Efficient reliability analysis via adaptive Kriging with dynamic optimization

Reliability analysis encounters efficiency limitations when addressing rare failure event scenarios. Although the surrogate model based method offers high accuracy, its computational cost escalates rapidly as the sample pool expands. A novel Dynamic Search Domain Genetic Algorithm (DSDGA) integrated with adaptive Kriging is introduced in this paper. The method employs a monotonically decaying domain constraint function to dynamically concentrate the search space, effectively reducing the optimization domain. Concurrently, the use of a genetic algorithm for optimal point selection eliminates the need for exhaustive evaluation of the U-function. Benchmark studies indicate a reduction in computational time by approximately 45 to 85 percent compared to the conventional adaptive Kriging-Monte Carlo Simulation (AK-MCS) approach, while preserving an accuracy of 99.1 percent in failure probability estimation. The proposed DSDGA-AK framework demonstrates significant efficiency and reliability. In this framework, the Kriging model comprises two components: a regression term, represented by a polynomial expression to capture the global trend, and a residual error term, modeled by a Gaussian process to simulate local variability.