突变控制机制及其在船舶非线性横摇运动中的应用研究
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摘要
人类对客观世界认知和改造的历史过程,是一个由低级到高级,由简单到复杂,由表及里的纵深发展过程,在控制领域中更是如此。由于人们对实际生产过程的精度要求越来越高以及受控对象的不断复杂化,原有的线性控制理论已不能满足需要,因此相继诞生了一系列的非线性控制方法,如变结构控制、自适应控制、鲁棒控制等。
突变控制是非线性控制的一种,其主要目的在于控制系统在平稳输入情况下产生的输出跳变问题。本文将致力于探索如何使突变理论同控制技术相结合,形成一套突变控制的方法,并试探性地应用到船舶横摇运动及稳定性控制中去,主要成果如下:
首先,对势函数具有多输入单输出形式的非线性系统,根据其输入变量的数目不同,分别提出了折叠突变建模、尖点突变建模、燕尾突变建模和蝴蝶突变建模的通用方法,并根据各个系统不同的突变特点,针对性的设计了线性控制器、非线性控制器与基于冲失滤波器辅助反馈的控制器对突变进行控制。
其次,将折叠突变建模的通用方法引入到船舶非线性横摇运动中,在定性地得出船舶非线性横摇运动具有突变特性后,采用非线性振动分析中的多尺度法对横摇方程加以解析,得出了横摇运动的幅频响应方程,并以数值仿真验证了横摇突变特性的存在。最后分别用线性控制器和非线性控制器对船舶非线性横摇运动的突变特性进行了控制,仿真结果表明这两种控制方法效果明显,能有效抑制船舶横摇运动时突变现象的发生。
然后,将尖点突变建模的通用方法引入到船舶无阻尼静水横摇运动中,详细地讨论了船舶倾覆的过程,并在对其突变流形解析的基础上得到了突变发生的临界条件。阐明了恢复力系数与横摇自然频率的改变是船舶无阻尼静水横摇运动突变发生的原因,并分别设计了非线性控制器和冲失滤波器进行突变控制,经仿真证明控制器效果明显。
最后,将蝴蝶突变建模的通用方法引入到船舶在长峰波海浪中的参数横摇运动中,在用突变模型定性地证明了其突变特性之后,采用多尺度法对横摇方程进行解析,定量地得出了船舶参数横摇的突变特性,并设计了线性反馈控制器,在讨论了控制参数选取范围的情况下,对横摇运动进行突变控制,仿真结果表明控制器简单有效。
The history course of human cognize and transform the objective world is a process which experience from lower to higher, simple to complex, outside to the inside, either the control area. For demanding higher accuracy in actual production process and the increasing complexity of the controlled object, the original linear control theory has been unable to meet the needs of people. So, a series of nonlinear control method were born in succession, such as variable structure control, adaptive control, robust control, etc.
Catastrophe control theory is a kind of nonlinear control theory, which main purpose is to control the output's jumping problem of the system when inputs are smooth. This article will explore how to make the catastrophe theory combined with the control technology to create a set of catastrophe control methods, and tentatively applied to the ship rolling motion and stability control.The main work are the as follows:
First, for a nonlinear system which potential energy function has multi-input and single-output style, catastrophe model can be built according to the numbers of input variables.They are fold, cusp, swallowtail and butterfly catastrophe models. And in accordance with the different characteristics of each system, linear controller, nonlinear controller and washout controller were designed to control the catastrophe phenomena.
Second, fold catastrophe model was introduced into the capsizing of nonlinear ship roll movement, then multi-scale method was used to get the amplitude frequency response equation, and the catastrohe characteristics were proved by numerical simulation. Finally, linear and nonlinear controllers were designed to control the catastrophe phenomena, and the effectiveness was proved by simulation.
Third, cusp catastrophe model was made to analyse the course of ship roll motion without damping in hydrostatic water, and the process of ship capsize caused by parameters changes were discussed in detail. Critical conditions were also discussed and the catastrophe cause was clarified. Finally, nonlinear controller and washout controller were designed.
At last, the ship’s nonlinear rolling motion under excition by longitudinal wave was fitted into butterfly catastrophe model, and the multi-scale method was used to get the catastrohe characteristics. Then the linear feedback controller was designed to restrain the catastrophe, and the result was great by simulation.
突变控制是非线性控制的一种,其主要目的在于控制系统在平稳输入情况下产生的输出跳变问题。本文将致力于探索如何使突变理论同控制技术相结合,形成一套突变控制的方法,并试探性地应用到船舶横摇运动及稳定性控制中去,主要成果如下:
首先,对势函数具有多输入单输出形式的非线性系统,根据其输入变量的数目不同,分别提出了折叠突变建模、尖点突变建模、燕尾突变建模和蝴蝶突变建模的通用方法,并根据各个系统不同的突变特点,针对性的设计了线性控制器、非线性控制器与基于冲失滤波器辅助反馈的控制器对突变进行控制。
其次,将折叠突变建模的通用方法引入到船舶非线性横摇运动中,在定性地得出船舶非线性横摇运动具有突变特性后,采用非线性振动分析中的多尺度法对横摇方程加以解析,得出了横摇运动的幅频响应方程,并以数值仿真验证了横摇突变特性的存在。最后分别用线性控制器和非线性控制器对船舶非线性横摇运动的突变特性进行了控制,仿真结果表明这两种控制方法效果明显,能有效抑制船舶横摇运动时突变现象的发生。
然后,将尖点突变建模的通用方法引入到船舶无阻尼静水横摇运动中,详细地讨论了船舶倾覆的过程,并在对其突变流形解析的基础上得到了突变发生的临界条件。阐明了恢复力系数与横摇自然频率的改变是船舶无阻尼静水横摇运动突变发生的原因,并分别设计了非线性控制器和冲失滤波器进行突变控制,经仿真证明控制器效果明显。
最后,将蝴蝶突变建模的通用方法引入到船舶在长峰波海浪中的参数横摇运动中,在用突变模型定性地证明了其突变特性之后,采用多尺度法对横摇方程进行解析,定量地得出了船舶参数横摇的突变特性,并设计了线性反馈控制器,在讨论了控制参数选取范围的情况下,对横摇运动进行突变控制,仿真结果表明控制器简单有效。
The history course of human cognize and transform the objective world is a process which experience from lower to higher, simple to complex, outside to the inside, either the control area. For demanding higher accuracy in actual production process and the increasing complexity of the controlled object, the original linear control theory has been unable to meet the needs of people. So, a series of nonlinear control method were born in succession, such as variable structure control, adaptive control, robust control, etc.
Catastrophe control theory is a kind of nonlinear control theory, which main purpose is to control the output's jumping problem of the system when inputs are smooth. This article will explore how to make the catastrophe theory combined with the control technology to create a set of catastrophe control methods, and tentatively applied to the ship rolling motion and stability control.The main work are the as follows:
First, for a nonlinear system which potential energy function has multi-input and single-output style, catastrophe model can be built according to the numbers of input variables.They are fold, cusp, swallowtail and butterfly catastrophe models. And in accordance with the different characteristics of each system, linear controller, nonlinear controller and washout controller were designed to control the catastrophe phenomena.
Second, fold catastrophe model was introduced into the capsizing of nonlinear ship roll movement, then multi-scale method was used to get the amplitude frequency response equation, and the catastrohe characteristics were proved by numerical simulation. Finally, linear and nonlinear controllers were designed to control the catastrophe phenomena, and the effectiveness was proved by simulation.
Third, cusp catastrophe model was made to analyse the course of ship roll motion without damping in hydrostatic water, and the process of ship capsize caused by parameters changes were discussed in detail. Critical conditions were also discussed and the catastrophe cause was clarified. Finally, nonlinear controller and washout controller were designed.
At last, the ship’s nonlinear rolling motion under excition by longitudinal wave was fitted into butterfly catastrophe model, and the multi-scale method was used to get the catastrohe characteristics. Then the linear feedback controller was designed to restrain the catastrophe, and the result was great by simulation.
引文
[1]王文锋.基于观测器的线性系统的正实控制研究.曲阜师范大学硕士学位论文.2006
[2] E.C Zeeman. Catastrophe Theory, Scientific American,1976
[3]凌复华.突变理论及其应用.上海:上海交通大学出版社,1987.1-225页
[4]汤丽平.突变控制机制及其应用研究.哈尔滨工程大学博士学位论文. 2004
[5] R.Thom.Structural stability.and morphogenesis. Benjam in-Addsion Wesley, NY, USA, 1975
[6] Pratt S.J. catastrophe theory:its application in operating system design.Oper.Syst.Rev.(ACM).1987,21(2):23-32P
[7] Clark J.J.Singularity theory and phantom edges In scale space.IEEE Trans.Pattern Anal Mach Intell.1989,10(5):720-727P
[8] Sallam A.A.Power system transient stability assessment using catastrophe theory .IEE Proc.1989,136 (2):108-114P
[9] Acha-Daza T.A, Hall F.L.Graphical comparison of predictions for speed given by catastrophe theory and some classic models.Trasp Res Rec,1993,n1398:119-124P
[10] Kuijper A, Florack L.M.J. The application of catastrophe theory to medical image analysis.UU-CS-2001-24 TR.1-9P
[11] Baurova N.I. Theoretical Foundations of Chemical Engineering.2009, 43(3):345-348P
[12] Kuijper A, Florack L.M.J. Journal of Mathematical Imaging and Vision. 2005, 23(3): 219-38P
[13] Barunik J, Vosvrda M. Journal of Economic Dynamics and Control. 2009, 33(10): 1824-1836P
[14] Nye J.F. Journal of Optics A: Pure and Applied Optics. 2008, 10(7): 9P
[15] Clark, A. European Physical Journal B.2006, 50(4): 4659-4669P
[16] Markova O, Zakrzhevsky M, Yevstignejevs V, Naumenko N. Journal of Vibroengineering. 2008, 10(4): 538-540P
[17] Weidlich W, Huebner H.Journal of Economic Behavior and Organization. 2008, 67(1): 1-26P
[18] Raftoyiannis I.G, Constantakopoulos T.G, Michaltsos G.T, Kounadis, A.N. International Journal of Mechanical Sciences. 2006,48(10): 1021-1030P
[19]钟声.基于突变理论的土钉支护体系的稳定分析研究.广州大学硕士学位论文.2006
[20]童华炜,周龙翔,钟声.基坑土钉支护的突变分析.西安建筑科技大学学报. 2007,39(4):485-490页
[21]童华炜,周龙翔,钟声.土钉支护突变稳定分析中能量方程的建立.广州大学学报. 2007,6(3):68-71页
[22]李萍.长江三峡库区链子崖危岩体的稳定性分析.天津大学硕士学位论文.2003
[23]张业民.突变理论在岩土与结构工程中的若干应用.大连理工大学博士学位论文.2008
[24]何广讷,张业民.土本构关系的尖点突变模式.固体力学学报. 1991,12(3):199-206页
[25]张业民,郝冬雪,栾茂田.尖点突变模型在平板荷载试验中应用及预测研究.大连理工大学学报. 2007,47(3):392-397页
[26]张业民,栾茂田,李顺群.尖点突变模型描述土应力应变特性的可行性.武汉理工大学学报. 2004,26(8):38-51页
[27] Zhang Ye-min, Luan Mao-tian, Li Shun-qun, HAO Dong-xue. Estimation of liquefaction based on catastrophe theory. Chinese Journal of Computational Mechanics. 2008,4:237-240P
[28]左宇军.动静组合加载下的岩石破坏特性研究.中南大学博士学位论文.2005
[29]李夕兵,左宇军,马春德.动静组合加载下岩石破坏的应变能密度准则及突变理论分析.岩石力学与工程学报. 2005,24(16):2814-2823页
[30]左宇军,李夕兵,赵国彦.受静载荷作用的岩石动态断裂的突变模型.煤炭学报. 2004,29(6):654-658页
[31]左宇军,李夕兵,马春德等.动静组合载荷作用下岩石失稳破坏的突变理论模型与试验研究.岩石力学与工程学报. 2005,24(5):741-746页
[32]闫长斌.爆破作用下岩体累积损伤效应及其稳定性研究.中南大学博士学位论文.2006
[33]闫长斌,徐国元.基于突变理论深埋硬岩隧道的失稳分析.工程地质学报. 2006,14(4):508-512页
[34]闫长斌,徐国元.动荷载诱发上下交叠硐室间顶柱失稳的突变理论分析.工程力学. 2007,24(4):46-51页
[35]张海龙.采煤沉陷中突变现象分析及预测.西安科技大学硕士学位论文.2009
[36]杨大为.突变理论在石油价值趋势分析中的应用.吉林大学硕士学位论文.2007
[37]郝继锋.矿井自然火灾的突变研究.太原理工大学硕士学位论文.2002
[38]张骐.基于突变理论的物流通道选择研究.大连海事大学硕士学位论文.2009
[39]胡晓婷.基于突变理论的复杂网络系统行为预测研究.西安建筑科技大学硕士学位论文.2006
[40]郭健.基于突变理论的复杂系统的脆性研究.哈尔滨工程大学硕士学位论文.2003
[41]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
[42]郭健.基于尖点突变势函数对复杂系统的脆性分析. 2007中国控制与决策学术年会论文集.2007,83-986页
[43]郭健.基于尖点突变模型对复杂系统脆性问题的研究.舰船电子工程. 2004, (2):1-4页
[44]樊松.基于突变理论的图像边缘检测技术研究.哈尔滨工程大学硕士学位论文.2008
[45]戚杰.突变理论在环境建模中的应用研究.华中科技大学硕士学位论文.2005
[46]戚杰,胡汉芳.尖点突变模型在环境领域中的应用研究.环境技术. 2005, (4):24-26页
[47]戚杰,周敬宣,陈云峰等.可持续发展的突变评判法.环境科学与技术. 2005,28(6):54-74页
[48]林建人.基于突变理论的近岸海域环境灾害风险评价.大连理工大学硕士学位论文.2009
[49]王文俊.基于突变理论的IP网络异常行为检测机制研究.电子科技大学硕士学位论文.2009
[50]曹珏.基于突变理论的高层建筑火灾危险性模糊综合评价方法研究.中南大学硕士学位论文.2008
[51]李春阳.基于突变理论的上市公司财务预警研究.大连理工大学硕士学位论文.2006
[52]孙尧.突变控制技术及其应用研究.哈尔滨工程大学博士学位论文. 2002
[53]孙尧.人工心脏控制系统势函数模型研究.哈尔滨工程大学学报. 2002,23(5):47-51页
[54]汤丽平,孙尧,刘成香.水下潜器垂直运动的突变特性及稳定性分析.哈尔滨工程大学学报. 2005,4(2):161-164页
[55]孙尧,汤丽平,李雪莲.突变控制及其在水下潜器中的应用.哈尔滨工程大学学报. 2004,25(5):569-573页
[56]王晓玢.突变控制体系及其在船舶运动中的应用研究.哈尔滨工程大学博士学位论文. 2009
[57]孙尧,王晓玢,莫宏伟.船舶横纵摇耦合运动突变特性分析.哈尔滨工程大学学报. 2009,30(5):527-530页
[58]王晓玢,孙尧,莫宏伟.潜艇垂直面运动突变分析.大连海事大学学报. 2008,34(4):55-58页
[59]赵国超.基于突变理论的神经网络自适应控制器设计.哈尔滨工程大学硕士学位论文. 2009
[60]丁庆华.基于突变理论的船舶非线性横摇运动分析.哈尔滨工程大学硕士学位论文. 2009
[61]褚亦清,李翠英.非线性振动分析.北京:北京理工大学出版社, 1996,9: 1-2页
[62] Virgin L.N.The nonlinear rolling response of a vessel including chaotic motions leading to capsize in regular seas.Applied Ocean Research.1987,9(2):331-352P
[63] Nayfeh A.H, Khdeir A.A.Nonlinear rolling of ships in regular beam seas.International Shipbuilding Progress.1986, 379 (33):40-49P
[64] Liaw Y, Bishop S.R.Nonlinear heave-roll coupling and ship rolling.Nonlinear Dynamics.1995,8(2):197-211P
[65] Sanchez N.E,Nayfeh A.H,Nonlinear rolling motions of ships in longitudinal waves.International Shipbuilding Progress.1990, 411(37):247-272P
[66] Taylan M.The effect of nonlinear damping and restoring in ship rolling. OceanEngineering.2000,27(9):921-932P
[67] Taylan M,Static and dynamic aspects of a capsize phenomenon.Oceanengineering.2003,30(3):331-350P
[68] Galeazzi Roberto,Vidic-Perunovic Jelena, Blanke Mogens. Stability Analysis of the Parametric Roll Resonance under Non-constant Ship Speed .2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis.2009,2(3): 743-750P
[69] Mamontov E, Naess A. The sea-wave elevation and multistability in a non-autonomous nonlinear It?’s stochastic differential equation for the rolling angle of a ship. Applied Mathematical Modelling.2009,33(11): 4153-4162P
[70] Kim Jae-Han, Kim Yonghwan, Kim Dae-Woong, Kim Yong-Soo. Study on Assessment of Comfortability and Roll Stabilization for Passenger Ship.Proceedings of the International Offshore and Polar Engineering Conference, 2009,722-727P
[71] Vidic-Perunovic Jelena, Jensen Jrgen Juncher. Non-linear springing excitation due to a bidirectional wave field. Proceedings of MARSTRUCT 2009, 2nd International Conference on Marine Structures-Analysis and Design of Marine Structures. 2009, 37-44P
[72] Sun Hui, Faltinsen Odd Water entry of a bow-flare ship section with roll angle.M.Journal of Marine Science and Technology. 2009,14(1): 69-79P
[73] Grace I.F. Ibrahim R.A. Modelling and analysis of ship roll oscillations interacting with stationary icebergs. Proceedings of the Institution of Mechanical Engineers. Journal of Mechanical Engineering Science. 2008,222(10): 1873-1884P
[74] Kamel M.M. Bifurcation analysis of a nonlinear coupled pitch-roll ship. Mathematics and Computers in Simulation. 2007,73(5): 300-308P
[75] Holden Christian, Galeazzi Roberto, Rodríguez Claudio. Nonlinear container ship model for the study of parametric roll resonance. Modeling, Identification and Control. 2007,28(4): 87-103P
[76]欧阳茹荃,朱继懋.船舶横摇运动的非线性振动与混沌.水动力学研究与进展. 1999,14(3):334-340页
[77]李远林,吴家鸣,王冬姣.波浪对船舶非线性横摇阻尼的影响.船舶工程. 2003,25(2):21-24页
[78]唐友刚,田凯强,董艳秋等船舶参数激励非线性运动升沉(纵摇)-横摇耦合关系的研究.中国造船. 2000,41(3): 23-27页
[79]李红霞,唐友刚,胡楠,郑宏宇.船舶横摇非线性阻尼系数识别.天津大学学报. 2005,38(12):1042-1045页
[80]徐德嘉,周庆根.船舶非线性横摇的精确模型.中国造船. 1990,(4): 11-23页
[81]余滋红,於家鹏.船舶横摇非线性运动最大值预报.中国造船. 1997, (2):26-31页
[82]张兢.关于船舶参激横摇船模试验的数据分析.武汉理工大学学报. 2001,25(2):172-175页
[83]张兢,张纬康.关于船舶参激横摇运动的试验研究.中国造船. 1991, (4):34-42页
[84]谷家扬.导致船舶倾覆的随机非线性横摇特性研究.天津大学硕士学位论文,2005
[85]杨绍普,申永军.滞后非线性系统的分岔与奇异性.北京:科学出版社, 1997,11:52,72-81页
[86]凌复华.突变理论及其应用.上海:上海交通大学出版社,1987:1-225页
[87]钱伟长.非线性力学的新发展-稳定性、分岔、突变、混沌.武汉:华中理工大学出版社,1988:199页
[88]桑博德.突变理论入门.上海:上海科学技术文献出版社, 1989,9:2-78页
[89]凌复华.非线性动力学系统的数值研究.上海:上海交通大学出版社, 1989,6:8-34页
[90]阿诺尔德著,周燕华译.突变理论.北京:高等教育出版社, 1990,6: 2页
[91]张琪昌,王洪礼,竺致文等.分岔与混沌理论及应用.天津:天津大学出版社, 2005, 35-45页
[92]陆启韶.分岔与奇异性.上海:上海科技教育出版社, 1995:9页
[93]萧寒.多自由度非线性系统的霍普分岔与鞍结分岔控制.湖南大学博士学位论文. 2008
[94]刘利琴.船舶非线性随机动力学行为的研究.天津大学博士学位论文. 2007
[95]欧阳克俭.非线性动力系统的两类分岔控制与混沌控制研究.湖南大学硕士学位论文. 2007
[96] Nayfeh A.H, Khdeir A.A. Nonlinear Rolling of Biased Ships In Regular Beam Waves. International Shipbuilding Progress.1986,33(381):84-93P
[97]金鸿章,李国斌.船舶特种装置控制系统.北京:国防工业出版社,1995:89-91页
[98]李积德.船舶耐波性.哈尔滨:哈尔滨工程大学出版社,2007:79-86页
[99]胡开业.船舶在波浪中的非线性横摇运动及其稳定性分析.哈尔滨工程大学硕士学位论文.2006
[100]杨博.船舶非线性横摇的近似解析.哈尔滨工程大学硕士学位论文.2005
[101]凌复华,魏焕明.初等突变理论在Hamiton系统中应用的一个例子.力学学报. 1985,17(1):34-40页
[102]李正文,唐建明等.油气储集层突变理论识别技术及其应用.矿物岩石.1998,18(3):87-93页
[103] Arnold V I. Catastrophe theory. Berlin: Springer Verlag,1986:10-14P
[104]金鸿章,姚绪梁.船舶控制原理.哈尔滨:哈尔滨工程大学出版社,2001,108-143页
[105]符文彬.非线性动力系统的分岔控制研究.湖南大学博士学位论文. 2004
[106]刘延柱,陈立群.非线性振动.北京:高等教育出版社, 2001,8:57-109页,179-243页,333-337页
[107]符文彬,唐驾时.强迫Duffing振动系统的主共振鞍结分岔控制.振动工程学报. 2004,17(3):365-368页
[108]何平,赵子都.突变理论及其应用.大连:大连理工大学出版社,1989:16-17页
[109]郭健,陈兴林,金鸿章.基于尖点突变对交通流模型的研究.控制与决策,2008,23(2):238-239页
[110]马骏,杨功流.导轨爬行分岔的Washout滤波器控制.农业机械学报. 2008,39(11):156-159页
[111] Blocki W. Ship safety inconnection with parametric resonance of the roll Int.Shipbuild.Progress.1980,306(27):36-53P
[112] Feat G, Jones D. Parametric excitation and the stability of a ship subjected to a steady heeling moment. Int.Shipbuild.Progress.1984,(28):263P
[113]陈启强.船模强迫横摇及其跳跃现象.力学学报.1983,(2):126-133页.
[114] Hua Jiaobo.A study of the Parametrically excited roll motion of a RoRo-Ship in following and heading waves. Int.Shipbuild.Progress.1992,(39):345-366P
[115]唐友刚,田凯强,张泽盛等.船舶参数激励非线性横摇运动方程.船舶工程. 1998, (6):16-18页
[116]张延峰,董艳秋,唐友刚等.纵浪上基本参数共振对船舶稳性的影响.船舶力学. 1998,2(3): 6-12页
[117] Sanchez N.E, Nayfeh A.H. Global behavior of a biased non-linear oscillator under external and parametric excitations. Journal of Sound and Vibration.1997,207(2):137-149P
[118]陈予恕.非线性振动系统的分岔和混沌理论.北京:高等教育出版社, 1993,7:53-96页
[2] E.C Zeeman. Catastrophe Theory, Scientific American,1976
[3]凌复华.突变理论及其应用.上海:上海交通大学出版社,1987.1-225页
[4]汤丽平.突变控制机制及其应用研究.哈尔滨工程大学博士学位论文. 2004
[5] R.Thom.Structural stability.and morphogenesis. Benjam in-Addsion Wesley, NY, USA, 1975
[6] Pratt S.J. catastrophe theory:its application in operating system design.Oper.Syst.Rev.(ACM).1987,21(2):23-32P
[7] Clark J.J.Singularity theory and phantom edges In scale space.IEEE Trans.Pattern Anal Mach Intell.1989,10(5):720-727P
[8] Sallam A.A.Power system transient stability assessment using catastrophe theory .IEE Proc.1989,136 (2):108-114P
[9] Acha-Daza T.A, Hall F.L.Graphical comparison of predictions for speed given by catastrophe theory and some classic models.Trasp Res Rec,1993,n1398:119-124P
[10] Kuijper A, Florack L.M.J. The application of catastrophe theory to medical image analysis.UU-CS-2001-24 TR.1-9P
[11] Baurova N.I. Theoretical Foundations of Chemical Engineering.2009, 43(3):345-348P
[12] Kuijper A, Florack L.M.J. Journal of Mathematical Imaging and Vision. 2005, 23(3): 219-38P
[13] Barunik J, Vosvrda M. Journal of Economic Dynamics and Control. 2009, 33(10): 1824-1836P
[14] Nye J.F. Journal of Optics A: Pure and Applied Optics. 2008, 10(7): 9P
[15] Clark, A. European Physical Journal B.2006, 50(4): 4659-4669P
[16] Markova O, Zakrzhevsky M, Yevstignejevs V, Naumenko N. Journal of Vibroengineering. 2008, 10(4): 538-540P
[17] Weidlich W, Huebner H.Journal of Economic Behavior and Organization. 2008, 67(1): 1-26P
[18] Raftoyiannis I.G, Constantakopoulos T.G, Michaltsos G.T, Kounadis, A.N. International Journal of Mechanical Sciences. 2006,48(10): 1021-1030P
[19]钟声.基于突变理论的土钉支护体系的稳定分析研究.广州大学硕士学位论文.2006
[20]童华炜,周龙翔,钟声.基坑土钉支护的突变分析.西安建筑科技大学学报. 2007,39(4):485-490页
[21]童华炜,周龙翔,钟声.土钉支护突变稳定分析中能量方程的建立.广州大学学报. 2007,6(3):68-71页
[22]李萍.长江三峡库区链子崖危岩体的稳定性分析.天津大学硕士学位论文.2003
[23]张业民.突变理论在岩土与结构工程中的若干应用.大连理工大学博士学位论文.2008
[24]何广讷,张业民.土本构关系的尖点突变模式.固体力学学报. 1991,12(3):199-206页
[25]张业民,郝冬雪,栾茂田.尖点突变模型在平板荷载试验中应用及预测研究.大连理工大学学报. 2007,47(3):392-397页
[26]张业民,栾茂田,李顺群.尖点突变模型描述土应力应变特性的可行性.武汉理工大学学报. 2004,26(8):38-51页
[27] Zhang Ye-min, Luan Mao-tian, Li Shun-qun, HAO Dong-xue. Estimation of liquefaction based on catastrophe theory. Chinese Journal of Computational Mechanics. 2008,4:237-240P
[28]左宇军.动静组合加载下的岩石破坏特性研究.中南大学博士学位论文.2005
[29]李夕兵,左宇军,马春德.动静组合加载下岩石破坏的应变能密度准则及突变理论分析.岩石力学与工程学报. 2005,24(16):2814-2823页
[30]左宇军,李夕兵,赵国彦.受静载荷作用的岩石动态断裂的突变模型.煤炭学报. 2004,29(6):654-658页
[31]左宇军,李夕兵,马春德等.动静组合载荷作用下岩石失稳破坏的突变理论模型与试验研究.岩石力学与工程学报. 2005,24(5):741-746页
[32]闫长斌.爆破作用下岩体累积损伤效应及其稳定性研究.中南大学博士学位论文.2006
[33]闫长斌,徐国元.基于突变理论深埋硬岩隧道的失稳分析.工程地质学报. 2006,14(4):508-512页
[34]闫长斌,徐国元.动荷载诱发上下交叠硐室间顶柱失稳的突变理论分析.工程力学. 2007,24(4):46-51页
[35]张海龙.采煤沉陷中突变现象分析及预测.西安科技大学硕士学位论文.2009
[36]杨大为.突变理论在石油价值趋势分析中的应用.吉林大学硕士学位论文.2007
[37]郝继锋.矿井自然火灾的突变研究.太原理工大学硕士学位论文.2002
[38]张骐.基于突变理论的物流通道选择研究.大连海事大学硕士学位论文.2009
[39]胡晓婷.基于突变理论的复杂网络系统行为预测研究.西安建筑科技大学硕士学位论文.2006
[40]郭健.基于突变理论的复杂系统的脆性研究.哈尔滨工程大学硕士学位论文.2003
[41]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
[42]郭健.基于尖点突变势函数对复杂系统的脆性分析. 2007中国控制与决策学术年会论文集.2007,83-986页
[43]郭健.基于尖点突变模型对复杂系统脆性问题的研究.舰船电子工程. 2004, (2):1-4页
[44]樊松.基于突变理论的图像边缘检测技术研究.哈尔滨工程大学硕士学位论文.2008
[45]戚杰.突变理论在环境建模中的应用研究.华中科技大学硕士学位论文.2005
[46]戚杰,胡汉芳.尖点突变模型在环境领域中的应用研究.环境技术. 2005, (4):24-26页
[47]戚杰,周敬宣,陈云峰等.可持续发展的突变评判法.环境科学与技术. 2005,28(6):54-74页
[48]林建人.基于突变理论的近岸海域环境灾害风险评价.大连理工大学硕士学位论文.2009
[49]王文俊.基于突变理论的IP网络异常行为检测机制研究.电子科技大学硕士学位论文.2009
[50]曹珏.基于突变理论的高层建筑火灾危险性模糊综合评价方法研究.中南大学硕士学位论文.2008
[51]李春阳.基于突变理论的上市公司财务预警研究.大连理工大学硕士学位论文.2006
[52]孙尧.突变控制技术及其应用研究.哈尔滨工程大学博士学位论文. 2002
[53]孙尧.人工心脏控制系统势函数模型研究.哈尔滨工程大学学报. 2002,23(5):47-51页
[54]汤丽平,孙尧,刘成香.水下潜器垂直运动的突变特性及稳定性分析.哈尔滨工程大学学报. 2005,4(2):161-164页
[55]孙尧,汤丽平,李雪莲.突变控制及其在水下潜器中的应用.哈尔滨工程大学学报. 2004,25(5):569-573页
[56]王晓玢.突变控制体系及其在船舶运动中的应用研究.哈尔滨工程大学博士学位论文. 2009
[57]孙尧,王晓玢,莫宏伟.船舶横纵摇耦合运动突变特性分析.哈尔滨工程大学学报. 2009,30(5):527-530页
[58]王晓玢,孙尧,莫宏伟.潜艇垂直面运动突变分析.大连海事大学学报. 2008,34(4):55-58页
[59]赵国超.基于突变理论的神经网络自适应控制器设计.哈尔滨工程大学硕士学位论文. 2009
[60]丁庆华.基于突变理论的船舶非线性横摇运动分析.哈尔滨工程大学硕士学位论文. 2009
[61]褚亦清,李翠英.非线性振动分析.北京:北京理工大学出版社, 1996,9: 1-2页
[62] Virgin L.N.The nonlinear rolling response of a vessel including chaotic motions leading to capsize in regular seas.Applied Ocean Research.1987,9(2):331-352P
[63] Nayfeh A.H, Khdeir A.A.Nonlinear rolling of ships in regular beam seas.International Shipbuilding Progress.1986, 379 (33):40-49P
[64] Liaw Y, Bishop S.R.Nonlinear heave-roll coupling and ship rolling.Nonlinear Dynamics.1995,8(2):197-211P
[65] Sanchez N.E,Nayfeh A.H,Nonlinear rolling motions of ships in longitudinal waves.International Shipbuilding Progress.1990, 411(37):247-272P
[66] Taylan M.The effect of nonlinear damping and restoring in ship rolling. OceanEngineering.2000,27(9):921-932P
[67] Taylan M,Static and dynamic aspects of a capsize phenomenon.Oceanengineering.2003,30(3):331-350P
[68] Galeazzi Roberto,Vidic-Perunovic Jelena, Blanke Mogens. Stability Analysis of the Parametric Roll Resonance under Non-constant Ship Speed .2008 Proceedings of the 9th Biennial Conference on Engineering Systems Design and Analysis.2009,2(3): 743-750P
[69] Mamontov E, Naess A. The sea-wave elevation and multistability in a non-autonomous nonlinear It?’s stochastic differential equation for the rolling angle of a ship. Applied Mathematical Modelling.2009,33(11): 4153-4162P
[70] Kim Jae-Han, Kim Yonghwan, Kim Dae-Woong, Kim Yong-Soo. Study on Assessment of Comfortability and Roll Stabilization for Passenger Ship.Proceedings of the International Offshore and Polar Engineering Conference, 2009,722-727P
[71] Vidic-Perunovic Jelena, Jensen Jrgen Juncher. Non-linear springing excitation due to a bidirectional wave field. Proceedings of MARSTRUCT 2009, 2nd International Conference on Marine Structures-Analysis and Design of Marine Structures. 2009, 37-44P
[72] Sun Hui, Faltinsen Odd Water entry of a bow-flare ship section with roll angle.M.Journal of Marine Science and Technology. 2009,14(1): 69-79P
[73] Grace I.F. Ibrahim R.A. Modelling and analysis of ship roll oscillations interacting with stationary icebergs. Proceedings of the Institution of Mechanical Engineers. Journal of Mechanical Engineering Science. 2008,222(10): 1873-1884P
[74] Kamel M.M. Bifurcation analysis of a nonlinear coupled pitch-roll ship. Mathematics and Computers in Simulation. 2007,73(5): 300-308P
[75] Holden Christian, Galeazzi Roberto, Rodríguez Claudio. Nonlinear container ship model for the study of parametric roll resonance. Modeling, Identification and Control. 2007,28(4): 87-103P
[76]欧阳茹荃,朱继懋.船舶横摇运动的非线性振动与混沌.水动力学研究与进展. 1999,14(3):334-340页
[77]李远林,吴家鸣,王冬姣.波浪对船舶非线性横摇阻尼的影响.船舶工程. 2003,25(2):21-24页
[78]唐友刚,田凯强,董艳秋等船舶参数激励非线性运动升沉(纵摇)-横摇耦合关系的研究.中国造船. 2000,41(3): 23-27页
[79]李红霞,唐友刚,胡楠,郑宏宇.船舶横摇非线性阻尼系数识别.天津大学学报. 2005,38(12):1042-1045页
[80]徐德嘉,周庆根.船舶非线性横摇的精确模型.中国造船. 1990,(4): 11-23页
[81]余滋红,於家鹏.船舶横摇非线性运动最大值预报.中国造船. 1997, (2):26-31页
[82]张兢.关于船舶参激横摇船模试验的数据分析.武汉理工大学学报. 2001,25(2):172-175页
[83]张兢,张纬康.关于船舶参激横摇运动的试验研究.中国造船. 1991, (4):34-42页
[84]谷家扬.导致船舶倾覆的随机非线性横摇特性研究.天津大学硕士学位论文,2005
[85]杨绍普,申永军.滞后非线性系统的分岔与奇异性.北京:科学出版社, 1997,11:52,72-81页
[86]凌复华.突变理论及其应用.上海:上海交通大学出版社,1987:1-225页
[87]钱伟长.非线性力学的新发展-稳定性、分岔、突变、混沌.武汉:华中理工大学出版社,1988:199页
[88]桑博德.突变理论入门.上海:上海科学技术文献出版社, 1989,9:2-78页
[89]凌复华.非线性动力学系统的数值研究.上海:上海交通大学出版社, 1989,6:8-34页
[90]阿诺尔德著,周燕华译.突变理论.北京:高等教育出版社, 1990,6: 2页
[91]张琪昌,王洪礼,竺致文等.分岔与混沌理论及应用.天津:天津大学出版社, 2005, 35-45页
[92]陆启韶.分岔与奇异性.上海:上海科技教育出版社, 1995:9页
[93]萧寒.多自由度非线性系统的霍普分岔与鞍结分岔控制.湖南大学博士学位论文. 2008
[94]刘利琴.船舶非线性随机动力学行为的研究.天津大学博士学位论文. 2007
[95]欧阳克俭.非线性动力系统的两类分岔控制与混沌控制研究.湖南大学硕士学位论文. 2007
[96] Nayfeh A.H, Khdeir A.A. Nonlinear Rolling of Biased Ships In Regular Beam Waves. International Shipbuilding Progress.1986,33(381):84-93P
[97]金鸿章,李国斌.船舶特种装置控制系统.北京:国防工业出版社,1995:89-91页
[98]李积德.船舶耐波性.哈尔滨:哈尔滨工程大学出版社,2007:79-86页
[99]胡开业.船舶在波浪中的非线性横摇运动及其稳定性分析.哈尔滨工程大学硕士学位论文.2006
[100]杨博.船舶非线性横摇的近似解析.哈尔滨工程大学硕士学位论文.2005
[101]凌复华,魏焕明.初等突变理论在Hamiton系统中应用的一个例子.力学学报. 1985,17(1):34-40页
[102]李正文,唐建明等.油气储集层突变理论识别技术及其应用.矿物岩石.1998,18(3):87-93页
[103] Arnold V I. Catastrophe theory. Berlin: Springer Verlag,1986:10-14P
[104]金鸿章,姚绪梁.船舶控制原理.哈尔滨:哈尔滨工程大学出版社,2001,108-143页
[105]符文彬.非线性动力系统的分岔控制研究.湖南大学博士学位论文. 2004
[106]刘延柱,陈立群.非线性振动.北京:高等教育出版社, 2001,8:57-109页,179-243页,333-337页
[107]符文彬,唐驾时.强迫Duffing振动系统的主共振鞍结分岔控制.振动工程学报. 2004,17(3):365-368页
[108]何平,赵子都.突变理论及其应用.大连:大连理工大学出版社,1989:16-17页
[109]郭健,陈兴林,金鸿章.基于尖点突变对交通流模型的研究.控制与决策,2008,23(2):238-239页
[110]马骏,杨功流.导轨爬行分岔的Washout滤波器控制.农业机械学报. 2008,39(11):156-159页
[111] Blocki W. Ship safety inconnection with parametric resonance of the roll Int.Shipbuild.Progress.1980,306(27):36-53P
[112] Feat G, Jones D. Parametric excitation and the stability of a ship subjected to a steady heeling moment. Int.Shipbuild.Progress.1984,(28):263P
[113]陈启强.船模强迫横摇及其跳跃现象.力学学报.1983,(2):126-133页.
[114] Hua Jiaobo.A study of the Parametrically excited roll motion of a RoRo-Ship in following and heading waves. Int.Shipbuild.Progress.1992,(39):345-366P
[115]唐友刚,田凯强,张泽盛等.船舶参数激励非线性横摇运动方程.船舶工程. 1998, (6):16-18页
[116]张延峰,董艳秋,唐友刚等.纵浪上基本参数共振对船舶稳性的影响.船舶力学. 1998,2(3): 6-12页
[117] Sanchez N.E, Nayfeh A.H. Global behavior of a biased non-linear oscillator under external and parametric excitations. Journal of Sound and Vibration.1997,207(2):137-149P
[118]陈予恕.非线性振动系统的分岔和混沌理论.北京:高等教育出版社, 1993,7:53-96页