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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 fourth-order Three-Point Boundary Value Problem Sign-Changing Green’s function Fixed Point Index Iterative Technique Monotone Positive Solution EXISTENCE
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Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Alhussein Mohamed 《Applied Mathematics》 2021年第4期311-321,共11页
In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style... In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style="white-space:normal;">where </span><span style="white-space:nowrap;"><em>f</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span></span> <em>C</em>([0,1]×[0,+∞),[0,+∞)) <span style="white-space:nowrap;"><em>α</em></span> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span> </span>[0,6)</span> and <img src="Edit_35fdded4-50be-48af-b9e0-1e97c719aeba.bmp" alt="" /> . The main point to emphasize is that although the corresponding Green’s function is changing signs, by applying the fixed point theorem, we can still obtain at least two positive solutions and degreased solutions under certain suitable conditions. 展开更多
关键词 fourth-order Fourth-Point Boundary Value Problem function Positive Solution EXISTENCE Fixed Point Greens function
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Analysis of Stability and Large Deflection Buckle of Rolled Strip by Third Power B-Spline Function Method
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作者 Bian Yuhong 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 1997年第2期24-28,共5页
A new method——the third power B-spline function method is developed to analyse the stability and the buckle of rolled strip under residual stress.The large deflection theory of thin plate is used to calculate the bu... A new method——the third power B-spline function method is developed to analyse the stability and the buckle of rolled strip under residual stress.The large deflection theory of thin plate is used to calculate the buckle of rolled strip and criterion of critical buckle is given.The computed results tally with those of experiment well,which provides theoretical basis and method for developing the mathematical model of flatness control. 展开更多
关键词 flatness control large deflection buckle critical buckle third power b-spline function
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Numerical Solution of Functional Integral and Integro-Differential Equations by Using B-Splines
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作者 Hesam-Eldien Derili Gherjalar Hossein Mohammadikia 《Applied Mathematics》 2012年第12期1940-1944,共5页
This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integ... This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integral and integro-differential equations. For showing efficiency of the method we give some numerical examples. 展开更多
关键词 LAGRANGE Interpolation b-spline functions functionAL Integral EQUATION functionAL Integro-Differential EQUATION functionAL Differential EQUATION
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The Investigation and Study of Hydrogen Atom in Spherical Cavity Using B-Spline Basis Functions: A Mathematical Approach
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作者 Alireza Heidari Foad Khademi Jahromi +1 位作者 Roozbeh Amiri Mohammadali Ghorbani 《Journal of Modern Physics》 2012年第4期334-339,共6页
The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific com... The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site. 展开更多
关键词 Hydrogen ATOM Spherical Cavity b-spline Basis functionS Quantum Systems Nanoscience VARIATIONAL Method Wave functionS b-splines’ Properties
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Intensity-curvature functional based digital high pass filter of the bivariate cubic B-spline model polynomial function
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作者 Carlo Ciulla Grace Agyapong 《Visual Computing for Industry,Biomedicine,and Art》 2019年第1期75-92,共18页
This research addresses the design of intensity-curvature functional(ICF)based digital high pass filter(HPF).ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF.In ord... This research addresses the design of intensity-curvature functional(ICF)based digital high pass filter(HPF).ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF.In order to calculate ICF,the model function needs to be second order differentiable and to have non-null classic-curvature calculated at the origin(0,0)of the pixel coordinate system.The theoretical basis of this research is called intensitycurvature concept.The concept envisions to replace signal intensity with the product between signal intensity and sum of second order partial derivatives of the model function.Extrapolation of the concept in two-dimensions(2D)makes it possible to calculate the ICF of an image.Theoretical treatise is presented to demonstrate the hypothesis that ICF is HPF signal.Empirical evidence then validates the assumption and also extends the comparison between ICF-based HPF and ten different HPFs among which is traditional HPF and particle swarm optimization(PSO)based HPF.Through comparison of image space and k-space magnitude,results indicate that HPFs behave differently.Traditional HPF filtering and ICF-based filtering are superior to PSO-based filtering.Images filtered with traditional HPF are sharper than images filtered with ICF-based filter.The contribution of this research can be summarized as follows:(1)Math description of the constraints that ICF need to obey to in order to function as HPF;(2)Math of ICF-based HPF of bivariate cubic B-spline;(3)Image space comparisons between HPFs;(4)K-space magnitude comparisons between HPFs.This research provides confirmation on the math procedure to use in order to design 2D HPF from a model bivariate polynomial function. 展开更多
关键词 Intensity-curvature functional High pass filter b-spline Particle swarm optimization K-SPACE
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Curve Classification Based onMean-Variance Feature Weighting and Its Application
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作者 Zewen Zhang Sheng Zhou Chunzheng Cao 《Computers, Materials & Continua》 SCIE EI 2024年第5期2465-2480,共16页
The classification of functional data has drawn much attention in recent years.The main challenge is representing infinite-dimensional functional data by finite-dimensional features while utilizing those features to a... The classification of functional data has drawn much attention in recent years.The main challenge is representing infinite-dimensional functional data by finite-dimensional features while utilizing those features to achieve better classification accuracy.In this paper,we propose a mean-variance-based(MV)feature weighting method for classifying functional data or functional curves.In the feature extraction stage,each sample curve is approximated by B-splines to transfer features to the coefficients of the spline basis.After that,a feature weighting approach based on statistical principles is introduced by comprehensively considering the between-class differences and within-class variations of the coefficients.We also introduce a scaling parameter to adjust the gap between the weights of features.The new feature weighting approach can adaptively enhance noteworthy local features while mitigating the impact of confusing features.The algorithms for feature weighted K-nearest neighbor and support vector machine classifiers are both provided.Moreover,the new approach can be well integrated into existing functional data classifiers,such as the generalized functional linear model and functional linear discriminant analysis,resulting in a more accurate classification.The performance of the mean-variance-based classifiers is evaluated by simulation studies and real data.The results show that the newfeatureweighting approach significantly improves the classification accuracy for complex functional data. 展开更多
关键词 functional data analysis CLASSIFICATION feature weighting b-splineS
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Wavelet-Based Fractal Function Approximation 被引量:1
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作者 Zhang Hejei Tao Ran Zhou Siyong & Wang Yue(Department of Electronic Engineering, Beijing Institute of Technology, 100081, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1999年第4期60-66,共7页
In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which th... In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression. 展开更多
关键词 b-spline Wavelet scaling function Fractal function APPROXIMATION Quadratic programming.
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A B-Spline Method Used to Calculate Added Resistance in Waves
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作者 Razieh Zangeneh Mahmood Ghiasi 《Journal of Marine Science and Application》 CSCD 2017年第1期20-26,共7页
Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation o... Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green's formula. The Kochin function is applied to compute added resistance using Maruo's far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss–Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results. 展开更多
关键词 Added resistance b-spline Kochin function Maruo's far-field method Gauss–Legendre quadrature
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Functional Analysis of Chemometric Data
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作者 Ana M. Aguilera Manuel Escabias +1 位作者 Mariano J. Valderrama M. Carmen Aguilera-Morillo 《Open Journal of Statistics》 2013年第5期334-343,共10页
The objective of this paper is to present a review of different calibration and classification methods for functional data in the context of chemometric applications. In chemometric, it is usual to measure certain par... The objective of this paper is to present a review of different calibration and classification methods for functional data in the context of chemometric applications. In chemometric, it is usual to measure certain parameters in terms of a set of spectrometric curves that are observed in a finite set of points (functional data). Although the predictor variable is clearly functional, this problem is usually solved by using multivariate calibration techniques that consider it as a finite set of variables associated with the observed points (wavelengths or times). But these explicative variables are highly correlated and it is therefore more informative to reconstruct first the true functional form of the predictor curves. Although it has been published in several articles related to the implementation of functional data analysis techniques in chemometric, their power to solve real problems is not yet well known. Because of this the extension of multivariate calibration techniques (linear regression, principal component regression and partial least squares) and classification methods (linear discriminant analysis and logistic regression) to the functional domain and some relevant chemometric applications are reviewed in this paper. 展开更多
关键词 functionAL Data ANALYSIS b-splineS functionAL Principal Component Regression functionAL Partial Least SQUARES functionAL LOGIT Models functionAL Linear DISCRIMINANT ANALYSIS Spectroscopy NIR Spectra
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Function-on-Partially Linear Functional Additive Models
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作者 Jinyou Huang Shuang Chen 《Journal of Applied Mathematics and Physics》 2020年第1期1-9,共9页
We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric... We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric and the nonparametric components proposed. In the final of this paper, as a result, we got the variance decomposition of the model and establish the asymptotic convergence rate for estimator. 展开更多
关键词 functionAL Data ANALYSIS functionAL Principal COMPONENT ANALYSIS PARTIAL Linear Regression Models Penalized b-splineS Variance Model
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Septic B-Spline Solution of Fifth-Order Boundary Value Problems
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作者 Bin Lin 《Journal of Applied Mathematics and Physics》 2016年第8期1446-1454,共9页
A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization tech... A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization technique to reduce the nonlinear problems to linear problems and use B-spline collocation method, which leads to a seven nonzero bands linear system. Illustrative example is included to demonstrate the validity and applicability of the proposed techniques. 展开更多
关键词 Septic b-spline function Fifth-Order Boundary Value Problems b-spline Collocation Method Nonlinear Problems
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B-Spline Collocation Method for Solving Singularly Perturbed Boundary Value Problems
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作者 Bin Lin 《Journal of Applied Mathematics and Physics》 2016年第9期1699-1704,共6页
We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The ac... We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical results are found in good agreement with exact solutions. 展开更多
关键词 Fifth Order b-spline functions b-spline Collocation Method Singularly Perturbed Boundary Value Problems
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Numerical Solution of the Seventh Order Boundary Value Problems Using B-Spline Method
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作者 Maryam Khazaei Yeganeh Karamipour 《Journal of Applied Mathematics and Physics》 2021年第12期3058-3066,共9页
We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of ord... We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using the seventh-degree B-Spline function. Formulation is based on particular terms of order of seventh order boundary value problem. We obtain Septic B-Spline formulation and the Collocation B-spline method is formulated as an approximation solution. We apply the presented method to solve an example of seventh order boundary value problem in which the result shows that there is an agreement between approximate solutions and exact solutions. Resulting in low absolute errors shows that the presented numerical method is effective for solving high order boundary value problems. Finally, a general conclusion has been included. 展开更多
关键词 Spline and b-spline functions Seventh Order Boundary Value Problem Septic b-spline Collocation Method
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Analysis of a Gyroscope′s Rotor Nonlinear Supported Magnetic Field Based on the B-Spline Wavelet-FEM
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作者 LIU Jian-feng YUAN Gan-nan +1 位作者 HUANG Xu YU Li 《International Journal of Plant Engineering and Management》 2005年第3期152-159,共8页
A supported framework of a gyroscope's rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling f... A supported framework of a gyroscope's rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor. 展开更多
关键词 nonlinear supported magnetic field b-spline wavelet FEM GYROSCOPE interpolation basis function boundary condition
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Knot Insertion Algorithms for ECT B-spline Curves
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作者 SONG Huan-huan TANG Yue-hong LI Yu-juan 《Computer Aided Drafting,Design and Manufacturing》 2013年第2期29-35,共7页
Knot insertion algorithm is one of the most important technologies of B-spline method. By inserting a knot the local prop- erties of B-spline curve and the control flexibility of its shape can be fiu'ther improved, a... Knot insertion algorithm is one of the most important technologies of B-spline method. By inserting a knot the local prop- erties of B-spline curve and the control flexibility of its shape can be fiu'ther improved, also the segmentation of the curve can be rea- lized. ECT spline curve is drew by the multi-knots spline curve with associated matrix in ECT spline space; Muehlbach G and Tang Y and many others have deduced the existence and uniqueness of the ECT spline function and developed many of its important properties .This paper mainly focuses on the knot insertion algorithm of ECT B-spline curve.It is the widest popularization of B-spline Behm algorithm and theory. Inspired by the Behm algorithm, in the ECT spline space, structure of generalized P61ya poly- nomials and generalized de Boor Fix dual functional, expressing new control points which are inserted after the knot by linear com- bination of original control vertex the single knot, and there are two cases, one is the single knot, the other is the double knot. Then finally comes the insertion algorithm of ECT spline curve knot. By application of the knot insertion algorithm, this paper also gives out the knot insertion algorithm of four order geometric continuous piecewise polynomial B-spline and algebraic trigonometric spline B-spline, which is consistent with previous results. 展开更多
关键词 ECT b-splines knot insertion geometric continuity generalized P61ya polynomial generalized de Boor-Fix functional
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Wind farm active power dispatching algorithm based on Grey Incidence 被引量:2
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作者 Binbin Zhang Mengxin Jia +2 位作者 Chaobo Chen Kun Wang Jichao Li 《Global Energy Interconnection》 EI CAS CSCD 2023年第2期175-183,共9页
This study proposes a wind farm active power dispatching(WFAPD) algorithm based on the grey incidence method, which does not rely on an accurate mathematical model of wind turbines. Based on the wind turbine start-sto... This study proposes a wind farm active power dispatching(WFAPD) algorithm based on the grey incidence method, which does not rely on an accurate mathematical model of wind turbines. Based on the wind turbine start-stop data at different wind speeds, the weighting coefficients, which are the participation degrees of a variable speed system and a variable pitch system in power regulation, are obtained using the grey incidence method. The incidence coefficient curve is fitted by the B-spline function at a full range of wind speeds, and the power regulation capacity of all wind turbines is obtained. Finally, the WFAPD algorithm, which is based on the regulating capacity of each wind turbine, is compared with the wind speed weighting power dispatching(WSWPD) algorithm in MATLAB. The simulation results show that the active power fluctuation of the wind farm is smaller, the rotating speed of wind turbines is smoother, and the fatigue load of highspeed turbines is effectively reduced. 展开更多
关键词 Wind farm Active power dispatching Grey incidence b-spline function
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Green Function of Fourth-order Differential Operator with Eigenparameter-dependent Boundary and Transmission Conditions
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作者 Xin-yan ZHANG Jiong SUN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第2期311-326,共16页
We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the... We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given. 展开更多
关键词 fourth-order differential operator eigenparameter-dependent boundary conditions transmission conditions EIGENVALUES Green function
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基于四阶B-样条最小二乘法的油气管道凹痕缺陷应变计算方法 被引量:6
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作者 张鹏 黄超 党思宏 《中国安全生产科学技术》 CAS CSCD 北大核心 2015年第1期52-58,共7页
针对油气管道上的凹痕缺陷,ASME B31.8提出采用基于应变的评价方法,但在内检测数据到应变求解的过程中,缺少噪声消除和轮廓拟合的相关方法。提出了采用四阶B-样条最小二乘拟合算法将检测数据进行噪声消除和轮廓拟合,实现从含有噪声的检... 针对油气管道上的凹痕缺陷,ASME B31.8提出采用基于应变的评价方法,但在内检测数据到应变求解的过程中,缺少噪声消除和轮廓拟合的相关方法。提出了采用四阶B-样条最小二乘拟合算法将检测数据进行噪声消除和轮廓拟合,实现从含有噪声的检测数据到应变求解的应变评价方法。采用文中所提方法和有限元方法,详细计算了几种典型凹痕的轴向弯曲应变、环向弯曲应变及其总应变。对比结果表明,该方法不仅能够较为精确的计算出弯曲应变值,还能得到较准确的弯曲应变分布情况。环向弯曲应变受在线检测工具精度的限制存在一定误差。计算发现,现有标准中忽略了环向薄膜应变分量,这使得总应变的计算结果不够准确。 展开更多
关键词 管道凹痕 四阶B-样条函数 最小二乘法 噪声消除 应变计算
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An adaptive generation method for free curve trajectory based on NURBS
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作者 朱昊 刘京南 +1 位作者 杨安康 汪木兰 《Journal of Southeast University(English Edition)》 EI CAS 2014年第3期296-301,共6页
To realize the high precision and real-time interpolation of the NURBS (non-uniform rational B-spline) curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate,... To realize the high precision and real-time interpolation of the NURBS (non-uniform rational B-spline) curve, a kinetic model based on the modified sigmoid function is proposed. The constraints of maximum feed rate, chord error, curvature radius and interpolator cycle are discussed. This kinetic model reduces the cubic polynomial S-shape model and the trigonometry function S-shape model from 15 sections into 3 sections under the precondition of jerk, acceleration and feedrate continuity. Then an optimized Adams algorithm using the difference quotient to replace the derivative is presented to calculate the interpolator cycle parameters. The higher-order derivation in the Taylor expansion algorithm can be avoided by this algorithm. Finally, the simplified design is analyzed by reducing the times of computing the low-degree zero-value B-spline basis function and the simplified De Boor-Cox recursive algorithm is proposed. The simulation analysis indicates that by these algorithms, the feed rate is effectively controlled according to tool path. The calculated amount is decreased and the calculated speed is increased while the machining precision is ensured. The experimental results show that the target parameter can be correctly calculated and these algorithms can be applied to actual systems. 展开更多
关键词 free curve NURBS (non-uniform rational b-spline sigmoid function Adams algorithm
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