The Extremal Index and the Maximum of a Dependent Stationary Pulse Load Process Observed above a High Threshold

Abstract

Observing a load process above high thresholds, modeling it as a pulse process with random occurrence times and magnitudes, and extrapolating life-time maximum or design loads from the data is a common task in structural reliability analyses. In this paper, we consider a stationary live load sequence that arrive according to a dependent point process and allow for a weakened mixing-type dependence in the load pulse magnitudes that asymptotically decreases to zero with increasing separation in the sequence. Inclusion of dependence in the model eliminates the unnecessary conservatism introduced by the i.i.d. (independent and identically distributed) assumption often made in determining maximum live load distribution. The scale of fluctuation of the loading process is used to identify clusters of exceedances above high thresholds which in turn is used to estimate the extremal index of the process. A Bayesian updating of the empirical distribution function, derived from the distribution of order statistics in a dependent stationary series, is performed. The pulse arrival instants are modeled as a Cox process goverened by a stationary lognormal intensity. An illustrative example utilizes in-service peak strain data from ambient traffic collected on a high volume highway bridge, and analyzes the asymptotic behavior of the maximum load.