Shape Control and Modification of Rational Cubic B-Spline Curves

This paper considers the construction of a rational cubic B-spline curve that willinterpolate a sequence of data points x'+ith specified tangent directions at those points. It is emphasisedthat the constraints are purely geometrical and that the pararnetric tangent magnitudes are notassigned as in many' curl'e manipulation methods. The knot vector is fixed and the unknowns are thecontrol points and x'eightsf in this respect the technique is fundamentally different from otherswhere knot insertion is allowed.First. the theoretical result3 for the uniform rational cubic B-spline are presented. Then. in theplanar case. the effect of changes to the tangent at a single point and the acceptable bounds for thechange are established so that all the weights and tangent magnitUdes remain positive. Finally, aninteractive procedure for controlling the shape of a planar rational cubic B-spline curve is presented.

An efficient cubic trigonometric B-spline collocation scheme for the time-fractional telegraph equation

In this paper,a proficient numerical technique for the time-fractional telegraph equation(TFTE)is proposed.The chief aim of this paper is to utilize a relatively new type of B-spline called the cubic trigonometric B-spline for the proposed scheme.This technique is based on finite difference formulation for the Caputo time-fractional derivative and cubic trigonometric B-splines based technique for the derivatives in space.A stability analysis of the scheme is presented to confirm that the errors do not amplify.A convergence analysis is also presented.Computational experiments are carried out in addition to verify the theoretical analysis.Numerical results are contrasted with a few present techniques and it is concluded that the presented scheme is progressively right and more compelling.

Performance of global look-up table strategy in digital image correlation with cubic B-spline interpolation and bicubic interpolation

Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.

Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation

This work is concerned with the application of a redefined set of extended uniform cubic B-spline(RECBS)functions for the numerical treatment of time-fractional Telegraph equation.The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid.Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure.The derivation of uniform convergence has also been presented.Some computational experiments are executed to verify the theoretical considerations.Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the complicated phase behavior and various multiphase flow characteristics,gas tends to break through early in production wells in heterogeneous formations because of overriding,fingering,and channeling,which may result in unfavorable recovery performance.On the basis of phase behavior studies,minimum miscibility pressure measurements,and immiscible WAG coreflood experiments,the cubic B-spline model（CBM） was employed to describe the three-phase relative permeability curve.Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially,optimization of production performance including pressure drop,water cut,and the cumulative gas-oil ratio was performed.A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process.Based on the quantitative characterization of major recovery mechanisms,the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment.The proposed method is reliable and can meet engineering requirements.It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve.

星载共口径多波束赋形反射面天线设计

为了满足星载通信中多任务并行需求,提出了一种由格里高利型反射面和三个馈源喇叭天线组成的共口径多波束反射面天线,该天线能够产生两个固定轮廓波束和一个点波束。天线设计是采用射线追踪法确定点波束馈源位置以建立天线基础结构,并通过Zernike多项式和Cubic B-splines函数共同对主、副反射面进行赋形优化来完成。为了验证该方法的有效性,对口径为1.1 m的天线进行仿真设计,结果表明两个赋形轮廓波束在Ku收、发频段边缘增益(EOC gain)分别为27.7、28.0、28.0、28.2 dBi,固定点波束在服务区EOC gain不低于34 dBi并且在0~6.5°范围内的扫描波束增益不低于35 dBi。

A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint;the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation.Experimental results are presented to show the advantages of the proposed algorithms.

一种基于相干积累CPF和NUFFT的机动目标ISAR成像新方法

机动目标的复杂运动导致散射体回波信号多普勒频率时变,给逆合成孔径雷达(ISAR)成像方位向处理带来困难.而传统的距离-多普勒(RD)成像方法、Wigner-Ville distribution(WVD)瞬时成像方法、Radon-Wigner等成像方法由于成像效果差或运算效率低等因素,不适合复杂运动目标的ISAR实时成像.针对这些问题,本文提出了一种基于相干积累三次相位函数(CPF)的机动目标ISAR成像新方法.首先,把平动补偿后的各距离单元数据,通过CPF变换到时间-调频率平面.然后,利用各散射体自项能量平行于时间轴分布特性,提出一种基于相干积累的交叉项和虚假伪峰抑制方法,进而得到各散射体在频率-调频率平面的高分辨分布特性.最后,通过向频率轴上的投影得到该距离单元目标的方位ISAR图像,并通过引入非均匀快速傅立叶变换(NUFFT)来降低算法计算复杂度.计算机仿真处理结果验证了该方法的有效性.

修正自适应Chirplet分解法及其快速实现

为克服时频关系为线性的基函数的不足,该文提出一种新的信号分解算法——修正自适应Chirplet分解法,将Chirplet基函数推广到三次相位信号的形式,因此可以逼近信号中的非线性时变结构成分。同时提出了一种快速分解算法,该算法通过计算信号的三次相位函数,可得到其能量分布集中于信号的瞬时频率变化率曲线上的结论,此时通过谱峰检测可同时获得基函数的二、三次相位系数,时间中心以及幅度的估计:进而通过解调频技术获得其初始频率和时间宽度的估计。文中给出了实现该方法的具体步骤,并分别以仿真信号和蝙蝠回声定位信号为例验证了该算法的有效性。

AISI 316奥氏体不锈钢等离子体源渗氮及其耐磨抗蚀性能

目前,对AISI 316奥氏体不锈钢单一面心结构γΝ相改性层耐磨抗蚀性能的报道差异较大,有些甚至相互矛盾。采用等离子体源渗氮技术,于450℃,6 h改性AISI 316奥氏体不锈钢,获得了厚度约为17μm、峰值氮浓度20%(原子分数)、最大显微硬度1 510 HV0.1 N、单一面心结构的γΝ相改性层。分别采用WTM-2E球盘式磨损仪和PARSTAT2273电化学工作站,研究了干摩擦条件下γN相/Si_3N_4陶瓷球的摩擦磨损行为和在3.5%NaCl溶液中的电化学腐蚀行为,揭示了γN相改性层的耐磨抗蚀机理。结果表明:γΝ相改性层的磨损机制由原不锈钢的黏着磨损转变为氧化磨损,摩擦系数由0.88降低至0.65,磨损体积由0.13 mm^3降低到9.50×10-3mm^3,耐磨性能显著提高;γΝ相改性层阳极极化曲线未发生点蚀击穿过程,容抗弧直径增大,相位角平台变宽;采用等效电路Rs-(Rct//CPE)拟合的电荷转移电阻Rct由原不锈钢的1.006×105Ω·cm^2增至1.377×106Ω·cm^2,计算的双电层电容Cdl由88.4m F/cm^2降低至77.8 m F/cm^2,抗蚀性能明显得到了改善。

Sn/Pt纳米立方体对乙醇电催化氧化的原位FTIR光谱研究

采用循环伏安电沉积方法制备了Sn修饰的铂纳米立方体,并研究其对乙醇的电催化氧化.结合传统的电化学方法和原位电化学红外光谱技术研究了Sn的作用机理.循环伏安研究表明,Sn修饰后使其对乙醇氧化的起始电位显著负移,Sn覆盖度～0.90时乙醇氧化的起始电位为-0.1 V.原位红外光谱结果表明,修饰Sn后极大地促进了乙酸的生成,更利于乙醇的直接氧化途径,但对乙醇的C—C键断裂促进作用不大.

沥青橡胶乳液改性机理研究

根据试验与观察，从理论上研究了沥青在沥青橡胶乳液破乳成膜后，沥青橡胶薄膜的结构．成膜后由于首次交联使橡胶首先形成立体网络结构，而后沥青质又和网络上的橡胶发生二次交联，加强了网络，从而提高与改善了乳化沥青的路用性能。

A Novel Approach for Numerical Computation of Fokker-Planck Equation

This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.

可调的类三次Bézier三角插值曲线

Bézier曲线是计算机辅助几何设计中的一类重要曲线,以可调的类三次Bézier三角曲线为例,对可调的类三次Bézier三角曲线的性质进行了分析,并由此推出可调的类三次Bézier三角曲线比三次Bézier曲线更光滑.然后,构造了可调的类三次Bézier三角插值曲线.该曲线继承了Bézier曲线的一些优良特性,并能充分克服Bézier曲线不能精确表示二次曲线曲面以及某些超越曲线曲面的弱点.最后实例表明了新的插值曲线应用于几何造型的有效性.

基于离散标准节理粗糙度系数曲线的粗糙单裂隙等效水力隙宽的确定

鉴于节理粗糙度、力学隙宽及迹线是影响确定粗糙单裂隙等效水力隙宽的三个关键因素,在既有研究的基础上,将光滑平行板和Barton提出的10条标准节理粗糙度系数曲线数字化,应用Fluent软件对不同节理粗糙度系数和不同力学隙宽模型进行数值模拟,探讨了节理粗糙度系数、力学隙宽、迹线与等效水力隙宽之间的关系。并与立方定理修正公式进行对比,结果表明等效水力隙宽随力学隙宽增大而线性增大,随节理粗糙度系数的增大而减小,并且考虑实际迹线情况的等效水力隙宽较不考虑的大。因此,在实际工程中,可采用所提出的拟合公式判断自然粗糙裂隙的渗透能力。

Reinforcement Learning Based Data Fusion Method for Multi-Sensors

In order to improve detection system robustness and reliability, multi-sensors fusion is used in modern air combat. In this paper, a data fusion method based on reinforcement learning is developed for multi-sensors. Initially, the cubic B-spline interpolation is used to solve time alignment problems of multisource data. Then, the reinforcement learning based data fusion(RLBDF) method is proposed to obtain the fusion results. With the case that the priori knowledge of target is obtained, the fusion accuracy reinforcement is realized by the error between fused value and actual value. Furthermore, the Fisher information is instead used as the reward if the priori knowledge is unable to be obtained. Simulations results verify that the developed method is feasible and effective for the multi-sensors data fusion in air combat.

UAV safe route planning based on PSO-BAS algorithm

In order to solve the current situation that unmanned aerial vehicles(UAVs)ignore safety indicators and cannot guarantee safe operation when operating in low-altitude airspace,a UAV route planning method that considers regional risk assessment is proposed.Firstly,the low-altitude airspace is discretized based on rasterization,and then the UAV operating characteristics and environmental characteristics are combined to quantify the risk value in the low-altitude airspace to obtain a 3D risk map.The path risk value is taken as the cost,the particle swarm optimization-beetle antennae search(PSO-BAS)algorithm is used to plan the spatial 3D route,and it effectively reduces the generated path redundancy.Finally,cubic B-spline curve is used to smooth the planned discrete path.A flyable path with continuous curvature and pitch angle is generated.The simulation results show that the generated path can exchange for a path with a lower risk value at a lower path cost.At the same time,the path redundancy is low,and the curvature and pitch angle continuously change.It is a flyable path that meets the UAV performance constraints.

The Color Calibration across Multi-Projector Display

Large plane displays are often achieved by combining tiled imaging elements, which give the appearance of a single, seamless display. However, this is difficult to realize in practical use, since differences in color will make the tiles dis-tinct even if the geometric calibration is perfect. The paper presents an approach of color calibration using cubic B- spline. According to the theory of cubic B-spline, we construct the color transfer function of each projector. This ap-proach reduces the color and photometric non-uniformities to achieve seamless tiled multi-projector display well. Finally, we propose the difference between blending region and overlapping region which can help to achieve a better effect of alpha blending.

A Differential Quadrature Based Approach for Volterra Partial Integro-Differential Equation with a Weakly Singular Kernel

Differential quadrature method is employed by numerous researchers due to its numerical accuracy and computational efficiency,and is mentioned as potential alternative of conventional numerical methods.In this paper,a differential quadrature based numerical scheme is developed for solving volterra partial integro-differential equation of second order having a weakly singular kernel.The scheme uses cubic trigonometric B-spline functions to determine the weighting coefficients in the differential quadrature approximation of the second order spatial derivative.The advantage of this approximation is that it reduces the problem to a first order time dependent integro-differential equation(IDE).The proposed scheme is obtained in the form of an algebraic system by reducing the time dependent IDE through unconditionally stable Euler backward method as time integrator.The scheme is validated using a homogeneous and two nonhomogeneous test problems.Conditioning of the system matrix and numerical convergence of the method are analyzed for spatial and temporal domain discretization parameters.Comparison of results of the present approach with Sinc collocation method and quasi-wavelet method are also made.

A numerical technique based on collocation method for solving modified Kawahara equation

In this article,a numerical solution of the modified Kawahara equation is presented by septic B-spline collocation method.Applying the von-Neumann stability analysis,the present method is shown to be unconditionally stable.L 2 and L∞error norms and conserved quantities are given at selected times.The accuracy of the proposed method is checked by test problems including motion of the single solitary wave,interaction of solitary waves and evolution of solitons.