High dimensional reliability analysis based on combinations of adaptive Kriging and dimension reduction technique

Abstract High dimensional reliability analysis is unavoidable if a structural system involving stochastic process because Karhunen–Loève (K‐L) expansion is commonly used. Reliability analysis for structural systems with computationally intensive numerical models and high dimensions is challenging. In this study, an effective high dimensional reliability analysis method is proposed based on principal components and active subspace (PCAS) and active Kriging, and is termed as PCAS‐AK. The proposed method can address two shortcomings existing in PCAS: the latter select training samples randomly and cannot deal with parallel processing. The proposed method, however, selects training samples adaptively, subsequently, the training samples that have high contribution to probability of failure are selected, which can improve computational efficiency. To reduce overall computational time and allow parallelization, K‐weighted‐means combined with learning function are used to select multiple samples at each iteration. After the dimension reduction of both input and output spaces, the samples selected by adaptive method are used to construct Kriging model in the latent low‐dimensional space. Three examples are used to demonstrate the applicability and accuracy of the proposed method. Results show that the proposed method can deal with parallel processing and is, generally, more effective than PCAS for high dimensional reliability problems.