Fueled by a growing number of applications in science and engineering, the development of stochastic simulation metamodeling methodologies has gained momentum in recent years. A majority of the existing methods, such as stochastic kriging (SK), only focus on efficiently metamodeling the mean response surface implied by a stochastic simulation experiment. As the simulation outputs are stochastic with the simulation variance varying significantly across the design space, suitable methods for variance modeling are required. This thesis takes a dual metamodeling perspective and aims at exploiting the benefits of fitting the mean and variance functions simultaneously for achieving an improved predictive performance. We first explore the effects of replacing the sample variances with various smoothed variance estimates on the performance of SK and propose a dual metamodeling approach to obtain an efficient simulation budget allocation rule. Second, we articulate the links between SK and least-square support vector regression and propose to use a ``dense and shallow'' initial design to facilitate selection of important design points and efficient allocation of the computational budget. Third, we propose a variational Bayesian inference-based Gaussian process (VBGP) metamodeling approach to accommodate the situation where either one or multiple simulation replications are available at every design point. VBGP can fit the mean and variance response surfaces simultaneously, while taking into full account the uncertainty in the heteroscedastic variance. Lastly, we generalize VBGP for handling large-scale heteroscedastic datasets based on the idea of ``transductive combination of GP experts.'' / Doctor of Philosophy / In solving real-world complex engineering problems, it is often helpful to learn the relationship between the decision variables and the response variables to better understand the real system of interest. Directly conducting experiments on the real system can be impossible or impractical, due to the high cost or time involved. Instead, simulation models are often used as a surrogate to model the complex stochastic systems for conducting simulation-based design and analysis. However, even simulation models can be very expensive to run. To alleviate the computational burden, a metamodel is often built based on the outputs of the simulation runs at some selected design points to map the performance response surface as a function of the controllable decision variables, or uncontrollable environmental variables, to approximate the behavior of the original simulation model. There has been a plethora of work in the simulation research community dedicated to studying stochastic simulation metamodeling methodologies suitable for analyzing stochastic simulation experiments in science and engineering. A majority of the existing methods, such as stochastic kriging (SK), have been known as effective metamodeling tool for approximating a mean response surface implied by a stochastic simulation. Despite that SK has been extensively used as an effective metamodeling methodology for stochastic simulations, SK and metamodeling techniques alike still face four methodological barriers: 1) Lack of the study in variance estimates methods; 2) Absence of an efficient experimental design for simultaneous mean and variance metamodeling; 3) Lack of flexibility to accommodate situations where simulation replications are not available; and 4) Lack of scalability. To overcome the aforementioned barriers, this thesis takes a dual metamodeling perspective and aims at exploiting the benefits of fitting the mean and variance functions simultaneously for achieving an improved predictive performance. We first explore the effects of replacing the sample variances with various smoothed variance estimates on the performance of SK and propose a dual metamodeling approach to obtain an efficient simulation budget allocation rule. Second, we articulate the links between SK and least-square support vector regression and propose to use a “dense and shallow” initial design to facilitate selection of important design points and efficient allocation of the computational budget. Third, we propose a variational Bayesian inference-based Gaussian process (VBGP) metamodeling approach to accommodate the situation where either one or multiple simulation replications are available at every design point. VBGP can fit the mean and variance response surfaces simultaneously, while taking into full account the uncertainty in the heteroscedastic variance. Lastly, we generalize VBGP for handling large-scale heteroscedastic datasets based on the idea of “transductive combination of GP experts.”
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/91482 |
| Date | 17 July 2019 |
| Creators | Wang, Wenjing |
| Contributors | Industrial and Systems Engineering, Chen, Xi, Yang, Feng, Sarin, Subhash C., Taaffe, Michael R. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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