Data-driven reduced order model and simplicial homology global optimization for reliability analysis and application

A novel framework of reliability analysis was developed in this study to consider the uncertainty of geomaterials and geological conditions by combining the reduced-order model (ROM), reliability analysis, and numerical model. The reliability method was used to determine the reliability index using the simplicial homology global optimization (SHGO) based on the ROM. The developed method was verified and illustrated using three numerical examples and a simple slope. The limit state curve in all three numerical examples was in excellent agreement with the actual curve. The reliability index and failure probability were also in excellent agreement with those of the actual limit state function using the first-order reliability method (FORM) and Monte Carlo simulation, respectively, indicating that the ROM method can present the limit state function well. The results showed that the developed method is feasible and effective for reliability analysis of geotechnical and geological engineering problems with a complex, nonlinear, and implicit limit state function. Furthermore, the developed method is effective, efficient, and accurate for reliability analysis. It provides an excellent way to approximate the limit state function to avoid the time-consuming numerical model in a practical engineering system.