Application of Radius-Determined Least Squares Circle Fitting Method in Cable Winding Monitoring

2019 ◽  
Vol 07 (04) ◽  
pp. 134-141
Author(s):  
巍 范
Keyword(s):  
Least Squares ◽  
Circle Fitting ◽  
Fitting Method

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.

Voltage Sag Source Localization Based on the Voltage Distance Function in Distribution Network

2013 ◽  
Vol 391 ◽  
pp. 607-610 ◽  
Author(s):  
Yu Liu ◽  
Jin Hao Wang ◽  
Chao Ying Yang
Keyword(s):  
Least Squares ◽  
Source Localization ◽  
Distance Function ◽  
Distribution Network ◽  
Voltage Sag ◽  
Sorting Algorithm ◽  
Line Voltage ◽  
Function Fitting ◽  
Fitting Method ◽  
Bus Voltage

To realize voltage sag source localization in distribution network, the paper proposes a function fitting method based on the least squares. Establish a voltage distance function in response to fault distance changes by the line voltage. According to the voltage distance function, combine with the bus voltage after fault to find out likely fault section and distance. Through the sorting algorithm to sort all possible results, weaken the effect of pseudo fault point on the judgment result. Finally the simulation verifies the effectiveness of the method.

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.

scholarly journals Generalized Inequalities to Optimize the Fitting Method for Track Reconstruction

Physics ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 608-623
Author(s):  
Gregorio Landi ◽  
Giovanni E. Landi
Keyword(s):  
Least Squares ◽  
Minimum Variance ◽  
Linear Estimator ◽  
Track Reconstruction ◽  
Gaussian Distributions ◽  
Least Squares Estimators ◽  
Optimal Estimator ◽  
Fitting Method ◽  
Optimal Estimators ◽  
The One

A standard criterium in statistics is to define an optimal estimator as the one with the minimum variance. Thus, the optimality is proved with inequality among variances of competing estimators. The demonstrations of inequalities among estimators are essentially based on the Cramer, Rao and Frechet methods. They require special analytical properties of the probability functions, globally indicated as regular models. With an extension of the Cramer–Rao–Frechet inequalities and Gaussian distributions, it was proved the optimality (efficiency) of the heteroscedastic estimators compared to any other linear estimator. However, the Gaussian distributions are a too restrictive selection to cover all the realistic properties of track fitting. Therefore, a well-grounded set of inequalities must overtake the limitations to regular models. Hence, the inequalities for least-squares estimators are generalized to any model of probabilities. The new inequalities confirm the results obtained for the Gaussian distributions and generalize them to any irregular or regular model. Estimators for straight and curved tracks are considered. The second part deals with the shapes of the distributions of simplified heteroscedastic track models, reconstructed with optimal estimators and the standard (non-optimal) estimators. A comparison among the distributions of these different estimators shows the large loss in resolution of the standard least-squares estimators.

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