朱位秋
非线性随机动力学
个性化签名
- 姓名:朱位秋
- 目前身份:
- 担任导师情况:
- 学位:
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学术头衔:
博士生导师, 享受国务院特殊津贴专家, 中国科学院院士
- 职称:-
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学科领域:
水文学
- 研究兴趣:非线性随机动力学
朱位秋教授是我国著名的力学专家。他1938年出生于浙江义乌;1961年于西北工业大学工程力学本科毕业;1964年西北工业大学研究生毕业;1967年至1975年任飞机结构强度研究所技术员;1975.10至今为浙江大学讲师、副教授、教授、博导;2003年当选为中国科学院院士。
1981.2―1981.8美国威斯康星大学工程力学系访问学者;1981.9―1983.5美国麻省理工学院机械系访问科学家;1989.10―1990.12美国佛罗里达大西洋大学应用随机研究中心访问副教授;1991.1―1992.6美国纽约州立大学土木系研究副教授;1996.7―1996.12美国纽约州立大学土木系研究教授;1999.3―1999.4法国伯莱塞?巴斯卡大学应用数学系访问教授;1999.6―2000.3日本京都大学防灾研究所访问教授;2002.8美国佛罗里达大西洋大学应用随机研究中心Schmidt杰出访问教授。现为国际结构安全与可靠性协会及其下属随机方法委员成员,第五届国际随机结构动力学会议主席,中国振动工程学会常务理事,中国力学学会一般力学专业委员会副主任,3种国际与5种国内学术刊物编委。科技成就:上世纪80年代在非线性随机振动、结构宽带随机振动、随机有限元及随机疲劳与断裂等方面做出了重要贡献,撰写了专著《随机振动》,概括了国际上包括他直至90年代初随机振动理论的精华。90年代以来,在国际上首创了一个崭新的非线性随机动力学与控制的哈密顿理论体系框架。国际上首次得到四类能量非等分精确平稳解,打破60多年来只有能量等分精确平稳解的局面;提出与发展了高斯白噪声激励下多自由度耗散哈密顿系统的等效非线性系统法;提出与发展了分别在白噪声、宽带噪声、窄带有界噪声及谐和与白噪声作用下多自由度拟哈密顿系统随机平均法;在平均方程基础上提出与发展了计算拟哈密顿系统最大李亚普诺夫指数的解析公式与方法;提出与发展了估计拟哈密顿系统首次穿越概率及平均首次穿越时间的方法;提出与发展了分别以响应最小为目标的非线性随机最优主动与半主动控制,以最大李亚普诺夫指数最小为目标的反馈稳定化及以可靠度最大或平均首次穿越时间最长为目标的最优控制理论方法。上述系统原创性研究成果为解决工程与科学中一系列极其重要而困难的非线性随机动力学与控制问题提供了一整套全新而有效的理论方法,并已应用于生物群体动力学与土木结构的动力学分析与控制。9次应邀在重要国际学术会议上作大会报告或特邀报告。发表论文150余篇,其中第一作者120余篇,SCI、EI及ISTP分别收录60、54、21篇。科学出版社出版专著2部,论著被他引538次,其中SCI他引283次,5篇论文被国外、内专著引用各成为书中一节。上述成果鉴定为"整体上达到了国际先进水平,其中若干方面达到国际领先水平。"美国工程院院士Y.K.Lin称专著《随机振动》"现今欧美日各国无类似专著可以比拟",称专著《非线性随机动力学与控制》"实属学术上重要贡献。书中理论之发展,以统一的哈密顿框架为基础,乃朱位秋教授之首创,尤属独特可贵",称被推荐人"在随机动力学领域,已成为国际著名专家之一"。西工大方同教授称该专著"反映了这一领域中当代最新成就,可谓非线性随机动力学发展过程中的一个新的里程碑"。
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607
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成果数
10
【期刊论文】Lyapunov exponent and stochastic stability of quasi-non-integrable Hamiltonian systems
朱位秋, W.Q. Zhu*
International Journal of Non-Linear Mechanics 39(2004)569-579,-0001,():
-1年11月30日
An n degree-of-freedom (DOF) non-integrable Hamiltonian system subject to light damping and weak stochastic excitation is called quasi-non-integrable Hamiltonian system. In the present paper, the stochastic averaging of quasi-non-integrable Hamiltonian systems is brie5y reviewed. A new norm in terms of the square root of Hamiltonian is introduced in the de6nitions of stochastic stability and Lyapunov exponent and the formulas for the Lyapunov exponent are derived from the averaged Itˆo equations of the Hamiltonian and of the square root of Hamiltonian. It is inferred that the Lyapunov exponent so obtained is the 6rst approximation of the largest Lyapunov exponent of the original quasi-non-integrable Hamiltonian systems and the necessary and su8cient condition for the asymptotic stability with probability one of the trivial solution of the original systems can be obtained approximately by letting the Lyapunov exponent to be negative. This inference is con6rmed by comparing the stability conditions obtained from negative Lyapunov exponent and by examining the sample behaviors of averaged Hamiltonian or the square root of averaged Hamiltonian at trivial boundary for two examples. It is also veri6ed by the largest Lyapunov exponent obtained using small noise expansion for the second example.
Non-linear system, Stochastic excitation, Stochastic averaging, Lyapunov exponent, Stochastic stability
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【期刊论文】Optimal bounded control for minimizing the response of quasi-integrable Hamiltonian systems
朱位秋, W.Q. Zhua;*, M.L. Dengb
International Journal of Non-Linear Mechanics 39(2004)1535-1546,-0001,():
-1年11月30日
A procedure for designing optimal bounded control to minimize the response of quasi-integrable Hamiltonian systems is proposed based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stochastic dynamical programming principle. The equations of motion of a controlled quasi-integrable Hamiltonian system are 5rst reduced to a set of partially completed averaged Itˆo stochastic di7erential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, the dynamical programming equation for the control problems of minimizing the response of the averaged system is formulated based on the dynamical programming principle. The optimal control law is derived from the dynamical programming equation and control constraints without solving the dynamical programming equation. The response of optimally controlled systems is predicted through solving the Fokker-Planck-Kolmogrov equation associated with fully completed averaged Ito equations. Finally, two examples are worked out in detail to illustrate the application and e7ectiveness of the proposed control strategy.
Non-linear system, Stochastic excitation, Stochastic averaging, Response, Stochastic optimal control, Dynamical programming
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朱位秋, W.Q. Zhua;b; *, Z.L. Huanga, M.L. Denga
International Journal of Non-Linear Mechanics 38(2003)1133-1148,-0001,():
-1年11月30日
An n degree-of-freedom Hamiltonian system with r (1<r<n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIto equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.
Non-linear system, Stochastic excitation, Stochastic averaging, First-passage failure, eliability, First-passage time, Stochastic optimal control, Dynamical programming
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【期刊论文】Stochastic averaging methods in random vibration
朱位秋, W Q Zhu
ASME Book No. AMR036. Reprinted from Appl Mech Rev vol 41, no 5, May 1988,-0001,():
-1年11月30日
A survey of stochastic averaging methods in random vibration is given. After a brief introduction to the basic ideas, the advantages and the history of the methods, three kinds of stochastic averaging methods are formulated, and their applicability and recent developments are stated. In the second part, the applications of the methods in response prediction, stability decision, and reliability estimation of randomly excited nonlinear and parametric systems are reviewed. The possibility of further developments and applications of the methods is also pointed out.
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【期刊论文】An Optimal Nonlinear Feedback Control Strategy for Randomly Excited Structural Systems
朱位秋, W. Q. ZHU and Z. G. YING, T. T. SOONG
Nonlinear Dynamics 24: 31-51, 2001.,-0001,():
-1年11月30日
A strategy for optimal nonlinear feedback control of randomly excited structural systems is proposed based on the stochastic averaging method for quasi-Hamiltonian systems and the stochastic dynamic programming principle. A randomly excited structural system is formulated as a quasi-Hamiltonian system and the control forces are divided into conservative and dissipative parts. The conservative parts are designed to change the integrability and resonance of the associated Hamiltonian system and the energy distribution among the controlled system. After the conservative parts are determined, the system response is reduced to a controlled diffusion process by using the stochastic averaging method. The dissipative parts of control forces are then obtained from solving the stochastic dynamic programming equation. Both the responses of uncontrolled and controlled structural systems can be predicted analytically. Numerical results for a controlled and stochastically excited Duffing oscillator and a two-degree-of-freedom system with linear springs and linear and nonlinear dampings, show that the proposed control strategy is very effective and efficient.
Nonlinear optimal control,, quasi-Hamiltonian systems,, random excitation,, stochastic averaging
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【期刊论文】Stochastic Hopf bifurcation of quasi-nonintegrable-Hamiltonian systems
朱位秋, W.Q. Zhu*, Z.L. Huang
International Journal of Non-Linear Mechanics 34(1999)437-447,-0001,():
-1年11月30日
A new procedure for analyzing the stochastic Hopf bifurcation of quasi-non-integrable-Hamiltonian systems is proposed. A quasi-non-integrable-Hamiltonian system is
Stochastic Hopf bifurcation, Stochastic stability, Quasi-integrable-Hamiltonian system, Stochastic averaging
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50浏览
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【期刊论文】Lyapunov exponents and stochastic stability of quasi- integrable-Hamiltonian systems
朱位秋
,-0001,():
-1年11月30日
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朱位秋, W.Q. Zhua, b, *, Z.L. Huanga, Y. Suzukib
International Journal of Non-Linear Mechanics 36(2001)773-786,-0001,():
-1年11月30日
An n-degree-of-freedom Hamiltonian system with r (1<r<n) integrals of motion which are in involution is called partially integrable Hamiltonian system. In the present paper, the exact stationary solutions of stochastically excited and dissipated partially integrable Hamiltonian systems are first reviewed. Then an equivalent non-linear system method for this class of systems in both nonresonant and resonant cases is developed. Three criteria are proposed to obtain the equivalent non-linear systems. The application and e!ectiveness of the method are illustrated by an example.
Hamiltonian system, Dissipation, Stochastic excitation, Equivalent non-linear system, Random vibration
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朱位秋, W.O. Zhu, Y. Q. Yang
JUNE 1996, Vol. 63/493,-0001,():
-1年11月30日
It is shown that the structure and property of the exact stationary solution of a stochastically excited and dissipated n-degree-of-freedom Hamiltonian system depend upon the integrability and resonant property of the Hamiltonian system modified by the Wong-Zakai correct terms. For a stochastically excited and dissipated nonintegra-ble Hamiltonian system, the exact stationary solution is a functional of the Hamilto-nian and has the protYerty of equipartition of energy. For a stochastically excited and dissipated integrable Hamiltonian system, the exact stationary solution is a functional of n independent integrals of motion or n action variables of the modified Hamiltonian system in nonresonant case, or a functional of both n action variables and binations of phase angles in resonant case with a (1≤α≤n-1) resonant relations, and has the property that the partition of the energy among n degrees-of-freedom can be adjusted by the magnitudes and distributions of dampings and stochastic excitations. All the exact stationary solutions obtained to date for nonlinear stochastic systems are those for stochastically excited and dissipated nonin-tegrable Hamiltonian systems, which are further generalized to account for the modi-fication of the Hamiltonian by Wong-Zakai correct terms. Procedures to obtain the exact stationary solutions of stochastically excited and dissipated integrable Hamilto-nian systems in both resonant and nonresonant cases are proposed and the conditions for such solutions to exist are deduced. The above procedures and results are further extended to a more general class of systems, which include the stochastically excited and dissipated Hamiltonian systems as special cases. Examples are given to illustrate the applications of the procedures.
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