Time-variant reliability model and its measure index of structures based on a non-probabilistic interval process

The study on reliability of an aging structure requires taking into account the influence of time. Typical approaches for performing time-variant reliability assessment are always based upon the random process model, where the dynamic distributions of uncertain parameters are determined by a substantial number of samples. In this paper, a new time-variant reliability measurement based on a non-probabilistic interval process model is proposed, in which we describe the time-varying uncertain variables at any time as intervals and define the corresponding auto-covariance function and correlation coefficient function to characterize the correlation between limit states at different times. By combining with the set-theory approach and the classical first-passage theory, a new non-probabilistic model of safety evaluation for time-dependent structures is established, and its measure index is then analytically calculated. The proposed model of time-variant reliability is suitable for both the cases of stationary process and non-stationary process. Moreover, the Monte Carlo method is also presented as a means of verification. The comparison between the presented model and the Monte Carlo-based model is eventually carried out on two application examples; the usage, efficiency and accuracy of the developed approach can be demonstrated.