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    Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems

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    Type
    Article
    Authors
    Contreras, Andres A.
    Le Maître, Olivier P.
    Aquino, Wilkins
    Knio, Omar
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Date
    2016-09-19
    Online Publication Date
    2016-09-19
    Print Publication Date
    2016-10
    Permanent link to this record
    http://hdl.handle.net/10754/622314
    
    Metadata
    Show full item record
    Abstract
    A method is presented for inferring the presence of an inclusion inside a domain; the proposed approach is suitable to be used in a diagnostic device with low computational power. Specifically, we use the Bayesian framework for the inference of stiff inclusions embedded in a soft matrix, mimicking tumors in soft tissues. We rely on a polynomial chaos (PC) surrogate to accelerate the inference process. The PC surrogate predicts the dependence of the displacements field with the random elastic moduli of the materials, and are computed by means of the stochastic Galerkin (SG) projection method. Moreover, the inclusion's geometry is assumed to be unknown, and this is addressed by using a dictionary consisting of several geometrical models with different configurations. A model selection approach based on the evidence provided by the data (Bayes factors) is used to discriminate among the different geometrical models and select the most suitable one. The idea of using a dictionary of pre-computed geometrical models helps to maintain the computational cost of the inference process very low, as most of the computational burden is carried out off-line for the resolution of the SG problems. Numerical tests are used to validate the methodology, assess its performance, and analyze the robustness to model errors. © 2016 Elsevier Ltd
    Citation
    Contreras AA, Le Maître OP, Aquino W, Knio OM (2016) Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems. Probabilistic Engineering Mechanics 46: 107–119. Available: http://dx.doi.org/10.1016/j.probengmech.2016.08.004.
    Sponsors
    We wish to thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the US Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Award Number DE-SC0008789. Support from the SRI Center for Uncertainty Quantification in Computational Science and Engineering at King Abdullah University of Science and Technology is also acknowledged.
    Publisher
    Elsevier BV
    Journal
    Probabilistic Engineering Mechanics
    DOI
    10.1016/j.probengmech.2016.08.004
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0266892016300261
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.probengmech.2016.08.004
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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