System reliability updating based on the rejection sampling algorithm

It studies the updating model of the reliability for structural systems considering the observation information and the corresponding rejection sampling strategy. The updating model of failure probabilities for structural systems is established based on the Bayesian theory. According to the type of observation information (i.e., inequality observation information and equality observation information), the likelihood function and the posterior probability density function for random variables are derived. The rejection sampling strategy of posterior samples for random variables is determined based on the observation information domain, and the efficiency of the rejection sampling strategy is illustrated. The estimated value and its standard deviation of updated failure probabilities for structural systems are formulated. To verify the availability of the proposed method, the failure probabilities of plane frames are updated based on the plastic theory considering various observation information. The results indicate that the conditional failure probability of the structural systems considering the observation information is the integral of the posterior joint probability density of random variables in the failure domain. The strategy is feasible for selecting the prior samples which satisfy the constructed observation information domain as the posterior samples for random variables. The proposed sampling strategy can be used to update the reliability of structural systems with multiple random variables and multiple types observation information. The updated failure probabilities of structural systems decrease as the detection values of the resistance-related random variables increase or as the proofed loads increase. To reduce the uncertainties of the observation information, standard derivations of detection error for resistance-related random variables should be well controlled. Copyright ©2022 Engineering Mechanics. All rights reserved.