Adaptive importance sampling of hybrid variable systems based on MCMC

The occurrence of key failures in a system may cause the system to degrade into different discrete states of performance. The classical importance sampling method based on Markov chain Monte Carlo (MCMC) can only be applied to a continuous variable system and cannot resolve the problem of mixed systems including discrete variables. Therefore, an improved adaptive importance sampling method based on MCMC is proposed to support the efficient simulation of system performance reliability. First, a failure space is constructed by combining different failure domains, and Markov simulation samples are achieved by the initial sample wandering in the failure space. Second, with a comprehensive consideration of continuous and discrete variables, a hybrid sampling density function is obtained through kernel density evaluation. Then, importance sampling simulation is operated according to the last hybrid sampling density function and the performance reliability is computed. Finally, the simulation efficiency is analyzed in theory. The validity and high efficiency of the proposed method are demonstrated by the case of an electro-hydrostatic actuator (EHA) system.