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Exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

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Science china(Technological Sciences) 2009年第8期52卷 2424-2431页

作者： HUANG ZhiLong1,2.& JIN XiaoLing1 1 department of mechanics, {2., hangzhou 31002., china 2.The state Key Laboratory of fluid power transmission and control, {2., hangzhou 31002., china department of mechanics Zhejiang University Hangzhou 310027 China The state Key Laboratory of fluid {2. transmission and control Zhejiang University Hangzhou 310027 China

A new procedure is proposed to construct strongly nonlinear systems of multiple degrees of freedom subjected to parametric and/or external Gaussian white noises, whose exact stationary solutions are independent of energy. Firstly, the equivalent Fokker-Planck-Kolmogorov (FPK) equations are derived by using exterior differentiation. The main difference between the equivalent FPK equation and the original FPK equation lies in the additional arbitrary antisymmetric diffusion matrix. Then the exact stationary solutions and the structures of the original systems can be obtained by using the coefficients of antisymmetric diffusion matrix. The obtained exact stationary solutions, which are generally independent of energy, are for the most general class of strongly nonlinear stochastic systems multiple degrees of freedom (MDOF) so far, and some classes of the known ones dependent on energy belong to the special cases of them.

关键词： exact stationary solution nonlinear stochastic system equivalent system independent of energy

Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems

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Acta Mechanica Sinica 2007年第4期23卷 437-444页

作者： Maolin Deng Weiqiu Zhu department of mechanics,{2. Key Laboratory of fluid power transmission and control,zhejiang university,hangzhou 31002.,china department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

Abstract A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems （multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations） is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The final dynamical programming equations for these control problems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynamical programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illustrate the application and effectiveness of the proposed control strategy.

关键词： Nonlinear stochastic system First-passage time Reliability Stochastic control Dynamical programming

Compensation for time-delayed feedback bang-bang control of quasi-integrable Hamiltonian systems

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Science china(Technological Sciences) 2009年第3期52卷 688-697页

作者： LIU ZhongHua1 & ZHU WeiQiu2.1 department of Civil Engineering, Xiamen university, Xiamen 361005, {2. 2.department of mechanics, state Key Laboratory of fluid power transmission and control, zhejiang university, hangzhou 31002., {2. department of Civil Engineering Xiamen University Xiamen 361005 China department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT), are proposed. The conditions applicable to each compensation method are discussed. Finally, an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation methods in combination.

关键词： time-delayed feedback control compensation method bang-bang control quasi-integrable Hamiltonian system

First passage failure of dynamical power systems under random perturbations

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Science china(Technological Sciences) 2010年第9期53卷 2495-2500页

作者： CHEN LinCong1 & ZHU WeiQiu2.1 College of Civil Engineering,Huaqiao university,Xiamen 36102.,china {2.,state Key Laboratory of fluid power transmission and control,zhejiang university,hangzhou 31002.,china 1. College of Civil Engineering Huaqiao University Xiamen 361021 China2. Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The first-passage problem of dynamical power system of a single-machine-infinite-bus (SMIB) system under random perturbations is ***,the stochastic averaging method for quasi non-integrable generalized Hamiltonian systems is applied to reduce the equations of the SMIB system under random perturbations to a set of averaged It ***,the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are established and solved numerically,***,the proposed method is verified by using the Monte Carlo simulation of the original system.

关键词： dynamical power system random perturbation stochastic averaging first passage failure

STABILITY IN THE CIRCULAR PIPE FLOW OF FIBER SUSPENSIONS

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Journal of Hydrodynamics 2003年第2期15卷 12-18页

作者： You Zhen jiang, Lin Jian zhong department of mechanics, {2. Key Laboratory of fluid power transmission and control, zhejiang university, hangzhou 31002., china departmentofmechanics StateKeyLaboratoryofFluidPowerTransmissionandControlZhejiangUniversityHangzhou310027China

A linear stability analysis on the circular pipe flow of fiber suspensions ispresented. The fiber orientation tensors are used to describe the characteristics of theorientation dislribution of fibers. The constitutive equation for the fiber suspensions is set upand the modified Orr-Sommerfeld stability equation is derived. An improved finite difference methodwith high order accuracy is employed to solve the e-quation. The Newtonian pipe Poiseuille flowcorresponding to H = 0 is also analyzed for comparison. The results reveal that the fiber additiveswill enhance the flow stability, the degree of enhancement becomes high with the increases of theparameter H which accounts for the fiber resistance to the stretching along its axis. Fibersuspensions with large H can suppress the influence of high Reynolds number on the flow ***, fibers give a higher attenuation of the short waves of disturbance.

关键词： flow stability circular pipe flow fiber suspensions numerical simulation

Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

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Science china(Physics,mechanics & Astronomy) 2010年第1期53卷 147-154页

作者： FENG Ju, ZHU WeiQiu & YING ZuGuang department of mechanics, {2. Key Laboratory of fluid power transmission and control, zhejiang university, hangzhou 31002., china 1. department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.

关键词： quasi-integrable Hamiltonian system partial observation stochastic optimal control

Theoretical model of particle orientation distribution function in a cylindrical particle suspension subject to turbulent shear flow

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Progress in Natural Science:Materials International 2006年第1期16卷 16-20页

作者： ZHANG Lingxin1, LIN Jianzhong1and ZHANG Weifeng 2.1.department of mechanics, {2. Key Laboratory of fluid power transmission and control, zhejiang university, hangzhou 31002., china 2. Institute of Marine and Coastal Sciences, Rutgers university, New Brunswick, New Jersey, USA) [a]department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou China [b]Institute of Marine and Coastal Sciences Rutgers University' New Brunswick New Jersey USA

The equation for the orientation probability function of slender cylindrical particles suspended in planar turbulent flows was investigated. After ensemble averaging, the equations for the mean and fluctuating probability function were derived. The equation for the fluctuating probability function appearing in the equation of mean probability function was solved by using the method of characteristics analysis. The orientational dispersion terms due to the random motion of cylindrical particles in the equation of mean probability function are related to the mean probability function and the Lagrangian fluid velocity correlations. The evolution of the mean probability function was described by a modified oriental ion-space-convection equation, where the dispersion terms account for the randomizing effect of the turbulence.

关键词： dispersion cylindrical particle suspensions turbulent flow probability function.

NUMERICAL SIMULATION ON VELOCITIES OF TWO INTERACTING FIBERS IN FIBER SUSPENSION

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Journal of Hydrodynamics 2003年第3期15卷 10-16页

作者： Lin Jian-zhong, Bao Fu-bing, Zhang Zhi-chao department of mechanics, {2. Key Laboratory of fluid power transmission and control, zhejiang university, hangzhou 31002., china, department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

A mathematical model was put forward to describe the mechanical interactionsof two contacting fibers, then a numerical simulation was carried out. The results of the simulationaccord with experimental results well. It turns out that the initial contacting point and theinitial orientation of the settling fiber have much effect on the translational and rotationalvelocities of the settling fiber, along with the increase in the length or the decrease in theradius of the fiber, the translational and rotational velocities of the settling fiber decrease; thesame trend remains when the viscosity of the solvent increases or the density of the fiberdecreases.

关键词： fiber suspension mechanical interaction numerical simulation

A　NEW　METHOD　FOR　SOLVING　TURBULENT　VELOCITY　CORRELATION　FUNCTIONS　AND　ITS　APPLICATION　TO　THE　CHANNEL　FLOW

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Journal of Hydrodynamics 1996年第4期8卷 69-77页

作者： Lin Jian-zhong Wang Yu-zhi(department of mechanics, the {2. Key Laboratory of fluid power transmission and control, zhejiang university hangzhou 31002., P. R. china) zhejiang Univ Hangzhou China

A new kind of method, the method of successive substitution, for solving velocity correlation functions is presented. As application of this method, the first order approximation solution in the turbulent channel flow is given numerically and then put into the equations of turbulent fluctuation which are solved numerically within the range of micro-scale by means of spectrum method and finite-difference method. By averaging fluctuating velocity, the second order approximation solutions of double fluctuating velocity correlation and other higher order correlations are obtained by computation. Putting the second approximation solution into equations of turbulent fluctuation, the solutions of different order correlations are given. These results are in good agreement with experimental results [1, 2. 3].

关键词： turbulence correlation functions computation method