Real-time Reliability Estimation for Serviceability Limit States in Structures with Uncertain Dynamical Excitation and Incomplete Output Data

Abstract

We present a novel technique for indirectly monitoring threshold exceedance in a partially instrumented structure represented by a linear structural model class subject to uncertainn Gaussian dynamic excitation. The goal of this technique is to answer the following question: given incomplete output data from a structure excited by uncertain dynamic loading, what Is the probability that any particular unobserved response of the structure exceeds a prescribed threshold? To apply this technique, it is assumed that a good probabilistic linear model class of the target structure has already been determined. The new technique is useful for monitoring the serviceability limit states of a structure subject to unmeasured small-amplitude excitation (e.g. wind excitation or non-damaging earthquake ground motions) or monitoring the damage status of equipment housed in the structure that is vulnerable to such excitation. The ISEE algorithm developed by Au and Beck in 2001 is used to estimate the threshold exceedance (first-passage) probability by stochastic simulation. Computational difficulties that arise in the current application are solved by using a state-estimation technique and a newly developed state-sampling technique. The efficiency of the new technique is demonstrated through two numerical examples, which show the approach is superior to Monte Carlo simulation in estimating the first-passage probability. Moreover, the approach produces useful byproducts, including estimates for the model state and the uncertain excitation.