Title page for ETD etd-07252001-160717

Type of Document Dissertation
Author Kim, Hongman
Author's Email Address kimhm@vt.edu
URN etd-07252001-160717
Title Statistical Modeling of Simulation Errors and Their Reduction via Response Surface Techniques
Degree PhD
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Mason, William H. Committee Chair
Cliff, Eugene M. Committee Member
Grossman, Bernard M. Committee Member
Haftka, Raphael T. Committee Member
Watson, Layne T. Committee Member
  • Weibull distribution
  • response surface technique
  • M-estimation
  • convergence error
  • discretization error
Date of Defense 2001-06-18
Availability unrestricted
Errors of computational simulations in design of

a high-speed civil transport (HSCT) are investigated.

First, discretization error from a supersonic panel code,

WINGDES, is considered. Second, convergence error from

a structural optimization procedure using GENESIS is

considered along with the Rosenbrock test problem.

A grid converge study is performed to estimate

the order of the discretization error in the lift

coefficient (CL) of the HSCT calculated from WINGDES.

A response surface (RS) model using several mesh sizes

is applied to reduce the noise magnification problem

associated with the Richardson extrapolation. The RS model

is shown to be more efficient than Richardson extrapolation

via careful use of design of experiments.

A programming error caused inaccurate optimization

results for the Rosenbrock test function, while

inadequate convergence criteria of the structural

optimization produced error in wing structural weight

of the HSCT. The Weibull distribution is successfully

fit to the optimization errors of both problems.

The probabilistic model enables us to estimate average

errors without performing very accurate optimization runs

that can be expensive, by using differences between

two sets of results with different optimization control

parameters such as initial design points or convergence


Optimization results with large errors, outliers,

produced inaccurate RS approximations. A robust regression

technique, M-estimation implemented by iteratively

reweighted least squares (IRLS), is used to identify

the outliers, which are then repaired by higher fidelity

optimizations. The IRLS procedure is applied to the

results of the Rosenbrock test problem, and wing structural

weight from the structural optimization of the HSCT.

A nonsymmetric IRLS (NIRLS), utilizing one-sidedness

of optimization errors, is more effective than IRLS in

identifying outliers. Detection and repair of the outliers

improve accuracy of the RS approximations. Finally,

configuration optimizations of the HSCT are performed

using the improved wing bending material weight RS models.

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