Efficient basis-adaptive Bayesian compressive sensing with fast leave-one-out cross-validation for reliability analysis of geotechnical engineering systems

For complex geotechnical engineering systems with highly non-stationary responses and computationally timeconsuming deterministic models, the estimation of failure probability poses a significant challenge in engineering. The non-parametric Bayesian compressive sensing (BCS)-based response surface method (RSM) has demonstrated its effectiveness as a surrogate modeling method for the reliability analysis of highly nonstationary systems. However, the performance of the BCS-based RSM heavily depends on the selection of basis functions. Incorporation of inappropriate basis functions can lead to under-fitting or over-fitting, particularly in cases of sparse sampling data. Therefore, selecting the optimal basis function is crucial to ensure the accuracy of the BCS-based response surface for reliability analysis of geotechnical systems. This study develops a novel BCSbased RSM, utilizing the analytical fast Leave-one-out cross-validation (LOOCV) method for the adaptive selection of basis functions, denoted as the BCS-LOOCV method, to effectively address this challenge in the reliability analysis of highly non-stationary geotechnical systems. In the proposed BCS-LOOCV method, the LOOCV error serves as the model selection criterion, and the optimal basis functions with the minimum LOOCV error are adaptively identified based on sparse sampling data through an efficient model comparison and selection process. Investigations using a highly non-stationary function and two slope reliability analysis problems demonstrate the reliable performance of the proposed BCS-LOOCV method.