The Maximum Entropy Estimation of Structural Reliability Based on Monte Carlo Simulation

Taking the advantage of the high efficiency of Monte Carlo simulation for events of high failure probability, it is adopted to estimate the probabilities of failure of the reduced safe margins of structures. By assuming that the low tail of the probabilistic distribution of the safe margin to follow a Weibull distribution, the failure probabilities simulated are taken as empirical data to extrapolate the Weibull parameters. Among the candidate Weibull distributions, the maximum entropy is used to identify the optimum one which is used to predict the truth probabilities of failure of structures. Two typical numerical examples are carried out to demonstrate the method developed.