Chapter2 On the Aggregation and Extrapolation of Uncertainty from Component to System Level Models Angel Urbina, Richard G. Hills, and Adam C. Hetzler Abstract The use of computational models to simulate the behavior of complex mechanical systems is ubiquitous in many high consequence applications such as aerospace systems. Results from these simulations are being used, among other things, to inform decisions regarding system reliability and margin assessment. In order to properly support these decisions, uncertainty needs to be accounted for. To this end, it is necessary to identify, quantify and propagate different sources of uncertainty as they relate to these modeling efforts. Some sources of uncertainty arise from the following: (1) modeling assumptions and approximations, (2) solution convergence, (3) differences between model predictions and experiments, (4) physical variability, (5) the coupling of various components and (6) and unknown unknowns. An additional aspect of the problem is the limited information available at the full system level in the application space. This is offset, in some instances, by information on individual components at testable conditions. In this paper, we focus on the quantification of uncertainty due to differences in model prediction and experiments, and present a technique to aggregate and propagate uncertainty from the component level to the full system in the applications space. A numerical example based on a structural dynamics application is used to demonstrate the technique. Keywords Aggregation • Extrapolation • Uncertainty propagation Nomenclature F Force fn Frequency of interest m Mass of test article — Instantaneous damping 2.1 Introduction The reliability of high consequence systems, such as aerospace components, has been traditionally established by testing individual systems and verifying their performance is within some acceptable limits. Although full scale testing is currently not feasible for some systems under actual use environments, some limited testing is often available for components, subsystems (i.e. groups of components) and a very limited number of tests of the full system in other use environments. Modeling and simulation attempt to fill the gap left by the lack of full scale testing for the actual use environments. Because component level data are usually cheaper and easier to obtain relative to the system data, it is advantageous to have the ability to build individual models of the component and/or subsystems using available data and incorporate them into a system level model. This leads to a hierarchical approach to building system level models and consequently the uncertainty in the system model is a function of the component level data and of the knowledge not captured in the component or subsystem level data. A. Urbina ( ) • R.G. Hills • A.C. Hetzler Sandia National Laboratories, P.O. Box 5800, MS 0828, Albuquerque, NM 87185, USA e-mail: aurbina@sandia.gov H.S. Atamturktur et al. (eds.), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04552-8__2, © The Society for Experimental Mechanics, Inc. 2014 11
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