基于MLS的三维扩展目标PMBM跟踪算法

针对传统三维扩展目标跟踪算法形状估计精度低的问题,提出了一种基于移动最小二乘的泊松多伯努利混合(Poisson multi-Bernoulli mixture based on the moving least square,MLS-PMBM)滤波跟踪算法。该算法基于MLS模型构建三维扩展目标的形状矩阵,通过PMBM滤波器预测和更新目标的运动状态,利用移动最小二乘算法更新形状矩阵,结合目标质心状态与形状估计完成对三维扩展目标的跟踪。仿真实验与实际点云数据的验证表明,与现有算法相比,本文所提算法在多扩展目标的形状估计方面具有更优的性能,具有较高的泛用性。

考虑法向离群的自适应双边滤波点云平滑及IMLS评价方法

针对目前在点云双边滤波平滑算法中,人工输入不合理参数导致的点云平滑效果不佳,且易导致体积收缩及现有去噪后点云质量评价方法存在表达局限性等问题,提出一种自适应参数的点云双边滤波算法和基于隐性移动最小二乘(IMLS)的质量评价方法。首先构建KD-tree数据结构用于点云拓扑,之后搜索各点邻域,利用奇异值分解法计算法向量信息,并在双边滤波公式中引入法向离群因子以剔除邻域内离群点,然后通过扩展高斯核函数的权值计算式,在点云邻域内自适应获取空间与法向特征参数,最后应用改进模型进行点云平滑并引入IMLS方法评价点云质量。实验结果表明,考虑法向离群的自适应双边滤波点云平滑算法具有良好的去噪效果,相比其他算法体积收缩更小,且IMLS评价方法客观有效。

基于改进型正则化MLS的风概率分布三维数值拟合方法

针对移动最小二乘法(MLS)存在的过拟合问题,以及传统正则化方法普遍采用单一的正则项系数,没有充分考虑不同阶次MLS基函数对过拟合产生不同程度的影响,文章提出了一种改进型正则化MLS方法,对不同阶次项采用了不同的正则项系数。将该方法应用于风电场风速风向概率分布的三维曲面拟合。该方法有效克服了传统MLS方法的过拟合问题;拟合后,所显示的风概率分布规律性得到增强;对3个不同区域风分布的拟合结果表明该方法具有较强的通用性。

基于改进MLS的铣齿刀具刃形曲线优化

为提高成形铣齿加工齿轮的齿廓形状精度,从刀具刃形曲线的设计角度入手,提出一种新的改进移动最小二乘法(MLS),以此来设计刀具的刃形曲线,并通过数值仿真和具体实验验证所提方法的正确性。首先,基于成形铣削加工机理,获取刀具理论廓形的数据点;其次,分别采用所提新方法和传统刀具刃形曲线设计方法对数据进行处理,利用MATLAB实现刀具刃形的拟合结果,并得到铣削齿廓余量偏差的整体水平;最后,以圆柱内齿轮加工为例进行实验验证,得到不同刀具加工齿轮之后的齿廓形状,并与理论模型进行对比。结果表明所提方法有效、可行,能够提高成形铣齿刀具刃形曲线的拟合精度,减少齿轮铣削加工之后的齿廓形状偏差。

A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

STUDY ON PARAMETERS FOR TOPOLOGICAL VARIABLES FIELD INTERPOLATED BY MOVING LEAST SQUARE APPROXIMATION

This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition,or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses,not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field,but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points,scaling parameter,weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the proposed method. The method is found robust and no numerical instabilities are found with proper parameters.

Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method

Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method （GMLSM） and then, discrete equations of motion based on Lagrange＇s equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.

ELASTO-PLASTICITY ANALYSIS BASED ON COLLOCATION WITH THE MOVING LEAST SQUARE METHOD

A meshless approach based on the moving least square method is developed for elasto-plasticity analysis,in which the incremental formulation is used.In this approach,the dis- placement shape functions are constructed by using the moving least square approximation,and the discrete governing equations for elasto-plastic material are constructed with the direct collo- cation method.The boundary conditions are also imposed by collocation.The method established is a truly meshless one,as it does not need any mesh,either for the purpose of interpolation of the solution variables,or for the purpose of construction of the discrete equations.It is simply formu- lated and very efficient,and no post-processing procedure is required to compute the derivatives of the unknown variables,since the solution from this method based on the moving least square approximation is already smooth enough.Numerical examples are given to verify the accuracy of the meshless method proposed for elasto-plasticity analysis.

Local geoid height approximation and interpolation using moving least squares approach

In this paper an introduction of the moving least squares approach is presented in the context of data approximation and interpolation problems in Geodesy.An application of this method is presented for geoid height approximation and interpolation using different polynomial basis functions for the approximant and interpolant,respectively,in a regular grid of geoid height data in the region 16.0417°≤φ≤47.9583°and 36.0417°≤λ≤69.9582°,with increment 0.0833°in both latitudal and longitudal directions.The results of approximation and interpolation are then compared with the geoid height data from GPS-Levelling approach.Using the standard deviation of the difference of the results,it is shown that the planar interpolant,with reciprocal of distance as weight function,is the best choice in this local approximation and interpolation problem.

公路路面LiDAR数据空洞插补的MLSPF方法

数字交通发展要求开展公路路面数字化,路面数字化主要采用车载或机载激光扫描,但由于遮挡等原因,路面扫描容易产生大小不一的数据空洞。为了处理激光扫描点云数据中空洞,文中提出公路路面空洞插补的移动最小二乘平面拟合方法,即将公路细分为许多格网区域,并视单个格网近似为平面,采用格网内实测点云拟合最佳平面方程,由平面方程插值完成公路路面数据空洞的填补,获得路面数字化初步模型。开展大量实验研究,并与具有代表性的最近邻插值法、克里金插值法、反距离加权插值等算法进行对比,结果表明本方法在计算效率与精度等两个方面都具有优势,是一种可行可靠的方法。

A meshless algorithm with moving least square approximations for elliptic Signorini problems

Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm.

Calculation of stratum surface principal curvature based on a moving least square method

With the east section of the Changji sag Zhunger Basin as a case study, both a principal curvature method and a moving least square method are elaborated. The moving least square method is introduced, for the first time, to fit a stratum surface. The results show that, using the same-degree base function, compared with a traditional least square method, the moving least square method can produce lower fitting errors, the fitting surface can describe the morphological characteristics of stratum surfaces more accurately and the principal curvature values vary within a wide range and may be more suitable for the prediction of the distribution of structural fractures. The moving least square method could be useful in curved surface fitting and stratum curvature analysis.

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

A global interpolating meshless shape function based on the generalized moving least-square （GMLS） is formulated by the transformation technique. Both the shape function and its derivatives meet the Kronecker delta function property. With the interpolating GMLS （IGMLS） shape function, an improved element-free Galerkin （EFG） method is proposed for the structural dynamic analysis. Compared with the conven- tional EFG method, the obvious advantage of the proposed method is that the essential boundary conditions including both displacements and derivatives can be imposed by the straightforward way. Meanwhile, it can greatly improve the ill-condition feature of the standard GMLS approximation, and provide good accuracy at low cost. The dynamic analyses of the Euler beam and Kirchhoff plate are performed to demonstrate the feasi- bility and effectiveness of the improved method. The comparison between the numerical results of the conventional method and the improved method shows that the proposed method has better stability, higher accuracy, and less time consumption.

Moving least squares-based multi-functional sensing technique for estimating viscosity and density of ternary solution

In the osmotic dehydration process of food,on-line estimation of concentrations of two components in ternary solution with NaCl and sucrose was performed based on multi-functional sensing technique.Moving Least Squares were adopted in approximation procedure to estimate the viscosity of such interested ternary solution with the given data set.As a result,in one mode of using total experimental data as calibration data and validation data,the relative deviations of estimated viscosities are less than ±1.24%.In the other mode,by taking total experimental data except the ones for estimation as calibration data,the relative deviations are less than ±3.47%.In the same way,the density of ternary solution can be also estimated with deviations less than ± 0.11% and ± 0.30% respectively in these two models.The satisfactory and accurate results show the extraordinary efficiency of Moving Least Squares behaved in signal approximation for multi-functional sensors.

A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation

An improved moving least square meshless method is developed for the numerical solution of the nonlinear improved Boussinesq equation. After the approximation of temporal derivatives, nonlinear systems of discrete algebraic equations are established and are solved by an iterative algorithm. Convergence of the iterative algorithm is discussed. Shifted and scaled basis functions are incorporated into the method to guarantee convergence and stability of numerical results. Numerical examples are presented to demonstrate the high convergence rate and high computational accuracy of the method.

Matrices Associated with Moving Least-Squares Approximation and Corresponding Inequalities

In this article, some properties of matrices of moving least-squares approximation have been proven. The used technique is based on known inequalities for singular-values of matrices. Some inequalities for the norm of coefficients-vector of the linear approximation have been proven.

基于MLS拟合带容差的测量数据加工刀位面生成算法

传统的刀位面生成算法无法直接生成存在缺陷的离散数据的刀位面,因此,针对球头铣刀提出了一种基于MLS拟合带容差的离散数据加工刀位面生成算法。该方法首先依据球头铣刀构造离散数据的点膨胀球模型,然后根据凸包原理获取该模型的最外层包络面,最终通过MLS投影拟合方法剔除奇异点、修补裂缝,生成刀位面网格模型。实例表明,该算法具有较高的稳定性,能够有效解决存在缺陷的离散数据刀位面生成问题,适用于实际工程应用加工。

二维MLSPH无网格方法

给出MLSPH无网格方法的控制方程、移动最小二乘近似、MLSPH守恒格式等,重点研究MLSPH守恒格式中MLS面积向量的数值求解方法,以提高求解的精度.对激波管问题和平面Noh问题进行模拟,得到较好的结果,确定用三次样条积分公式计算面积向量.

新型无网格法(IMLS方形域法)的研究及其应用

根据最新无网格法的前沿研究,提出了一种新型无网格法-IMLS方形域法。该法在场函数近似、权函数选取以及方形域数值积分等方面给出了全新的格式。方法中未知变量的近似采用IMLS技术,局部影响域形状采用方形几何形态。这些技术的具体实施展现了节点布置和数值积分的无网格特点,并自然满足Dirichlet边界条件。该方法可以容易求解偏微分方程初值或边值问题上实现,此外,计算了一维固结问题、二维弹性力学平面问题的算例,所得计算结果证明:该方法是一种具有收敛快、精度高、简便有效的通用方法,在工程中具有广阔的应用前景。

基于MLS改进算法的曲线拟合技术研究

针对散乱点拟合曲线的算法问题,分析了移动最小二乘逼近法(MLS)的特点,提出了用MLS改进算法对散乱点进行曲线拟合,并结合实例进行了验证.结果表明,MLS改进算法在拟合曲线时,选取不同阶的基函数和不同的权函数,在保证精度和光滑度的基础上,解决了传统曲线拟合方法在拟合曲线时出现的运算不稳定现象,显示了MLS改进算法在曲线拟合中的优越性.