Abstract:To develop the lightning physics and the new lightning protection theory and technology, inversion of thunderstorm charged model was done based on E-field data at the ground level, which is a practical way to study the thunderstorm charged structure. Traditional inversion methods always fail, for actual thunderstorm charged structure is extraordinarily complex and objective functions are strongly non-linear. To solve this problem, quantum inversion methods were tried. We summed up and analyzed the quantum genetic algorithm(QGA), quantum annealing algorithm (QA) and quantum particle swarm optimization (QPSO) which were developed fast in these last few years. Inversion model was established based on charged disk thunderstorm model introduced by Amoruso and Lattarulo, and then a theoretic model was inversed by three kinds of improved quantum inversion methods. The results show that improved QA adapts to this model best and convergent velocity of QGA is the fastest. A group of E-field data at ground level was used to invert for three-layer, four-layer and five-layer models by improved QGA. The results show that inversion result with actual data strongly depends on the model structure.
[1] Golde R H. Physics of Lightning. London:Academy Press Inc,1977
[2] 陈渭民. 雷电学原理. 北京:气象出版社,2006 Chen W M. Lightning Theory(in Chinese). Beijing:China Meteorological Press,2006
[3] Rakov Vl A,Uman M A. Lightning:Physics and Effects. Cambridge:Cambridge University Press,2003
[4] Edward R Mansell,Donald R, Conrad L Ziegler. Charge structure and lightning sensitivity in a simulated multicell thunderstorm. Journal of Geophysical Research,2005, 110,D12O1,doi:10.1029/2004JD005278
[5] 王家映. 地球物理反演方法概述. 工程地球物理学报,2007,4(1): 1~3 Wang J Y. Introduction to Geophysical Inverse Problems. Chinese Journal of Engineering Geophysics (in Chinese),2007,4(1): 1~3
[6] 李士勇,李盼池. 量子计算与量子优化算法. 哈尔滨:哈尔滨工业大学出版社,2009 Li S Y,Li P C. Quantum Computation and Quantum Optimization Algorithms(in Chinese). Harbin:Harbin Institute of Technology Press,2009
[7] Francesco Lattarulo. 李庆民,李清泉译. 电力系统中的电磁兼容. 北京:机械工业出版社,2008 Francesco Lattarulo. Li Q M,Li Q Q trans. Electromagnetic Compatibility in Power System(in Chinese). Beijing:China Machine Press,2008
[8] Amoruso V,Lattarulo F. Thundercloud pre-stroke electrostatic modeling. Electrostatics,2002,56: 255~260
[9] Van Bladel. Singular Electromagnetic Fields and Sources. New York:IEEE Press,1991
[10] 王竹溪,郭敦仁. 特殊函数概论. 北京:北京大学出版社,2000 Wang Z X,Guo D R. An Introduction to Special Functions (in Chinese). Beijing:Peking University Press,2000
[11] Lajos Diósi. A Short Course in Quantum Information Theory. New York:Springer,2007
[12] 李承祖. 量子通信和量子计算. 长沙:国防科学技术大学出版社,2000 Li C Z. Quantum Communication and Quantum Computation(in Chinese). Changsha:National University of Defense Technology Press,2000
[13] Han K H,Kim J H. Genetic algorithm and its application to combinational optimization problem. Proceedings of the International Congress on Evolutionary Computation. IEEE Press,2000
[14] Han K H,Kim J H. Quantum-Inspired Evolutionary Algorithm for a Class of Combinational Optimization. IEEE Trans on Evolutionary Computation,2002
[15] Khorsand A R,Akbarzadeh M R. Quantum Gate Optimization in a Meta-level Genetic Quantum Algorithm. 2005 IEEE International Conference on Systems, Man and Cybernetics,2005
[16] 罗红明,王家映,朱培民等. 量子遗传算法在大地电磁反演中的应用. 地球物理学报,2009,52(1): 260~267 Luo H M,Wang J Y,Zhu P M, et al. Quantum genetic algorithm and its application in magnetotelluric data inversion. Chinese Journal of Geophysics (in Chinese),2009,52(1): 260~267
[17] 杜卫林,李 斌,田 宇. 量子退火算法研究进展. 计算机研究与发展,2008,45(9): 1501~1508 Du W L,Li B,Tian Y. Quantum annealing algorithms: state of art. Journal of Computer Research and Development (in Chinese),2008,45(9): 1501~1508
[18] Tadashi K,Hidetoshi N. Study of optimization problem by quantum annealing. Tokyo: Tokyo Institute of Technology,1998
[19] Lee Y,Berne B J. Global optimization: quantum thermal annealing with path integral Monte Carlo. Journal of Physical Chemistry A,2000, 104:86~95
[20] Liu P,Berne B J. Quantum path minimization: an efficient method for global optimization. Chemical Physics,2003, 118:2999~3005
[21] 魏 超,朱培民,王家映. 量子退火反演的原理和实现. 地球物理学报,2006,49(2): 578~583 Wei C,Zhu P M,Wang J Y. Quantum annealing inversion and its implementation. Chinese J. Geophys. (in Chinese),2006,49(2): 578~583
[22] 魏 超,李小凡,张美根. 量子退火最优化与地球物理反演方法. 地球物理学进展,2007,22(3): 785~789 Wei C,Li X F,Zhang M G. Quantum annealing optimization and geophysical inverse method. Progress in Geophysics (in Chinese),2007,22(3): 785~789
[23] 李盼池. 基于量子位Bloch坐标的量子遗传算法及其应用. 控制理论与应用,2008,25(6): 985~989 Li P C. Quantum genetic algorithm based on Bloch coordinates of qubits and its application. Control Theory and Applications (in Chinese),2008,25(6): 985~989
[24] 罗红明,王家映,师学明等. 量子路径积分算法及其在大地电磁反演中的应用. 地球物理学报,2007,50(4): 1268~1276 Luo H M,Wang J Y,Shi X M, et al. Quantum path integral algorithm and its application in magnetotelluric inversion. Chinese J. Geophys. (in Chinese),2007,50(4): 1268~1276
[25] 白铭复,陈健华,田成林. 高等量子力学. 长沙:国防科学技术大学出版社,1994 Bai M F,Chen J H,Tian C L. Advanced Quantum Mechanics(in Chinese). Changsha:National University of Defense Technology Press,1994
[26] Mikki S M,Kishk A A. Quantum Particle Swarm Optimization for Electromagnetic. IEEE Trans on Antennas and Propagation,2006