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.

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.

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.

A segment feedrate profile fitting method for parametric interpolation

2016 ◽  
Vol 232 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Lei Lu ◽  
Lei Zhang ◽  
Shijun Ji ◽  
Dunlan Song ◽  
Ji Zhao
Keyword(s):  
Tool Path ◽  
Least Squares Method ◽  
Machining Accuracy ◽  
The Novel ◽  
Profile Fitting ◽  
Fitting Method ◽  
Calculation Process ◽  
Data Points ◽  
Simulation And Experiment ◽  
Parametric Interpolation

There are many researches in scheduling an optimal feedrate profile under various constraints by numerical calculation. A large number of discrete feedrate data points are obtained. They are inconvenient for the parametric interpolator. Therefore, these discrete feedrate data points need to be fitted by parameter curves. Different from the regular curve fitting, the inappropriate feedrate fitting method can generate larger acceleration and jerk that seriously affect the machining accuracy and stability, although the feedrate satisfies the error requirements. In order to generate a suitable feedrate profile, a segment feedrate profile fitting method using B-spline is proposed in this article. The discrete feedrate data points are segmented in the jerk discontinuous points. In each segment, the feedrate profile is fitted by the linear least squares method. These fitted feedrate profiles are combined to generate a unified feedrate profile. The unified fitted feedrate profile and the tool path trajectory are used in the controller to command the axis. In this article, the process of parametric interpolation is separated into the arc-length calculation process and the curve parameter calculation process. Using parallel computation, the two processes are calculated simultaneously in the controller, and the computational efficiency is improved. Both simulation and experiment are carried out to verify that the fitted feedrate profile satisfies the error requirements, and the novel interpolation can be applied to the controller appropriately.

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.

Crystal-structure refinement by profile fitting and least-squares analysis of powder diffractometer data

1983 ◽  
Vol 16 (6) ◽  
pp. 611-622 ◽  
Author(s):  
G. Will ◽  
W. Parrish ◽  
T. C. Huang
Keyword(s):  
Least Squares ◽  
Structure Refinement ◽  
Specimen Preparation ◽  
Crystal Structure Refinement ◽  
Instrument Function ◽  
X Ray ◽  
Profile Fitting ◽  
Fitting Method ◽  
The Individual ◽  
Integrated Intensities

The refinement of crystal structures using X-ray powder data in a two-stage method is described. (1) The integrated intensities of the individual reflections are derived by a profile fitting method in which the profile shapes are accurately defined using an experimentally determined instrument function and the sum of Lorentzian curves. (2) These values are then used in a powder least-squares refinement for structure determination. The results obtained with three simple structures (silicon, quartz and corundum) gave R(Bragg) values of 0.7 to 2.5%. The necessity of correcting for preferred orientation and the importance of proper specimen preparation are also discussed.

scholarly journals Extended Peridynamics and Parameter Optimization Study Based on Moving Least Squares Method

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jingwei Xu ◽  
Wei Hou ◽  
Shoucheng Luan ◽  
Shuting Mao ◽  
Guowei Liu ◽  
...  
Keyword(s):  
Weight Function ◽  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Weight Functions ◽  
Optimization Study ◽  
Fitting Method ◽  
Moving Least Squares Method ◽  
Physical Information ◽  
The One

Based on the theory of peridynamics, the least squares and the moving least squares method are proposed to fit the physical information at nondiscrete points. It makes up for the shortcomings of the peridynamic method that only solves the discrete nodes and cannot obtain the physical information of other blank areas. The extended method is used to fit the one-way vibration problem of the rod, and the curve of the displacement of a nondiscrete node in the rod is extracted with time. The fitted displacement results are compared with the theoretical results to verify the feasibility of the fitting method. At the same time, the parameters in the fitting of the moving least squares method are optimized, and the effects of different tight weight functions and influence ranges on the results are analyzed. The results show that when the weight function is a power exponential function, the fitting effect increases with the decrease in the coefficient. When the weight function is a cubic spline weight function, a better fitting effect is obtained. And in the case of ensuring the fitting result, the affected area should be reduced as much as possible, and the calculation efficiency and precision can be improved.

EFFECT OF WAVELENGTH FILTERING ON THE SHAPE OF THE RESIDUAL ANOMALY

Geophysics ◽  
1968 ◽  
Vol 33 (6) ◽  
pp. 1015-1018 ◽  
Author(s):  
T. J. Ulrych
Keyword(s):  
Least Squares ◽  
Computational Scheme ◽  
Polynomial Fitting ◽  
Aeromagnetic Anomalies ◽  
Residual Gravity ◽  
Fitting Method ◽  
Wavelength Filtering

Recently Skeels (1967) has considerably clarified the concept of the term “residual gravity” and has proposed a modified polynomial fitting method as a computational scheme. In the article Skeels refers to wavelength (or wavenumber) filtering discussed by Byerly (1965). Wavelength filtering has been recently applied by Zurflueh (1967) to the determination of residual aeromagnetic anomalies. Although Zurflueh compares wavelength filtering and least‐squares polynomial fitting methods and mentions the pseudo anomalies introduced by the latter method, he does not discuss the effect of wavelength filtering on the shape of the residual anomaly.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

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