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Galerkin approximationwith Legendre polynomials for a continuous-time nonlinear optimal control problem Article

Xue-song CHEN

Frontiers of Information Technology & Electronic Engineering 2017, Volume 18, Issue 10,   Pages 1479-1487 doi: 10.1631/FITEE.1601101

Abstract: The approach derived from the Galerkin approximation is used to solve the generalized Hamilton-Jacobi-Bellman

Keywords： Generalized Hamilton-Jacobi-Bellman equation     Nonlinear optimal control     Galerkin approximation     Legendre    

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Indirect adaptive fuzzy-regulated optimal control for unknown continuous-time nonlinear systems

Haiyun Zhang, Deyuan Meng, Jin Wang, Guodong Lu,gray_sun@zju.edu.cn,tinydreams@126.com,dwjcom@zju.edu.cn,lugd@zju.edu.cn

Frontiers of Information Technology & Electronic Engineering 2021, Volume 22, Issue 2,   Pages 141-286 doi: 10.1631/FITEE.1900610

Abstract: Initially, the Hamilton-Jacobi-Bellman (HJB) equation associated with its performance function is derivedweighting matrix of the performance function for the purpose of approximating and balancing the HJB equationadaptive optimal feedback controller is developed as the actor with a new form of augmented Riccati equation

Keywords： Indirect adaptive optimal control     Hamilton-Jacobi-Bellman equation     Fuzzy-regulated critic     Adaptive    

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Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

Frontiers of Mechanical Engineering 2006, Volume 1, Issue 2,   Pages 131-145 doi: 10.1007/s11465-006-0018-y

Abstract: one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobipartial differential equation.By making a connection between the velocity field in the Hamilton-Jacobi partial differential equationtransform the optimization problem into that of finding a steady-state solution of the partial differential equation

Keywords： splitting     minimum     dimensional optimization     Hamilton-Jacobi     topological    

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Comparison of the performance of traditional advection-dispersion equation and mobile-immobile model

Haizhu HU,Xiaomin MAO

Frontiers of Agricultural Science and Engineering 2016, Volume 3, Issue 3,   Pages 241-248 doi: 10.15302/J-FASE-2016108

Abstract: The traditional advection-dispersion equation (ADE) and the mobile-immobile model (MIM) are widely used

Keywords： solute transport     advection dispersion equation (ADE)     mobile-immobile model (MIM)     conservative solute    

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Optimal design of extractive dividing-wall column using an efficient equation-oriented approach

Yingjie Ma, Nan Zhang, Jie Li, Cuiwen Cao

Frontiers of Chemical Science and Engineering 2021, Volume 15, Issue 1,   Pages 72-89 doi: 10.1007/s11705-020-1977-y

Abstract: The extractive dividing-wall column (EDWC) is one of the most efficient technologies for separation of azeotropic or close boiling-point mixtures, but its design is fairly challenging. In this paper we extend the hybrid feasible path optimisation algorithm (Ma Y, McLaughlan M, Zhang N, Li J. Computers & Chemical Engineering, 2020, 143: 107058) for such optimal design. The tolerances-relaxation integration method is refined to allow for long enough integration time that can ensure the solution of the pseudo-transient continuation simulation close to the steady state before the required tolerance is used. To ensure the gradient and Jacobian information available for optimisation, we allow a relaxed tolerance for the simulation in the sensitivity analysis mode when the simulation diverges under small tolerance. In addition, valid lower bounds on purity of the recycled entrainer and the vapour flow rate in column sections are imposed to improve computational efficiency. The computational results demonstrate that the extended hybrid algorithm can achieve better design of the EDWC compared to those in literature. The energy consumption can be reduced by more than 20% compared with existing literature report. In addition, the optimal design of the heat pump assisted EDWC is achieved using the improved hybrid algorithm for the first time.

Keywords： design     extractive dividing-wall column     equation-oriented optimisation     pseudo-transient continuation model    

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Calculation and research on deepwater drilling riser flexural equation and natural frequency

Jiang Wei

Strategic Study of CAE 2011, Volume 13, Issue 5,   Pages 66-73

Abstract:

Flexural equation was established in this paper, which was based on applicationFree-hinged beam was taken as constraint condition of flexural equation combined with drilling string

Keywords： deepwater drilling     drilling riser     flexural equation     natural frequency     shape function    

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Parametric analysis and design equation of ultimate capacity for unstiffened overlapped CHS K-joints

CHEN Yu, ZHAO Xianzhong, CHEN Yiyi

Frontiers of Structural and Civil Engineering 2008, Volume 2, Issue 2,   Pages 107-115 doi: 10.1007/s11709-008-0014-x

Abstract: Finally, based on the design equation of gap joints, a formula predicting the ultimate capacity of overlappedResults from the proposed design equation are consistent with experimental results.

Keywords： regression analysis     consistent     unstiffened     plasticity     overlapped    

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Research of the Damage Evolution Equation and Spallation Criterion

Cao Jiedong,Li Yongchi

Strategic Study of CAE 2006, Volume 8, Issue 1,   Pages 40-45

Abstract:

In this paper, a new kind of damage evolution equation is presented by the method of phenomenologicalthe computational results and the experimental ones, the material parameters in the damage evolution equationbetween the computational results and the experimental ones show that the new form of damage evolution equation

Keywords： damage evolution equation     spallation criterion     numerical simulation    

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Modal disturbance investigation of rod-shaped ultrasonic motor using bending vibrations

ZHANG Jiantao, ZHU Hua, ZHAO Chunsheng

Frontiers of Mechanical Engineering 2008, Volume 3, Issue 3,   Pages 343-347 doi: 10.1007/s11465-008-0058-6

Abstract: a dynamic analysis model of a stator is created on the basis of the finite element method (FEM) and Hamilton

Keywords： Hamilton principle     disturbance     separation     frequency separation     dynamic analysis    

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Numerical Study on the Parabolic Mild-slope Equation

Shen Yongming,Zheng Yonghong,Wu Xiuguang

Strategic Study of CAE 2004, Volume 6, Issue 3,   Pages 30-35

Abstract:

Two kinds of parabolic mild-slope equations are studied systematically. By numerical modeling wave transformation over four typical topographies, the accuracy of numerical schemes, the effect of grid number on the solution accuracy, the sensitiveness of the models to the incident wave angle and the effect of weakly nonlinear terms on the numerical results are discussed in detail. These results can give some theoretical guidance to the applications of parabolic mild slope equations to wave propagation over complex topography in large coastal areas.

Keywords： parabolic mild-slope equation     numerical study     wave    

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The experimental study on the equation of state for polyester

Lin Peng,Wang Changli,Li Yan,Liu Wenxiang,Wang Dengwang

Strategic Study of CAE 2009, Volume 11, Issue 4,   Pages 63-66

Abstract: The polynomial equation of state is obtained by regression of the experimental data and the Grüneisen

Keywords： polyester     equation of state     Hugoniot     the shock wave    

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Simulation of Wave Propagation Over a Submerged Bar Using a Modified Boussinesq Equation

Zheng Yonghong,Shen Yongming,Wu Xiuguang,You Yage

Strategic Study of CAE 2004, Volume 6, Issue 4,   Pages 34-40

Abstract:

A modified Boussinesq equation is numerically studied.Comparison of numerical results with experimental data shows that the modified Boussinesq equation itselfThese results can give some theoretical guidance to the applications of Boussinesq equation to wave propagation

Keywords： modified Boussinesq equation     numerical simulation     wave propagation     submerged bar    

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A New Explicit Equation for Calculating the Friction Factor for the Turbulent Flow in Pipes

Wang Yong,Yuan Qi

Strategic Study of CAE 2006, Volume 8, Issue 6,   Pages 83-88

Abstract: Calculating friction factor by implicit Colebrook equation have to use iterative algorithm, which isFitting the data calculated by Colebrook equation with the above method, a new explicit equation forThe new equation can reproduce the Colebrook equation with average deviation of 0.5% and the maximumThe new equation has the advantages such as simple form, high precise, wide range of application, andcan be simplified to the equation for calculating the friction factor in the range of smooth pipe and

Keywords： turbulent flow     friction factor     implicit Colebrook equation     genetic algorithms     intelligent fitting method     explicit equation    

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Application of Zero Equation Turbulence Model for Numerical Simulation of Air Distribution in Train Compartment

Yang Peizhi,Gu Xiaosong

Strategic Study of CAE 2006, Volume 8, Issue 1,   Pages 26-29

Abstract: numerical simulation of air distribution in train compartment using k - ε turbulence model, so zero equationIn this paper, zero equation turbulence model and k - ε turbulence model were applied for numericalcomparison, the results come from these two. methods are inosculated very well, and the time cost by zero equationSo zero equation turbulence model has the merit of simpleness and quickness, it will provide a simple

Keywords： air-conditioning     zero equation turbulence model     numerical simulation     train    

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Iteration framework for solving mixed lubrication computation problems

Frontiers of Mechanical Engineering 2021, Volume 16, Issue 3,   Pages 635-648 doi: 10.1007/s11465-021-0632-8

Abstract: The general discrete scheme of time-varying Reynolds equation loses the information of the previous stepA discretization formula of the Reynolds equation, which is based on the Crank–Nicolson method, is proposedframework is developed to investigate the relative error of the most important term in the Reynolds equation

Keywords： mixed lubrication     discretization formula     relative error     Reynolds equation     asperity    

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Title Author Date Type Operation

Galerkin approximationwith Legendre polynomials for a continuous-time nonlinear optimal control problem

Xue-song CHEN

Journal Article

Indirect adaptive fuzzy-regulated optimal control for unknown continuous-time nonlinear systems

Haiyun Zhang, Deyuan Meng, Jin Wang, Guodong Lu,gray_sun@zju.edu.cn,tinydreams@126.com,dwjcom@zju.edu.cn,lugd@zju.edu.cn

Journal Article

Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

Journal Article

Comparison of the performance of traditional advection-dispersion equation and mobile-immobile model

Haizhu HU,Xiaomin MAO

Journal Article

Optimal design of extractive dividing-wall column using an efficient equation-oriented approach

Yingjie Ma, Nan Zhang, Jie Li, Cuiwen Cao

Journal Article

Calculation and research on deepwater drilling riser flexural equation and natural frequency

Jiang Wei

Journal Article

Parametric analysis and design equation of ultimate capacity for unstiffened overlapped CHS K-joints

CHEN Yu, ZHAO Xianzhong, CHEN Yiyi

Journal Article

Research of the Damage Evolution Equation and Spallation Criterion

Cao Jiedong,Li Yongchi

Journal Article

Modal disturbance investigation of rod-shaped ultrasonic motor using bending vibrations

ZHANG Jiantao, ZHU Hua, ZHAO Chunsheng

Journal Article

Numerical Study on the Parabolic Mild-slope Equation

Shen Yongming,Zheng Yonghong,Wu Xiuguang

Journal Article

The experimental study on the equation of state for polyester

Lin Peng,Wang Changli,Li Yan,Liu Wenxiang,Wang Dengwang

Journal Article

Simulation of Wave Propagation Over a Submerged Bar Using a Modified Boussinesq Equation

Zheng Yonghong,Shen Yongming,Wu Xiuguang,You Yage

Journal Article

A New Explicit Equation for Calculating the Friction Factor for the Turbulent Flow in Pipes

Wang Yong,Yuan Qi

Journal Article

Application of Zero Equation Turbulence Model for Numerical Simulation of Air Distribution in Train Compartment

Yang Peizhi,Gu Xiaosong

Journal Article

Iteration framework for solving mixed lubrication computation problems

Journal Article