Détermination directe des coefficients du potentiel de Dunham par une méthode de moindres carrés non linéaire appliquée aux nombres d'ondes des raies. Application au cas de la molécule HBr

1977 ◽  
Vol 55 (21) ◽  
pp. 1829-1834 ◽  
Author(s):  
P. Niay ◽  
P. Bernage ◽  
C. Coquant ◽  
A. Fayt
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Iterative Process ◽  
Nonlinear Least Squares ◽  
Theoretical Framework ◽  
New Method

In this paper, the Dunham potential coefficients are numerically determined by using a nonlinear least squares routine applied directly to the line experimental wave numbers.The results are compared to the ones obtained when using the usual iterative process applied to the H81Br Yi0 and Yi1 equilibrium constants.The al determination new method assumes a theoretical framework (B.O., adiabatic or non-adiabatic) to be valid. One can test this assumption by comparing the experimental data to the calculated ones.

Deformation Identification and Tank Capacity Table Calibration of the Storage Tank

2012 ◽  
Vol 184-185 ◽  
pp. 110-113
Author(s):  
Zhi Peng Yao ◽  
Sheng Shuang Chen
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Storage Tank ◽  
Nonlinear Least Squares ◽  
Integral Model ◽  
Tank Capacity

We build the deformation integral model of the actual storage tank and estimate the deflection parameters by using nonlinear least squares based on experimental data. The accurate calibration value of the tank capacity table of the actual storage tank is calculated.

Discharge Coefficients for Circular Side Outlets

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Laszlo Czetany ◽  
Peter Lang
Keyword(s):  
Experimental Data ◽  
Genetic Algorithm ◽  
Least Squares ◽  
Discharge Coefficient ◽  
Nonlinear Least Squares ◽  
Fluid Distribution ◽  
Vast Amount ◽  
Discharge Coefficients ◽  
New Equation

Fluid distributors are widely used in various industrial and ventilation applications. For the appropriate design of such distributors, the discharge coefficient has to be known to predict the energy and fluid distribution performance. Despite the vast amount of experimental data published, no generally applicable equations are available. Therefore, a new equation is presented for sharp-edged circular side outlets, which can be widely used for calculating the discharge coefficient. The equation is developed by regression with nonlinear least squares combined with genetic algorithm on experimental data available in the literature. The equation covers a wider range than the others presented in the literature.

The Area-Coarea Method for the Estimation of Power-Law Constitutive Parameters

1989 ◽  
Vol 111 (3) ◽  
pp. 295-297 ◽  
Author(s):  
T. Y. Peterson ◽  
K. A. Stelson
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Real Time ◽  
Power Law ◽  
New Method ◽  
Least Squares Fitting ◽  
Excessive Weight ◽  
Amplitude Data ◽  
Low Amplitude ◽  
Constitutive Parameters

A new method for estimating the power-law constitutive parameters from experimental data is presented. The algorithm is well suited to real time computation because the integrals employed can be continuously updated with new data. The method requires less computation than least squares fitting and avoids the problem of excessive weight being put on low amplitude data that is present in logarithmic least squares fitting. Because the method employs integrals, it smooths noise in the data. The method can also be extended to linear plus power-law fitting.

Optimum Levenberg–Marquardt constant determination for nonlinear least-squares

2018 ◽  
Vol 51 (2) ◽  
pp. 428-435 ◽  
Author(s):  
Alan Anthony Coelho
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Matrix Equation ◽  
Nonlinear Least Squares ◽  
Computational Effort ◽  
New Method ◽  
Constant Determination ◽  
Levenberg Marquardt ◽  
The Matrix ◽  
Parameter Values

A new method for determining an approximate optimum value for the Levenberg–Marquardt constant has been shown to improve the convergence rate of nonlinear least-squares problems including complex X-ray powder diffraction and single-crystal structural refinements. In the Gauss–Newton method of nonlinear least squares, a lower value for the objective function is occasionally not realized after solving the matrix equationAΔp=b. This situation occurs when either the objective function is at a minimum or theAmatrix is ill conditioned. Invariably the Levenberg–Marquardt method is used, where the matrix equation is reformulated to (A+ λI)Δp=band λ is the Levenberg–Marquardt constant. The values chosen for λ depend on whether the objective function increases or decreases. This paper describes a new method for setting the Levenberg–Marquardt constant, as implemented in the computer programTOPAS-AcademicVersion 7, which in general results in an increased rate of convergence and additionally a lowering of the objective function as a function of starting parameter values. The reduction in computation is problem dependent and ranges from 10% for typical crystallographic refinements to 50% for large refinements. In addition, the method can be applied to general functions including cases where the objective function comprises both the sum of squares and penalties including functions with discontinuities. Of significance is the trivial extra computational effort required in determining λ as well as the simplicity in carrying out the calculation; the latter should allow for easy implementation in refinement programs.

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