Session: Validation Methods

Paper Number: 152195

152195 - Estimating Modeling Errors at an Application Point Using Regression 

Abstract: 

Estimating modeling errors at an application point cannot be made with the V&V20 validation approach because experimental data are not available at the application point. However, in many practical situations it is important to assess the accuracy of a model result at an application point. Therefore, it is useful to develop techniques that use the data available at the setpoints of the validation space to estimate modeling errors at an application point.

This paper discusses a regression method to interpolate/extrapolate the validation data available at setpoints of a validation space to estimate an interval that should contain the modeling error at an application point. This material is currently being developed as a supplement to the ASME V&V20 Standard.

Regression is applied to the upper (d_M,U,i =E_i+u_val,i) and lower (d_M,L,i =E_i-u_val,i) bounds of the modeling error estimated at the validation setpoints. The method accounts for added uncertainty associated with regression, which depends on the validation uncertainties (u_val,i) at the validation space setpoints and numerical and input uncertainties at the application point. For purposes of this discussion, we assume that the sensitivity to primary model parameters is accounted for in the validation cases and that the setpoint conditions for the application are known exactly, therefore, the input uncertainties at the application point are zero.

The procedure for regression includes the following steps:

1.     regress the upper and lower bounds for model error from the validation setpoints to the application setpoint to obtain d_M,U,A and d_M,L,A; 

2.     quantify uncertainty due to non-zero regression residuals and due to uncertainty in the regression coefficients, u_U,regr,A and u_L,regr,A;

3.     Estimate numerical uncertainty u_num,A at the application point;

4.     Calculate added uncertainty at application point, u_U,A and u_L,,A, assuming uncertainties at validation and application are not correlated.

                                            u_U,A=((u_{U,regr,A)²+(}u_{num,A)²)^0.5}

                                            u_L,A=((u_{L,regr,A)²+(}u_{num,A)²)^0.5}

The result from regression is quantification of the range for modeling error at the application point, d_M,A, expressed as

                                           d_M,L,A-u_L,A  <  d_M,A  <  d_M,U,A+u_U,A

Least-squares weighted linear regression is adopted using the inverse of the validation uncertainties u_val,i as weights. Therefore, the determination of the regression coefficients requires the solution of a linear system of equations. 

The paper presents the mechanics of regression and calculation of uncertainty due to regression in matrix form and illustrates the application of the technique to example problems.

 

Presenting Author: Joel Peltier Betchel

Presenting Author Biography: Joel is a Principal Engineer in Bechtel's Nuclear, Security & Environmental (NS&E) Advanced Simulation and Analysis (ASA) group, serving as the technical lead for computational fluid mechanics and numerical heat transfer.

Joel has over 25 years of experience as a fluid dynamics specialist in industry and academia with specializations in physics modeling, computational fluid dynamics, numerical heat transfer, and model verification and validation. He has extensive experience in atmospheric boundary layer physics, marine hydrodynamics, industrial gas/solids/liquid flows, verification and validation of computational results, and data analysis.

Authors:

L. Joel Peltier Betchel
Urmila Ghia University of Cincinnati Office of Research
Nima Fathi Texas A&M University at Galveston
Laura Savoldi Politecnico di Torino
Kevin Dowding Sandia National Laboratories, New Mexico
Luis Eca IST