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Stochastic reduced order models for inverse problems under uncertainty.

Publication ,  Journal Article
Warner, JE; Aquino, W; Grigoriu, MD
Published in: Computer methods in applied mechanics and engineering
March 2015

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well.

Duke Scholars

Published In

Computer methods in applied mechanics and engineering

DOI

EISSN

1879-2138

ISSN

0045-7825

Publication Date

March 2015

Volume

285

Start / End Page

488 / 514

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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ICMJE
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Warner, J. E., Aquino, W., & Grigoriu, M. D. (2015). Stochastic reduced order models for inverse problems under uncertainty. Computer Methods in Applied Mechanics and Engineering, 285, 488–514. https://doi.org/10.1016/j.cma.2014.11.021
Warner, James E., Wilkins Aquino, and Mircea D. Grigoriu. “Stochastic reduced order models for inverse problems under uncertainty.Computer Methods in Applied Mechanics and Engineering 285 (March 2015): 488–514. https://doi.org/10.1016/j.cma.2014.11.021.
Warner JE, Aquino W, Grigoriu MD. Stochastic reduced order models for inverse problems under uncertainty. Computer methods in applied mechanics and engineering. 2015 Mar;285:488–514.
Warner, James E., et al. “Stochastic reduced order models for inverse problems under uncertainty.Computer Methods in Applied Mechanics and Engineering, vol. 285, Mar. 2015, pp. 488–514. Epmc, doi:10.1016/j.cma.2014.11.021.
Warner JE, Aquino W, Grigoriu MD. Stochastic reduced order models for inverse problems under uncertainty. Computer methods in applied mechanics and engineering. 2015 Mar;285:488–514.

Published In

Computer methods in applied mechanics and engineering

DOI

EISSN

1879-2138

ISSN

0045-7825

Publication Date

March 2015

Volume

285

Start / End Page

488 / 514

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences