Type of Document Master's Thesis Author Price, Darryl Brian Author's Email Address email@example.com 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 Keywords
- center of gravity
- 8-post test
- polynomial chaos expansion
- Galerkin method
Date of Defense 2008-06-03 Availability unrestricted AbstractThe 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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