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fitting methods for relaxation modulus of viscoelastic materials

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Journal of Central South University of Technology 2007年第2期14卷 248-250页

作者：段吉安杨成林帅词俊 School of Mechanical and Electrical Engineering Central South University

Based on viscoelastic theory, two new computational methods of solving linear equations and minimum value of the l-norm were put forward for transforming Kohlransch-William-Watts （KWW） function of viscoelastic materials to the generalized Maxwell model. The computational methods for the Maxwell model fitting were achieved in MATLAB software. It is found that fitting precision of the two methods is very high. The method of solving linear equations needs more fitting points and more numbers of Maxwell units. It makes the program of finite element analysis complex. While the method of solving minimum value of 1-norm can obtain very high precision only using less fitting points. These methods can fit not only experimental curve of KWW function, but also the experimental data directly.

关键词： viscoelastic material relaxation modulus Maxwell model fitting

A general, fast and robust B-spline fitting scheme for micro-line tool path under chord error constraint

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Science China(Technological Sciences) 2019年第2期62卷 321-332页

作者： BI QingZhen HUANG Jie LU YaoAn ZHU LiMin DING Han State Key Laboratory of Mechanical System and Vibration School of Mechanical Engineering Shanghai Jiao Tong University School of Electromechanical Engineering Guangdong University of Technology

The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local transition method or the global fitting method. For micro-line tool path, the transition method will significantly decrease the machining efficiency and introduce feedrate fluctuation. The global fitting method cannot be directly used in the NC interpolation because the indispensable chord error checking and iterative fitting processes are computation-intensive. This paper presents a general, fast and robust B-spline fitting scheme under chord error constraint for high speed interpolation of micro-line tool path. The proposed fitting method guarantees the chord error by utilizing the strong convex hull property of B-spline curves. The knot vector and control points are initially generated by a progressive iterative approximation method and locally refined to conform to the chord error constraint by using an analytical method. The analytical approximation and refining methods avoid solving a linear system of equations that is necessary in the standard B-spline fitting method. The feasibility and efficiency of the proposed scheme has been verified via simulations and experiments. Compared with the traditional fitting method, the proposed scheme can strictly constrain the chord error and can significantly decrease the computational load. Compared with the transition scheme, the proposed scheme can significantly increase the machining efficiency for the same micro-line tool path under the same chord error tolerance.

关键词： NC interpolation high speed machining micro-line segments path smoothing B-spline fitting

The Convergence of Least-Squares Progressive Iterative Approximation for Singular Least-Squares fitting System

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Journal of Systems Science & Complexity 2018年第6期31卷 1618-1632页

作者： LIN Hongwei CAO Qi ZHANG Xiaoting School of Mathematical Science State Key Laboratory of CAD&CG Zhejiang University

Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more least-squares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the least- squares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.

关键词： Data fitting geometric modeling LSPIA singular least-squares fitting system.

A new method for fitting the complicated water level process of the lower Yellow River

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Science China(Technological Sciences) 2009年第10期52卷 2997-3003页

作者： YongSheng Yuan JiChun Wu YiJun Zuo JieRen Chen College of Sciences Hohai University Nanjing 210098 China Department of Earth Sciences Nanjing University Nanjing 210093 China Department of Statistics and Probability Michigan State University East Lansing MI 48824 USA College of Water Conservancy and Hydropower Engineering Hohai University Nanjing 210098 China

With the view of effectively fitting the complicated water level process of the lower Yellow River, polynomial regression, stepwise regression, parameters by ridge estimate and so on, are logically integrated. And the progressive transformation is introduced. Then a new method is put forward. The core difference of this new method from the same kind of methods lies in that in this method the strong coupling effect of weak influencing factors which is common in a complicated water level process is considered, that many effective methods are synthetically used to reduce the fitting model error, and that the necessary progressive transformation is introduced. The advantages of many theories and methods are logically integrated in this method, and the method can be easily used. The rationality and necessity of each step in this method are ensured by sufficient theories, so this method can be widely used to effectively simulate the inherent relations in the same kind of complicated data. Furthermore, many complicated water level processes of the lower Yellow River are fitted by this method, and all the fitting precisions are markedly higher than the precision by the other existing methods. Every component term in the fitting model has clear physical meaning.

关键词： complicated water level process high sediment content nonlinearity stepwise transforming-filtrating fitting method heavy sediment-laden river

fitting method of pseudo-polynomial for solving nonlinear parametric adjustment

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中国有色金属学会会刊：英文版 2001年第2期11卷 311-314页

作者：陶华学宫秀军郭金运 Shandong Univ Sci & Technol Inst Geosci & Technol Taian 271019 Peoples R China

The optimal condition and its geometrical characters of the least square adjustment were proposed. Then the relation between the transformed surface and least squares was discussed. Based on the above, a non iterative method, called the fitting method of pseudo polynomial, was derived in detail. The final least squares solution can be determined with sufficient accuracy in a single step and is not attained by moving the initial point in the view of iteration. The accuracy of the solution relys wholly on the frequency of Taylor’s series. The example verifies the correctness and validness of the method. [

关键词： nonlinear parametric adjustment fitting method of pseudo-polynomial transformed surface

Transmitting electric power system dynamics in SCADA using polynomial fitting

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Science China(Technological Sciences) 2009年第4期52卷 937-943页

作者： DUAN XianZhong SU Sheng MEI Nian College of Electrical and Electronic Engineering Huazhong University of Science and TechnologyWuhan 430074China

The paper proposes an approach to transmit electric power system dynamics in the SCADA. With the prevalent application of digital substation automation system, it is feasible for the remote terminal units (RTUs) to collect phasors within a substation. However, limited communication capacity remains the bottleneck that prevents SCADA from transmitting system dynamics. This paper proposes to compress dynamics data with curve fitting in the RTUs and reconstruct the dynamics in the SCADA server for reducing communication demand. Dispatchers in the control center can thus get system dynamics with a delay of several seconds. Simulation result shows that for a power system under disturbance with short-circuit that once occurred and was cleared, the SCADA can approximate the original dynamics with satisfying precision using limited degree polynomial fitting. The approach is highly scalable and adaptable, and can be implemented on existing communication infrastructure with a few software modifications. The approach has extensive application potential.

关键词： SCADA WAMS (wide area measurement system) polynomial fitting system dynamics

Iterative circle fitting based on circular attracting factor

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Journal of Central South University 2013年第10期20卷 2663-2675页

作者：王恒升张强王福亮 College of Mechanical and Electrical Engineering Central South University State Key Laboratory for High Performance Complex Manufacturing (Central South University)

An intuitive method for circle fitting is proposed. Assuming an approximate circle(CA,n) for the fitting of some scattered points, it can be imagined that every point would apply a force to CA,n, which all together form an overall effect that "draws" CA,n towards best fitting to the group of points. The basic element of the force is called circular attracting factor(CAF) which is defined as a real scalar in a radial direction of CA,n. An iterative algorithm based on this idea is proposed, and the convergence and accuracy are analyzed. The algorithm converges uniformly which is proved by the analysis of Lyapunov function, and the accuracy of the algorithm is in accord with that of geometric least squares of circle fitting. The algorithm is adopted to circle detection in grayscale images, in which the transferring to binary images is not required, and thus the algorithm is less sensitive to lightening and background noise. The main point for the adaption is the calculation of CAF which is extended in radial directions of CA,n for the whole image. All pixels would apply forces to CA,n, and the overall effect of forces would be equivalent to a force from the centroid of pixels to CA,n. The forces from would-be edge pixels would overweigh that from noisy pixels, so the following approximate circle would be of better fitting. To reduce the amount of calculation, pixels are only used in an annular area including the boundary of CA,n just in between for the calculation of CAF. Examples are given, showing the process of circle fitting of scattered points around a circle from an initial assuming circle, comparing the fitting results for scattered points from some related literature, applying the method proposed for circular edge detection in grayscale images with noise, and/or with only partial arc of a circle, and for circle detection in BGA inspection.

关键词： circle detection circle fitting grayscale image iterative algorithm least squares fitting(LSF) circular attracting factor(CAF) BGA inspection

ANNUAL VARIATIONS OF TEMPERATURE ON FOUR URBAN UNDERLYING SURFACES AND fitting ANALYSIS

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Journal of Tropical Meteorology 2013年第2期19卷 138-144页

作者：刘霞王春林景元书麦博儒 Haikou Meteorology Bureau Climate Center of Guangdong Province College of Applied Meteorology Nanjing University of Information Scienceand Technology Guangzhou Institute of Tropical and Marine Meteorology China Meteorological Administration

Based on the observed 2-year temperature data for four kinds of typical urban underlying surfaces,including asphalt, cement, bare land and grass land, the annual variations and influencing factors of landsurface temperature are analyzed. Then fitting equations for surface temperature are established. It is shownthat the annual variation of daily average, maximum and minimum temperature and daily temperature rangeon the four urban underlying surfaces is consistent with the change in air temperature. The difference oftemperature on different underlying surfaces in the summer half year (May to October) is much moreevident than that in the winter half year (December to the following April). The daily average and maximumtemperatures of asphalt, cement, bare land and grass land are higher than air temperature due to theatmospheric heating in the daytime, with that of asphalt being the highest, followed in turn by cement, bareland and grass land. Moreover, the daily average, maximum and minimum temperature on the four urbanunderlying surfaces are strongly impacted by total cloud amount, daily average relative humidity andsunshine hours. The land surface can be cooled (warmed) by increased total cloud amount (relativehumidity). The changes in temperature on bare land and grass land are influenced by both the total cloudamount and the daily average relative humidity. The temperature parameters of the four land surfaces aresignificantly correlated with daily average, maximum and minimum temperature, sunshine hours, dailyaverage relative humidity and total cloud amount, respectively. The analysis also indicates that the range offitting parameter of a linear regression equation between the surface temperature of the four kinds of typicalland surface and the air temperature is from 0.809 to 0.971, passing the F-test with a confidence level of 0.99.

关键词： fitting analysis urban underlying surface land surface temperature

Relative position fitting based control strategy for thruster point assembly mechanism of electric propulsion

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International Journal of Intelligent Computing and Cybernetics 2016年第1期9卷 69-82页

作者： Xiaohui Li Jie Geng Qiang Zhang Jing Sun Beijing Institute of Control Engineering BeijingChina

Purpose-Thruster point assembly mechanism(TPAM)of the electric propulsion system allows to adjust the thrust vector,sothat the thrust vectorisdirectedtothesatellitecenterof gravity(COG)during the satellite on-orbit working *** this way the impact of disturbance torque caused by deviation of the thrust vector from the satellite COG during thruster ignition can be ***,the control accuracy of satellite is influenced directly by the control accuracy of *** the other hand,the on-orbit application of TPAM is restricted to the on-orbit computer ***,the purpose of this paper is to design a control strategy for TPAM,and the strategy should not only be able to control the TPAM precisely but also be easily implemented by the on-board ***/methodology/approach-First,the structure and work principle of TPAM are discussed,and the mathematical model based on D-H coordinate system is built for *** the fitting methods are utilized to design the control strategy of *** position fitting-based control strategy and relative position fitting-based control strategy are designed,and the least squares algorithm is introduced for parameter ***-Simulations and tests are provided for the *** with the state-of-the-art PD controller,the proposed control strategy shows smaller overshoot and more simple *** experiment results are matched with the simulation results and both the experiment and simulation results show the validity of the proposed control *** implications-The designed control strategies can be used for the TPAM of some satellite’s electric propulsion ***/value-The mathematical model of the TPAM based on D-H coordinate system is *** absolute position fitting-based control strategy and relative position fitting-based control strategy are *** with existing methods,the two control strategies have more simple structure and smaller amoun

关键词： Control strategy Nonlinear control D-H coordinate system fitting Thruster point assembly mechanism TPAM Electric propulsion system