A new adaptive importance sampling Monte Carlo method for structural reliability

Monte Carlo simulation is a useful method for reliability analysis. But in Monte Carlo, a large number of simulations are required to assess small failure probabilities. Many methods, such as Importance sampling, have been proposed to reduce the computational time. In this paper, a new importance sampling Monte Carlo method is proposed that reduces the numbers of calculation of the limit state function. On the other hand, the proposed algorithm does not need the knowledge about the position of the design point or the shape of the limit state function. The key-idea of the proposed algorithm is that the mean of sampling density function is changed throughout the simulation. In fact, in random point generating process each point with lower absolute value of limit state function and nearer distance from space center is considered the mean of the sampling density function. Based on this, the centralization of the sampling will be on the important area.