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.

Real-Time Prediction Method for Performance Degradation Trend Based on Reliability Experimental Data

2013 ◽  
Vol 321-324 ◽  
pp. 757-761 ◽  
Author(s):  
Chen Liang Song ◽  
Zhen Liu ◽  
Bin Long ◽  
Cheng Lin Yang
Keyword(s):  
Experimental Data ◽  
Real Time ◽  
Field Data ◽  
Prediction Method ◽  
Field Method ◽  
Performance Degradation ◽  
New Method ◽  
Time Prediction ◽  
Prediction Result ◽  
The Relationship

According to the real-time prediction for performance degradation trend, the commonly used method is just based on field data. But this methods prediction result will not be so much ideal when the fitting of degradation trend of field data is not good. To solve the problem, the paper introduces a new method which is not only based on field method but also based on reliability experimental data coming from the history experiment. We use the relationship between the field data and reliability experimental data to get the result of the two kinds of data respectively and then get the weights according to the two prediction results. Finally, the final real-time prediction result for performance degradation tendency can obtain by allocating the weights to the two prediction results.

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.

Improved Tooth Crown Edge Smoothing Method Based on Noise Classification and Fitting

2020 ◽  
Vol 10 (11) ◽  
pp. 2609-2619
Author(s):  
Tian Ma ◽  
Yurong Li
Keyword(s):  
3D Reconstruction ◽  
Least Squares ◽  
Rate Increase ◽  
Removal Rate ◽  
Noise Removal ◽  
New Method ◽  
Boundary Line ◽  
Tooth Crown ◽  
Least Squares Fitting ◽  
Noise Classification

Because three-dimensional (3D) models of teeth are currently obtained via oral scanning, there are only the tooth crown and gingival surface part, lack of data on the roots of teeth, which is not conducive to the 3D reconstruction of teeth. In order to help doctors to carry out virtual tooth correction, this paper studies the edge characteristics of the tooth crown model, removes the edge noise, which can better carry out the 3D reconstruction of teeth. Therefore, this paper proposes an improved method of tooth crown edge smoothing based on noise classification and fitting. First, according to the characteristics of the tooth crown edge, the method of noise classification is proposed after fitting analysis. The noise can be divided into two types: the noise in the boundary line and the noise in the fitting curve. Then, the noise can be identified according to the Gaussian curvature. Finally, the improved Laplacian smoothing and least squares fitting methods are used to remove the two types of noise, and the denoised tooth crown model is the output. The smoothing effect of the method is verified in terms of the noise removal rate, the patch filling rate, and the patch deletion rate. Compared with the traditional Laplacian smoothig, the new method exhibited a noise removal rate increase of 86.0%, a probability of patch filling that approximately doubled, and a probability of patch deletion that basically remained the same. Compared with the least squares fitting method, the new method exhibited a noise removal rate increase of 75.9%, a patch filling reduction of 22.61%, and a patch deletion reduction of 22.14%.

scholarly journals What is the best fractional derivative to fit data?

2017 ◽  
Vol 11 (2) ◽  
pp. 358-368 ◽  
Author(s):  
Ricardo Almeida
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Fractional Derivative ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Fractional Derivatives ◽  
Least Squares Fitting ◽  
Different Types ◽  
Fractional Differential

The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the order of the fractional differential equation that better describes the experimental data, for different types of fractional derivatives.

Improved Tooth Crown Edge Smoothing Method Based on Noise Classification and Fitting

2020 ◽  
Vol 10 (11) ◽  
pp. 2609-2619
Author(s):  
Tian Ma ◽  
Yurong Li
Keyword(s):  
3D Reconstruction ◽  
Least Squares ◽  
Rate Increase ◽  
Removal Rate ◽  
Noise Removal ◽  
New Method ◽  
Boundary Line ◽  
Tooth Crown ◽  
Least Squares Fitting ◽  
Noise Classification

Because three-dimensional (3D) models of teeth are currently obtained via oral scanning, there are only the tooth crown and gingival surface part, lack of data on the roots of teeth, which is not conducive to the 3D reconstruction of teeth. In order to help doctors to carry out virtual tooth correction, this paper studies the edge characteristics of the tooth crown model, removes the edge noise, which can better carry out the 3D reconstruction of teeth. Therefore, this paper proposes an improved method of tooth crown edge smoothing based on noise classification and fitting. First, according to the characteristics of the tooth crown edge, the method of noise classification is proposed after fitting analysis. The noise can be divided into two types: the noise in the boundary line and the noise in the fitting curve. Then, the noise can be identified according to the Gaussian curvature. Finally, the improved Laplacian smoothing and least squares fitting methods are used to remove the two types of noise, and the denoised tooth crown model is the output. The smoothing effect of the method is verified in terms of the noise removal rate, the patch filling rate, and the patch deletion rate. Compared with the traditional Laplacian smoothig, the new method exhibited a noise removal rate increase of 86.0%, a probability of patch filling that approximately doubled, and a probability of patch deletion that basically remained the same. Compared with the least squares fitting method, the new method exhibited a noise removal rate increase of 75.9%, a patch filling reduction of 22.61%, and a patch deletion reduction of 22.14%.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

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