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
Keywords	center of gravity 8-post test polynomial chaos expansion Galerkin method
Date of Defense	2008-06-03
Availability	unrestricted
Abstract 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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