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A PCE-based multiscale framework for the characterization of uncertainties in complex systems

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Abstract

This paper presents a framework for the modeling and analysis of material systems that exhibit uncertainties in their constituents at all scales. The framework integrates multiscale formalism with a polynomial chaos construction enabling an explicit representation of quantities of interests, at any scale, in terms of any form of underlying uncertain parameters, a key feature to model multiscale dependencies. It is demonstrated how the framework can successfully tackle settings where a hierarchy of scales must be explicitly modeled. The application of this framework is illustrated in the construction of stochastic models of mesoscale and macroscale properties of non-crimp fabric composites. Joint statistical properties of upscaled components of the composite, including properties of tow, laminae and laminate, are computed.

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Acknowledgements

The information, data, or work presented herein was funded in part by the Office of Energy Efficiency and Renewable Energy (EERE), U.S. Department of Energy, under Award Number DE-EE0006826. The information, data, or work presented herein was funded in part by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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Authors and Affiliations

  1. Viterbi School of Engineering, University of Southern California, Los Angeles, CA, 90089, USA

    Loujaine Mehrez & Roger Ghanem

  2. Altair Engineering, Inc., Troy, MI, 48083, USA

    Jacob Fish

  3. GM R&D Technical Center, General Motors Company, 30500 Mound Rd, Warren, MI, 48092, USA

    Venkat Aitharaju & Will R. Rodgers

Authors
  1. Loujaine Mehrez
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  2. Jacob Fish
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  3. Venkat Aitharaju
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  4. Will R. Rodgers
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  5. Roger Ghanem
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Correspondence to Loujaine Mehrez.

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Mehrez, L., Fish, J., Aitharaju, V. et al. A PCE-based multiscale framework for the characterization of uncertainties in complex systems. Comput Mech 61, 219–236 (2018). https://doi.org/10.1007/s00466-017-1502-4

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  • DOI: https://doi.org/10.1007/s00466-017-1502-4

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