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    Statistical Analysis and Bayesian Methods for Fatigue Life Prediction and Inverse Problems in Linear Time Dependent PDEs with Uncertainties

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    Dissertation
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    Type
    Dissertation
    Authors
    Sawlan, Zaid A cc
    Advisors
    Tempone, Raul cc
    Committee members
    Knio, Omar cc
    Rue, Haavard cc
    Le Maitre, Olivier
    Scavino, Marco cc
    Prudhomme, Serge
    Nobile, Fabio
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2018-11-10
    Permanent link to this record
    http://hdl.handle.net/10754/629731
    
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    Abstract
    This work employs statistical and Bayesian techniques to analyze mathematical forward models with several sources of uncertainty. The forward models usually arise from phenomenological and physical phenomena and are expressed through regression-based models or partial differential equations (PDEs) associated with uncertain parameters and input data. One of the critical challenges in real-world applications is to quantify uncertainties of the unknown parameters using observations. To this purpose, methods based on the likelihood function, and Bayesian techniques constitute the two main statistical inferential approaches considered here. Two problems are studied in this thesis. The first problem is the prediction of fatigue life of metallic specimens. The second part is related to inverse problems in linear PDEs. Both problems require the inference of unknown parameters given certain measurements. We first estimate the parameters by means of the maximum likelihood approach. Next, we seek a more comprehensive Bayesian inference using analytical asymptotic approximations or computational techniques. In the fatigue life prediction, there are several plausible probabilistic stress-lifetime (S-N) models. These models are calibrated given uniaxial fatigue experiments. To generate accurate fatigue life predictions, competing S-N models are ranked according to several classical information-based measures. A different set of predictive information criteria is then used to compare the candidate Bayesian models. Moreover, we propose a spatial stochastic model to generalize S-N models to fatigue crack initiation in general geometries. The model is based on a spatial Poisson process with an intensity function that combines the S-N curves with an averaged effective stress that is computed from the solution of the linear elasticity equations.
    Citation
    Sawlan, Z. A. (2018). Statistical Analysis and Bayesian Methods for Fatigue Life Prediction and Inverse Problems in Linear Time Dependent PDEs with Uncertainties. KAUST Research Repository. https://doi.org/10.25781/KAUST-8422C
    DOI
    10.25781/KAUST-8422C
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-8422C
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; PhD Dissertations; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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