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Model Validation of Dynamic Engineering Models Under Uncertainty

[+] Author Affiliations
Zequn Wang, Wei Chen

Northwestern University, Evanston, IL

Yan Fu, Ren-Jye Yang, Saeed Barbat

Ford Motor Company, Dearborn, MI

Paper No. DETC2016-59437, pp. V02BT03A048; 11 pages
doi:10.1115/DETC2016-59437
From:
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2B: 42nd Design Automation Conference
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5011-4
  • Copyright © 2016 by ASME

abstract

Validating dynamic engineering models is critically important in practical applications by assessing the agreement between simulation results and experimental observations. Though significant progresses have been made, the existing metrics lack the capability of managing uncertainty in both simulations and experiments, which may stem from computer model instability, imperfection in material fabrication and manufacturing process, and variations in experimental conditions. In addition, it is challenging to validate a dynamic model aggregately over both the time domain and a model input space with data at multiple validation sites. To overcome these difficulties, this paper presents an area-based metric to systemically handle uncertainty and validate computational models for dynamic systems over an input space by simultaneously integrating the information from multiple validation sites. To manage the complexity associated with a high-dimensional data space, Eigen analysis is performed for the time series data from simulations at each validation site to extract the important features. A truncated Karhunen-Loève (KL) expansion is then constructed to represent the responses of dynamic systems, resulting in a set of uncorrelated random coefficients with unit variance. With the development of a hierarchical data fusion strategy, probability integral transform is then employed to pool all the resulting random coefficients from multiple validation sites across the input space into a single aggregated metric. The dynamic model is thus validated by calculating the cumulative area difference of the cumulative density functions. The proposed model validation metric for dynamic systems is illustrated with a mathematical example, a supported beam problem with stochastic loads, and real data from the vehicle occupant restraint system.

Copyright © 2016 by ASME

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