scholarly journals Statistically Generated Weighted Curve Fit of Residual Functions for Modal Analysis of Structures

1997 ◽  
Vol 4 (4) ◽  
pp. 211-222
Author(s):  
Paul Stanley Bookout
Keyword(s):  
Weighting Function ◽  
Second Order ◽  
Test Method ◽  
Mode Shapes ◽  
Modal Parameter ◽  
Residual Function ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Residual Functions ◽  
Order Polynomial

A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure to modal test large structures in a free-free environment to measure the effects of higher order modes and stiffness at distinct degree of freedom interfaces. Due to the present damping estimate limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of irregular data, which should be a smooth curve in a second-order polynomial form. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure, which is used to predict constrained mode shapes.

Curve Fit and Form Design Procedure Using Rotated Parabolas

1983 ◽  
Vol 27 (02) ◽  
pp. 93-102
Author(s):  
C. Myrianthis
Keyword(s):  
Future Development ◽  
Digital Computer ◽  
Design Procedure ◽  
Smooth Curve ◽  
Second Order ◽  
Interactive Applications ◽  
Curve Fit ◽  
Order Polynomial ◽  
Data Points ◽  
Form Design

A method for curve fitting and form design using rotated second-order polynomial segments is presented. The segments, which are referred to axes of common origin but different rotation, are generated to connect known adjoining data points with slope conditions imposed where necessary. The use of second-order polynomials precludes the possibility of oscillations and it is shown how the number of data points required for any segment is related to the requirements imposed at the segment. The resulting smooth curve fit can represent a wide variety of shapes within the overall curve and permit the presence of discontinuities. The method is thus versatile and flexible and can be used for form design purposes. Applications of the method are given using a digital computer program. Future development and elaboration are discussed and reference is made to interactive applications.

Improvements to Common Data Reduction and Calibration Methods for Seven Hole Probes

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
James Crawford ◽  
A. Michael Birk
Keyword(s):  
Calibration Data ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Calibration Methods ◽  
Polynomial Extrapolation ◽  
Order Polynomial ◽  
Physical Response ◽  
Probe Response ◽  
Fourth Order Polynomial ◽  
Data Sorting

The influence of calibration data sorting procedures and the order of polynomial curve fit used to calibrate seven hole pressure probes in subsonic, incompressible flow are discussed. It is shown that the inclusion of fourth order polynomial terms is necessary to properly model the physical response of the probe. It is also shown that the uniformity of probe response error is significantly affected by polynomial extrapolation near sector boundaries, and that the uniformity can be improved by using some calibration points in multiple sectors.

Improvements to Common Data Reduction and Calibration Methods for Seven Hole Probes

2012 ◽  
Author(s):  
James Crawford ◽  
A. M. Birk
Keyword(s):  
Calibration Data ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Calibration Methods ◽  
Polynomial Extrapolation ◽  
Order Polynomial ◽  
Physical Response ◽  
Probe Response ◽  
Fourth Order Polynomial ◽  
Data Sorting

The influence of calibration data sorting procedures and the order of polynomial curve fit used to calibrate seven hole pressure probes in subsonic, incompressible flow are discussed. It is shown that the inclusion of fourth order polynomial terms is necessary to properly model the physical response of the probe. It is also shown that the uniformity of probe response error is be significantly affected by polynomial extrapolation near sector boundaries, and that the uniformity can be improved by using some calibration points in multiple sectors.

Integrating Second-order Moving Average and Over-sampling Algorithm to Predict Apoptosis Protein Subcellular Localization

2020 ◽  
Vol 15 (6) ◽  
pp. 517-527
Author(s):  
Yunyun Liang ◽  
Shengli Zhang
Keyword(s):  
Subcellular Localization ◽  
Moving Average ◽  
Subcellular Location ◽  
Second Order ◽  
Test Method ◽  
Support Vector ◽  
Protein Subcellular Localization ◽  
Protein Subcellular Location ◽  
Apoptosis Protein ◽  
Leibler Divergence

Background: Apoptosis proteins have a key role in the development and the homeostasis of the organism, and are very important to understand the mechanism of cell proliferation and death. The function of apoptosis protein is closely related to its subcellular location. Objective: Prediction of apoptosis protein subcellular localization is a meaningful task. Methods: In this study, we predict the apoptosis protein subcellular location by using the PSSMbased second-order moving average descriptor, nonnegative matrix factorization based on Kullback-Leibler divergence and over-sampling algorithms. This model is named by SOMAPKLNMF- OS and constructed on the ZD98, ZW225 and CL317 benchmark datasets. Then, the support vector machine is adopted as the classifier, and the bias-free jackknife test method is used to evaluate the accuracy. Results: Our prediction system achieves the favorable and promising performance of the overall accuracy on the three datasets and also outperforms the other listed models. Conclusion: The results show that our model offers a high throughput tool for the identification of apoptosis protein subcellular localization.

scholarly journals Method for Measuring the Second-Order Moment of Atmospheric Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 564
Author(s):  
Hong Shen ◽  
Longkun Yu ◽  
Xu Jing ◽  
Fengfu Tan
Keyword(s):  
Atmospheric Turbulence ◽  
Weighting Function ◽  
Structure Constant ◽  
Turbulence Models ◽  
Second Order ◽  
Index Structure ◽  
Order Moment ◽  
Site Testing ◽  
Optical Effects ◽  
Novel Method

The turbulence moment of order m (μm) is defined as the refractive index structure constant Cn2 integrated over the whole path z with path-weighting function zm. Optical effects of atmospheric turbulence are directly related to turbulence moments. To evaluate the optical effects of atmospheric turbulence, it is necessary to measure the turbulence moment. It is well known that zero-order moments of turbulence (μ0) and five-thirds-order moments of turbulence (μ5/3), which correspond to the seeing and the isoplanatic angles, respectively, have been monitored as routine parameters in astronomical site testing. However, the direct measurement of second-order moments of turbulence (μ2) of the whole layer atmosphere has not been reported. Using a star as the light source, it has been found that μ2 can be measured through the covariance of the irradiance in two receiver apertures with suitable aperture size and aperture separation. Numerical results show that the theoretical error of this novel method is negligible in all the typical turbulence models. This method enabled us to monitor μ2 as a routine parameter in astronomical site testing, which is helpful to understand the characteristics of atmospheric turbulence better combined with μ0 and μ5/3.

Development of a new combined heat source model for welding based on a polynomial curve fit of the experimental fusion line

2016 ◽  
Vol 87 (5-8) ◽  
pp. 1985-1997 ◽  
Author(s):  
Junqiang Wang ◽  
Jianmin Han ◽  
Joseph P. Domblesky ◽  
Zhiyong Yang ◽  
Yingxin Zhao ◽  
...  
Keyword(s):  
Heat Source ◽  
Source Model ◽  
Fusion Line ◽  
Heat Source Model ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Experimental Fusion

An alternating coupled two-unequal residual functions algorithm for second-order calibration

2014 ◽  
Vol 6 (16) ◽  
pp. 6322 ◽  
Author(s):  
Yong Li ◽  
Hai-Long Wu ◽  
Chong-Chong Nie ◽  
Hui-Wen Gu ◽  
Xiang-Dong Qing ◽  
...  
Keyword(s):  
Second Order ◽  
Residual Functions ◽  
Second Order Calibration
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