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Uncertainty Quantification and Propagation in Materials Modeling Using a Bayesian Inferential Framework

Ricciardi, Denielle E
http://orcid.org/0000-0003-4921-9030
http://rave.ohiolink.edu/etdc/view?acc_num=osu1587473424147276

Abstract Details

2020, Doctor of Philosophy, Ohio State University, Materials Science and Engineering.
In the past several decades, there has been an unprecedented demand for the discovery and design of new materials to support rapidly advancing technology. This demand has fueled a push for Integrated Computational Materials Engineering (ICME), an engineering approach whereby model linkages as well as experimental and computational integration are exploited in order to efficiently explore materials processing-to-performance relationships. Tailored simulations allow for the reduction of expensive and lengthy experiments, emphasizing the need to establish a statistical confidence in component designs and manufacturing processes from the simulations, rather than experiments, in a principled way. Since many materials models and simulations are deterministic in nature, the use of sophisticated tools and techniques are required. Achieving a statistical confidence in a simulation output requires, first, the identification of the various sources of error and uncertainty affecting the simulation results. These sources include machine and user error in collecting calibration data, uncertain model parameters, random error from natural processes, and model inadequacy in capturing the true material property or behavior. Statistical inference can then be used to recover information about unknown model parameters by conditioning on available data while taking into account the various sources of uncertainty. In this work, Bayesian inference is used to quantify and propagate uncertainty in simulations of material behavior. More specifically, a random effects hierarchical framework is used since it provides a way to account for uncertainty stemming from random natural processes or conditions. This is especially important in many materials modeling applications where the random microstructure plays an important role in dictating material behavior. In addition to this, in many cases experiments are quite costly, so in order to obtain sufficient data for calibration, a compilation of data from multiple sources (i.e, labs, publications, experimental techniques) may be necessary. As a result, there is a not only error within each experiment due to noise, resolution or machine/user error, but also variations in the data from sample-to-sample (or experiment-to-experiment). The random effects model allows for the consideration of this variability that occurs between samples to robustly calibrate model parameters and predict material behavior. The statistical framework is first demonstrated for parameter estimation and response prediction in the phenomenological viscoplastic self-consistent (VPSC) crystal plasticity model [1]. Inference is performed under two different scenarios: 1) with the consideration of model discrepancy, modeled through a Gaussian process and 2) without the consideration of model discrepancy. Second, uncertainty quantification and propagation is demonstrated for calculations of phase equilibrium for the binary AgCu system. In all cases, uncertainty due to uncertain model inputs, observation error, as well as sample-to-sample variability are considered. A Metropolis-Hastings Markov chain Monte Carlo algorithm is used to estimate model parameters with a quantified level of uncertainty. This uncertainty is then propagated to induce a probability distribution in the simulation output and quantified using posterior summaries such as the mean, mode, and highest posterior intervals (HPI).
Stephen Niezgoda (Advisor)
Oksana Chkrebtii (Committee Member)
Yunzhi Wang (Committee Member)
Alan Luo (Committee Member)
231 p.
Materials Science; Statistics
Uncertainty Quantification; Bayesian Inference; Random Effects; Crystal Plasticity; VPSC; CALPHAD; Model Discrepancy, Gaussian Process

Recommended Citations

Citations

  • Ricciardi, D. E. (2020). Uncertainty Quantification and Propagation in Materials Modeling Using a Bayesian Inferential Framework [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587473424147276

    APA Style (7th edition)

  • Ricciardi, Denielle. Uncertainty Quantification and Propagation in Materials Modeling Using a Bayesian Inferential Framework. 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1587473424147276.

    MLA Style (8th edition)

  • Ricciardi, Denielle. "Uncertainty Quantification and Propagation in Materials Modeling Using a Bayesian Inferential Framework." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587473424147276

    Chicago Manual of Style (17th edition)

osu1587473424147276
246
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This open access ETD is published by The Ohio State University and OhioLINK.