Using Predictive Models in Engineering Design: Metamodeling, Uncertainty Quantification, and Model Validation

Ying Xiong

doi:https://doi.org/10.21985/N2NX60

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Using Predictive Models in Engineering Design: Metamodeling, Uncertainty Quantification, and Model Validation

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Predictive modeling has emerged as a new research subject that studies a broad range of modeling techniques to provide confident prediction of the phenomenon of interest by integrating scientific principles together with both computer models and observed physical experiments. Motivated by overcoming the existing challenges, the objective in this dissertation is to develop methodology and techniques to facilitate the use of predictive models in engineering design. To develop an improved metamodeling technique that better captures changing smoothness behavior in high-dimensional engineering applications, a Kriging method with sparse yet flexible parameterization of non-stationary covariance is investigated. To efficiently yield an improved predictive model, a bias-correction approach is examined considering two scenarios by combining either computer and physical experimental data or data from variable fidelity computer models. A Bayesian approach is applied to the Gaussian process model to assess the uncertainty of the bias-corrected model. To achieve a better understanding of the various model updating strategies, we examine different model updating formulations as well as different solution methods. As opposed to traditional calibration approaches we pay particular attention to the situations in which certain computer model parameters vary from trial to trial. A maximum likelihood estimation approach for parameter estimation s developed toward the best agreement between physical and computer observations. Motivated by the need for validating predictive models in engineering design, a design-driven Bayesian model validation procedure is employed. With the quantified uncertainty of Bayesian prediction models, decision validation metrics are proposed to provide confidence measures in making a design choice. To facilitate resource allocation in updating a predictive model, a new objective oriented sequential sampling approach is developed for computer experiments, by employing a periodical switching criterion in sampling for balancing the needs of optimizing a design objective versus reducing the metamodel uncertainty. A design confidence metric is proposed as the stopping criterion to facilitate design decision making. Through various example problems, it is illustrated that the research developments in this dissertation are applicable to various engineering applications, thus providing useful techniques in metamodeling, uncertainty quantification, and model validation that are critical to using predictive models in engineering design.

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