Multi-point Bayesian active learning reliability analysis

Authored by

Tong Zhou, Xujia Zhu, Tong Guo, You Dong, Michael Beer

Abstract

This manuscript presents a novel Bayesian active learning reliability method integrating both Bayesian failure probability estimation and Bayesian decision-theoretic multi-point enrichment process. First, an epistemic uncertainty measure called integrated margin probability (IMP) is proposed as an upper bound for the mean absolute deviation of failure probability estimated by Kriging. Then, adhering to the Bayesian decision theory, a look-ahead learning function called multi-point stepwise margin reduction (MSMR) is defined to quantify the possible reduction of IMP brought by adding a batch of new samples in expectation. The cost-effective implementation of MSMR-based multi-point enrichment process is conducted by three key workarounds: (a) Thanks to analytical tractability of the inner integral, the MSMR reduces to a single integral. (b) The remaining single integral in the MSMR is numerically computed with the rational truncation of the quadrature set. (c) A heuristic treatment of maximizing the MSMR is devised to fastly select a batch of best next points per iteration, where the prescribed scheme or adaptive scheme is used to specify the batch size. The proposed method is tested on two benchmark examples and two dynamic reliability problems. The results indicate that the adaptive scheme in the MSMR gains a good balance between the computing resource consumption and the overall computational time. Then, the MSMR fairly outperforms those existing leaning functions and parallelization strategies in terms of the accuracy of failure probability estimate, the number of iterations, as well as the number of performance function evaluations, especially in complex dynamic reliability problems.

Details

Organisation(s): Institute for Risk and Reliability
External Organisation(s): Hong Kong University of Science and Technology
CentraleSupelec
Université Paris-Saclay
CNRS Open Research Data Department (DDOR)
Southeast University (SEU)
Hong Kong Polytechnic University
University of Liverpool
Tongji University
Type: Article
Journal: Structural safety
Volume: 114
No. of pages: 24
ISSN: 0167-4730
Publication date: 05.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Building and Construction, Safety, Risk, Reliability and Quality
Electronic version(s): https://doi.org/10.1016/j.strusafe.2024.102557 (Access: Closed )
https://hal.science/hal-04896079 (Access: Open )