Research on Establishing Assessment Datum Plane of Three Dimensional Surface Micro-Topography

2010 ◽  
Vol 455 ◽  
pp. 435-438
Author(s):  
Feng Kui Cui ◽  
Y.X. Li ◽  
X.Q. Wang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Mathematic Model ◽  
Maximum Error ◽  
Accurate Assessment ◽  
Fitting Method ◽  
Fitting Error ◽  
Micro Topography ◽  
Dimensional Surface

For making accurate assessment about each characteristics paramete of three-dimensional surface micro-topography, mathematic model for the datum plane of three-dimensional surface micro-topography assessment was established with least squares method, the relational expression of the average fitting error and maximum error were made. The datum plane equation was found by processing experimental data with least squares fitting method. The rationality and feasibility of the algorithm which is used to establish datum plane were verified through error calculation and analysis of the datum plane equation. The research provides the foundation for parametric assessment of 3D surface micro-topography and provides a method for datum surface establishment of curved surface.

scholarly journals Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

2022 ◽  
Vol 10 (1) ◽  
pp. 102
Author(s):  
Zhiyao Zhu ◽  
Huilong Ren ◽  
Xiuhuan Wang ◽  
Nan Zhao ◽  
Chenfeng Li
Keyword(s):  
Least Squares ◽  
Residual Strength ◽  
Least Squares Method ◽  
Limit State ◽  
Nonlinear Least Squares ◽  
State Function ◽  
Limit State Function ◽  
Distribution Models ◽  
Sample Distribution ◽  
Fitting Method

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

Structure cristalline et moléculaire du cyclopentadiényle dicarbonyle triphénylphosphine manganèse, MnC5H5(CO)2P(C6H5)3

1973 ◽  
Vol 51 (18) ◽  
pp. 3027-3031 ◽  
Author(s):  
Claude Barbeau ◽  
Klaus Sorrento Dichmann ◽  
Louis Ricard
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Triphenyl Phosphine ◽  
Triclinic Space Group ◽  
Space Group ◽  
Bond Lengths ◽  
Atomic Parameter

The crystalano molecular structure of cyclopentadienyl manganese dicarbonyl-triphenyl phosphine has been determined by means of three dimensional data obtained by a Buerger precession camera. 2931 independent intensities were utilized in the refinement of the structure using the least-squares method. The final disagreement factor is 0.11. MnC5H5(CO)2P(C6H5)3 crystallizes in the triclinic space group.[Formula: see text]The molecule shows atomic parameter almost identical to those of MnC5H5(CO)3 except for the Mn—C bond lengths which change from 1.80 to 1.73 Å. The Mn—P distance (2.236 Å) and the unchanged parameters for the Mn—C5H5 group confirm the strong donating power of the cyclopentadienyl group. [Journal translation]

Application of Legendre Polynomial in Predicting Total Energy Consumption

2015 ◽  
Vol 713-715 ◽  
pp. 1627-1630
Author(s):  
Hong Qin Zhang ◽  
Lai Bin Gao
Keyword(s):  
Energy Consumption ◽  
Total Energy ◽  
Least Squares ◽  
Legendre Polynomial ◽  
Statistical Data ◽  
Least Squares Method ◽  
Total Energy Consumption ◽  
Least Squares Fitting ◽  
Fitting Method

Based on statistical data of National Statistical Bureau of China, and given the least-squares fitting of Legendre polynomial, the data of total energy consumption from 1978 to 2012 is analyzed by least squares method and Legendre polynomial least squares method respectively. The results showed that Legendre polynomial least squares fitting method is excellent and the data of total energy consumption from 2013 to 2016 is predicted by this method.

scholarly journals Exponential Polynomial Fitting for Fibre Spectrum CCD Profiles

2010 ◽  
Vol 27 (3) ◽  
pp. 290-295 ◽  
Author(s):  
Zhangqin Zhu ◽  
Jia Zhu ◽  
Hanqin Qin ◽  
Chong Wang ◽  
Zhongfu Ye
Keyword(s):  
Least Squares ◽  
Spatial Orientation ◽  
Least Squares Method ◽  
Exponential Polynomial ◽  
Exponential Functions ◽  
Polynomial Fitting ◽  
Gaussian Functions ◽  
Profile Fitting ◽  
Fitting Method

AbstractA fibre spectrum profile fitting method based on the least-squares method is presented in this article. For each spectrum of one fibre in spatial orientation, two exponential functions are employed to approximate the profile. Experiments are performed with both simulated profiles and observed profiles to demonstrate the effectiveness of the algorithm. Specially, the proposed method has a better performance for profiles that are asymmetric or composed of multi-Gaussian functions.

A Three-Dimensional Generalization of Reuleaux’s Method Based on Line Geometry

2006 ◽  
Author(s):  
Jasem Baroon ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Line Geometry ◽  
Basic Form ◽  
Motion Reconstruction ◽  
Linear Solution ◽  
On Line

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much if not all of the previous work in this area has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. An elegant geometric method is developed based on line geometry that can be considered as a generalization of the classical Reuleaux’s method used in 2D kinematics. The case of over determined system is also considered a linear solution is presented based on least squares method.

N-way partial least squares combined with new self-construction strategy—A promising approach of using near infrared spectral data for quantitative determination of multiple compounds

2019 ◽  
Vol 28 (2) ◽  
pp. 113-121
Author(s):  
Xiang-Zhi Zhang ◽  
Ai-Jun Ma ◽  
Na Feng ◽  
Bao Qiong Li
Keyword(s):  
Quantitative Analysis ◽  
Least Squares ◽  
Partial Least Squares ◽  
Near Infrared ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Near Infrared Spectra ◽  
Infrared Spectral ◽  
Construction Strategy ◽  
Partial Least Squares Method

Because of the complexity of near infrared spectral data, effective strategies are necessary proposed for accurate quantitative analysis purpose. This work explores a new self-construction strategy for the arrangement of conventional near infrared two-dimensional spectra into new self-constructed three-dimensional spectra, and investigate the feasibility of N-way partial least squares combined with the new self-constructed three-dimensional near infrared spectra for obtaining accurate quantitative determination results. A proof-of-concept model system, the quantitative analysis of four components (moisture, oil, protein, and starch) in corn samples, was applied to evaluate the performance of the proposed strategy. The ability of the newly proposed approach to predict the target compounds was checked with test samples. The established models have good predictive power for the target compounds with acceptable values of Rp (range from 0.82 to 0.997) and RMSEP (range from 0.03 to 0.47). Compared with partial least squares method on pretreated near infrared spectra and N-way partial least squares method on the basis of near infrared self-constructed three-dimensional spectra, the proposed method is competitive.

Total Least-Squares Methods for Active View Registration of Three-Dimensional Line Laser Scanning Data

2004 ◽  
Vol 127 (1) ◽  
pp. 50-56 ◽  
Author(s):  
F. Xi ◽  
D. Nancoo ◽  
G. Knopf
Keyword(s):  
Least Squares ◽  
Laser Scanning ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Measurement Data ◽  
Ordinary Least Squares ◽  
Total Least Squares ◽  
Position Measurement ◽  
Point Position ◽  
Ordinary Least Squares Method

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

Three Dimensional Simulation of the Heat Dissipation of an Automotive Radiator Based on Porous Media Method

2014 ◽  
Vol 543-547 ◽  
pp. 207-210
Author(s):  
Ning Kang ◽  
Ni Ka Mo ◽  
Wei Qi Zheng
Keyword(s):  
Porous Media ◽  
Least Squares ◽  
Heat Dissipation ◽  
Least Squares Method ◽  
Cell Model ◽  
Three Dimensional ◽  
Cell Models ◽  
Air Inlet ◽  
Dimensional Simulation ◽  
Porous Media Method

12 kinds of automotive radiator cell models were simulated at different air inlet velocities using CFD software Fluent. The distributed drag coefficients of each cell model were obtained by least squares method. Then the whole radiator model whose fins region was replaced by the porous media was simulated. The numerical results were validated by experiments which indicate that the porous media method is reliable. The study shows that the radiator heat dissipation is significantly influenced by fin structure and the model with a fin space of 1.4mm and a louver angle of 23o has the best cooling effect.

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