弹性半空间单一覆盖层表面振源的虚拟反演
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摘要
交通拥挤正成为制约我国城市发展的重要问题之一,发展城市轨道交通是一个有效的解决方案。轨道交通引起的环境振动与防治研究,越来越迫切地成为亟待解决的问题。
用台阵观测方法反演城市轨道交通振源函数是一个崭新的课题,本文采用虚拟反演方法,给定振源函数,计算台阵各点的振动,再反演振源参数,比较结果和给定输入的差别,论证这个思路的可行性。
首先,简化场地条件为弹性半空间单一覆盖层模型。利用传递矩阵法及Laplace-Hankel联合变换技术,推导出层间完全接触的弹性半空间单一覆盖层模型表面作用脉冲荷载时,覆盖层表面竖向位移场解析解。接着,详细阐述了数值化实现该解析解的方案,分五种情况考虑数值计算可能出现的问题,分别提出了解决方案,编制了Fortran程序。通过退化为弹性半空间问题,与经典解对比,验证了数值计算的准确性。
然后,简要评述了遗传算法的研究历程及发展现状、基本遗传算法原理及其存在的问题。详细介绍了微遗传算法的要点和步骤,构造了反演的遗传策略,编制了振源反演计算程序,通过四个测试函数验证了整个反演程序的可靠性。
最后,给定弹性半空间单一覆盖层具体的场地模型、三角脉冲振源模型和台阵布置的方案,计算了矩形台阵六个点的位移时程。分析了时程表达的信息,借助频率-波数谱分析,得到场地的频散曲线,与用频散方程得到的频散曲线对比说明计算的可靠性。利用微遗传算法虚拟反演振源参数,分别采用单点时程段、单点自功率谱、两点自功率谱联合、两点互功率谱与其中一点自功率谱联合作目标曲线反演振源参数,结果与给定输入脉冲的参数比对,表明反演结果稳定,效率较高;利用两个点的信息,反演结果更为稳定,反演效率高。论证了根据台阵各点的竖向位移时程构造适当的目标函数,反演准确的振源参数的思路是可行的。
Traffic congestion is now one of the most important problems in city development of our country. An effective method to solve this problem is developing urban track traffic. Thus, study on environmental vibration and its prevention has been an urgent problem.
Inversion of vibration source from urban track traffic by observed data on an array is a quite new idea. The virtual inversion is adopted in this dissertation, in the process, a vibration source function is given, and vibration on each point in the array is calculated then. Based on the vibrations at the array, the parameters of the source function are inversed and are furthermore checked with the given ones to validate the feasibility of this idea.
Firstly, site condition is simplified as a model with single soil layer overlaid on elastic homogeneous half-space. The analytical solution of vertical displacement field on the surface of the model from pulse loading on the surface is derived by means of transfer matrix and Laplace-Hankel combined transform. In the derivation all layers contacted with each other completely. Afterwards, the numerical realization of the solution is introduced in detail, five possible problems in the process are discussed and the method to manage them is presented, and a Fortran program is compiled. The numerical result by degenerating the model into elastic half-space is checked with classical solution to validate the reliability of the calculation in this dissertation.
Then, the evolution and the state-of-the art of Genetic Algorithm are reviewed briefly, as well as the principles and existing problems in the basic Genetic Algorithm. The gist and the procedure in the Micro Genetic Algorithm are introduced in detail, the generic strategy for inversion is designed, the program for inversion is also compiled. The reliability of the program is verified by four test functions.
Finally, displacement time histories at six points in a rectangular array are calculated from the given site model with single soil layer overlaid on elastic half-space, given array layout and given triangular pulse input. The information in the time histories are analyzed, frequency dispersion curve at the site is acquired and is checked with those derived directly from frequency dispersion equation. Micro Genetic Algorithm is adopted in the virtual inversion of source parameters. Target curves are constructed respectively by the time history at a point, the auto-power spectrum at a point, the cross-power spectrum between a pair of points in the array. The results are checked with the given source parameters, and show a good stability and efficacy. The information on two points can improve the inversion results. As a conclusion, the idea to inverse traffic vibration source from the observation data at an array is feasible, if the target function is constructed well.
用台阵观测方法反演城市轨道交通振源函数是一个崭新的课题,本文采用虚拟反演方法,给定振源函数,计算台阵各点的振动,再反演振源参数,比较结果和给定输入的差别,论证这个思路的可行性。
首先,简化场地条件为弹性半空间单一覆盖层模型。利用传递矩阵法及Laplace-Hankel联合变换技术,推导出层间完全接触的弹性半空间单一覆盖层模型表面作用脉冲荷载时,覆盖层表面竖向位移场解析解。接着,详细阐述了数值化实现该解析解的方案,分五种情况考虑数值计算可能出现的问题,分别提出了解决方案,编制了Fortran程序。通过退化为弹性半空间问题,与经典解对比,验证了数值计算的准确性。
然后,简要评述了遗传算法的研究历程及发展现状、基本遗传算法原理及其存在的问题。详细介绍了微遗传算法的要点和步骤,构造了反演的遗传策略,编制了振源反演计算程序,通过四个测试函数验证了整个反演程序的可靠性。
最后,给定弹性半空间单一覆盖层具体的场地模型、三角脉冲振源模型和台阵布置的方案,计算了矩形台阵六个点的位移时程。分析了时程表达的信息,借助频率-波数谱分析,得到场地的频散曲线,与用频散方程得到的频散曲线对比说明计算的可靠性。利用微遗传算法虚拟反演振源参数,分别采用单点时程段、单点自功率谱、两点自功率谱联合、两点互功率谱与其中一点自功率谱联合作目标曲线反演振源参数,结果与给定输入脉冲的参数比对,表明反演结果稳定,效率较高;利用两个点的信息,反演结果更为稳定,反演效率高。论证了根据台阵各点的竖向位移时程构造适当的目标函数,反演准确的振源参数的思路是可行的。
Traffic congestion is now one of the most important problems in city development of our country. An effective method to solve this problem is developing urban track traffic. Thus, study on environmental vibration and its prevention has been an urgent problem.
Inversion of vibration source from urban track traffic by observed data on an array is a quite new idea. The virtual inversion is adopted in this dissertation, in the process, a vibration source function is given, and vibration on each point in the array is calculated then. Based on the vibrations at the array, the parameters of the source function are inversed and are furthermore checked with the given ones to validate the feasibility of this idea.
Firstly, site condition is simplified as a model with single soil layer overlaid on elastic homogeneous half-space. The analytical solution of vertical displacement field on the surface of the model from pulse loading on the surface is derived by means of transfer matrix and Laplace-Hankel combined transform. In the derivation all layers contacted with each other completely. Afterwards, the numerical realization of the solution is introduced in detail, five possible problems in the process are discussed and the method to manage them is presented, and a Fortran program is compiled. The numerical result by degenerating the model into elastic half-space is checked with classical solution to validate the reliability of the calculation in this dissertation.
Then, the evolution and the state-of-the art of Genetic Algorithm are reviewed briefly, as well as the principles and existing problems in the basic Genetic Algorithm. The gist and the procedure in the Micro Genetic Algorithm are introduced in detail, the generic strategy for inversion is designed, the program for inversion is also compiled. The reliability of the program is verified by four test functions.
Finally, displacement time histories at six points in a rectangular array are calculated from the given site model with single soil layer overlaid on elastic half-space, given array layout and given triangular pulse input. The information in the time histories are analyzed, frequency dispersion curve at the site is acquired and is checked with those derived directly from frequency dispersion equation. Micro Genetic Algorithm is adopted in the virtual inversion of source parameters. Target curves are constructed respectively by the time history at a point, the auto-power spectrum at a point, the cross-power spectrum between a pair of points in the array. The results are checked with the given source parameters, and show a good stability and efficacy. The information on two points can improve the inversion results. As a conclusion, the idea to inverse traffic vibration source from the observation data at an array is feasible, if the target function is constructed well.
引文
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2马筠等.我国铁路环境振动现状及传播规律[J].中国环境科学. 1987, 7(6): 70~74
3公害防止の技术と法规编辑委员会.公害防止の技术と法规振动篇[S].丸善株式会社, 1984
4陶夏新.国家自然科学基金重点项目“城市轨道交通引起的环境振动与防治”申请书.国家自然科学基金委员会. 2005:5～17
5陶夏新.国家自然科学基金重点项目“城市轨道交通引起的环境振动及传播规律”(50538030)计划书.国家自然科学基金委员会. 2005:2～5
6 D. M. Burmister. The general theory of stresses and displacements in layered systems. Journal of Applied Physics[J]. 1945, (16): 89~96
7王凯. N层弹性连续体在圆形均布垂直荷载作用下的力学计算[J].土木工程学报, 1982
8王林生.求解层状地基空间轴对称问题的初参数法[J].力学学报, 1986
9 H. Lamb. On the propagation of tremors over the surface of an elastic solid [J]. Philosophical Transactions of the Royal Society(London). 1904, A203: 1~42
10杨宝俊,王宝昌,张伯军.弹性波理论[M].长春:东北师范大学出版社, 1990
11 Y. Shekhter.‘Consideration of inertial properties of soil in the computation of vertical forced vibrations of massive foundations’[C]. NII Symposium 12, Vibratsii Osnovaniy I Fundamentov. Moscow, 1948
12 G. R. Franssens. Calculation of the elasto-dynamic Green’s functions in layered media by means of a modified propagator matrix method [J]. Geophysical Journal of the Royal Astronomical Society. 1983, 75, 669~691
13 R. J. Apsel, J. E. Luco. On the Green's function for a layered half-space (PartⅠ)[J]. Bulletin of Seismological Society of America. 1983, 73(4): 909~929
14 J. E. Luco, R. J. Apsel. On the Green's function for a layered half-space (PartⅡ) [J]. Bulletin of Seismological Society of America. 1983, 73(4): 931~951
15 E. Kausel, R. Peek. Dynamic loads in the interior of a layered stratum: an explicit solution [J]. Bulletin of Seismological Society of America. 1982, 72(5): 1459~1481
16曾三平,曹志远.层状弹性半空间轴对称动力问题的奇异解[J].力学学报, 1992, 24(4): 446~457
17孟凡顺,郭海燕,叶天麒.用传递矩阵法求解多层层状弹性半空间轴对称动力问题的奇异解[J].地震工程与工程振动, 1995, 15(2): 44~51
18黄菊花,何成宏,杨国泰.任意激励下层状粘弹性地基表面振动的解析解[J].塑性工程学报, 1999, 6(1): 74~80
19 H. Yamamaka, H. Ishida. Application of genetic algorithms to an inversion of surface-wave dispersion data. Bulletin of Seismological Society of America[J]. 1996, 86(2): 436~444
20 D. E. Goldberg. Sizing Populations for Serial and Parallel Genetic Algorithms[C]. In J. David Schafer, editor, Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, California, 1989. Morgan Kaufmann Publishers, 1989, 70~79
21 K. Krishnakumar. Micro-genetic algorithms for stationary and non-stationary function optimization[C]. In SPIE Proceedings: Intelligent Control and Adaptive Systems, 1989, 1196:289~296
22关志华.面向多目标优化问题的遗传算法的理论及应用研究[D].天津大学博士论文. 2002
23陶夏新,师黎静.利用地脉动台阵观测推断场地速度结构的虚拟反演.《新世纪地震工程与防灾减灾-庆贺胡聿贤院士八十寿辰》论文集.北京:地震出版社. 2002: 443~452
24师黎静,陶夏新.地脉动台阵方法的有效性分析[J].岩石力学与工程学报, 2006, 25(8): 1683~1690
25王元汉,谢诗伟,谢洪阳.计算层状地基板的半解析数值方法[J].岩石力学与工程学报, 2002, 21(增2): 2447~2450
26尹一平,王元汉.传递矩阵法的Zn误差分析[J].岩土力学, 2001, 22(4):440~442
27尹一平,王元汉.传递矩阵法的ξ误差分析[J].岩土力学, 2002, 23(5): 608~611
28沈永欢,梁在中等编.数学手册[M].北京:科学出版社, 2002: 670~675
29邓学钧,黄卫等编.路面结构计算和设计电算方法[M].南京:东南大学出版社, 1997: 117~118
30 F. Durbin. Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method [J]. The computer Journal, 1974, 17(6): 371~376
31 Zeng Sanping, Liang Robert. A fundamental solution of a multilayered half-space due to an impulsive ring source[J]. Soil Dynamics and Engineering, 2002, (22): 541~550
32杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社, 1988
33 C. L. Pekeris. The seismic surface pulse[C]. Proceedings of the National Academy of Sciences, 1955, (41): 469~480
34刘凯欣,刘广裕.垂直点源的一个精确解[J].科学通报. 2004, 49(5): 419~423
35 J. D. Achenbach. Wave propagation in elastic solid [M]. Great Britain: North-Holland Publishing Company. 1973, 310~317
36王小平.遗传算法:理论应用及软件实现[M].西安交通大学出版社, 2002
37周明,孙树栋等.遗传算法原理及应用[M].北京:国防工业出版社, 1999
38 David L. Carroll. Chemical Laser Modeling with Genetic Algorithms [J]. American Institute of Aeronautics and Astronautics Journal, 1996, 34(2): 338~346
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51郑薇.列车经过对周边建筑的影响分析[D].浙江大学硕士学位论文. 2006
52 C. A. Moya, J. Aguirre, K. Irikura. Inversion of source parameters and site effects from strong ground motions records using genetic algorithms [J]. Bulletin of Seismological Society of America. 2000, 90(4): 977~992.
53 Chen S Z, G M Atkinson. Global Comparasions of Earthquake Source Spectra [J]. Bulletin of Seismological Society of America. 2002, 92(3): 885~895
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2马筠等.我国铁路环境振动现状及传播规律[J].中国环境科学. 1987, 7(6): 70~74
3公害防止の技术と法规编辑委员会.公害防止の技术と法规振动篇[S].丸善株式会社, 1984
4陶夏新.国家自然科学基金重点项目“城市轨道交通引起的环境振动与防治”申请书.国家自然科学基金委员会. 2005:5～17
5陶夏新.国家自然科学基金重点项目“城市轨道交通引起的环境振动及传播规律”(50538030)计划书.国家自然科学基金委员会. 2005:2～5
6 D. M. Burmister. The general theory of stresses and displacements in layered systems. Journal of Applied Physics[J]. 1945, (16): 89~96
7王凯. N层弹性连续体在圆形均布垂直荷载作用下的力学计算[J].土木工程学报, 1982
8王林生.求解层状地基空间轴对称问题的初参数法[J].力学学报, 1986
9 H. Lamb. On the propagation of tremors over the surface of an elastic solid [J]. Philosophical Transactions of the Royal Society(London). 1904, A203: 1~42
10杨宝俊,王宝昌,张伯军.弹性波理论[M].长春:东北师范大学出版社, 1990
11 Y. Shekhter.‘Consideration of inertial properties of soil in the computation of vertical forced vibrations of massive foundations’[C]. NII Symposium 12, Vibratsii Osnovaniy I Fundamentov. Moscow, 1948
12 G. R. Franssens. Calculation of the elasto-dynamic Green’s functions in layered media by means of a modified propagator matrix method [J]. Geophysical Journal of the Royal Astronomical Society. 1983, 75, 669~691
13 R. J. Apsel, J. E. Luco. On the Green's function for a layered half-space (PartⅠ)[J]. Bulletin of Seismological Society of America. 1983, 73(4): 909~929
14 J. E. Luco, R. J. Apsel. On the Green's function for a layered half-space (PartⅡ) [J]. Bulletin of Seismological Society of America. 1983, 73(4): 931~951
15 E. Kausel, R. Peek. Dynamic loads in the interior of a layered stratum: an explicit solution [J]. Bulletin of Seismological Society of America. 1982, 72(5): 1459~1481
16曾三平,曹志远.层状弹性半空间轴对称动力问题的奇异解[J].力学学报, 1992, 24(4): 446~457
17孟凡顺,郭海燕,叶天麒.用传递矩阵法求解多层层状弹性半空间轴对称动力问题的奇异解[J].地震工程与工程振动, 1995, 15(2): 44~51
18黄菊花,何成宏,杨国泰.任意激励下层状粘弹性地基表面振动的解析解[J].塑性工程学报, 1999, 6(1): 74~80
19 H. Yamamaka, H. Ishida. Application of genetic algorithms to an inversion of surface-wave dispersion data. Bulletin of Seismological Society of America[J]. 1996, 86(2): 436~444
20 D. E. Goldberg. Sizing Populations for Serial and Parallel Genetic Algorithms[C]. In J. David Schafer, editor, Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, California, 1989. Morgan Kaufmann Publishers, 1989, 70~79
21 K. Krishnakumar. Micro-genetic algorithms for stationary and non-stationary function optimization[C]. In SPIE Proceedings: Intelligent Control and Adaptive Systems, 1989, 1196:289~296
22关志华.面向多目标优化问题的遗传算法的理论及应用研究[D].天津大学博士论文. 2002
23陶夏新,师黎静.利用地脉动台阵观测推断场地速度结构的虚拟反演.《新世纪地震工程与防灾减灾-庆贺胡聿贤院士八十寿辰》论文集.北京:地震出版社. 2002: 443~452
24师黎静,陶夏新.地脉动台阵方法的有效性分析[J].岩石力学与工程学报, 2006, 25(8): 1683~1690
25王元汉,谢诗伟,谢洪阳.计算层状地基板的半解析数值方法[J].岩石力学与工程学报, 2002, 21(增2): 2447~2450
26尹一平,王元汉.传递矩阵法的Zn误差分析[J].岩土力学, 2001, 22(4):440~442
27尹一平,王元汉.传递矩阵法的ξ误差分析[J].岩土力学, 2002, 23(5): 608~611
28沈永欢,梁在中等编.数学手册[M].北京:科学出版社, 2002: 670~675
29邓学钧,黄卫等编.路面结构计算和设计电算方法[M].南京:东南大学出版社, 1997: 117~118
30 F. Durbin. Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method [J]. The computer Journal, 1974, 17(6): 371~376
31 Zeng Sanping, Liang Robert. A fundamental solution of a multilayered half-space due to an impulsive ring source[J]. Soil Dynamics and Engineering, 2002, (22): 541~550
32杨桂通,张善元.弹性动力学[M].北京:中国铁道出版社, 1988
33 C. L. Pekeris. The seismic surface pulse[C]. Proceedings of the National Academy of Sciences, 1955, (41): 469~480
34刘凯欣,刘广裕.垂直点源的一个精确解[J].科学通报. 2004, 49(5): 419~423
35 J. D. Achenbach. Wave propagation in elastic solid [M]. Great Britain: North-Holland Publishing Company. 1973, 310~317
36王小平.遗传算法:理论应用及软件实现[M].西安交通大学出版社, 2002
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