An investigation of the robustness of the nonlinear least-squares sphere fitting method to small segment angle surfaces

2008 ◽  
Vol 32 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Wenjuan Sun ◽  
Martyn Hill ◽  
John W. McBride
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Small Segment ◽  
Fitting Method ◽  
Sphere Fitting

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.

Mueller Matrix Ellipsometer Based on Nonlinear Least Squares Fitting Method

2013 ◽  
Vol 40 (4) ◽  
pp. 0408004
Author(s):  
侯俊峰 Hou Junfeng ◽  
王东光 Wang Dongguang ◽  
邓元勇 Deng Yuanyong ◽  
孙英姿 Sun Yingzi ◽  
张志勇 Zhang Zhiyong
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Mueller Matrix ◽  
Least Squares Fitting ◽  
Fitting Method

A new high-precision sphere-fitting method with small segment angles

2020 ◽  
Vol 32 (1) ◽  
pp. 015012
Author(s):  
Zhigen Fei ◽  
Jixiang Fu ◽  
Jun Ma ◽  
Wenbin He ◽  
Yanqiu Xiao
Keyword(s):  
High Precision ◽  
Small Segment ◽  
Fitting Method ◽  
Sphere Fitting
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