An Efficient Adaptive Response Surface Method for Reliability Analysis of Geotechnical Engineering Systems Using Adaptive Bayesian Compressive Sensing and Monte Carlo Simulation (ABCS-MCS)

Geotechnical reliability-based design method provides a systematic framework to consider the effect of input parameter uncertainty on geotechnical structure design. A main challenge of reliability-based design for geotechnical engineering systems is the computational power required for reliability assessment when time-consuming geotechnical deterministic models are used, for example, finite element model. Direct use of Monte Carlo simulation (MCS) would lead to significant computational cost, which is inefficient and even unrealistic. Response surface methods (RSMs) have been developed to improve the efficiency of reliability analysis. However, most RSMs cannot self-evaluate the accuracy of reliability analysis results. Therefore, this renders a challenging question in RSMs applications that how to determine whether the number of sampling points is sufficient to achieve a target accuracy of reliability analysis. Using the advantage of self-estimated uncertainty of Kriging method, adaptive Kriging MCS (AK-MCS) method adopts the Kriging model to construct a response surface 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, AK-MCS requires extensive sampling data to construct the reliable trend function and auto-correlation structure function, and it is also not applicable to highly non-stationary data. To address these challenges, an innovative adaptive response surface method is developed using adaptive Bayesian compressive sensing (ABCS) and Monte Carlo simulation (MCS), called ABCS-MCS. ABCS-MCS can self-evaluate the uncertainty of predictions and combine a learning function to adaptively determine the minimum number of sampling points and their locations for achieving a target accuracy of reliability analysis. ABCS-MCS is directly applicable to non-stationary data because it is a purely non-parametric method. A two-layered slope reliability analysis problem with consideration of spatial variability in soil properties is illustrated. Results demonstrate that ABCS-MCS outperforms AK-MCS in terms of accuracy and efficiency of reliability analysis.

Keywords: Reliability analysis, small failure probability, adaptive response surface method, Bayesian compressive sensing, non-parametric method