对偶基函数的升阶算法

由对偶泛函得到幂函数的对偶基,根据对偶基函数的升阶算法得到其高阶对偶基函数.升阶算法与传统的算法相比,省去系数矩阵求逆,同时也不要求其基函数的正交性,可提高计算机辅助几何设计及图形绘制系统的效率.     

An extension of Bernstein-Bézier surface over the triangular domain

In this paper, a set of quasi-Bernstein polynomials of degree n with one parameter is presented, which is an extension of the Bernstein polynomials over the triangular domain. Using the presented polynomials as basis functions, we construct a class of shape adjusting surfaces defined over the triangular domain with a shape parameter, namely, quasi-B-B parametric surfaces. These surfaces share many properties with the B-B parametric surfaces. In particular, when shape parameters equal 1, they degenerate to be the B-B parametric surfaces. By changing the value of the shape parameter, we can get different surfaces under the fixed control net.     

An extension of Bernstein-Bézier surface over the triangular domain

In this paper, a set of quasi-Bernstein polynomials of degree n with one parameter is presented, which is an extension of the Bernstein polynomials over the triangular domain. Using the presented polynomials as basis functions, we construct a class of shape adjusting surfaces defined over the triangular domain with a shape parameter, namely, quasi-B-B parametric surfaces. These surfaces share many properties with the B-B parametric surfaces. In particular, when shape parameters equal 1, they degenerate to be the B-B parametric surfaces. By changing the value of the shape parameter, we can get different surfaces under the fixed control net.     

Design of Fault Detection Observer Based on Hyper Basis Function

In this paper, we propose the Hyper Basis Function(HBF) neural network on the basis of Radial Basis Function(RBF) neural network. Compared with RBF, HBF neural networks have a more generalized ability with different activation functions. A decision tree algorithm is used to determine the network center. Subsequently, we design an adaptive observer based on HBF neural networks and propose a fault detection and diagnosis method based on the observer for the nonlinear modeling ability of the neural network. Finally, we apply this method to nonlinear systems. The sensitivity and stability of the observer for the failure of the nonlinear systems are proved by simulation, which is beneficial for real-time online fault detection and diagnosis.     

A polynomial smooth epsilon-support vector regression based on cubic spline interpolation

Regression analysis is often formulated as an optimization problem with squared loss functions.Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support vector regression models,this study takes cubic spline interpolation to generate a new polynomial smooth function |x|_ε~2 in ε-insensitive support vector regression.Theoretical analysis shows that S_ε~2-function is better than p_ε~2-function in properties,and the approximation accuracy of the proposed smoothing function is two order higher than that of classical p_ε~2-function.The experimental data shows the efficiency of the new approach.     

Interior-point algorithm for linear optimization based on a new kernel function

In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, and . This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other primal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.     

Prediction of Flexural Deformation of Reinforcement Concrete Beams with Polynomial Tension Stiffening Model

Based on an assumption of parabolic bond stress distribution,a simplified model with quartic polynomial function of the relative slip of steel bar and surrounding concrete for reinforced concrete (RC)tensile member was proposed. The post-cracking behavior as well as tension stiffening effect was considered in the new model. The relative slip of bending member could also be determined through the extension of the new model,which could be applied to obtaining the concentrated rotations at certain sections in order to predict the flexural deformation of RC beam. Several examples of four-point bending RC beams were approached to verify the new model,and the predictions of the flexural deflections of RC beams agreed well with experimental results. The new model can be extended to the application of partially corroded RC beam.     

Adaptive Stabilization of Neural Control for Robot Trajectory Tracking *

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一类广义的三角多项式均匀B样条曲线

为了实现从均匀B样条曲线到三角多项式均匀B样条曲线的过渡,定义了一种n阶广义的三角多项式均匀B样条曲线.这种样条曲线包含了n阶均匀B样条曲线和n阶三角多项式均匀B样条曲线以及介于它们之间的无数曲线,随着阶数的升高,形状参数的取值范围也将扩大.     

带形状参数的三角曲线曲面

为了保留B样条曲线的优点,同时克服B样条曲线在控制顶点给定的情况下不具备形状可调性、不能精确表示椭圆(圆)的缺点,定义了一种带形状参数的三角样条曲线.新曲线具有与三次B样条曲线相同的结构与基本性质,但因为引入了形状参数,并采用三角函数作为基底,新曲线还具备了三次B样条曲线不具备的两个性质,即形状可调性和可以精确表示椭圆(圆).另外,新曲线还具有比三次B样条曲线更好的连续性和对控制多边形的逼近性.     

一类带形状参数的三次均匀B样条曲线

利用三次多项式调配函数构造三次均匀B样条基,基于该基函数建立了一类带形状参数的三次均匀B样条曲线,形状参数的值用于调整曲线的形状,描述曲线接近其控制多边形的程度;选取的形状参数不同,得到的连续曲线不同.最后给出曲线设计的实例.     

均匀结点情形下的两类二阶三角B-样条曲线

给出两类均匀结点情形下二阶三角B-样条基函数的定义,分析它们的构造过程,性质,并分别用其生成二阶三角B-样条函数和二阶三角B-样条曲线.其中第一类曲线是三点分段的,即由前后相继3个控制点决定一段曲线,与二阶B-样条曲线类似,第二类曲线是四点分段的,即由前后相继4个控制点决定一段曲线,与三阶B-样条曲线类似.讨论这两类曲线的性质及它们之间的关系.针对第一类曲线,还给出了重结点情形下基函数的定义并分析了这种情形下曲线的情况.将第一类二阶三角B-样条曲线与一阶三角B-样条曲线进行了对比,得出相同结点向量下,二阶三角B-样条曲线更加接近控制多边形的结论.     

3种带形状参数的二次三角样条曲线

构造了3种带参数的三角样条基,基于这3组基定义了3种三角样条曲线。与二次B样条曲线类似,这3种曲线的每一段都由相继的3个控制顶点生成。这3种曲线具有许多与二次B样条曲线类似的性质,但它们的连续性都比二次B样条曲线更好。对于等距节点,在一般情况下,这3种曲线都整体C2连续,在特殊条件下它们都可达C3连续。另外,这3种曲线都具有比二次B样条曲线更好的对控制多边形的逼近性。     

均匀混合三角多项式B-样条曲线

提出一种新的均匀样条曲线,均匀混合三角多项式B-样条.它是建立在空间{sint,cost,tsint,tcost,1,t,…,tk-5}上,其中k是任意大于等于5的整数.这种曲线与传统的B-样条曲线有很多相似的性质,给出了它具体的性质.基于曲线的明确的表述之上,也给出了这种新曲线的细分公式.由于新样条把多项式曲线、三角曲线以及三角多项式B-样条曲线做为其特殊情况,所以它是CAD/CAM领域中一种新的有效的新模型.     

均匀混合三角多项式B-样条曲线

提出一种建立在空间Ω={sint,cost,tsint,tcost,1,t,…t^k-s）上的新的均匀样条曲线——均匀混合三角多项式B样条．给出了这种新曲线的细分公式．     

多形状参数的均匀B样条曲线

利用分段积分的方法并引入多个形状参数,将单形状参数的均匀B样条曲线推广到多形状参数的情形;这类曲线具有标准的均匀B样条曲线及单形状参数的均匀B样条曲线的主要性质,如连续性、凸包性等;根据形状参数的各种不同取值,这类曲线既能整体地又能局部地调控其形状,由此生成的曲线与曲面,作为一种新的几何造型方法,可应用于CAD/CAM领域。     

多形状参数的双曲多项式均匀B样条

文章利用分段积分的思想并引入多个形状参数,给出了双曲多项式均匀B样条曲线的扩展,该类曲线具有标准的和单形状参数的双曲多项式均匀B样条曲线的主要性质;改变形状参数的值能整体或局部调控其形状,有利于双曲多项式均匀B样条曲线的设计;并给出了多形状参数的均匀B样条曲线,体现了曲线的整体与局部调控.     

可调控C2连续三次三角多项式样条曲线

文章提出一类C2连续带有形状参数的三次三角多项式样条曲线.该曲线对给定的多边形具有保形性,通过改变形状参数的取值,可以局部或整体调整曲线逼近其控制多边形的程度.所得结论具有明确的几何意义,有效增强了控制及表达曲线形状的能力.最后用实例表明了该方法的有效性.