A multi-objective-optimization based importance sampling method and its application in seismic stability analysis of gravity dam

Abstract

The stable reliability analysis of dams is a challenging topic in geotechnical engineering safety. Because there are more complex system failure modes and high-dimensional parameters in large solid structures, it is difficult to calculate failure probability efficiently and accurately using general reliability analysis methods. Most methods suffer from complex iterative processes and the curse of dimensionality. In this study, an improved importance sampling method based on multi-objective optimization is proposed and applied to reliability analysis for dam sliding. The optimization function is constructed from the limit state surface and the original probability density. The optimal sampling center is selected from the optimization results by considering the dominant performance function as well as the coefficient of variation of the weight function. Four numerical examples and a case study of the sliding stability of a gravity dam demonstrate the accuracy and efficiency of the proposed method. The results show that the proposed method is not sensitive to the specific multi-objective optimization algorithm used. Simulations using multiple sampling centers perform better overall than simulations using a single sampling center. In particular, the proposed method remains applicable to parallel systems with 20 high-dimensional parameters that are virtually immune to the curse of dimensionality.