On the ensemble crossing rate approach to time variant reliability analysis of uncertain structures

The ‘ensemble’ up-crossing rate technique consists of averaging the rate at which a random load process up-crosses a deterministic barrier level over the resistance distribution at successive time points. Averaging over the resistance makes the assumption of independent up-crossings less appropriate. As a result, first passage failure probabilities may become excessively conservative in problems with other than extremely low failure probabilities. The ensemble up-crossing rate technique has a significant potential in simplifying the solution of time variant reliability problems under resistance degradation. However, little is known about the quality of this approximation or its limits of application. In the paper, a Monte Carlo simulation-based methodology is developed to predict the error in the approximation. An error parameter is identified and error functions are constructed. The methodology is applied to a range of time-invariant and time-variant random barriers, and it is shown that the error in the original ensemble up-crossing rate approximation is largely reduced. The study provides unprecedented insight into characteristics of the ensemble up-crossing rate approximation.