A high-dimensional reliability analysis method via subspace updating and Gaussian process

The subspace-based surrogate modeling method has become increasingly popular in high-dimensional reliability analysis due to its effectiveness in mitigating the “curse of dimensionality.” Establishing an accurate subspace through dimensionality reduction is crucial for ensuring reliable outcomes in these methodologies. However, traditional approaches often perform dimensionality reduction solely based on sample responses and gradients, which can compromise subspace accuracy. To address this issue, this paper presents a novel high-dimensional reliability analysis method that integrates manifold optimization with Gaussian process (GP). Initially, the slice inverse regression technique is used to determine the parameter s of the initial projection matrix, and an initial GP model is constructed within the projected subspace. To enhance the precision of dimensionality reduction, the projection matrix is evaluated using responses from the GP model within the subspace, followed by calibration through manifold optimization techniques. Finally, Monte Carlo simulation is performed using the subspace GP model to estimate the failure probability. The proposed method’s effectiveness is validated through two high -dimensional case studies.