Algorithms of calculating of approximating spline functions with optimization of the location of spline nodes

The problem of computing spline approximation functions taking into account the possibility of optimizing the location of spline nodes is considered. Algorithms are developed to compute spline approximation functions with free conditions at the ends of observation intervals, with controlling of splines by the zero and first derivatives at the ends of observation intervals, and with the provision of optimal locations of spline nodes. The results of mathematical modeling of the algorithms for computing spline approximation functions are presented.     

New digital filter for the analysis of experimental data

The extremely simple mathematical technique called 'straightening through smoothing,' which is a numerical frequency filter, is generalized in order to provide a transmission function having any shape. This frequency filter requires such a small memory that it can be performed using a minicomputer or even a programmable hand held calculator and the number of channels used is not limited to a power of 2, as in the case of the fast Fourier transform. For some filtering functions the number of operations required is smaller than with the fast Fourier transform.     

A simple point cloud data reduction method based on Akima spline interpolation for digital copying manufacture

Point cloud data acquisition is the first key step in digital copying manufacture. In order to reduce extremely dense acquired data while maintaining data accuracy, this paper presents a simple and practical on-line point cloud data reduction method for digital copying manufacture, which is based on Akima spline interpolation. The basic idea of this method is similar to sketch painting: Outline the broad contour of the curve first and then revise local details until the interpolated curve satisfies the required accuracy. In this method, Akima spline interpolation is adopted to connect acquired points for CNC machining in digital copying process. It obtains a smaller data reduction ratio and a smoother machined surface than conventional methods. Experimental results indicate that the proposed Akima reduction method is able to eliminate redundant data effectively under different required accuracy. The reduction performance of this method is superior to equal ATCD reduction method obviously under the same required accuracy. The proposed method can be used in the real-time data acquisition process of digital copying manufacture to replace traditional methods.     

Construction of wavelet filtration algorithms with two-parameter threshold functions

A class of wavelet filtration algorithms with two-parameter threshold functions is considered. An algorithm is proposed for solving the problem of choosing two threshold values, which allows estimating their optimal values with acceptable accuracy.     

非完整单足跳跃机器人姿态运动控制的样条逼近方法

讨论非完整单足跳跃机器人姿态运动规划的最优控制问题。在机器人无外力矩作用时,其系统相对于总质心的角动量守恒而成为一类典型的非完整系统。由于非完整约束的不可积特性,对该类系统的运动控制问题比一般系统要困难得多。为解决这一问题,首先导出机器人姿态运动方程,根据系统的非完整约束特性,在系统角动量为零的情况下,将非完整机器人的姿态运动规划问题转化为最优控制问题,利用样条逼近方法和粒子群优化算法实现机器人姿态运动的最优控制。该方法的主要特点是所得到的控制输入的初值和终值均为零,解决了以往文献中控制输入的初值和终值不为零的问题,便于利用伺服电机实现机器人运动的控制。文末数值仿真表明了该方法的有效性。     

Method of face recognition with the use of scalar perturbation functions and a set-theoretic operation of subtraction

The problem of face recognition is discussed. For this purpose, a method based on scalar perturbation functions and a set-theoretic operation of subtraction is proposed. It is shown that all surface points and the mask volume are used in the process of sample testing for more accurate identification.     

三次B样条曲线数据采样插补器的研究

针对复杂轮廓零件数控加工的实际需求，基于数据采样插补原理，提出 了一种改进的三次B样条曲线插补器。利用此B样条曲线插补器进行数控加工，能够保证在整个加工过程中加工效率和加工质量的一致性，三次B样条曲线插补技术的实现将大大提高曲线，曲面零件数控加工的效率和加工质量。     

样条函数最小二乘拟合法在寻求打纬凸轮机构运动规律中的应用

分析未知运动规律的凸轮机构时,传统的方法具有很大的局限性,计算量和误差都很大。根据凸轮廓线实测值,采用样条函数最小二乘拟合法分析凸轮机构,可以为寻找凸轮机构的运动规律提供一种新的思路。     

融合波动率的时序数据符号聚合近似方法探究

为解决传统符号聚合近似方法分析时序数据时丢失序列波动形态信息的问题,提出一种融合波动信息的时间序列符号聚合近似方法.该方法在传统符号化方法的基础上定义波动率指标来同时量化时间序列的波动幅度和变化趋势信息,用融合波动率的符号矢量近似刻画子序列,在此基础上给出一种新的时间序列距离度量方法.以此度量方法为基础,提出时间序列的相似性计算和分类方法,并在公开数据集上进行了分类学习实验.实验结果表明,所提方法在绝大部分数据集上获得了较传统符号聚合近似方法更好的分类准确率,尤其在时间序列具有明显的局部波动或明显的上升、下降趋势时.     

精确逼近密集散乱点数据的矩形网格

基于自组织特征映射(Self-Organizing Feature Map,SOFM)神经网络构建的矩形网格模型可以实现密集散乱点数据自组织压缩,生成双有序点列,但该模型存在矩形网格的逼近误差和边缘误差。为减小矩形网格的逼近误差和边缘误差,改进了矩形网格模型的训练模式。首先采用整个测量点集对矩形网格模型中的所有神经元进行整体训练;然后对矩形网格中的网格神经元的位置权重,沿网格顶点法矢方向进行修正;最后采用测量点集中的边界点集,对矩形网格模型中的网格边界神经元进行训练。算例表明,应用该训练模式,可以有效减小矩形网格的边缘误差,矩形网格逼近散乱数据点集的逼近精度得到大幅提高并覆盖散乱数据点集整体分布范围。     

Processing of incomplete data with the use of ternary logic

A data processing method based on one variant of ternary logic, which allows considering unreliable and incomplete information, is presented. An example of practical application of the proposed method in the development of the Novosibirsk subway supervisory train control system is given.     

Method of choosing the best distribution law for a random variable based on experimental data

This paper describes a new method for choosing a distribution law from a given set of experimental data that provides the best fit to a measured random variable. The method is based on a comparison of empirical distributions constructed for the original sample with the set of given laws using a continuous mapping of the distribution function onto the interval [0, 1]. As a result, the distribution for which the corresponding value of the functional is maximal is taken as the most probable distribution law for the original sample. Examples of implementing the method using statistical Monte Carlo simulation are given.     

磁悬浮轴承数字控制器的设计

以数字信号处理器TMS320F2812和复杂可编程器件EPM7128为控制核心,设计了四自由度磁悬浮轴承系统的控制硬件电路。在CCS环境中用C语言编写了系统的程序,采用抗积分饱和的增量式积分分离PID系统控制算法实现系统的控制。针对实验室的四自由度轴承进行了悬浮试验,试验结果表明系统悬浮动态性能良好,达到了控制性能的要求。     

套管螺纹全参数化几何模型的建立

根据圆锥螺旋面形成理论,推导出了构成ＡＰＩ圆套管螺纹四段圆锥螺旋面的方程,建立了套管螺纹全参数化的几何模型,以此模型研制了接箍和套管内外螺纹旋合过程的计算机仿真系统,可用于研究套管螺纹设计参数的变化对接箍和套管内外螺纹旋合几何接触性能的影响。     

基于工业数字模型的数据共享分析

随着CAD软件的发展,产生了名目繁多的工业模型格式,给转换各种工业模型造成了很大困惑和麻烦。主要通过阐述计算机辅助设计产生的两大类模型的形成原理和需求分析,从虚拟制作的角度分析各种格式下工业数字模型的优劣,研讨工业数字模型的数据共享分析的方法论,解决从工业模型到展示表现类模型的转换,利用前期设计师制作的工业三维模型为后续的3D动画和虚拟仿真项目制作节省大量的人力、物力和时间,更为大数据量模型虚拟仿真项目提供了保障。     

基于分段多项式的直接数字频率合成器设计

为提高直接数字频率合成器（DDS）系统的性能,将分段多项式逼近算法应用于优化相幅转换电路中,实现了基于此结构的直接数字频率合成器设计。提出了适合在流行的现场可编程门阵列（FPGA）平台上实现的电路结构方案,进行了硬件实验,给出了在Altera Cyclone II器件中的实现结果,并在性能和资源消耗方面与基于ROM查找表的方案作了比较。研究结果表明,由于避免了庞大的查找表,这一方案大大减小了电路面积,提高了系统性能。     

Modular system for data acquisition and control of experiments with digital output

In the present work, the design of an efficient, modular, and scalable data acquisition and control system is described. It consists of an array of microcontrollers and memories, which feed a single concentrating unit whose information can be accessed by means of a universal series bus (USB) interface to be processed later on. Signal levels can be controlled through a set of digital potentiometers. This system is ideal for experiments with a large number of digital outputs.     

B样条列表曲线直线插补的自适应算法

给出了一种根据零件加工精度要求,对三次Ｂ样条列表曲线进行直线插补,自动生成变步长刀位轨迹的算法,简称自适应算法。该算法当列表曲线曲率大时,使步长变小,反之使步长变大,同时使逼近误差满足要求。该算法稳定、可靠,便于在列表曲线、列表曲面的数控加工中推广应用。