Dimensional decomposition-aided metamodels for uncertainty quantification and optimization in engineering: A review

Quantitative analysis and optimal design under uncertainty are active research areas in modern engineering structures and systems. A metamodel, as an effective mathematical modelling tool, plays an important role in it. With the deepening understanding of the complexity of practical problems, the dimensionality of uncertainties in engineering problems is also increasing, which poses a great challenge on effective high-dimensional metamodeling. To handle this issue, researchers have modified metamodeling methods using various techniques to reduce dimensionality of data requirements in high-dimensional engineering applications. We review advances in dimensional decomposition-aided metamodels for high-dimensional uncertainty quantification and optimization in engineering. First, we review the theoretical frameworks and methods for classifying and modelling uncertainty according to its sources and nature. Second, the theoretical foundations and applications of five popular metamodels are presented, and their advantages and limitations are summarized. Third, the basic theories, properties, and applications of dimensional decomposition techniques in uncertainty quantification and optimization are discussed. Different integration methods of dimensional decomposition techniques and metamodels, and their applications in uncertainty quantification are subsequently reviewed and summarized. In addition, the applications of the dimensional decomposition-aided metamodels in uncertainty optimization design are reviewed. Finally, recent research progress is summarized, and future research directions are outlined. This review aims to provide guidance and offer insightful perspectives to researchers in the field of high-dimensional uncertainty quantification, revealing areas where further work is needed.