scholarly journals Calibration Method of Orthogonally Splitting Imaging Pose Sensor Based on KDFcmPUM

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4991
Author(s):  
Na Zhao ◽  
Changku Sun ◽  
Peng Wang
Keyword(s):  
Weight Function ◽  
Clustering Algorithm ◽  
Interpolation Method ◽  
Partition Of Unity ◽  
Calibration Method ◽  
Test Accuracy ◽  
Dense Matrix ◽  
Partition Of Unity Method ◽  
The Mathematical Model ◽  
Local Expression

This paper proposes a partition of unity method (PUM) based on KDFCM (KDFcmPUM) that can be implemented to solve the dense matrix problem that occurs when the radial basis function (RBF) interpolation method deals with a large amount of scattered data. This method introduces a kernel fuzzy clustering algorithm to improve clustering accuracy and achieve the partition of unity. The local compact support RBF is used to construct the weight function, and local expression is obtained from the interpolation of the global RBF. Finally, the global expression is constructed by the weight function and local expression. In this paper, the method is applied to the orthogonally splitting imaging pose sensor to establish the mathematical model and the calibration and test experiments are carried out. The calibration and test accuracy both reached ±0.1 mm, and the number of operations was reduced by 4% at least. The experimental results show that KDFcmPUM is effective.

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

scholarly journals A Nonlinear Calibration Method Based on Sinusoidal Excitation and DFT Transformation for High-Precision Power Analyzers

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Wenjian Zhou ◽  
Sheng Yang ◽  
Li Wang ◽  
Hanmin Sheng ◽  
Yang Deng
Keyword(s):  
High Precision ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Calibration Method ◽  
Calibration Error ◽  
Initial Moment ◽  
Calibration Process ◽  
Calibration Methods ◽  
Nonlinear Calibration ◽  
Sinusoidal Excitation

For most high-precision power analyzers, the measurement accuracy may be affected due to the nonlinear relationship between the input and output signal. Therefore, calibration before measurement is important to ensure accuracy. However, the traditional calibration methods usually have complicated structures, cumbersome calibration process, and difficult selection of calibration points, which is not suitable for situations with many measurement points. To solve these issues, a nonlinear calibration method based on sinusoidal excitation and DFT transformation is proposed in this paper. By obtaining the effective value data of the current sinusoidal excitation from the calibration source, the accurate calibration process can be done, and the calibration efficiency can be improved effectively. Firstly, through Fourier transform, the phase value at the initial moment of the fundamental frequency is calculated. Then, the mapping relationship between the sampling value and the theoretical calculation value is established according to the obtained theoretical discrete expression, and a cubic spline interpolation method is used to further reduce the calibration error. Simulations and experiments show that the calibration method presented in this paper achieves high calibration accuracy, and the results are compensation value after calibration with a deviation of ± 3 × 10 − 4 .

A parallel partition of unity method for the unsteady Stokes equations

2017 ◽  
Vol 27 (9) ◽  
pp. 2105-2114
Author(s):  
Xiaoying Zhao ◽  
Yanren Hou ◽  
Guangzhi Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Partition Of Unity ◽  
Time Dependent ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Content Type ◽  
Standard Galerkin Method ◽  
Unsteady Stokes Equations

Purpose The purpose of this paper is to propose a parallel partition of unity method to solve the time-dependent Stokes problems. Design/methodology/approach This paper solved the time-dependent Stokes equations using the finite element method and the partition of unity method. Findings The proposed method in this paper obtained the same accuracy as the standard Galerkin method, but it, in general, saves time. Originality/value Based on a combination of the partition of unity method and the finite element method, the authors, in this paper, propose a new parallel partition of unity method to solve the unsteady Stokes equations. The idea is that, at each time step, one need to only solve a series of independent local sub-problems in parallel instead of one global problem. Numerical tests show that the proposed method not only reaches the same convergence orders as the fully discrete standard Galerkin method but also saves ample computing time.

Research on Mathematical Model and Calibration of Weighing System by Digital Addition

2012 ◽  
Vol 151 ◽  
pp. 101-104
Author(s):  
Chao Fu Zhu ◽  
Shu Jian Ji ◽  
Jin Long Zhao
Keyword(s):  
Mathematical Model ◽  
Calibration Method ◽  
Optimization Method ◽  
Load Cells ◽  
On Line ◽  
The Mathematical Model ◽  
Multiple Load

In practice the method is widely used, by which a gravity is measured using multiple load cells. A weighing system is introduced in this paper, in which a gravity is measured by multiple load cells with digital addition. The mathematical model of weighing system with digital addition is established. Normal calibration method is not suitable for the on-line calibration of weighing system with digital addition. When the mathematical model is given, the accurate on-line calibration of weighing system with digital addition is achieved by using optimization method.

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