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Author: Jin, Ruichen
Supervisor: Chen, Wei
Institution: Graduate College, University of Illinois at Chicago
The effectiveness of using Computer Aided Engineering (CAE) tools to support design decisions is often hindered by the enormous computational costs of complex analysis models, especially when uncertainty is considered. Approximations of analysis models, also known as “metamodels”, are widely used to replace analysis models for design concept exploration and optimization. However, challenges still remain to efficiently and effectively utilize metamodels in real-world design problems. The goal of this dissertation is to advance the use of metamodeling techniques in engineering design by developing efficient and robust methods for constructing metamodels and further exploiting metamodels to gain design knowledge and to facilitate uncertainty analysis. Research developments have been made in the following three main areas.
In the area of optimal design of computer experiments, an efficient algorithm is developed for constructing optimal design of computer experiments. There are two major developments involved. One is on developing an efficient global optimal search algorithm, i.e., the enhanced stochastic evolutionary (ESE) algorithm. The other is on developing efficient methods for evaluating optimality criteria to facilitate the search of optimal experimental designs. Based on a comprehensive statistical comparison, it is found that the proposed algorithm is much more efficient than existing techniques. Specifically, the computation time has been cut from hours to merely minutes if not seconds, which makes the just-in-time generation of large size optimal designs possible. Furthermore, the algorithm is very flexible to work on various optimality criteria and different classes of designs while maintaining desirable special structural properties.
In the area of model-fitting techniques and procedure, an efficient hybrid global-local search strategy is first developed for estimating the parameters in Kriging models. Numerical techniques are proposed to further improve the efficiency and robustness of Kriging model-fitting. In the second part of this research area, a generic sequential metamodeling procedure is proposed. Building upon the earlier proposed optimal experimental design algorithm, sample data are collected in sequential steps and fully utilized for both model-fitting and model-assessing purposes. The sequential procedure provides designers the flexibility of terminating a metamodeling process whenever the quality of a metamodel is good enough.
Finally, analytical techniques are developed for global sensitivity analysis and uncertainty analysis via the use of metamodels. The proposed approaches provide more accurate as well as more efficient techniques for evaluating the statistical quantities involved in both global sensitivity analysis and uncertainty analysis. Analytical global sensitivity analysis is particularly beneficial in engineering design to gain insights into the effects of inputs on outputs. Analytical uncertainty analysis eliminates the noises associated with sampling methods and greatly facilitates the convergence of robust design optimization. It is demonstrated that the proposed methods can be applied to a variety of commonly used metamodeling techniques.
Through example problems from literature and industrial applications, it is illustrated that the research developments in this dissertation can be integrated to provide efficient and reliable techniques for advancing the application of metamodeling techniques in real world engineering design problems.