A Methodology for Determining Experimental Uncertainties in Regressions

1998 ◽  
Vol 120 (3) ◽  
pp. 445-456 ◽  
Author(s):  
K. K. Brown ◽  
H. W. Coleman ◽  
W. Glenn Steele
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Regression Analysis ◽  
Discharge Coefficient ◽  
Linear Regression Analysis ◽  
Uncertainty Propagation ◽  
Experimental Information ◽  
Uncertainty Sources ◽  
Systematic Uncertainties ◽  
Proper Estimation

A methodology to determine the experimental uncertainties associated with regressions is presented. When a regression model is used to represent experimental information, the uncertainty associated with the model is affected by random, systematic, and correlated systematic uncertainties associated with the experimental data. The key to the proper estimation of the uncertainty associated with a regression is a careful, comprehensive accounting of systematic and correlated systematic uncertainties. The methodology presented in this article is developed by applying uncertainty propagation techniques to the linear regression analysis equations. The effectiveness of this approach was investigated and proven using Monte Carlo simulations. The application of that methodology to the calibration of a venturi flowmeter and its subsequent use to determine flowrate in a test is demonstrated. It is shown that the previously accepted way of accounting for the contribution of discharge coefficient uncertainty to the overall flowrate uncertainty does not correctly account for all uncertainty sources, and the appropriate approach is developed, discussed, and demonstrated.

Discharge coefficients for ogee weirs including the effects of a sloping upstream face

2020 ◽  
Vol 20 (4) ◽  
pp. 1493-1508 ◽  
Author(s):  
Farzin Salmasi ◽  
John Abraham
Keyword(s):  
Gene Expression ◽  
Experimental Data ◽  
Regression Analysis ◽  
Discharge Coefficient ◽  
Gene Expression Programming ◽  
Linear Interpolation ◽  
Performance Criteria ◽  
Upstream Face ◽  
Discharge Coefficients ◽  
Regression Techniques

Abstract Discharge coefficients (C0) for ogee weirs are essential factors for predicting the discharge-head relationship. The present study investigates three influences on the C0: effect of approach depth, weir upstream face slope, and the actual head, which may differ from the design head. This study uses experimental data with multiple non-linear regression techniques and Gene Expression Programming (GEP) models that are applied to introduce practical equations that can be used for design. Results show that the GEP method is superior to the regression analysis for predicting the discharge coefficient. Performance criteria for GEP are R2 = 0.995, RMSE = 0.021 and MAE = 0.015. Design examples are presented that show that the proposed GEP equation correlates well with the data and eliminates linear interpolation using existing graphs.

Full-field numerical differentiation

1978 ◽  
Vol 13 (3) ◽  
pp. 177-183 ◽  
Author(s):  
R E Rowlands ◽  
K D Winters ◽  
J A Jensen
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Regression Analysis ◽  
Numerical Differentiation ◽  
Experimental Information ◽  
Numerical Representation ◽  
Spline Regression ◽  
Full Field ◽  
Independent Variables ◽  
Two Independent Variables

The numerical representation and differentiation of experimental information is extended to full-field capability involving two independent variables. Bicubic spline, regression analysis and finite-element concepts are employed. Smoothing of the experimental data is accomplished mathematically. The technique are demonstrated by analysing loaded plates.

The Elovich equation and chemisorption kinetics

1966 ◽  
Vol 19 (11) ◽  
pp. 2015 ◽  
Author(s):  
JA Allen ◽  
PH Scaife
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Regression Analysis ◽  
Numerical Methods ◽  
Linear Regression ◽  
Apparent Activation Energy ◽  
Linear Regression Analysis ◽  
Systematic Procedure ◽  
Elovich Equation

A generalized Elovich equation which takes account of features of chemi- sorption not previously included is presented and discussed. A systematic procedure for determining the parameters, the initial rates, and the corresponding apparent activation energy is described. A method based on a linear regression analysis which is capable of evaluating the parameters more satisfactorily than graphical and numerical methods is proposed and applied to a range of existing experimental data.

Evaluation of Measurement Uncertainty from Imperfect Data

2013 ◽  
Vol 457-458 ◽  
pp. 815-820
Author(s):  
Xiao Zhang Zhang ◽  
Ai Dong Ge ◽  
Jian Wei Ma ◽  
Yu Jie Bai
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Method ◽  
Uncertainty Propagation ◽  
Evaluation Process ◽  
Process Data ◽  
Imperfect Data ◽  
Probability Propagation ◽  
The Mean

The uncertainty evaluation process of imperfect experimental data is presented in this paper. In the process, data neither in steady state nor under normal distribution compared with the conventional assumptions are considered. Results of the evaluation show that the uncertainty is asymmetry to the mean of the data while symmetry in conventional way. Furthermore, three ways to deal with the uncertainty propagation are discussed, and the probability propagation is simulated by Monte Carlo method.

scholarly journals Port-Hamiltonian Mathematical Model of a Fluid Ring Attitude System

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6906
Author(s):  
Juan Cristobal Alcaraz Alcaraz Tapia ◽  
Carlos E. Castañeda ◽  
Héctor Vargas-Rodríguez
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Linear Regression ◽  
Turbulent Flows ◽  
Linear Regression Analysis ◽  
Hamiltonian Formalism ◽  
System Model ◽  
Energy Shaping ◽  
Spatial Environment

In this article, we propose a mathematical model using the port-Hamiltonian formalism for a satellite’s three-axis attitude system comprising fluid rings. Fluid rings are an alternative to reaction wheels used for the same purpose, since, for the same mass, they can exert a greater torque than a reaction wheel as the fluid can circulate the periphery of the satellite. The port-Hamiltonian representation lays the foundation for a posterior controller that is feasible, stable, and robust based on the interconnection of the system to energy shaping and/or damping injection components, and by adding energy routing controllers. The torques exerted by the fluid rings are modeled using linear regression analysis on the experimental data got from a prototype of a fluid ring. Since the dynamics of turbulent flows is complex, the torques obtained by the prototype lead to a simpler first approach, leaving its uncertainties to a controller. Thus, the attitude system model could be tested in a future prototype before considering a spatial environment.

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