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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. [ABSTRACT FROM AUTHOR]

To address the issue of low accuracy resulting from approximation errors in conventional interval finite element methods, this study presents an ɛ -accelerated bivariate dimension-reduction interval finite element method. The proposed method aims to accurately and efficiently predict the static response of structures with high dimensionality and large uncertainty parameters. We first approximate the structural interval equilibrium equation using a bivariate dimension-reduction method. An explicit expression for the sequence of displacements is derived by approximating the inverse of the structural interval stiffness matrix using the Neumann series. Adjoint-based sensitivity analysis can effectively avoid the response interval expansion caused by parameter coupling. For improving the convergence speed and computational accuracy, the displacement response sequence is accelerated by a vector ɛ acceleration algorithm and an adaptive strategy. Finally, three engineering structures with uncertain-but-bounded parameters are analyzed with the proposed method. Compared with conventional interval analysis methods, the proposed method effectively balances computational accuracy and efficiency, making it more suitable for non-linear and large uncertainty problems with multiple interval parameters. The study shows that ɛ -accelerated bivariate dimension-reduction interval finite element method has a promising application. • An interval finite element method based on bivariate dimension-reduction is proposed. • Explicit sequences and errors for the bounds of displacements were derived. • Dependencies between parameters are addressed by adjoint-based sensitivity analysis. • Convergence speed and accuracy are improved by the adaptive ɛ algorithm. • Structural response intervals are efficiently and accurately predicted. [ABSTRACT FROM AUTHOR]