Title page for ETD etd-06172008-195556

Type of Document Master's Thesis
Author Price, Darryl Brian
Author's Email Address dbprice@vt.edu
URN etd-06172008-195556
Title Estimation of Uncertain Vehicle Center of Gravity using Polynomial Chaos Expansions
Degree Master of Science
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Southward, Steve C. Committee Chair
Sandu, Adrian Committee Member
Sandu, Corina Committee Member
  • center of gravity
  • 8-post test
  • polynomial chaos expansion
  • Galerkin method
Date of Defense 2008-06-03
Availability unrestricted
The main goal of this study is the use of polynomial chaos expansion (PCE) to analyze

the uncertainty in calculating the lateral and longitudinal center of gravity for a vehicle

from static load cell measurements. A secondary goal is to use experimental testing as a

source of uncertainty and as a method to confirm the results from the PCE simulation.

While PCE has often been used as an alternative to Monte Carlo, PCE models have

rarely been based on experimental data. The 8-post test rig at the Virginia Institute for

Performance Engineering and Research facility at Virginia International Raceway is the

experimental test bed used to implement the PCE model. Experimental tests are

conducted to define the true distribution for the load measurement systems’ uncertainty.

A method that does not require a new uncertainty distribution experiment for multiple

tests with different goals is presented. Moved mass tests confirm the uncertainty analysis

using portable scales that provide accurate results.

The polynomial chaos model used to find the uncertainty in the center of gravity

calculation is derived. Karhunen-Loeve expansions, similar to Fourier series, are used to

define the uncertainties to allow for the polynomial chaos expansion. PCE models are

typically computed via the collocation method or the Galerkin method. The Galerkin

method is chosen as the PCE method in order to formulate a more accurate analytical

result. The derivation systematically increases from one uncertain load cell to all four

uncertain load cells noting the differences and increased complexity as the uncertainty

dimensions increase. For each derivation the PCE model is shown and the solution to the

simulation is given. Results are presented comparing the polynomial chaos simulation to

the Monte Carlo simulation and to the accurate scales. It is shown that the PCE

simulations closely match the Monte Carlo simulations.

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