A PC-Kriging-HDMR integrated with an adaptive sequential sampling strategy for high-dimensional approximate modeling

High-dimensional complex multi-parameter problems are prevalent in engineering, exceeding the capabilities of traditional surrogate models designed for low/medium-dimensional problems. These models face the curse of dimensionality, resulting in decreased modeling accuracy as the design parameter space expands. Furthermore, the lack of a parameter decoupling mechanism hinders the identification of couplings between design variables, particularly in highly nonlinear cases. To address these challenges and enhance prediction accuracy while reducing sample demand, this paper proposes a PC-Kriging-HDMR approximate modeling method within the framework of Cut-HDMR. The method leverages the precision of PC-Kriging and optimizes test point placement through a multi-stage adaptive sequential sampling strategy. This strategy encompasses a first-stage adaptive proportional sampling criterion and a second-stage central-based maximum entropy criterion. Numerical tests and a practical application involving a cantilever beam demonstrate the advantages of the proposed method. Key findings include: (1) The performance of traditional single-surrogate models, such as Kriging, significantly deteriorates in high-dimensional nonlinear problems compared to combined surrogate models under the Cut-HDMR framework (e.g., Kriging-HDMR, PCE-HDMR, SVR-HDMR, MLS-HDMR, and PC-Kriging-HDMR); (2) The number of samples required for PC-Kriging-HDMR modeling increases polynomially rather than exponentially as the parameter space expands, resulting in substantial computational cost reduction; (3) Among existing Cut-HDMR methods, no single approach outperforms the others in all aspects. However, PC-Kriging-HDMR exhibits improved modeling accuracy and efficiency within the desired improvement range compared to PCE-HDMR and Kriging-HDMR, demonstrating robustness.Comment: 17 pages with 7 figures and 9 table

Data-driven approaches for improving failure resilience of engineered systems

Since the 1980s, major industries and government agencies worldwide have faced increasing challenges in ensuring the reliability and resilience of engineered systems. The goal of this dissertation is to create novel probabilistic analysis and design methodologies that enable engineered systems to achieve and sustain near-zero breakdown performance. Specifically, this dissertation is focused on developing new methods for simulation-based design and sensor-based diagnostics and prognostics that can be used to design engineered systems for failure resilience. The research contributions are in the areas of engineering design under uncertainty and post-design fault diagnostics which focuses on applications within wind turbines (energy generation), rotating machinery, and large-scale structural systems