A dimension reduction metamodeling approach for hybrid uncertainties quantification and response prediction

In this paper, a novel hierarchical Polynomial chaos-Legendre metamodel based on the high-dimensional model representation (PCLM-HDMR) approach is proposed to conquer the computational challenges of multi-degree-of-freedom systems with high-dimensional hybrid uncertain parameters. Firstly, a high-dimensional model representation-based decomposition method is extended to mitigate sample point requirements in hybrid uncertainty problems. Secondly, an adaptive orthogonal polynomial selection method is introduced based on variable-type-specific basis selection rules to approximate response components and establish PCLM-HDMR surrogate model. The complete PCLM-HDMR model provides accurate and efficient estimation of both statistical characteristics and boundary conditions for dynamic responses. A dynamic response prediction approach is then developed to efficiently approximate high-dimensional black-box input–output problems. Finally, the effectiveness of the proposed PCLM-HDMR method is validated through two numerical examples. Compared with polynomial chaos-Legendre metamodel, the proposed method requires only 4% of the sample size and reduces computational time by 92% while maintaining equivalent accuracy.