基于元胞自动机的复杂系统脆性研究
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摘要
随着社会的进步、科学技术的发展,以及控制论、信息论、系统论和计算机技术的飞速发展。我们所面对的控制对象也越来越复杂,因此对于复杂系统的研究成为了当前的研究热点。元胞自动机是模拟复杂性行为,研究复杂系统的一种有效的工具。它能通过简单的基元和简单的规则产生复杂现象,从而具有模拟复杂系统的能力。而复杂系统脆性作为复杂系统的一个重要性质被提出。
本文首先对复杂系统的定义进行了一些改进,并提出了具有普适性一般系统数学描述。其次,应用元胞自动机建立起了复杂系统脆性的几种常见脆性模型,进一步说明了复杂系统脆性的发生过程。再次,对脆性源、脆性接收者、脆性过程所组成的脆性表现基本单元进行分析;最后,以恶性传染病的传播为例,应用元胞自动机对复杂系统脆性发生的演化过程进行仿真。
Along with the development of society and the improvement in technology, systems become huger and huger, more and more complex. Therefore the study of complex system becomes the hot spot. Cellular Automation is one of available tools which to simulate the complex behavior and study complex system. It can cause complex phenomenon by simple cell and simple rule, so it is applied to the study of the complex system extensively. The brittleness is an important characteristic.At first, I ameliorate the definition of brittleness, and give common mathematic description of the brittleness. Secondly set up some familiar brittleness model applying the cellular automation, and explain the brittleness process. Then analyze the brittleness unit that is made of the brittle source, brittle receiver and brittle action. Finally regard the diffusion of an infectious disease as the example, and apply cellular automation to simulate the evolvement of complex system brittleness.
本文首先对复杂系统的定义进行了一些改进,并提出了具有普适性一般系统数学描述。其次,应用元胞自动机建立起了复杂系统脆性的几种常见脆性模型,进一步说明了复杂系统脆性的发生过程。再次,对脆性源、脆性接收者、脆性过程所组成的脆性表现基本单元进行分析;最后,以恶性传染病的传播为例,应用元胞自动机对复杂系统脆性发生的演化过程进行仿真。
Along with the development of society and the improvement in technology, systems become huger and huger, more and more complex. Therefore the study of complex system becomes the hot spot. Cellular Automation is one of available tools which to simulate the complex behavior and study complex system. It can cause complex phenomenon by simple cell and simple rule, so it is applied to the study of the complex system extensively. The brittleness is an important characteristic.At first, I ameliorate the definition of brittleness, and give common mathematic description of the brittleness. Secondly set up some familiar brittleness model applying the cellular automation, and explain the brittleness process. Then analyze the brittleness unit that is made of the brittle source, brittle receiver and brittle action. Finally regard the diffusion of an infectious disease as the example, and apply cellular automation to simulate the evolvement of complex system brittleness.
引文
[1] 尼科里斯,普利高津.探索复杂性.四川:四川教育出版社,1989:1-23页
[2] 钱学森,于景元,戴汝为.一个科学的新领域——开放的复杂巨系统及其方法论.自然杂志,1990,13(3):3-10页
[3] 韦琦,金鸿章,姚绪梁,郭建.基于脆性的复杂系统崩溃的研究.哈尔滨工程大学学报,2003,24(2):161-165页
[4] 韦琦,金鸿章,郭建.复杂系统崩溃的脆性致因的研究.系统工程,2003,21(4):1-5页
[5] WEI Qi, JlN Hongzhang, JI Ming. THE RESEARCH ON BRITTLE CATASTROPHE OF COMPLEX GIANT SYSTEM. IEEE Region 10 Technical Conference on Computers, Communications, Control and Power Engineering (TENCON'02) October 28-31, 2002 Beijing, CHINA.
[6] 霍兰.涌现.陈禹等译.上海:上海科学出版社,2001:4-9页
[7] 戴汝为,操龙兵.一个开放的复杂巨系统.系统工程学报.2001,16(5):76-81页
[8] 王迪兴.复杂适应系统的共性描述.系统辩证学学报.2001,9(4):40-43页
[9] Holland, J.H. Hidden Order: How Adaptation Builds Complexity. Perseus Books, Reading, Massachusetts, 1995: 185 P
[10] Holland, J.H. Emergence: From Chaos to Order. HelixBooks, Reading, Massachusetts, 1998: 258 P
[11] Tero Ojanpera,Ramjee Prased著.朱旭红,卢学军等译.宽带CDMA:第三代移动通信技术.北京:人民邮电出版社,2001:1-23页
[12] 张嗣赢.复杂系统与复杂性科学简介.青岛大学学报.2001,16(4):25-28页
[13] 颜泽贤,陈忠,胡皓编.复杂系统演化论.人民出版社,1993年:40-70 页
[14] 姜璐.复杂系统的层次结构.自然辩证法研究.1994,10(2):16-21页
[15] Domenico Famularo, Peter Dorato. Robust non-fragile LQ controllers: the ststic state feedback case. International journal of control. 2000, 73(2): 159-165P
[16] Celmins, Aivars. Vulnerability assessment of fuzzy targets. Fuzzy Sets and Systems. 1994, 68(1): 29-38P
[17] Ang, A.H.S. Pires, J.A. A model for the seismic reliability assessment of electric power transmission systems. Reliability Engineering &system safety. 1996, 51(1): 7-22P
[18] Einarsson, Stefan. Comparision of QRA and Vulnerability analysis: does analysis lead to more robust and resilient systems? Acta Polytechnica Scandinavica, Civil Engineering and Building Construction Series. 1999, (114): 1-27P
[19] Rennaker, P.R. Richardson, S. New approach to vulnerability assessment. Journal of the American Helicoper Society. 1999, 44(1): 38-41P
[20] Reese, Ronald M. Calvano, Charles N. Hopkins, Th. Operationally oriented vulnerability requirements in the ship design process. Naval Engineers Journal. 1998, 110(1): 19-34P
[21] Soutter, Marc Musy, andre. Global sensitivity analyses of three pesticide leaching models using a Monte-Carlo approach. Journal of Environmental Quality. 1999, 28(4): 1290-1297P
[22] Soutter, Marc Musy, Andre. Coupling 1D Monte-Carlo simulations and geostatistics to assess groundwater vulnerability to pesticide contamination on a regional scale. Journel of Contaminant Hydrology. 1998, 32(1-2): 25-29P
[23] 王经民,王有科.黄土高原生态环境脆弱性计算方法探讨.水土保持通报.1996(32):36-43页
[24] Willianmsen, Joel Blacklock, Kevin Evans, Hilary. Quantifying and reducing International Space Station vulnerability following orbital debris penetration. Journal of Spacecraft and Rockets. 1999, 56(1): 133-141P
[25] Said, Michael O. Theory and practice of total ship survivability for ship design Naval Engineers Journal.1995, 107(4): 191-203P
[26] Technology overview for a proposed navy surface combatant DC zonal electric distribution system Ciezki, J.G., Ashton, R.W. Conference Naval Engineers Journal.1999, 111(3): 59-69P
[27] Operationally oriented vulnerability requirements in the ship design process Reese, Ronald M., Calvano, Charles N., Hopkins, Th Naval Engineers Journal. 1998, 110(1): 19-34P
[28] Vassalos, D., Turan, O., Konovessis, D., Tuzcu, C. Comparison between prescriptive and performance-based criteria for assessing ro-ro damage survivability International Shipbuilding Progress. 1998, 45(444): 351-382P
[29] Vassalos, Dracos, Turan, Osman, Pawlowski, Maciej. Dynamic stability assessment of damaged passenger/ro-ro ships and proposal of rational survival criteria Marine Technology. 1997, 34(4): 241-266P
[30] Said, Michael O. Theory and practice of total shipsurvivability for ship design. Naval Engineers Journal. 1995, 107(4): 191-203P
[31] Holland J.H. Escaping Brittleness: The possibilities of General Purpose Learning Algorithms Applied to Parallel Rule-Based Systems. In: Michals Ki R S, Carbonell J G, Mitchell T M(Eds), Machine Learning Ⅱ, Los Altos, CA: Morgan Kaufmann. 1986: 593-623P
[32] Lind, Niels C. Measure of vulnerability and damage tolerance. Reliability Engineering & System Safety. 1995, 48(1): 1-6P
[33] 韦琦.复杂系统脆性理论及其在危机控制中的应用.哈尔滨工程大学博士学位论文.2004.1-94页
[34] 郭健.突变理论在复杂系统脆性理论研究中的应用.哈尔滨工程大学博士学位论文,2004.1-109页
[35] J. V. Neumann. Theory of Self-reproducing Automata. edited and completed by A. W. Burks, Champaign, University of Illinois Press, Ⅱ[c], 1966: 1-21P
[36] S. Wolfram. Theory and Applications of Cellular Automata. Singapore, World Scientific, 1986: 12-57P
[37] A. Eizenberg, Y. Kifer. Large Deviations for Probabilistic Cellular Automata. Journal of Statistical Physics, 2002, 108(5-6): 1255-1280P
[38] Norio Konno. Dualities for a Class of Finite Range Probabilistic Cellular Automata in One Dimension. Journal of Statistical Physics, 2002, 106(5-6): 915-922P
[39] 张永安,白学志.复杂系统的重要研究工具——细胞自动机及其应用.自然杂志,1998,20(4):192-196页
[40] 应尚军,魏一鸣,范英,蔡嗣经.基于元胞自动机的股票市场投资行为模拟.系统工程学报,2001,16(5):382-388页
[41] 戴汝为.人工生命.模式识别与人工智能,1998,11(4):412-419页
[42] 李夏,戴汝为.系统科学与复杂性.自动化学报.1998,24(2):200-207页
[43] 肖帕德,德罗斯.物理系统的元胞自动机模拟.北京:清华大学出版社,2003:1-239页
[44] 昝廷全.复杂系统的一般数学框架.应用数学和力学.1993,14(4):367-374页
[45] 谢惠民.复杂性与动力系统.上海:上海科技教育出版社,1994:151-184页
[46] 布里渊.物理熵与信息(Ⅱ).系统论控制论信息论经典文献选编.北京:求实出版社,1989:649-664页
[47] 中华人民共和国卫生部.非典型肺炎疫情通报.http://www.moh.gov.cn/news/more_index.aspx?tp_class=C602.2003.3.31-2003.5.23
[2] 钱学森,于景元,戴汝为.一个科学的新领域——开放的复杂巨系统及其方法论.自然杂志,1990,13(3):3-10页
[3] 韦琦,金鸿章,姚绪梁,郭建.基于脆性的复杂系统崩溃的研究.哈尔滨工程大学学报,2003,24(2):161-165页
[4] 韦琦,金鸿章,郭建.复杂系统崩溃的脆性致因的研究.系统工程,2003,21(4):1-5页
[5] WEI Qi, JlN Hongzhang, JI Ming. THE RESEARCH ON BRITTLE CATASTROPHE OF COMPLEX GIANT SYSTEM. IEEE Region 10 Technical Conference on Computers, Communications, Control and Power Engineering (TENCON'02) October 28-31, 2002 Beijing, CHINA.
[6] 霍兰.涌现.陈禹等译.上海:上海科学出版社,2001:4-9页
[7] 戴汝为,操龙兵.一个开放的复杂巨系统.系统工程学报.2001,16(5):76-81页
[8] 王迪兴.复杂适应系统的共性描述.系统辩证学学报.2001,9(4):40-43页
[9] Holland, J.H. Hidden Order: How Adaptation Builds Complexity. Perseus Books, Reading, Massachusetts, 1995: 185 P
[10] Holland, J.H. Emergence: From Chaos to Order. HelixBooks, Reading, Massachusetts, 1998: 258 P
[11] Tero Ojanpera,Ramjee Prased著.朱旭红,卢学军等译.宽带CDMA:第三代移动通信技术.北京:人民邮电出版社,2001:1-23页
[12] 张嗣赢.复杂系统与复杂性科学简介.青岛大学学报.2001,16(4):25-28页
[13] 颜泽贤,陈忠,胡皓编.复杂系统演化论.人民出版社,1993年:40-70 页
[14] 姜璐.复杂系统的层次结构.自然辩证法研究.1994,10(2):16-21页
[15] Domenico Famularo, Peter Dorato. Robust non-fragile LQ controllers: the ststic state feedback case. International journal of control. 2000, 73(2): 159-165P
[16] Celmins, Aivars. Vulnerability assessment of fuzzy targets. Fuzzy Sets and Systems. 1994, 68(1): 29-38P
[17] Ang, A.H.S. Pires, J.A. A model for the seismic reliability assessment of electric power transmission systems. Reliability Engineering &system safety. 1996, 51(1): 7-22P
[18] Einarsson, Stefan. Comparision of QRA and Vulnerability analysis: does analysis lead to more robust and resilient systems? Acta Polytechnica Scandinavica, Civil Engineering and Building Construction Series. 1999, (114): 1-27P
[19] Rennaker, P.R. Richardson, S. New approach to vulnerability assessment. Journal of the American Helicoper Society. 1999, 44(1): 38-41P
[20] Reese, Ronald M. Calvano, Charles N. Hopkins, Th. Operationally oriented vulnerability requirements in the ship design process. Naval Engineers Journal. 1998, 110(1): 19-34P
[21] Soutter, Marc Musy, andre. Global sensitivity analyses of three pesticide leaching models using a Monte-Carlo approach. Journal of Environmental Quality. 1999, 28(4): 1290-1297P
[22] Soutter, Marc Musy, Andre. Coupling 1D Monte-Carlo simulations and geostatistics to assess groundwater vulnerability to pesticide contamination on a regional scale. Journel of Contaminant Hydrology. 1998, 32(1-2): 25-29P
[23] 王经民,王有科.黄土高原生态环境脆弱性计算方法探讨.水土保持通报.1996(32):36-43页
[24] Willianmsen, Joel Blacklock, Kevin Evans, Hilary. Quantifying and reducing International Space Station vulnerability following orbital debris penetration. Journal of Spacecraft and Rockets. 1999, 56(1): 133-141P
[25] Said, Michael O. Theory and practice of total ship survivability for ship design Naval Engineers Journal.1995, 107(4): 191-203P
[26] Technology overview for a proposed navy surface combatant DC zonal electric distribution system Ciezki, J.G., Ashton, R.W. Conference Naval Engineers Journal.1999, 111(3): 59-69P
[27] Operationally oriented vulnerability requirements in the ship design process Reese, Ronald M., Calvano, Charles N., Hopkins, Th Naval Engineers Journal. 1998, 110(1): 19-34P
[28] Vassalos, D., Turan, O., Konovessis, D., Tuzcu, C. Comparison between prescriptive and performance-based criteria for assessing ro-ro damage survivability International Shipbuilding Progress. 1998, 45(444): 351-382P
[29] Vassalos, Dracos, Turan, Osman, Pawlowski, Maciej. Dynamic stability assessment of damaged passenger/ro-ro ships and proposal of rational survival criteria Marine Technology. 1997, 34(4): 241-266P
[30] Said, Michael O. Theory and practice of total shipsurvivability for ship design. Naval Engineers Journal. 1995, 107(4): 191-203P
[31] Holland J.H. Escaping Brittleness: The possibilities of General Purpose Learning Algorithms Applied to Parallel Rule-Based Systems. In: Michals Ki R S, Carbonell J G, Mitchell T M(Eds), Machine Learning Ⅱ, Los Altos, CA: Morgan Kaufmann. 1986: 593-623P
[32] Lind, Niels C. Measure of vulnerability and damage tolerance. Reliability Engineering & System Safety. 1995, 48(1): 1-6P
[33] 韦琦.复杂系统脆性理论及其在危机控制中的应用.哈尔滨工程大学博士学位论文.2004.1-94页
[34] 郭健.突变理论在复杂系统脆性理论研究中的应用.哈尔滨工程大学博士学位论文,2004.1-109页
[35] J. V. Neumann. Theory of Self-reproducing Automata. edited and completed by A. W. Burks, Champaign, University of Illinois Press, Ⅱ[c], 1966: 1-21P
[36] S. Wolfram. Theory and Applications of Cellular Automata. Singapore, World Scientific, 1986: 12-57P
[37] A. Eizenberg, Y. Kifer. Large Deviations for Probabilistic Cellular Automata. Journal of Statistical Physics, 2002, 108(5-6): 1255-1280P
[38] Norio Konno. Dualities for a Class of Finite Range Probabilistic Cellular Automata in One Dimension. Journal of Statistical Physics, 2002, 106(5-6): 915-922P
[39] 张永安,白学志.复杂系统的重要研究工具——细胞自动机及其应用.自然杂志,1998,20(4):192-196页
[40] 应尚军,魏一鸣,范英,蔡嗣经.基于元胞自动机的股票市场投资行为模拟.系统工程学报,2001,16(5):382-388页
[41] 戴汝为.人工生命.模式识别与人工智能,1998,11(4):412-419页
[42] 李夏,戴汝为.系统科学与复杂性.自动化学报.1998,24(2):200-207页
[43] 肖帕德,德罗斯.物理系统的元胞自动机模拟.北京:清华大学出版社,2003:1-239页
[44] 昝廷全.复杂系统的一般数学框架.应用数学和力学.1993,14(4):367-374页
[45] 谢惠民.复杂性与动力系统.上海:上海科技教育出版社,1994:151-184页
[46] 布里渊.物理熵与信息(Ⅱ).系统论控制论信息论经典文献选编.北京:求实出版社,1989:649-664页
[47] 中华人民共和国卫生部.非典型肺炎疫情通报.http://www.moh.gov.cn/news/more_index.aspx?tp_class=C602.2003.3.31-2003.5.23