An active learning reliability analysis method using adaptive Bayesian compressive sensing and Monte Carlo simulation (ABCS-MCS)

Response surface methods (RSMs) have been developed to improve the efficiency of reliability analysis for computationally time-consuming systems. Most RSMs cannot self-evaluate the accuracy of reliability analysis results and rely on Monte Carlo simulation (MCS) for verification. Therefore, this renders a challenging question in RSM applications that how to determine whether the number of sampling points is sufficient to achieve target accuracy of reliability analysis. Adaptive Kriging MCS (AK-MCS) utilizes the advantage of self-estimated uncertainty in Kriging method and combines a learning function to sequentially select additional sampling points to improve the accuracy of reliability analysis until a target accuracy is achieved. However, extensive sampling data are required to ensure that the trend function and auto-correlation structure function of AK-MCS are reliable, and AK-MCS does not work with high-dimensional or highly non-stationary data. To address these challenges, this study develops an active learning reliability analysis method using adaptive Bayesian compressive sensing (ABCS) and MCS, denoted ABCS-MCS. ABCS-MCS can self-evaluate the uncertainty of predictions and combines a learning function to adaptively determine the minimum number of sampling points and their locations for achieving a target accuracy of reliability analysis. This approach is directly applicable to non-stationary data because BCS is non-parametric and data-driven, and thus does not incorporate a trend function or an auto-correlation function. Investigations using two highly non-stationary analytical functions and a slope reliability analysis problem reveal that ABCS-MCS outperforms AK-MCS.