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

The "ensemble" up-crossing rate technique consists of averaging the up-crossing rate of a random load process, for a deterministic barrier level, over the resistance distribution at discrete time points. Averaging over the resistance makes the assumption of independent up-crossings less appropriate. As a result the first passage failure probabilities may become excessively conservative in problems with other than extremely low failure probabilities. The technique has received little attention from the structural reliability community, and hence little is known about the quality of this approximation or its limits of application. In the paper, Monte Carlo simulation results are used to predict the error introduced by this approach and to derive a correction to the ensemble up-crossing rate solution. The methodology is tested on a range of time-invariant and time-variant random barriers. Results shown that, using the developed correction, the error in the original ensemble up-crossing rate approximation is largely reduced. The error expressions are derived using simple analytical random barriers and limited sampling intervals, but can be applied to problems with more complex, numerically evaluated random barriers and extended beyond the simulated time interval.