An efficient method for time-dependent reliability problems with high-dimensional outputs based on adaptive dimension reduction strategy and surrogate model. (1st February 2023) - Ji, Yuxiang; Liu, Hui; Xiao, Ning-Cong; Zhan, Hongyou
Highlights: A new adaptive dimension reduction strategy for high dimensional problems is proposed. The selection of training sample, dimension reduction and Kriging modelling are well-combined at each iteration; The proposed method bridges dimension reduction and Kriging modeling and is a single loop process. The proposed method is effective for time-dependent reliability analysis with high dimensional outputs. Abstract: Time-dependent reliability analysis with high dimensional outputs is a challenge because of 'curse of dimensionality' and accurate reliability estimation over entire time interval is computationally expensive. In this paper, an efficient time-dependent reliability analysis method is proposed for systems with high dimensional outputs based on adaptive dimension reduction strategy and Kriging. The adaptive Kriging model is constructed in low-dimensional space after performing principal component analysis (PCA) on original time-dependent output. A new learning function and corresponding stopping criterion are developed as the guideline for selecting training samples at each iteration. The proposed learning function focuses on prediction accuracy over the entire time interval and the stopping criterion is directly linked to failure probability. Subsequently, fewer number of function evaluations is required compared with existing competitive works. Moreover, the key advantage of the proposed method is that it is a single-loop process, i.e., the selection of training samples, dimension reduction and Kriging modeling have been combined simultaneously at each iteration with adaptive manner. However, the existing competitive methods, generally, have two independent stages, i.e., stage one is collecting training samples and stage two is performing PCA and Kriging modelling for time-dependent reliability analysis. Thus, these methods cannot fully utilize the information provided by PCA to find optimal training samples. It is noteworthy that the dimension reduction is also an adaptive process in the proposed method, i.e., dimension reduction changes with the training samples at each iteration. The applicability, accuracy and efficiency of the proposed method are validated through three numerical examples and one engineering example.