Line sampling based on Markov Chain simulation

For reliability analysis of implicit non-linear limit state function with high dimensionality of basic variables and small failure probability in engineering, a novel numerical simulation is presented on the combination of Markov Chain simulation and line sampling. In the presented method, Markov Chain simulation is used to draw samples in the failure domain rapidly, and important direction for the line sampling is determined by these samples. Then the line sampling technique is employed to take samples according to the important direction, and the failure probability can be evaluated by line sampling with high efficiency. Comparing to the finite differential method for obtaining the important direction, higher accuracy and higher robustness of the important direction result are obtained by the presented method. These advantages brought to the line sampling result in precision improvement of the failure probability evaluation. The application of the presented method in the reliability analysis of low cycle fatigue life of an engine turbine disc structure, which is applied by multiple cyclic loads, demonstrates the efficiency and feasibility.