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Annals of Differential Equations 2001年第2期17卷 159-161页

作者：刘朝杰孙瑞德 ***

This paper gives a theorem about the uniqueness of the solutions of Lienard system to the initial value problem.

关键词： uniqueness solution Lienard system initial value

The Relationship between Nonconservative Schemes and initial values of Nonlinear Evolution Equations

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Advances in Atmospheric Sciences 2004年第2期21卷 277-282页

作者：林万涛 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029

For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensional shallow water wave equation as an example, the necessary conditions of computational stability are given. Based on numerical tests, the relationship between the nonlinear computational stability and the construction of difference schemes, as well as the form of initial values, is further discussed. It is proved through both theoretical analysis and numerical tests that if the construction of difference schemes is definite, the computational stability of nonconservative schemes is decided by the form of initial values.

关键词： nonlinear evolution equation nonconservative scheme initial value

THE SENSITIVITY INFLUENCE OF NUMERICAL MODEL initial valueS ON FOUR-DIMENSIONAL ASSIMILATION—STUDY BASED ON LORENZ SYSTEM

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Acta meteorologica Sinica 1995年第3期9卷 278-287页

作者：郜吉东邱崇践丑纪范 Department of Atmospheric Sciences Lanzhou UniversityLanzhou 730000

Numerical experiments of adjoint variational assimilation have been performed using the known Lorenz *** the increase of sensitivity of model's initial values,it is more and more difficult to use the adjoint method to get the initial values which are consistent with the dynamics of the fore- cast *** some circumstances the algorithm completely *** shows that four-dimen- sional assimilation is related to the limit of *** the other *** the increase of model equation's error,the result of variational assimilation may become worse and worse so that the prediction has no *** if the model parameters are corrected when variational assimilation is made,the forecast results can be greatly improved based on Lorenz model.

关键词： adjoint variational assimilation Lorenz system initial value numerical model

Algorithm for Calculating Torque Base in Vehicle Traction Control System

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Chinese Journal of Mechanical Engineering 2012年第6期25卷 1130-1137页

作者： LI Hongzhi LI Liang SONG Jian WU Kaihui QIAO Yanjuan LIU Xingchun XIA Yongguang State Key Laboratory of Automotive Safety and Energy Tsinghua University Beijing 100084 China Chang'an Automotive Engineering General Research Institute Chongqing 400023 China

Existing research on the traction control system（TCS） mainly focuses on control methods, such as the PID control, fuzzy logic control, etc, aiming at achieving an ideal slip rate of the drive wheel over long control periods. The initial output of the TCS （referred to as the torque base in this paper）, which has a great impact on the driving performance of the vehicle in early cycles, remains to be investigated. In order to improve the control performance of the TCS in the first several cycles, an algorithm is proposed to determine the torque base. First, torque bases are calculated by two different methods, one based on states judgment and the other based on the vehicle dynamics. The confidence level of the torque base calculated based on the vehicle dynamics is also obtained. The final torque base is then determined based on the two torque bases and the confidence level. Hardware-in-the-loop（HIL） simulation and vehicle tests emulating sudden start on low friction roads have been conducted to verify the proposed algorithm. The control performance of a PID-controlled TCS with and without the proposed torque base algorithm is compared, showing that the proposed algorithm improves the performance of the TCS over the first several cycles and enhances about 5% vehicle speed by contrast. The proposed research provides a more proper initial value for TCS control, and improves the performance of the first several control cycles of the TCS.

关键词： traction control system torque base torque control initial value

Improving convergence of incremental harmonic balance method using homotopy analysis method

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Acta Mechanica Sinica 2009年第5期25卷 707-712页

作者： Yanmao Chen Jike Liu State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University 800 Dongchuan Road 200240 Shanghai China Department of Mechanics Sun Yat-sen University 510275 Guangzhou China

We have deduced incremental harmonic balance an iteration scheme in the （IHB） method using the harmonic balance plus the Newton-Raphson method. Since the convergence of the iteration is dependent upon the initial values in the iteration, the convergent region is greatly restricted for some cases. In this contribution, in order to enlarge the convergent region of the IHB method, we constructed the zeroth-order deformation equation using the homotopy analysis method, in which the IHB method is employed to solve the deformation equation with an embedding parameter as the active increment. Taking the Duffing and the van der Pol equations as examples, we obtained the highly accurate solutions. Importantly, the presented approach renders a convenient way to control and adjust the convergence.

关键词： Incremental harmonic balance method Homotopy analysis method initial value Convergence

Sensitivity studies of a high accuracy surface modeling method

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Science China Earth Sciences 2014年第10期57卷 2386-2396页

作者： ZHAO Na YUE TianXiang ZHAO MingWei DU ZhengPing FAN ZeMeng CHEN ChuanFa State Key Laboratory of Resources and Environmental Information System Institute of Geographic Sciences and Natural Resources Research Chinese Academy of Sciences Geomatics College Shandong University of Science and Technology

The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling(HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely ***, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951–2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of ***. It is found that sampling information plays an important role in the simulation accuracy of ***. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.

关键词： HASM spatial interpolation initial value sensitivity accuracy temperature

High Accuracy On-line Measurement Method of Motion Error on Machine Tools Straight-going Parts

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Journal of Donghua University(English Edition) 2003年第1期20卷 109-114页

作者：苏恒洪迈生魏元雷李自军 School of Mechanical Engineering Shanghai Jiaotong University Shanghai 200030

Harmonic suppression, non-periodic and non-closing in straightness profile error that will bring about harmonic component distortion in measurement result are analyzed. The countermeasure-a novel accurate two-probe method in time domain is put forward to measure straight-going component motion error in machine tools based on the frequency domain 3-point method after symmetrical continuation of probes' primitive signal. Both straight-going component motion error in machine tools and the profile error in workpiece that is manufactured on this machine can be measured at the same time. The information is available to diagnose the fault origin of machine tools. The analysis result is proved to be correct by the experiment.

关键词： Tendency profile Symmetry continuation initial value Motion error Error separation technology.

A Comparative Study of Conservative and Nonconservative Schemes

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Advances in Atmospheric Sciences 2003年第5期20卷 810-814页

作者：林万涛王春华陈兴蜀 LASG Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing100029 Agricultural College Xinjiang Agricultural UniversityUrumqi830052 School of Computer Science and Engineering Sichuan UniversityChengdu610064

For the conservative and non-conservative schemes of nonlinear evolution equations, by taking the two-dimensional shallow water wave equations as an example, a comparative analysis on computational stability is carried out. The relationship between the nonlinear computational stability, the structure of the difference schemes, and the form of initial values is also discussed.

关键词： conservative scheme nonconservative scheme computational stability initial value

Extended digital image correlation method for micro-region deformation measurement

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Science China(Technological Sciences) 2011年第6期54卷 1355-1361页

作者： CHEN JinLong ZHANG XiaoChuan ZHAN Nan Department of Mechanics Tianjin University Tianjin 300072 China Tianjin Key Laboratory of Modern Engineering Mechanics Tianjin 300072 China

Extended digital image correlation(X-DIC) method is one novel test method in experimental *** this paper,the principle of the X-DIC method was introduced in detail.A selection scheme of the initial value of Newton iteration method was proposed when Newton iteration method was applied to solve the partial differential *** scheme could make the X-DIC method suitable for the large deformation measurement and avoid the non-convergence phenomenon *** performance of the X-DIC method was verified by simulated *** the pixel point with the maximum absolute error occurred mainly at the corner or on the interface of the region of interest(ROI,region used for correlation calculation),measured deformation of the core area(area surrounding the center point of the ROI with a smaller size) was taken as the reliable measured *** measurement accuracy of the X-DIC method could be improved greatly by using the core *** with a long-distance microscope,the X-DIC method could be used in the deformation measurement of the *** deformation experiment was done to test the precision of the measurement ***,the X-DIC method was applied to measure the micro-region deformation of the specimen with a *** value was proved to be in accordance with the actual deformation,showing that the X-DIC method is suitable for the research of microscale mechanical behavior of materials.

关键词： extended digital image correlation(X-DIC) initial value core area micro-region deformation

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一类多维BBM型方程组初值问题的整体强解

郑州大学学报(理学版) 1988年第2期 18-23页

作者：邢家省

一、引言在一系列实际问题的研究中经常出现主部含u1-uxxt项的偏微分方程。例如研究小振幅水波时出现的方程 ut+ux+uux-βuxx=αuxxt以及非线性色散系统中的长波方程 ut+ψ(u)x=uxxt等。在文献[2]中研究了如下一类BBM型方程的初值问题 u... 详细信息

一、引言在一系列实际问题的研究中经常出现主部含u1-uxxt项的偏微分方程。例如研究小振幅水波时出现的方程 ut+ux+uux-βuxx=αuxxt以及非线性色散系统中的长波方程 ut+ψ(u)x=uxxt等。在文献[2]中研究了如下一类BBM型方程的初值问题 ut+f(u)x+u-uxx-uxxt=0,(x,t)∈R×(0,T], u(x,0)=u0(X),X∈R.的弱解。文献[3]中研究了如下一类多维GBBM型方程组的初边值问题

关键词： multidimensional BBM system initial value Galerkin method.