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

TL;DR

This paper models dependent stationary load processes exceeding high thresholds, estimating the extremal index to improve maximum load predictions in structural reliability, using Bayesian methods and Cox process modeling.

Contribution

It introduces a dependent load process model with weakened dependence, incorporating the extremal index and Bayesian updating to better estimate maximum loads.

Findings

Dependence reduces conservatism in load maximum estimates.

Extremal index effectively captures clustering of exceedances.

Bayesian updating improves distribution estimation accuracy.

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.