Combined dimensionality reduction based adaptive polynomial chaos expansion for high-dimensional reliability analysis

Polynomial chaos expansion (PCE) is increasingly used for structural reliability analysis in various engineering fields. However, due to the curse of dimensionality, full PCE computation is often unaffordable for high-dimensional problems. In this paper, a combined dimensionality reduction based adaptive polynomial chaos expansion (CDR-PCE) is proposed for high-dimensional reliability analysis. Taking advantage of different kernel functions and low-fidelity model gradients to construct transformation matrix, a combined dimensionality reduction (CDR) method is first introduced to map high-dimensional input data to a low-dimensional space for effective dimension reduction. Then, an adaptive PCE model is constructed by employing the sparrow search algorithm to optimize the polynomial order and regularization parameter in the solving process of recently developed Bregman-iterative greedy coordinate descent. A novel CDR-PCE framework is finally conceived by incorporating the CDR method into the adaptive PCE model for enhancing both efficiency and accuracy. The performance of the proposed CDR-PCE is evaluated on five numerical examples of varying dimensionality and complexity through comparison with several state-of-the-art methods. Results show that the proposed method is superior to the benchmark algorithms in terms of accuracy, efficiency and robustness for high-dimensional reliability analysis, and its superiority becomes more significant for complex engineering structures with high nonlinearities.