site:A case study using 3D GPR, magnetic, and high-resolution topographic data [J]. Geophysics,2010,75(4):169-176.
[39]Xu X X, Zeng Q S, Li D, et al. GPR detection of several common subsurface voids inside dikes and dams [J]. Engineering Geology,2010,111(1-4):31-42.
[40]Hubbard S, Chen J S, Williams K, et al. Environmental and agricultural applications of GPR[C]. Proceedings of the 3rd International Workshop on Advanced Ground Penetrating Radar, IWAGPR 2005, Delft, Netherlands,2005:45-49.
[41]徐朝红.二维块状模型射线追踪方法设计与实现[D]：(硕士学位论文).西安：长安大学,2009.
[42]刘军.基于射线追踪的微地震模型多波场正演模拟[D]：(硕士学位论文).北京：中国石油大学,2009.
[43]魏亦文.基于复杂介质最短路径射线追踪层析成像正演研究[D]：(硕士学位论文).长沙：中南大学,2007.
[44]邓世坤,王惠濂.探地雷达图像的正演合成与偏移处理[J].地球物理学报,1993,36(04)：528-536.
[45]Goodman D. Ground-penetrating radar simulation in engineer in gand archaeology [J]. Geophysics, 1994,59(2):224-232.
[46]Cai J, McMechan G A. Ray based synthesis of bistatic ground-penetrating radar profiles [J]. Geophysics,1995,60(1):87-96.
[47]曾昭发,高尔根.三维介质中探地雷达(GPR)波传播逐段迭代射线追踪方法研究和应用[J].吉林大学学报(地球科学版),2005,35(sup)：119-123.
[48]Huang Y Q, Zhang J Z, Liu Q H. Three-dimensional GPR ray tracing based on wavefront expansion with irregular cells[J]. IEEE Transaction on Geoscience and Remote Sensing,2011,49(2):679-687.
[49]王长清.现代计算电磁学基础[M].北京：北京大学出版社,2005.
[50]Gurel L, Aksun M I. Electromagnetic scattering solution of conducting strips in layered media using the fast multipole method [J]. IEEE Microwave and Guided Wave Letters,1998,6(8):277-279.
[51]Geng N, Sullivan A, Carin L. Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space [J]. IEEE Transactions on Antennas and Propagation,2001, 49(5):740-748.
[52]Vande Ginste D, Rogier H, Olyslager F, et al. A fast multipole method for layered media based on the application of perfectly matched layers-the 2-D case [J]. IEEE Transactions on Antennas and Propagation,2004,52(10):2631-2640.
[53]于继军,盛新庆.地下三维目标电磁散射的矩量法计算[J].电子与信息学报,2008,28(5)：950-954.
[54]Wang A Q, Guo L X, Chai C. Fast numerical method for electromagnetic scattering from an object above a large-scale layered rough surface at large incident angle vertical polarization [J]. Applied Optics,2011,50(4):500-508.
[55]马弘炯.瞬态电磁脉冲的时域伪谱方法：研究、改进及应用[D]：(博十学位论文).成都：电子科技大学,2005.
[56]杨虎.多区域时域伪谱算法在电磁分析中的理论和应用研究[D]：(博士学位论文).长沙：国防科技大学,2006.
[57]粟毅,黄春林,雷文太.探地雷达理论与应用[M].北京：科学出版社,2006.
[58]Casper D A, Samuel Kung K J. Simulation of ground-penetrating radar waves in a 2-D soil model [J]. Geophysics,1996,61(4):1034-1049.
[59]Liu Q H, Fan G X. Simulations of GPR in dispersive media using a frequency-dependent PSTD algorithm[J]. IEEE Transaction on Geoscience and Remote Sensing,1999,37(5):2317-2324.
[60]Fan G X, Liu Q H, Hesthaven J S. Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media [J]. IEEE Transaction on Geoscience and Remote Sensing,2002,40(6):1366-1373.
[61]姜永金,刘立业,杨虎等.有耗媒质中目标体散射特性的TSNU_PSTD模拟[J].国防科技大学学报,2005,27(6)：88-92.
[62]吕英华.计算电磁学的数值方法[M].北京：清华大学出版社,2006.
[63]王建国,葛德彪(泽).电磁场有限元方法[M].西安：西安电子科技大学出版社,1998.
[64]沈飙,孙忠良,曲孝良.探地雷达波波动方程研究及其正演模拟[J].东南大学学报,1994,24(2)：114-117.
[65]底青云,王妙月.雷达波有限元仿真模拟[J].地球物理学报,1999,42(6)：818-825.
[66]谢辉,钟燕辉,蔡迎春.电磁场有限元法在GPR正演模拟中的应用[J].河南科学,2003,21(3)：295-298.
[67]Zhang X J, Huang J H, Song L. Application of ground penetrating radar (GPR) exploration in Karst mountain areas[C] 2010 13th International Conference on Ground Penetrating Radar (GPR), Lecce, 2010:21-25.
[68]陈承申.探地雷达二维有限元正演模拟[D]：(硕十学位论文).K沙：中南大学,2011.
[69]葛德彪,闫玉波.电磁场时域有限差分法[M].西安：西安电子科技大学出版社,2002.
[70]Wang T, Oristaglio M L.3-D simulation of GPR surveys over pipes in dispersive soils [J]. Geophysics,2000,65(5):1560-1568.
[71]詹毅.复杂有耗色散地层中的FDTD方法以及在冲击探地雷达中的应用[D]：(博十学位论文)西安：电子科技大学,2000.
[72]Moss C D, Teixeira F L, Kong J A. Analysis and compensation of numerical dispersion in the FDTD method for layered, anisotropic media [J]. IEEE Transactions on Antennas and Propagation, 2002,50(9):1174-1184.
[73]Irving J, Knight R. Numerical modeling of ground-penetrating radar in 2-D using MATLAB [J]. Computers & Geosicences,32(9):1247-1258.
[74]冯德山,戴前伟,何继善.探地雷达的正演模拟及有限差分波动方程偏移处理[J].中南大学学报(自然科学版),2006,27(2)：361-365.
[75]Cassidy N J, Millington T M. The application of finite-difference time-domain modeling for the assessment of GPR in magnetically lossy materials[J]. Journal of Applied Geophysics,2009,67(4): 296-308.
[76]Zhu Z Q, Lu G Y, Lu Q. The FDTD modeling of GPR for tunnel inspection[C]. International Conference on Information Engineering and Computer Science, WuHan,2009. ICIECS,2009:1-4.
[77]Diamanti N. A study of GPR vertical crack responses in pavement using field data and numerical modeling[C].2010 13th International Conference on Ground Penetrating Radar (GPR), Lecce, 2010:1-6.
[78]汤炜ADI_FDTD及其混合算法在电磁散射中的应用[D]：(博士学位论文).西安：电子科技大学,2005.
[79]Xiao F, Tang X H, Du G H, et al. Improvement on the numerical dispersion inherent in the ADI-FDTD Method [C]. Proceedings of Asia-Pacific Microwave Conference 2007, Bangkok, 2007:1-4.
[80]Diamanti N, Giannopoulos A. Implementation of ADI-FDTD subgrids in ground penetrating radar FDTD models[J] Journal of Applied Geophysics,2009,67(4):309-317.
[81]Feng D S, Dai Q W. GPR numerical simulation of full wave field based on UPML boundary condition of ADI-FDTD [J]. NDT&E International,2011,44(6):495-504.
[82]冯德山,谢源.基于单轴各向异性完全匹配层边界条件的ADI_FDTD三维GPR全波场正演[J].中南大学学报(自然科学版),2011,42(8)：2363-2371.
[83]张玉廷,蔡智,刘胜.交替隐式时域有限差分分析有耗介质电磁波传播[J].电波科学学报,2011,26(6)：1088-1094.
[84]Sarrafi P, Li Q. Modeling of Pulse Propagation in Layered Structures With Resonant Nonlinearities Using a Generalized Time-Domain Transfer Matrix Method [J]. IEEE Journal of Quantum Electronics,2012,48(5):559-567.
[85]Cao Q S, Chen Y C. Application of an anisotropic perfectly matched layer absorber for open boundary truncation in the multiresolution time domain scheme[J] IEEE Transactions on Antennas and Propagation,2003,51(2):350-357.
[86]Ghasemia F A, Abrishamian M S. A novel method for FDTD numerical GPR imaging of arbitrary shapes based on Fourier transform [J]. NDT&E International,2007,40(2):140-146.
[87]文舸一.辛算法及其在电磁场方程中的应用[J].微波学报,1999,15(1)：68-79.
[88]文舸一.电磁理论新进展[M].北京：国防工业出版社,1999.
[89]Hirono T, Lui W W, Yokoyama K. Time-domain simulation of electromagnetic field using a symplectic integrator[J]. IEEE Microwave and Guided Wave Letters,1997,7(9):279-281.
[90]Hirono T, Lui W W, Yokoyama K, et al. Stability and numerical dispersion of symplectic fourth-order time-domain schemes for optical field simulation[J]. Journal of Lightwave Technology, 1998,16(10):1915-1920.
[91]Hirono T, Lui W W, Yokoyama K. Successful applications of PML-ABC to the symplectic FDTD scheme with 4th-order accuracy in time and space [C].1999 IEEE MTT-S International Microwave Symposium Digest Anaheim, CA,1999:1293-1296.
[92]Saitoh I, Takahashi N. Stability of symplectic finite-difference time-domain methods[J]. IEEE Transactions on Magnetics,2002,38(2):665-668.
[93]Huang Z X, Wu X L. Symplectic partitioned Runge-Kutta scheme for Maxwell's equations[J]. International Journal of Quantum Chemistry,2006,106:839-842.
[94]Jiang L L, Mao J F, Wu X L. Symplectic finite-difference time-domain method for Maxwell equations[J] IEEE Transactions on Magnetics,2006,42(8):1991-1995.
[95]钟万勰.分离变量法与哈密尔顿体系[J].计算结构力学及其应用,1991,8(3)：229-240.
[96]钟万勰.条形域平面弹性问题与哈密尔顿体系[J].大连理工大学学报,1991,31(4)：373-384.
[97]钟万勰.弹性力学求解辛体系[M].大连：大连理工大学出版社,1995.
[98]Zhong W X. Combined method for the solution of asymmetric Riccati differential equations [J]. Computer Methods in Applied Mechanics and Engineering,2001,191(1-2):93-102.
[99]钟万勰.电磁波导的辛体系[J].大连理工大学学报,2001,41(4)：378-387.
[100]陈杰大,郑长良,钟万勰.电磁波导的辛分析与对偶棱边元[J].物理学报,2006,55(5)：2340-2346.
[101]Yao Z, Zhong W X. Symplectic analysis for optical waveguides in layered media[J] Computational Methods,2006,1567-1579.
[102]孙耿.波动方程的一类显式辛格式[J].计算数学,1997,1：1-10.
[103]Gioda G, Pnadolfi A, Cividini A. A comparative evaluation of some backanalysis algorithms and their application to in-situ load tests [C]. Proc.2nd Int.Symp.on Field Measurement in Geom,1987:1131-1144.
[104]Harada H, Wall D J N, Takenaka T, et al. Conjugate gradient method applied to inverse scattering problem[J]. IEEE Transactions on Antennas and Propagation,1995,43(8):784-792.
[105]杨桦,王守东,刘家琦等.电法测井反演的离散牛顿法[J].测井技术,1996,20(1)：53-58.
[106]吕爱钟.地下巷道弹性位移反分析各种优化方法的探讨[J].岩土力学,1996,17(2)：29-34.
[107]吴小平,徐果明.利用共轭梯度法的电阻率三维反演研究[J].地球物理学报,2000,43(3)：421-427.
[108]凡友华,刘雪峰,陈晓非.面波频散反演地下层状结构的拟牛顿法[J].物探与化探,2006,30(5)：456-459.
[109]钟燕辉.层状体系介电特性反演及其工程应用[D]：(博十学位论文).大连：大连理工大学,2006.
[110]Kirkpatrick S, Gelatt C D, Vecchi M P. Equation of state calculations by fast computing machines Optimization by simulated annealing[J].Science,1983(220):671-680.
[111]姚姚.地球物理反演基本理论与应用方法[M].武汉：中国地质大学出版社,2002.
[112]项宝卫.结构优化中的模拟退火算法研究和应阳[D]：(硕十学位论文).大连：大连理工大学,2004.
[113]陈科.基于模拟退火的谱反演方法研究[D]：(硕士学位论文).北京：中国石油大学,2010.
[114]MA X Q. Simultaneous inversion of prestack seismic data for rock properties using simulated annealing[J].Geophysics,2002,67(6):1877-1885.
[115]李守巨,刘迎曦,何翔等.基于模拟退火算法的边坡最小安全系数全局搜索方法[J].岩石力学与工程学报,2003,22(2)：236-240.
[116]Lindwall D, Brozena J. Inversion of sonobuoy data from shallow-water sites with simulated annealing[J]. Journal of the Acoustical Society of America,2005,117(2):809-817.
[117]曹文贵,卢山,胡坚丽.地下工程围岩位移反分析的改进模拟退火算法[J].水文地质工程地质,2006,2：50-54.
[118]包龙生,祝孝成,叶磊等.模拟退火算法在桥梁结构可靠度分析中的应用[J].公路,2011,5：77-80.
[119]张赛民,陈灵君,刘海飞,等.基于模型分块交义移动的学习型模拟退火算法地震反演[J].中南大学学报(自然科学版),2012,43(3)：1046-1040.
[120]陈华根,吴健生,王家林等.模拟退火算法机理研究[J].同济大学学报(自然科学版),2004,32(6)：802-805.
[121]陆晓芳.改进的非常快速模拟退火算法反演四川盆地主要构造界面形态[D]：(硕士学位论文)西安：西北大学,2011.
[122]Holland J H. Adaptation in natural and artificial systems [M]. MIT Press,1975.
[123]唐文燕.结构优化中的遗传算法研究和应用[D]：(博士学位论文).大连：大连理工大学,2002.
[124]黄卡玛,赵翔.电磁场中的逆问题及应用[M].北京：科学出版社,2005.
[125]Stoffa P L, Sen M K. Nonlinear multiparameter optimization using genetic algorithms:Inversion of plane-wave seismograms[J].Geophysics,1991,56(11):1794-1810.
[126]Boschetti F, Dentith M C, List R D. Inversion of seismic refraction data using genetic algorithms [J]. Geophysics,1996,61 (6):1715-1727.
[127]徐军,邵军,郑颖人.遗传算法在岩土工程可靠度分析中的应用[J].岩土工程学报,2000,22(5)：586-589.
[128]王登刚,刘迎曦,李守巨.岩土工程位移反分析的遗传算法[J].岩石力学与工程学报,2000,19(增)：979-982.
[129]Qing A. An experimental study on electromagnetic inverse scattering of a perfectly conducting cylinder by using the real-coded genetic algorithm[J]. Microwave and Optical Technology Letters, 2001,30(5):315-320.
[130]高位,郑颖人.采用快速遗传算法进行岩土工程反分析[J].岩土工程学报,2001,23(1)：120-122.
[131]颜俊.遗传算法反演工程水文地质参数[J].铁道工程学报,2007,7：20-23.
[132]Dong E. The inversion of the coefficient of permeability with genetic algorithm[C].2011 Second International Conference on Mechanic Automation and Control Engineering (MACE), Hohhot, 2011:2722-2725.
[133]孙思扬.基于改进遗传算法的小型化宽带微带天线设计[D]：(博士学位论文).北京：北京邮电大学，2001.
[134]邢文训,谢金星.现代优化计算方法[M].北京：清华大学出版社,2005.
[135]Hopfield J, Tank D. "Neural" computation of decisions in optimization problems[J]. Biological Cybernetics,1985,52:141-152.
[136]Hopfield J, Tank D. Computing with neural circuits:a model[J]. Science,1986,233(4764):625-633.
[137]刘争平,何永富.人工神经网络在测井解释中的应用[J].地球物理学报,1995,38(增)：323-330.
[138]Rizzo D M, Dougherty, D E. Solving groundwater inverse problems using artificial neural networks[C]. International Conference on Computational Methods in Water Resources, CMWR, 1996:313-319.
[139]Caorsi S, Gamba P. Electromagnetic detection of dielectric cylinders by a neural network approach[J]. IEEE Transactions on Geoscience and Remote Sensing,1999,37(21):820-827.
[140]孙钧,袁金荣.盾构施工扰动与地层移动及其智能神经网络预测[J].岩石工程学报,2011,23(3)：261-267.
[141]Darabi A, Maldague X. Neural network based defect detection and depth estimation in TNDE[J]. NDT and E International,2002,35(3):165-175.
[142]樊琨,杨涛,李国维.公路软基沉降函数干涉神经网络预测模型[J].岩土力学,2004,25(2)：301-307.
[143]金长宇,马震岳,张运良等.神经网络在岩体力学参数和地应力场反演中的应用[J].岩十力学,2006,27(8)：1264-1271.
[144]闫滨.大坝安全监控及评价的智能神经网络模型研究[D]：(博士学位论文).大连：大连理工大学,2006.
[145]Dorigo M. Optimization, learning and natural algorithms [D]:(PhD thesis). Italy:Politecnico di Milano,1992.
[146]陈昌富,龚晓南,王贻荪.自适应蚁群算法及其在边坡工程中的应用[J].浙江大学学报(工学版),2003,37(5)：566-569.
[147]Oscar Q T, Eval R I. Application of ant colony optimization based algorithm to solve different electromagnetic problems[C]. Proceedings of The European Conference on Antennas and Propagation:EuCAP 2006, Nice, France,2006:6-10.
[148]Xu J Q, Song X H. Ant Colony Optimization for Nonlinear Inversion of Rayleigh Waves[C]. Bio-Inspired Computing and Applications-7th International Conference on Intelligent Computing, ICIC 2011, Revised Selected Papers, Zhengzhou,2011:370-377.
[149]王复明,刘小梅,蔡迎春.蚁群算法在路面模量反演中的研究与应用[J].路基工程,2009,4：74-75.
[150]韦凯,宫全美,周顺华.软土盾构隧道不均匀沉降预测的蚁群算法改进及参数选取[J].岩石力学与工程学报,2011,30(增1)：3022-3031.
[151]吴小利.祁连山北缘断裂滑动参数的GPS数据蚁群算法反演研究[J].工程地球物理学报,2011.8(2)：182-186.
[152]刘彦鹏.蚁群优化算法的理论研究及其应阳[D]：(博十学位论文).浙江：浙江大学,2007.
[153]Li S J, Liu Y X, Yu H. Parameter estimation approach in groundwater hydrology using hybrid ant colony system[C]. Computational Intelligence and Bioinformatics International Conference on Intelligent Computing, ICIC 2006, Proceedings, Kunming,2006:182-191.
[154]姚磊华.用改进的遗传算法和高斯牛顿法联合反演三维地下水流模型参数[J].计算物理,2002,22(4)：311-318.
[155]朱合华,刘学增.基于遗传算法的混合优化反分析及比较研究[J].岩石力学与工程学报,2003,22(2)：197-202.
[156]张新明,周超英,刘家琦等.流体饱和多孔隙介质多参数反演的小波多尺度_正则化高斯牛顿法[J].应用基础与工程科学学报,2009,17(4)：580-589.
[157]刘鹏程,纪晨.改进的模拟退火_单纯形综合反演方法[J].地球物理学报,1995,38(2)：199-205.
[158]高玮,冯夏庭.基于免疫连续蚁群算法的岩土工程反分析研究[J].岩石力学与工程学报,2005,24(23)：4266-4271.
[159]石露,李小春,任伟等.蚁群算法与遗传算法融合及其在边坡临界滑动面搜索中的应用[J].岩土力 学,2009,30(11)：3486-3492.
[160]Rabbani M, Noroozi S, Vinney J, et al. An inverse method of load determination using hybrid genetic algorithms, artificial neural networks and finite element analysis[C] Proceedings of the 5th International Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain,2006:54.
[161]Tang R Y, Li Y, Wen G, et al. Combined strategy of improved simulated annealing and genetic algorithm for inverse problem[J] IEEE Transactions on Magnetics,1996,32(3):1326-1329.
[162]Kennedy J, Eerhart R C. Particle swarm optimization[C] Proceedings of the IEEE International Conserence on Neural Networks. Perth, Australia,1995:1942-1948.
[163]李丽,牛奔.粒子群优化算法[M].北京：冶金工业出版社,2010.
[164]Cheu R L, Srinivasan D, Loo W H. Traffic incident detection using particle swarm optimization[J] Transportation Research Record,2004,1867:11-18.
[165]高玮.基于粒子群优化的岩土工程反分析研究[J].岩土力学,2006,27(25)：795-798.
[166]姜谙男,梁冰.基于粒子群支持向量机的三维含水层渗流参数反馈识别[J].岩土力学,2009,30(5)：1527-1531.
[167]徐飞,徐卫亚.岩爆预测的粒子群优化投影寻踪模型[J].岩土工程学报,2010,32(5)：718-723.
[168]Sun C H, Chiu C C, Li C L. Time-domain inverse scattering of a two-dimensional metallic cylinder in slab medium using asynchronous particle swarm optimization[J] Progress In Electromagnetics Research M,2010,14:85-100.
[169]周永祖.非均匀介质中的场与波[M]北京：电子工业出版社,1992.
[170]郑宏兴,葛德彪 广义传播矩阵法分析分层各向异性材料对电磁波的反射与透射[J]物理学报2000,49(9)：1702-1706.
[171]张剑锋.非均匀吸收介质中地震波的广义传递矩阵解法[J].计算结构力学及其应用,1996,13(2)：201-207.
[172]张剑锋,刘书，各向异性展状介质中弹性波的传播矩阵解法[J].固体力学学报,1996,17(3)：273-277.
[173]Vashishth A K, Khurana P S. Waves in stratified anisotropic poroelastic media:a transfer matrix approach[J] Journal of Sound and Vibration,2004,277(1-2):239-275.
[174]高强.辛体系算法在波的传播与振动问题中的应用[D]：(博十学位论文).大连：大连理工大学,2006.
[175]邓子辰,欧阳华江,钟万勰.奇异条件下Riccati代数方程的求解[J].计算结构力学及其应用,1993,10(1)：1-6.
[176]钟万勰,朱建平.黎卡提微分方程的精细积分[J].数值计算与计算机应用,1996,1：26-35.
[177]钟万勰.矩阵黎卡提方程的精细积分法.[J].计算结构力学及其应用,1994,11(2)：113-119.
[178]钟万勰.矩阵黎卡提(Riccati)微分方程的分析解[J].力学季刊,2000,21(1)：1-7.
[179]赵丽滨,张建宇,王寿梅.精细积分方法的稳定性和精度分析[J].北京航空航天大学学报,2000,26(5)：569-572.
[180]钟万勰,林家浩,高强.分层介质中非平稳随机波的精细求解[J].动力学与控制学报,2003,1(1)：2-8.
[181]高强,钟万勰,林家浩.分层介质中Love波的扩展w-w算法[J].固体力学学报,2007,28(2)：132-136.
[182]钟万勰.应阳力学的辛数学方法[M].北京：高等教育出版社,2006.
[183]Zhong W X, Lin J H, Gao Q. The precise computation for wave propagation in a stratified materials[J] Journal for Numerical Methods in Engineering,2004,60:11-25.
[184]Gao Q, Lin J H, Zhong W X, et al. Random wave propagation in a viscoelastic layered half space[J]. International Journal of Solids and Structures,2006,43(21):6453-6471.
[185]Gao Q, Lin J H, Zhong W X, et al. Propagation of partially coherent non-stationary random waves in a viscoelastic layered half-space[J]. Soil Dynamics and Earthquake Engineering,2008,28(4): 305-320.
[186]Gao Q, Lin J H, Zhong W X, et al. Propagation of non-stationary random waves in viscoelastic stratified solids[J]. Computers and Geotechnics,2006,33(8):444-453.
[187]Gao Q, Lin J H, Zhong W X, et al. Isotropic layered soil-structure interaction caused by stationary random excitations[J]. International Journal of Solids and Structures.2009,46(3-4):455-463.
[188]Zhong W X, Williams F W, Bennett P N. Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems[J]. Journal of Vibration and Acoustics, Transactions of the ASME,1997, 119(3):334-340.
[189]Gao Q, Lin J H, Zhong W X, et al. A precise numerical method for Rayleigh waves in a stratified half space[J] Journal for Numerical Methods in Engineering,2006,67(6):771-786.
[190]G Q, Zhong W X, Howson W P. A precise method for solving wave propagation problems in layered anisotropic media.[J] Wave Motion,2004,40(3):191-207.
[191]姚征.辛体系算法在波的传播与振动问题中的应用[D]：(博十学位论文).大连：大连理工大学,2006.
[192]Gao Q.Lin J H. Stationary random waves Propagation in 3D viscoelastic stratified solid[J]. Applied Mathematics and Mechanics,2005,26(6):785-796.
[193]Feng K, Wang D L. A note on conservation laws of symplectic difference schemes for Hamiltonian systems[J] Journal of Computational Mathematics,1991,9(3):229-237.
[194]Sun G. A simple way of constructing symplectic Runge-Kutta methods[J]. Journal of Computational Mathematics,2000,18(1):61-68.
[195]Lu X W, Schmid R. A symplectic algorithm for wave equations[J]. Mathematics and Computers in Simulation,1997,43(1):29-38.
[196]Sun G. Construction of high order Symplectic PRK methods[J]. Journal of Computational Mathematics,1995,13(1),40-50.
[197]Qin M Z, Zhang M Q. Multi-stage symplectic schemes of two kinds of Hamiltonian systems for wave equations[J]. Computers & Mathematics with Applications,1990,19(10):51-62.
[198]Feng K. On difference schemes and symplectic geometry[C]. Proceedings of the 1984 Beijing symposium on differential geometry and differential equations, Beijing,1985:42-58.
[199]Sanz-Serna J M, Calvo M P. Numerical Hamilton Problems[M]. London, UK:Chapman & Hall. 1994.
[200]Higueras I, Rold'an T. Starting algorithms for partitioned Runge-Kutta methods:the pair Lobatto ⅢA-ⅢB [C]. Monograf (?)as de la Real Academia de Ciencias de Zaragoza,2004,25:149-158.
[201]Jay L. Symplectic Partitioned Runge-Kutta Methods for Constrained Hamiltonian Systems[J]. SIAM Journal on Numerical Analysis,1996,33(1):368-387.
[202]Liu H Y, Sun G. Symplectic RK method and symplectic PRK methods with real eigenvalues[J]. Journal of Computational Mathematics,2004,22(5):769-776.
[203]Sun G. Symplectic partitioned Runge-Kutta method[J]. Journal of Computational Mathematics, 1993,11(4):365-372,
[204]Sanz-Serna J M. Symplectic integrations for Hamiltonian problems:an overview[J] Acta Numerica,1992,1:243-286.
[205]Sanz-Serna J M. Runge-Kutta schemes for Hamiltonian systems[J]. BIT Numerical Mathematics 1988,28:877-883.
[206]冯康,秦孟兆.哈密尔顿系统的辛几何算法[M].杭州：浙江科学技术出版社,2003.
[207]李世雄.波动方程的高频近似与辛几何算法[M].北京：科学出版社,2001.
[208]施妙根,顾丽珍.科学和工程计算基础[M].北京：清华大学出版社,1999.
[209]施吉林,张宏伟,金光日.计算机科学计算[M].北京：高等教育出版社,2005.
[210]黄志祥.辛算法在时域电磁散射计算中的应用[D]：(博士学位论文).合肥：安徽大学,,2007.
[211]蒋乐乐.基于辛几何算法的电磁散射数值方法的研究[D]：(硕士学位论文).合肥：安徽大学,2004.
[212]Mur G. Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations [J]. IEEE Transactions on Electromagnetic Compatibility 1981,4: 377-382.
[213]Liao Z P. Normal transmitting boundary conditions [J]. Science in China(series E),1996,39(3): 244-254.
[214]Liao Z P. Extrapolation non-reflecting boundary conditions [J]. Wave Motion,1996,24(2): 117-138.
[215]廖振鹏.工程波动理论导论[M].北京：科学出版社,2002.
[216]Liao Z P, Wong H L, Yang B P, et al. A transmitting boundary for transient wave analysis[J]. Scienta Sinica series A,1984,17 (10):1063-1076.
[217]Liao Z P, Wong H L. A transmitting boundary for the numerical simulation of elastic wave propagation [J]. Soil Dynamics and Earthquake Engineering,1984,3(4):174-183.
[218]Liao Z P, Yang G. Multi-directional transmitting boundaries for steady-state sh wave [J]. Earthquake Engineering and Structural Dynamics,1995,24(3):361-371.
[219]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现[J].地球物理学报,2002,45(4)：533-545.
[220]谢志南,廖振鹏.多次透射公式在波动数值模拟中的一种实现方案[J].固体力学学报,2010,41(4)：422-426.
[221]Higdon R L. Absorbing boundary conditions for elastic waves [J]. Geophysics,1991,56(2):231-241.
[222]孙卫涛.弹性波动方程的有限差分方法[M].北京：清华大学出版社,2009.
[223]Taflove A, Hagness S C. Computational electrodynamics the finite-difference time-domain method[M]. Norwood, USA:Artech House.
[224]Capoglu I R, Smith G S. A Total-Field Scattered-Field Plane-Wave Source for the FDTD Analysis of Layered Media[J]. IEEE Transaction on Antenna and Propagation,2008,56(1):158-169
[225]Sullivan D M. Electromagnetic simulation using the FDTD method[M]. New York, U.S.A:IEEE Press.
[226]Schneider J B. Plane waves in FDTD simulations and a nearly perfect total-field scattered-field boundary [J]. IEEE Transactions on Antennas and Propagation,2004,52(12):3280-3287.
[227]Sha W, Huang Z X, Wu X L, et al. Total field and scattered field technique for fourth-order symplectic finite difference time domain method [J]. Chinese Physics Letters,2006,23(1): 103-105.
[228]黄志祥,沙威,吴先良等.高阶辛算法的稳定性与数值色散性分析[J].计算物理,2010,27(1)：82-88.
[229]黄志祥,吴先良.辛算法的稳定性及数值色散性分析[J].电子学报,2006,34(3)：535-538.
[230]Saitoh I, Takahashi N. Stability of symplectic finite-difference time-domain methods[J]. IEEE Transactions on Magnetics,2002,38(2):665-668.
[231]纪震,廖慧连,吴青华.粒子群算法及应用[M].北京：科学出版社,2009.
[232]刘波.粒子群优化算法及其工程应用[M].北京：电子工业出版社,2010.
[233]Shi Y H, Eberhart R C. A modified particle swarm optimizer [J]. The 1998 IEEE International Conference on Evolutionary Computation Proceedings,1998. IEEE World Congress on Computational Intelligence, Anchorage, AK,1998:69-73.
[234]Shi Y H, Eberhart R C. Empirical study of particle swarm optimization [C]. Proceedings of the 1999 Congress on Evolutionary Computation,1999. CEC 99. Washington, DC,1999:1945-1950.
[235]Shi Y H, Eberhart R C. Fuzzy adaptive particle swarm optimization [C]. Proceedings of the 2001 Congress on Evolutionary Computation, Seoul,2001:101-106.
[236]刘建华,樊晓平，瞿志华.一种惯性权重动态调整的新型粒子群算法[J].计算机工程与应阳,2007,43(7)：68-70.
[237]黄轩,张军,詹志辉.基于随机惯量权重的快速粒子群优化算法[J].计算机工程与设计,2009,30(3)：647-650.
[238]邓爱萍,王会芳.动态改变惯性权重的自适应粒子群算法[J].计算机工程与设计,2010,31(13)：3062-3065.
[239]李军,许丽佳,游志宇.一种带压缩因子的自适应权重粒子群算法[J].西南大学学报(自然科学版),2011,33(7)：118-122.
[240]姜长元,赵曙光,沈十根等.惯性权重正弦调整的粒子群算法[J].计算机工程与应用,2012,48(8)：40-42.
[241]M. Clerc. The swarm and the queen:towards a deterministic and adaptive particle swarm optimization[C] Proceedings of IEEE international conference on evolutionary computation, Washington, DC,1999:1951-1957
[242]Ratnaweera A, Halgamuge S K, Watson H C. Self-organizing hierarchical particle swarm optimizer with time-varying [J]. IEEE Transactions on Evolutionary Computation,2004,8(3):240-255
[243]冯翔,陈国龙,郭文忠.粒子群优化算法中加速因子的设置与试验分析[J].集美大学学报(自然科学版),2005,11(2)：146-150.
[244]孙湘.非线性动态加速系数对粒子群算法的影响[J].计算机工程与科学.2011,33(10)：131-134.
[245]陈水利,蔡国榕,郭文忠等.PSO算法加速因子的非线性策略研究[J].长江大学学报(自科版)理工卷,2007,4(4)：1-4.
[246]Zhang L P, Yu H J, Hu S X. Optimal choice of parameters for particle swarm optimization [J]. Journal of Zhejiang University SCIENCE A,2005,6(6):528-534.
[247]M. Clerc. The swarm and the queen:towards a deterministic and adaptive particle swarm optimization[C] Proceedings of the 1999 congress on evolutionary computation, Piscataway NJ USA,1999:1927-1930.
[248]Fieldsend J E, Singh S. A multi-objective algorithm based upon particle swarm optimization[C] An efficient data structure and turbulence, proceedings of UK workshop on computational intelligence: 2002:37-44.
[249]庞巍,王康平,周春光等.模糊离散粒子群优化算法求解旅行商问题[J].小型微型计算机系统,2005,26(8)：1331-1334.
[250]刘建华,樊晓平,瞿志华.一种基于相似度的新型粒子群算法[J].控制与决策,2007,22(10)：1155-1159.
[251]张英男.改进的粒子群优化算法(APSO和DPSO)研究[D]：(硕士学位论文).大连：大连理工大学,2008.
[252]张艳琼.改进的云自适应粒子群优化算法[J].计算机应用研究,2010,27(9)：3250-3252.
[253]顾大为,凌君.一种改进的新颖的粒子群优化算法[J].计算机工程与应用,2011,47(6)：50-51.
[254]Yang Y H, Zhao F Q, Yao Y P, et al. A PSO and simulated annealing hybrid algorithm to task allocation problem for holonic manufacturing system [C]. The Sixth World Congress on Intelligent Control and Automation,2006. WCICA 2006, Dalian,2006:6767-6771.
[255]Zhao X C, Song B Q, Huang P Y, et al. An improved discrete immune optimization algorithm based on PSO for QoS-driven web service composition [J]. Applied Soft Computing,2012,12(8): 2208-2216.
[256]Yu S W, Wei Y M, Wang K. A PSO-GA optimal model to estimate primary energy demand of China [J]. Energy Policy,2012,42:329-340.
[257]Liu R H, Wang H. A novel auto calibration of 3-axis MEMS accelerometers based on improved PSO algorithm [J]. Advanced Materials Research,2012,403-408:4572-4579.
[258]李晓龙.基于支持向量机的岩体力学参数反演及工程应用[D]：(博士学位论文).郑州：郑州大学,2009.
[259]李晓龙,王复明.岩土工程弹塑性反分析的改进粒子群算法[J].采矿与安全工程学报,2009,26(1)：50-54.
[2]曾昭发,刘四新,王者江.探地雷达方法原理及应用[M].北京：科学出版社,2006.
[3]张蓓.路面结构层材料介电特性及其厚度反演分析的系统识别方法[D]：(博士学位论文).重庆：重庆大学,2003.
[4]Saarenketo T, Scullion T. Road evaluation with ground penetrating radar [J]. Journal of Applied Geophysics,2000,43(2-4):119-138.
[5]Saarenketo T, Hietala K, Salmi T. GPR application in geotechnical investigations of peat for road survey purposes [C]. Fourth International Conference on Ground Penetrating Radar, Rovaniemi, Finland,1992:293-305.
[6]Saarenketo T, Scullion T. Laboratory and GPR tests to evaluate electrical and mechanical properties of Texas and Finnish base course aggregates [C]. Proceeding of the Sixth International Conference on Ground Penetrating Radar, Sendai, Japan.1996:477-482.
[7]Saarenketo T. Using Ground Penetrating Radar and dielectric probe measurements in pavement density quality control [C].1997 Annual Meeting of the Transportation Research Board, Washington D C, USA,1997:34-41.
[8]Saarenketo T, Roimela P. Ground Penetrating Radar technique in asphalt pavement density quality control [C]. Proceeding of the Seventh International Conference on Ground Penetrating Radar, Lawrence KS,1998:461-466.
[9]Saarenketo T, Nikkinen T, Lotvonen S. The use of Ground Penetrating Radar for monitoring water movement in road structures [C]. Proceedings of Fifth International Conference on Ground Penetrating Radar, Ontario, Canada,1994:1181-1192.
[10]Lau C L, Scullion T, Chan P. Using Ground Penetrating Radar technology for pavement evaluations in Texas [C]. Proceedings 4th International Conference on Ground Penetrating Radar, Rovaniemi, Finland,1992:277-283.
[11]Scullion T, Saarenketo T. Application of Ground Penetrating Radar technology for network and project level pavement management systems [C]. Proceedings of the Fourth International Conference on Managing Pavements, Durban, South Africa,1998:254-268.
[12]Scullion T, Saarenketo T. Integrating Ground Penetrating Radar and falling weight deflectometer technology in pavement evaluation [C]. Proceedings of the Third ASTM Symposium of Nondestructive Testing of Pavements and Backcalculation of Moduli, Seattle,Washington, 2000:23-37.
[13]Rmeili E, Scullion T. Detecting stripping in asphalt concrete layers using Ground Penetrating Radar [C].1997 Annual Meeting of Transportation Research Board, Washington D C USA,1997:165-174.
[14]Saarenketo T, Scullion T. Moisture susceptibility and electrical properties of base course aggregates [C]. Proceedings of BCRA,Trondheim, Norway,1998:1401-1410.
[15]Lau C L.Scullion T, Chan P. Modeling of Ground Penetrating Radar wave propagation in pavement systems [C].72nd Annual Meeting, Washington D C,1992:99-107.
[16]Cuvillier M, Boaddard J F, Retour P. New methods developed in France for road network survey and maintenance [C]. Proc.6th Conf. Struct. Des. of Asphalt Pavements, Univ. of Michigan, Ann Arbor, MI,1987:562-573.
[17]Attoh-Okine B N. Time series analysis for ground penetrating radar (GPR) asphalt thickness profile [J]. Applied Stochastic Models and Data Analysis,1994,10(3):153-167.
[18]Fernando E, Liu W T, Dietrich B. Computer program for network level determination of pavement layer thicknesses[C], Proceedings of SPIE-The International Society for Optical Engineering, Gold Coast, Australia,2000:194-199.
[19]Loulizi A, Al-Qadi I L, Lahouar S. Optimization of ground-penetrating radar data to predict layer thicknesses in flexible pavements [J]. Journal of Transportation Engineering,2003,129(1):93-99.
[20]Huang C L, Su Y. A new GPR calibration method for high accuracy thickness and permittivity measurement of multi-layered pavement [C]. Proceedings of the Tenth International Conference on Ground Penetrating Radar, Delft, The Netherlands,2004:627-630.
[21]Willett D A., Mahbou K C, Rister B. Accuracy of ground-penetrating radar for pavement-layer thickness analysis [J].Journal of Transportation Engineering,2006,132(1):96-103.
[22]Maser K R, Holland T J, Roberts R. NDE methods for quality assurance of new pavement thickness [J].International Journal of Pavement Engineering,2006,7(1):1-10.
[23]Malva L J, Cline G D. Detecting voids under airfield pavements[C]. Proceedings of the Specialty Conference, Las Vegas, Nevada, United States,2003:366-377.
[24]Saarenketo T, Soderqvist M K. Ground penetrating radar applications for bridge deck evaluations in Finland [J]. Insight-Non-Destructive Testing and Condition Monitoring,1994,36(7):496-50.
[25]Chen Roger H L, Chen H U, Pei L F, et al. An experimental evaluation of concrete bridge decks and pavements using ground penetrating radar[C]. Structures Congress-Proceedings, Building to Last, Portland, Oregon,1997:1508-1512.
[26]Narayanan R M, Hudson S G, Kumke C J. Detection of rebar corrosion in bridge decks using statistical variance of radar reflected pulses[C]. GPR 98, Proc.7th Intl. Conf. on GPR, Lawrence, Kansas,1998:601-605.
[27]Du S, Rummel P. Reconnaissance studies of moisture in the subsurface with GPR[C].GPR 94, Proc. 5th Intl. Conf. on GPR, Kitchener, Ontario,1994:1241-1248.
[28]Greaves R J, Lesmes D P, Lee J M, et al. Velocity variations and water content estimated from multioffset ground penetrating radar [J]. Geophysics,1996(61):683-695.
[29]Hubbard S, Grote K, Rubin Y, Estimation of near subsurface water content using high frequency GPR ground wave [J]. Leading Edge of Exploration, Society of Exploration Geophysics,2002, 21(6):552-559.
[30]Maser Kenneth R. Condition assessment of transportation infrastructure using ground-penetrating radar [J]. Journal of Infrastructure Systems,1996,2(2):94-101.
[31]Maser K R, Sande I. Application of ground penetrating radar for evaluation of sub-surface airfield pavement conditions [J].Insight:Non-Destructive Testing and Condition Monitoring,2000, 42(7):451-453.
[32]李大心.探地雷达方法与应用[M].北京：地质出版社,1994.
[33]Cook J C. Radar exploration through rock in advance of mining [J], Transactions of AIME, Society of Mining Engineers,1973,254:140-146.
[34]Holser W T, Brown R J, Roberts F A, et al. Radar logging of a salt dome [J]. Geophycics, 37(5):889-906.
[35]Simmons G, Strangway D, Annan A P, et al. Surface electrical properties experiment [R] in Apollo 17:preliminary science report, scientific and technical office, NASA, Washington D C, 1973:15-1-15-14.
[36]Coon J B, Fowler J C, Schafers C J. Experimental uses of short pulse radar in coal seams [J]. Geophysics,1981,46(8):1163-1168.
[37]Davis J L, Annan A P. Ground penetrating radar for high-resolution mapping of soil and rock stratigraphy [J]. Geophysical prospecting,1989,37:531-551.
[38]Boniger U, Tronicke J. Integrated data analysis at an archaeological site:A case study using 3D GPR, magnetic, and high-resolution topographic data [J]. Geophysics,2010,75(4):169-176.
[39]Xu X X, Zeng Q S, Li D, et al. GPR detection of several common subsurface voids inside dikes and dams [J]. Engineering Geology,2010,111(1-4):31-42.
[40]Hubbard S, Chen J S, Williams K, et al. Environmental and agricultural applications of GPR[C]. Proceedings of the 3rd International Workshop on Advanced Ground Penetrating Radar, IWAGPR 2005, Delft, Netherlands,2005:45-49.
[41]徐朝红.二维块状模型射线追踪方法设计与实现[D]：(硕士学位论文).西安：长安大学,2009.
[42]刘军.基于射线追踪的微地震模型多波场正演模拟[D]：(硕士学位论文).北京：中国石油大学,2009.
[43]魏亦文.基于复杂介质最短路径射线追踪层析成像正演研究[D]：(硕士学位论文).长沙：中南大学,2007.
[44]邓世坤,王惠濂.探地雷达图像的正演合成与偏移处理[J].地球物理学报,1993,36(04)：528-536.
[45]Goodman D. Ground-penetrating radar simulation in engineer in gand archaeology [J]. Geophysics, 1994,59(2):224-232.
[46]Cai J, McMechan G A. Ray based synthesis of bistatic ground-penetrating radar profiles [J]. Geophysics,1995,60(1):87-96.
[47]曾昭发,高尔根.三维介质中探地雷达(GPR)波传播逐段迭代射线追踪方法研究和应用[J].吉林大学学报(地球科学版),2005,35(sup)：119-123.
[48]Huang Y Q, Zhang J Z, Liu Q H. Three-dimensional GPR ray tracing based on wavefront expansion with irregular cells[J]. IEEE Transaction on Geoscience and Remote Sensing,2011,49(2):679-687.
[49]王长清.现代计算电磁学基础[M].北京：北京大学出版社,2005.
[50]Gurel L, Aksun M I. Electromagnetic scattering solution of conducting strips in layered media using the fast multipole method [J]. IEEE Microwave and Guided Wave Letters,1998,6(8):277-279.
[51]Geng N, Sullivan A, Carin L. Fast multipole method for scattering from an arbitrary PEC target above or buried in a lossy half space [J]. IEEE Transactions on Antennas and Propagation,2001, 49(5):740-748.
[52]Vande Ginste D, Rogier H, Olyslager F, et al. A fast multipole method for layered media based on the application of perfectly matched layers-the 2-D case [J]. IEEE Transactions on Antennas and Propagation,2004,52(10):2631-2640.
[53]于继军,盛新庆.地下三维目标电磁散射的矩量法计算[J].电子与信息学报,2008,28(5)：950-954.
[54]Wang A Q, Guo L X, Chai C. Fast numerical method for electromagnetic scattering from an object above a large-scale layered rough surface at large incident angle vertical polarization [J]. Applied Optics,2011,50(4):500-508.
[55]马弘炯.瞬态电磁脉冲的时域伪谱方法：研究、改进及应用[D]：(博十学位论文).成都：电子科技大学,2005.
[56]杨虎.多区域时域伪谱算法在电磁分析中的理论和应用研究[D]：(博士学位论文).长沙：国防科技大学,2006.
[57]粟毅,黄春林,雷文太.探地雷达理论与应用[M].北京：科学出版社,2006.
[58]Casper D A, Samuel Kung K J. Simulation of ground-penetrating radar waves in a 2-D soil model [J]. Geophysics,1996,61(4):1034-1049.
[59]Liu Q H, Fan G X. Simulations of GPR in dispersive media using a frequency-dependent PSTD algorithm[J]. IEEE Transaction on Geoscience and Remote Sensing,1999,37(5):2317-2324.
[60]Fan G X, Liu Q H, Hesthaven J S. Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media [J]. IEEE Transaction on Geoscience and Remote Sensing,2002,40(6):1366-1373.
[61]姜永金,刘立业,杨虎等.有耗媒质中目标体散射特性的TSNU_PSTD模拟[J].国防科技大学学报,2005,27(6)：88-92.
[62]吕英华.计算电磁学的数值方法[M].北京：清华大学出版社,2006.
[63]王建国,葛德彪(泽).电磁场有限元方法[M].西安：西安电子科技大学出版社,1998.
[64]沈飙,孙忠良,曲孝良.探地雷达波波动方程研究及其正演模拟[J].东南大学学报,1994,24(2)：114-117.
[65]底青云,王妙月.雷达波有限元仿真模拟[J].地球物理学报,1999,42(6)：818-825.
[66]谢辉,钟燕辉,蔡迎春.电磁场有限元法在GPR正演模拟中的应用[J].河南科学,2003,21(3)：295-298.
[67]Zhang X J, Huang J H, Song L. Application of ground penetrating radar (GPR) exploration in Karst mountain areas[C] 2010 13th International Conference on Ground Penetrating Radar (GPR), Lecce, 2010:21-25.
[68]陈承申.探地雷达二维有限元正演模拟[D]：(硕十学位论文).K沙：中南大学,2011.
[69]葛德彪,闫玉波.电磁场时域有限差分法[M].西安：西安电子科技大学出版社,2002.
[70]Wang T, Oristaglio M L.3-D simulation of GPR surveys over pipes in dispersive soils [J]. Geophysics,2000,65(5):1560-1568.
[71]詹毅.复杂有耗色散地层中的FDTD方法以及在冲击探地雷达中的应用[D]：(博十学位论文)西安：电子科技大学,2000.
[72]Moss C D, Teixeira F L, Kong J A. Analysis and compensation of numerical dispersion in the FDTD method for layered, anisotropic media [J]. IEEE Transactions on Antennas and Propagation, 2002,50(9):1174-1184.
[73]Irving J, Knight R. Numerical modeling of ground-penetrating radar in 2-D using MATLAB [J]. Computers & Geosicences,32(9):1247-1258.
[74]冯德山,戴前伟,何继善.探地雷达的正演模拟及有限差分波动方程偏移处理[J].中南大学学报(自然科学版),2006,27(2)：361-365.
[75]Cassidy N J, Millington T M. The application of finite-difference time-domain modeling for the assessment of GPR in magnetically lossy materials[J]. Journal of Applied Geophysics,2009,67(4): 296-308.
[76]Zhu Z Q, Lu G Y, Lu Q. The FDTD modeling of GPR for tunnel inspection[C]. International Conference on Information Engineering and Computer Science, WuHan,2009. ICIECS,2009:1-4.
[77]Diamanti N. A study of GPR vertical crack responses in pavement using field data and numerical modeling[C].2010 13th International Conference on Ground Penetrating Radar (GPR), Lecce, 2010:1-6.
[78]汤炜ADI_FDTD及其混合算法在电磁散射中的应用[D]：(博士学位论文).西安：电子科技大学,2005.
[79]Xiao F, Tang X H, Du G H, et al. Improvement on the numerical dispersion inherent in the ADI-FDTD Method [C]. Proceedings of Asia-Pacific Microwave Conference 2007, Bangkok, 2007:1-4.
[80]Diamanti N, Giannopoulos A. Implementation of ADI-FDTD subgrids in ground penetrating radar FDTD models[J] Journal of Applied Geophysics,2009,67(4):309-317.
[81]Feng D S, Dai Q W. GPR numerical simulation of full wave field based on UPML boundary condition of ADI-FDTD [J]. NDT&E International,2011,44(6):495-504.
[82]冯德山,谢源.基于单轴各向异性完全匹配层边界条件的ADI_FDTD三维GPR全波场正演[J].中南大学学报(自然科学版),2011,42(8)：2363-2371.
[83]张玉廷,蔡智,刘胜.交替隐式时域有限差分分析有耗介质电磁波传播[J].电波科学学报,2011,26(6)：1088-1094.
[84]Sarrafi P, Li Q. Modeling of Pulse Propagation in Layered Structures With Resonant Nonlinearities Using a Generalized Time-Domain Transfer Matrix Method [J]. IEEE Journal of Quantum Electronics,2012,48(5):559-567.
[85]Cao Q S, Chen Y C. Application of an anisotropic perfectly matched layer absorber for open boundary truncation in the multiresolution time domain scheme[J] IEEE Transactions on Antennas and Propagation,2003,51(2):350-357.
[86]Ghasemia F A, Abrishamian M S. A novel method for FDTD numerical GPR imaging of arbitrary shapes based on Fourier transform [J]. NDT&E International,2007,40(2):140-146.
[87]文舸一.辛算法及其在电磁场方程中的应用[J].微波学报,1999,15(1)：68-79.
[88]文舸一.电磁理论新进展[M].北京：国防工业出版社,1999.
[89]Hirono T, Lui W W, Yokoyama K. Time-domain simulation of electromagnetic field using a symplectic integrator[J]. IEEE Microwave and Guided Wave Letters,1997,7(9):279-281.
[90]Hirono T, Lui W W, Yokoyama K, et al. Stability and numerical dispersion of symplectic fourth-order time-domain schemes for optical field simulation[J]. Journal of Lightwave Technology, 1998,16(10):1915-1920.
[91]Hirono T, Lui W W, Yokoyama K. Successful applications of PML-ABC to the symplectic FDTD scheme with 4th-order accuracy in time and space [C].1999 IEEE MTT-S International Microwave Symposium Digest Anaheim, CA,1999:1293-1296.
[92]Saitoh I, Takahashi N. Stability of symplectic finite-difference time-domain methods[J]. IEEE Transactions on Magnetics,2002,38(2):665-668.
[93]Huang Z X, Wu X L. Symplectic partitioned Runge-Kutta scheme for Maxwell's equations[J]. International Journal of Quantum Chemistry,2006,106:839-842.
[94]Jiang L L, Mao J F, Wu X L. Symplectic finite-difference time-domain method for Maxwell equations[J] IEEE Transactions on Magnetics,2006,42(8):1991-1995.
[95]钟万勰.分离变量法与哈密尔顿体系[J].计算结构力学及其应用,1991,8(3)：229-240.
[96]钟万勰.条形域平面弹性问题与哈密尔顿体系[J].大连理工大学学报,1991,31(4)：373-384.
[97]钟万勰.弹性力学求解辛体系[M].大连：大连理工大学出版社,1995.
[98]Zhong W X. Combined method for the solution of asymmetric Riccati differential equations [J]. Computer Methods in Applied Mechanics and Engineering,2001,191(1-2):93-102.
[99]钟万勰.电磁波导的辛体系[J].大连理工大学学报,2001,41(4)：378-387.
[100]陈杰大,郑长良,钟万勰.电磁波导的辛分析与对偶棱边元[J].物理学报,2006,55(5)：2340-2346.
[101]Yao Z, Zhong W X. Symplectic analysis for optical waveguides in layered media[J] Computational Methods,2006,1567-1579.
[102]孙耿.波动方程的一类显式辛格式[J].计算数学,1997,1：1-10.
[103]Gioda G, Pnadolfi A, Cividini A. A comparative evaluation of some backanalysis algorithms and their application to in-situ load tests [C]. Proc.2nd Int.Symp.on Field Measurement in Geom,1987:1131-1144.
[104]Harada H, Wall D J N, Takenaka T, et al. Conjugate gradient method applied to inverse scattering problem[J]. IEEE Transactions on Antennas and Propagation,1995,43(8):784-792.
[105]杨桦,王守东,刘家琦等.电法测井反演的离散牛顿法[J].测井技术,1996,20(1)：53-58.
[106]吕爱钟.地下巷道弹性位移反分析各种优化方法的探讨[J].岩土力学,1996,17(2)：29-34.
[107]吴小平,徐果明.利用共轭梯度法的电阻率三维反演研究[J].地球物理学报,2000,43(3)：421-427.
[108]凡友华,刘雪峰,陈晓非.面波频散反演地下层状结构的拟牛顿法[J].物探与化探,2006,30(5)：456-459.
[109]钟燕辉.层状体系介电特性反演及其工程应用[D]：(博十学位论文).大连：大连理工大学,2006.
[110]Kirkpatrick S, Gelatt C D, Vecchi M P. Equation of state calculations by fast computing machines Optimization by simulated annealing[J].Science,1983(220):671-680.
[111]姚姚.地球物理反演基本理论与应用方法[M].武汉：中国地质大学出版社,2002.
[112]项宝卫.结构优化中的模拟退火算法研究和应阳[D]：(硕十学位论文).大连：大连理工大学,2004.
[113]陈科.基于模拟退火的谱反演方法研究[D]：(硕士学位论文).北京：中国石油大学,2010.
[114]MA X Q. Simultaneous inversion of prestack seismic data for rock properties using simulated annealing[J].Geophysics,2002,67(6):1877-1885.
[115]李守巨,刘迎曦,何翔等.基于模拟退火算法的边坡最小安全系数全局搜索方法[J].岩石力学与工程学报,2003,22(2)：236-240.
[116]Lindwall D, Brozena J. Inversion of sonobuoy data from shallow-water sites with simulated annealing[J]. Journal of the Acoustical Society of America,2005,117(2):809-817.
[117]曹文贵,卢山,胡坚丽.地下工程围岩位移反分析的改进模拟退火算法[J].水文地质工程地质,2006,2：50-54.
[118]包龙生,祝孝成,叶磊等.模拟退火算法在桥梁结构可靠度分析中的应用[J].公路,2011,5：77-80.
[119]张赛民,陈灵君,刘海飞,等.基于模型分块交义移动的学习型模拟退火算法地震反演[J].中南大学学报(自然科学版),2012,43(3)：1046-1040.
[120]陈华根,吴健生,王家林等.模拟退火算法机理研究[J].同济大学学报(自然科学版),2004,32(6)：802-805.
[121]陆晓芳.改进的非常快速模拟退火算法反演四川盆地主要构造界面形态[D]：(硕士学位论文)西安：西北大学,2011.
[122]Holland J H. Adaptation in natural and artificial systems [M]. MIT Press,1975.
[123]唐文燕.结构优化中的遗传算法研究和应用[D]：(博士学位论文).大连：大连理工大学,2002.
[124]黄卡玛,赵翔.电磁场中的逆问题及应用[M].北京：科学出版社,2005.
[125]Stoffa P L, Sen M K. Nonlinear multiparameter optimization using genetic algorithms:Inversion of plane-wave seismograms[J].Geophysics,1991,56(11):1794-1810.
[126]Boschetti F, Dentith M C, List R D. Inversion of seismic refraction data using genetic algorithms [J]. Geophysics,1996,61 (6):1715-1727.
[127]徐军,邵军,郑颖人.遗传算法在岩土工程可靠度分析中的应用[J].岩土工程学报,2000,22(5)：586-589.
[128]王登刚,刘迎曦,李守巨.岩土工程位移反分析的遗传算法[J].岩石力学与工程学报,2000,19(增)：979-982.
[129]Qing A. An experimental study on electromagnetic inverse scattering of a perfectly conducting cylinder by using the real-coded genetic algorithm[J]. Microwave and Optical Technology Letters, 2001,30(5):315-320.
[130]高位,郑颖人.采用快速遗传算法进行岩土工程反分析[J].岩土工程学报,2001,23(1)：120-122.
[131]颜俊.遗传算法反演工程水文地质参数[J].铁道工程学报,2007,7：20-23.
[132]Dong E. The inversion of the coefficient of permeability with genetic algorithm[C].2011 Second International Conference on Mechanic Automation and Control Engineering (MACE), Hohhot, 2011:2722-2725.
[133]孙思扬.基于改进遗传算法的小型化宽带微带天线设计[D]：(博士学位论文).北京：北京邮电大学，2001.
[134]邢文训,谢金星.现代优化计算方法[M].北京：清华大学出版社,2005.
[135]Hopfield J, Tank D. "Neural" computation of decisions in optimization problems[J]. Biological Cybernetics,1985,52:141-152.
[136]Hopfield J, Tank D. Computing with neural circuits:a model[J]. Science,1986,233(4764):625-633.
[137]刘争平,何永富.人工神经网络在测井解释中的应用[J].地球物理学报,1995,38(增)：323-330.
[138]Rizzo D M, Dougherty, D E. Solving groundwater inverse problems using artificial neural networks[C]. International Conference on Computational Methods in Water Resources, CMWR, 1996:313-319.
[139]Caorsi S, Gamba P. Electromagnetic detection of dielectric cylinders by a neural network approach[J]. IEEE Transactions on Geoscience and Remote Sensing,1999,37(21):820-827.
[140]孙钧,袁金荣.盾构施工扰动与地层移动及其智能神经网络预测[J].岩石工程学报,2011,23(3)：261-267.
[141]Darabi A, Maldague X. Neural network based defect detection and depth estimation in TNDE[J]. NDT and E International,2002,35(3):165-175.
[142]樊琨,杨涛,李国维.公路软基沉降函数干涉神经网络预测模型[J].岩土力学,2004,25(2)：301-307.
[143]金长宇,马震岳,张运良等.神经网络在岩体力学参数和地应力场反演中的应用[J].岩十力学,2006,27(8)：1264-1271.
[144]闫滨.大坝安全监控及评价的智能神经网络模型研究[D]：(博士学位论文).大连：大连理工大学,2006.
[145]Dorigo M. Optimization, learning and natural algorithms [D]:(PhD thesis). Italy:Politecnico di Milano,1992.
[146]陈昌富,龚晓南,王贻荪.自适应蚁群算法及其在边坡工程中的应用[J].浙江大学学报(工学版),2003,37(5)：566-569.
[147]Oscar Q T, Eval R I. Application of ant colony optimization based algorithm to solve different electromagnetic problems[C]. Proceedings of The European Conference on Antennas and Propagation:EuCAP 2006, Nice, France,2006:6-10.
[148]Xu J Q, Song X H. Ant Colony Optimization for Nonlinear Inversion of Rayleigh Waves[C]. Bio-Inspired Computing and Applications-7th International Conference on Intelligent Computing, ICIC 2011, Revised Selected Papers, Zhengzhou,2011:370-377.
[149]王复明,刘小梅,蔡迎春.蚁群算法在路面模量反演中的研究与应用[J].路基工程,2009,4：74-75.
[150]韦凯,宫全美,周顺华.软土盾构隧道不均匀沉降预测的蚁群算法改进及参数选取[J].岩石力学与工程学报,2011,30(增1)：3022-3031.
[151]吴小利.祁连山北缘断裂滑动参数的GPS数据蚁群算法反演研究[J].工程地球物理学报,2011.8(2)：182-186.
[152]刘彦鹏.蚁群优化算法的理论研究及其应阳[D]：(博十学位论文).浙江：浙江大学,2007.
[153]Li S J, Liu Y X, Yu H. Parameter estimation approach in groundwater hydrology using hybrid ant colony system[C]. Computational Intelligence and Bioinformatics International Conference on Intelligent Computing, ICIC 2006, Proceedings, Kunming,2006:182-191.
[154]姚磊华.用改进的遗传算法和高斯牛顿法联合反演三维地下水流模型参数[J].计算物理,2002,22(4)：311-318.
[155]朱合华,刘学增.基于遗传算法的混合优化反分析及比较研究[J].岩石力学与工程学报,2003,22(2)：197-202.
[156]张新明,周超英,刘家琦等.流体饱和多孔隙介质多参数反演的小波多尺度_正则化高斯牛顿法[J].应用基础与工程科学学报,2009,17(4)：580-589.
[157]刘鹏程,纪晨.改进的模拟退火_单纯形综合反演方法[J].地球物理学报,1995,38(2)：199-205.
[158]高玮,冯夏庭.基于免疫连续蚁群算法的岩土工程反分析研究[J].岩石力学与工程学报,2005,24(23)：4266-4271.
[159]石露,李小春,任伟等.蚁群算法与遗传算法融合及其在边坡临界滑动面搜索中的应用[J].岩土力 学,2009,30(11)：3486-3492.
[160]Rabbani M, Noroozi S, Vinney J, et al. An inverse method of load determination using hybrid genetic algorithms, artificial neural networks and finite element analysis[C] Proceedings of the 5th International Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain,2006:54.
[161]Tang R Y, Li Y, Wen G, et al. Combined strategy of improved simulated annealing and genetic algorithm for inverse problem[J] IEEE Transactions on Magnetics,1996,32(3):1326-1329.
[162]Kennedy J, Eerhart R C. Particle swarm optimization[C] Proceedings of the IEEE International Conserence on Neural Networks. Perth, Australia,1995:1942-1948.
[163]李丽,牛奔.粒子群优化算法[M].北京：冶金工业出版社,2010.
[164]Cheu R L, Srinivasan D, Loo W H. Traffic incident detection using particle swarm optimization[J] Transportation Research Record,2004,1867:11-18.
[165]高玮.基于粒子群优化的岩土工程反分析研究[J].岩土力学,2006,27(25)：795-798.
[166]姜谙男,梁冰.基于粒子群支持向量机的三维含水层渗流参数反馈识别[J].岩土力学,2009,30(5)：1527-1531.
[167]徐飞,徐卫亚.岩爆预测的粒子群优化投影寻踪模型[J].岩土工程学报,2010,32(5)：718-723.
[168]Sun C H, Chiu C C, Li C L. Time-domain inverse scattering of a two-dimensional metallic cylinder in slab medium using asynchronous particle swarm optimization[J] Progress In Electromagnetics Research M,2010,14:85-100.
[169]周永祖.非均匀介质中的场与波[M]北京：电子工业出版社,1992.
[170]郑宏兴,葛德彪 广义传播矩阵法分析分层各向异性材料对电磁波的反射与透射[J]物理学报2000,49(9)：1702-1706.
[171]张剑锋.非均匀吸收介质中地震波的广义传递矩阵解法[J].计算结构力学及其应用,1996,13(2)：201-207.
[172]张剑锋,刘书，各向异性展状介质中弹性波的传播矩阵解法[J].固体力学学报,1996,17(3)：273-277.
[173]Vashishth A K, Khurana P S. Waves in stratified anisotropic poroelastic media:a transfer matrix approach[J] Journal of Sound and Vibration,2004,277(1-2):239-275.
[174]高强.辛体系算法在波的传播与振动问题中的应用[D]：(博十学位论文).大连：大连理工大学,2006.
[175]邓子辰,欧阳华江,钟万勰.奇异条件下Riccati代数方程的求解[J].计算结构力学及其应用,1993,10(1)：1-6.
[176]钟万勰,朱建平.黎卡提微分方程的精细积分[J].数值计算与计算机应用,1996,1：26-35.
[177]钟万勰.矩阵黎卡提方程的精细积分法.[J].计算结构力学及其应用,1994,11(2)：113-119.
[178]钟万勰.矩阵黎卡提(Riccati)微分方程的分析解[J].力学季刊,2000,21(1)：1-7.
[179]赵丽滨,张建宇,王寿梅.精细积分方法的稳定性和精度分析[J].北京航空航天大学学报,2000,26(5)：569-572.
[180]钟万勰,林家浩,高强.分层介质中非平稳随机波的精细求解[J].动力学与控制学报,2003,1(1)：2-8.
[181]高强,钟万勰,林家浩.分层介质中Love波的扩展w-w算法[J].固体力学学报,2007,28(2)：132-136.
[182]钟万勰.应阳力学的辛数学方法[M].北京：高等教育出版社,2006.
[183]Zhong W X, Lin J H, Gao Q. The precise computation for wave propagation in a stratified materials[J] Journal for Numerical Methods in Engineering,2004,60:11-25.
[184]Gao Q, Lin J H, Zhong W X, et al. Random wave propagation in a viscoelastic layered half space[J]. International Journal of Solids and Structures,2006,43(21):6453-6471.
[185]Gao Q, Lin J H, Zhong W X, et al. Propagation of partially coherent non-stationary random waves in a viscoelastic layered half-space[J]. Soil Dynamics and Earthquake Engineering,2008,28(4): 305-320.
[186]Gao Q, Lin J H, Zhong W X, et al. Propagation of non-stationary random waves in viscoelastic stratified solids[J]. Computers and Geotechnics,2006,33(8):444-453.
[187]Gao Q, Lin J H, Zhong W X, et al. Isotropic layered soil-structure interaction caused by stationary random excitations[J]. International Journal of Solids and Structures.2009,46(3-4):455-463.
[188]Zhong W X, Williams F W, Bennett P N. Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems[J]. Journal of Vibration and Acoustics, Transactions of the ASME,1997, 119(3):334-340.
[189]Gao Q, Lin J H, Zhong W X, et al. A precise numerical method for Rayleigh waves in a stratified half space[J] Journal for Numerical Methods in Engineering,2006,67(6):771-786.
[190]G Q, Zhong W X, Howson W P. A precise method for solving wave propagation problems in layered anisotropic media.[J] Wave Motion,2004,40(3):191-207.
[191]姚征.辛体系算法在波的传播与振动问题中的应用[D]：(博十学位论文).大连：大连理工大学,2006.
[192]Gao Q.Lin J H. Stationary random waves Propagation in 3D viscoelastic stratified solid[J]. Applied Mathematics and Mechanics,2005,26(6):785-796.
[193]Feng K, Wang D L. A note on conservation laws of symplectic difference schemes for Hamiltonian systems[J] Journal of Computational Mathematics,1991,9(3):229-237.
[194]Sun G. A simple way of constructing symplectic Runge-Kutta methods[J]. Journal of Computational Mathematics,2000,18(1):61-68.
[195]Lu X W, Schmid R. A symplectic algorithm for wave equations[J]. Mathematics and Computers in Simulation,1997,43(1):29-38.
[196]Sun G. Construction of high order Symplectic PRK methods[J]. Journal of Computational Mathematics,1995,13(1),40-50.
[197]Qin M Z, Zhang M Q. Multi-stage symplectic schemes of two kinds of Hamiltonian systems for wave equations[J]. Computers & Mathematics with Applications,1990,19(10):51-62.
[198]Feng K. On difference schemes and symplectic geometry[C]. Proceedings of the 1984 Beijing symposium on differential geometry and differential equations, Beijing,1985:42-58.
[199]Sanz-Serna J M, Calvo M P. Numerical Hamilton Problems[M]. London, UK:Chapman & Hall. 1994.
[200]Higueras I, Rold'an T. Starting algorithms for partitioned Runge-Kutta methods:the pair Lobatto ⅢA-ⅢB [C]. Monograf (?)as de la Real Academia de Ciencias de Zaragoza,2004,25:149-158.
[201]Jay L. Symplectic Partitioned Runge-Kutta Methods for Constrained Hamiltonian Systems[J]. SIAM Journal on Numerical Analysis,1996,33(1):368-387.
[202]Liu H Y, Sun G. Symplectic RK method and symplectic PRK methods with real eigenvalues[J]. Journal of Computational Mathematics,2004,22(5):769-776.
[203]Sun G. Symplectic partitioned Runge-Kutta method[J]. Journal of Computational Mathematics, 1993,11(4):365-372,
[204]Sanz-Serna J M. Symplectic integrations for Hamiltonian problems:an overview[J] Acta Numerica,1992,1:243-286.
[205]Sanz-Serna J M. Runge-Kutta schemes for Hamiltonian systems[J]. BIT Numerical Mathematics 1988,28:877-883.
[206]冯康,秦孟兆.哈密尔顿系统的辛几何算法[M].杭州：浙江科学技术出版社,2003.
[207]李世雄.波动方程的高频近似与辛几何算法[M].北京：科学出版社,2001.
[208]施妙根,顾丽珍.科学和工程计算基础[M].北京：清华大学出版社,1999.
[209]施吉林,张宏伟,金光日.计算机科学计算[M].北京：高等教育出版社,2005.
[210]黄志祥.辛算法在时域电磁散射计算中的应用[D]：(博士学位论文).合肥：安徽大学,,2007.
[211]蒋乐乐.基于辛几何算法的电磁散射数值方法的研究[D]：(硕士学位论文).合肥：安徽大学,2004.
[212]Mur G. Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations [J]. IEEE Transactions on Electromagnetic Compatibility 1981,4: 377-382.
[213]Liao Z P. Normal transmitting boundary conditions [J]. Science in China(series E),1996,39(3): 244-254.
[214]Liao Z P. Extrapolation non-reflecting boundary conditions [J]. Wave Motion,1996,24(2): 117-138.
[215]廖振鹏.工程波动理论导论[M].北京：科学出版社,2002.
[216]Liao Z P, Wong H L, Yang B P, et al. A transmitting boundary for transient wave analysis[J]. Scienta Sinica series A,1984,17 (10):1063-1076.
[217]Liao Z P, Wong H L. A transmitting boundary for the numerical simulation of elastic wave propagation [J]. Soil Dynamics and Earthquake Engineering,1984,3(4):174-183.
[218]Liao Z P, Yang G. Multi-directional transmitting boundaries for steady-state sh wave [J]. Earthquake Engineering and Structural Dynamics,1995,24(3):361-371.
[219]廖振鹏,周正华,张艳红.波动数值模拟中透射边界的稳定实现[J].地球物理学报,2002,45(4)：533-545.
[220]谢志南,廖振鹏.多次透射公式在波动数值模拟中的一种实现方案[J].固体力学学报,2010,41(4)：422-426.
[221]Higdon R L. Absorbing boundary conditions for elastic waves [J]. Geophysics,1991,56(2):231-241.
[222]孙卫涛.弹性波动方程的有限差分方法[M].北京：清华大学出版社,2009.
[223]Taflove A, Hagness S C. Computational electrodynamics the finite-difference time-domain method[M]. Norwood, USA:Artech House.
[224]Capoglu I R, Smith G S. A Total-Field Scattered-Field Plane-Wave Source for the FDTD Analysis of Layered Media[J]. IEEE Transaction on Antenna and Propagation,2008,56(1):158-169
[225]Sullivan D M. Electromagnetic simulation using the FDTD method[M]. New York, U.S.A:IEEE Press.
[226]Schneider J B. Plane waves in FDTD simulations and a nearly perfect total-field scattered-field boundary [J]. IEEE Transactions on Antennas and Propagation,2004,52(12):3280-3287.
[227]Sha W, Huang Z X, Wu X L, et al. Total field and scattered field technique for fourth-order symplectic finite difference time domain method [J]. Chinese Physics Letters,2006,23(1): 103-105.
[228]黄志祥,沙威,吴先良等.高阶辛算法的稳定性与数值色散性分析[J].计算物理,2010,27(1)：82-88.
[229]黄志祥,吴先良.辛算法的稳定性及数值色散性分析[J].电子学报,2006,34(3)：535-538.
[230]Saitoh I, Takahashi N. Stability of symplectic finite-difference time-domain methods[J]. IEEE Transactions on Magnetics,2002,38(2):665-668.
[231]纪震,廖慧连,吴青华.粒子群算法及应用[M].北京：科学出版社,2009.
[232]刘波.粒子群优化算法及其工程应用[M].北京：电子工业出版社,2010.
[233]Shi Y H, Eberhart R C. A modified particle swarm optimizer [J]. The 1998 IEEE International Conference on Evolutionary Computation Proceedings,1998. IEEE World Congress on Computational Intelligence, Anchorage, AK,1998:69-73.
[234]Shi Y H, Eberhart R C. Empirical study of particle swarm optimization [C]. Proceedings of the 1999 Congress on Evolutionary Computation,1999. CEC 99. Washington, DC,1999:1945-1950.
[235]Shi Y H, Eberhart R C. Fuzzy adaptive particle swarm optimization [C]. Proceedings of the 2001 Congress on Evolutionary Computation, Seoul,2001:101-106.
[236]刘建华,樊晓平，瞿志华.一种惯性权重动态调整的新型粒子群算法[J].计算机工程与应阳,2007,43(7)：68-70.
[237]黄轩,张军,詹志辉.基于随机惯量权重的快速粒子群优化算法[J].计算机工程与设计,2009,30(3)：647-650.
[238]邓爱萍,王会芳.动态改变惯性权重的自适应粒子群算法[J].计算机工程与设计,2010,31(13)：3062-3065.
[239]李军,许丽佳,游志宇.一种带压缩因子的自适应权重粒子群算法[J].西南大学学报(自然科学版),2011,33(7)：118-122.
[240]姜长元,赵曙光,沈十根等.惯性权重正弦调整的粒子群算法[J].计算机工程与应用,2012,48(8)：40-42.
[241]M. Clerc. The swarm and the queen:towards a deterministic and adaptive particle swarm optimization[C] Proceedings of IEEE international conference on evolutionary computation, Washington, DC,1999:1951-1957
[242]Ratnaweera A, Halgamuge S K, Watson H C. Self-organizing hierarchical particle swarm optimizer with time-varying [J]. IEEE Transactions on Evolutionary Computation,2004,8(3):240-255
[243]冯翔,陈国龙,郭文忠.粒子群优化算法中加速因子的设置与试验分析[J].集美大学学报(自然科学版),2005,11(2)：146-150.
[244]孙湘.非线性动态加速系数对粒子群算法的影响[J].计算机工程与科学.2011,33(10)：131-134.
[245]陈水利,蔡国榕,郭文忠等.PSO算法加速因子的非线性策略研究[J].长江大学学报(自科版)理工卷,2007,4(4)：1-4.
[246]Zhang L P, Yu H J, Hu S X. Optimal choice of parameters for particle swarm optimization [J]. Journal of Zhejiang University SCIENCE A,2005,6(6):528-534.
[247]M. Clerc. The swarm and the queen:towards a deterministic and adaptive particle swarm optimization[C] Proceedings of the 1999 congress on evolutionary computation, Piscataway NJ USA,1999:1927-1930.
[248]Fieldsend J E, Singh S. A multi-objective algorithm based upon particle swarm optimization[C] An efficient data structure and turbulence, proceedings of UK workshop on computational intelligence: 2002:37-44.
[249]庞巍,王康平,周春光等.模糊离散粒子群优化算法求解旅行商问题[J].小型微型计算机系统,2005,26(8)：1331-1334.
[250]刘建华,樊晓平,瞿志华.一种基于相似度的新型粒子群算法[J].控制与决策,2007,22(10)：1155-1159.
[251]张英男.改进的粒子群优化算法(APSO和DPSO)研究[D]：(硕士学位论文).大连：大连理工大学,2008.
[252]张艳琼.改进的云自适应粒子群优化算法[J].计算机应用研究,2010,27(9)：3250-3252.
[253]顾大为,凌君.一种改进的新颖的粒子群优化算法[J].计算机工程与应用,2011,47(6)：50-51.
[254]Yang Y H, Zhao F Q, Yao Y P, et al. A PSO and simulated annealing hybrid algorithm to task allocation problem for holonic manufacturing system [C]. The Sixth World Congress on Intelligent Control and Automation,2006. WCICA 2006, Dalian,2006:6767-6771.
[255]Zhao X C, Song B Q, Huang P Y, et al. An improved discrete immune optimization algorithm based on PSO for QoS-driven web service composition [J]. Applied Soft Computing,2012,12(8): 2208-2216.
[256]Yu S W, Wei Y M, Wang K. A PSO-GA optimal model to estimate primary energy demand of China [J]. Energy Policy,2012,42:329-340.
[257]Liu R H, Wang H. A novel auto calibration of 3-axis MEMS accelerometers based on improved PSO algorithm [J]. Advanced Materials Research,2012,403-408:4572-4579.
[258]李晓龙.基于支持向量机的岩体力学参数反演及工程应用[D]：(博士学位论文).郑州：郑州大学,2009.
[259]李晓龙,王复明.岩土工程弹塑性反分析的改进粒子群算法[J].采矿与安全工程学报,2009,26(1)：50-54.