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Research Papers

An Enhanced Bayesian Based Model Validation Method for Dynamic Systems

[+] Author and Article Information
Zhenfei Zhan

School of Mechanical Engineering,  Shanghai Jiao Tong University, Shanghai 200240, P. R. Chinaflee@sjtu.edu.cn

Yan Fu

Research and Advanced Engineering, Ford Motor Company, Dearborn, MI 48121yfu4@ford.com

Ren-Jye Yang1

Research and Advanced Engineering, Ford Motor Company, Dearborn, MI 48121ryang@ford.com

Yinghong Peng

School of Mechanical Engineering,  Shanghai Jiao Tong University, Shanghai 200240, P. R. Chinayhpeng@sjtu.edu.com

1

Corresponding author.

J. Mech. Des 133(4), 041005 (May 09, 2011) (7 pages) doi:10.1115/1.4003820 History: Received February 23, 2010; Revised February 14, 2011; Accepted March 10, 2011; Published May 09, 2011; Online May 09, 2011

Validation of computational models with multiple correlated functional responses requires the consideration of multivariate data correlation, uncertainty quantification and propagation, and objective robust metrics. This paper presents an enhanced Bayesian based model validation method together with probabilistic principal component analysis (PPCA) to address these critical issues. The PPCA is employed to handle multivariate correlation and to reduce the dimension of the multivariate functional responses. The Bayesian interval hypothesis testing is used to quantitatively assess the quality of a multivariate dynamic system. The differences between the test data and computer-aided engineering (CAE) results are extracted for dimension reduction through PPCA, and then Bayesian interval hypothesis testing is performed on the reduced difference data to assess the model validity. In addition, physics-based threshold is defined and transformed to the PPCA space for Bayesian interval hypothesis testing. This new approach resolves some critical drawbacks of the previous methods and adds some desirable properties of a model validation metric for dynamic systems, such as symmetry. Several sets of analytical examples and a dynamic system with multiple functional responses are used to demonstrate this new approach.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Bayesian based multivariate model validation process

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Figure 2

Enhanced Bayesian based multivariate model validation process

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Figure 3

Test and selective CAE data for magnitude changes

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(Color online) Bayesian confidence results of magnitude changes

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Figure 5

Test and selective CAE data for phase shifts

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(Color online) Bayesian confidence results of phase shifts

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Test and selective CAE data for mean shifts

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(Color online) Bayesian confidence results of mean shifts

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Figure 9

(Color online) Functional responses of test and CAE results

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Figure 10

(Color online) Histograms and normal distribution fitting curves of difference data

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Figure 11

(Color online) PPCA dimension reduction

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Figure 12

(Color online) Bayesian confidence result

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