Real-time reliability estimation for serviceability limit states in structures with uncertain dynamic excitation and incomplete output data

A novel technique is presented for indirectly monitoring threshold exceedance in a sparsely-instrumented structure represented by a linear dynamic model subject to uncertain excitation modeled as a Gaussian process. The goal 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? It is assumed that a good linear dynamic model of the target structure has previously been identified using dynamic test data. The technique is useful for monitoring the serviceability limit states of a structure subject to unmeasured “small-amplitude” ambient excitation (e.g. wind excitation or non-damaging earthquake ground motions), or for 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 2000 is used to efficiently estimate the threshold exceedance (first-passage) probability by stochastic simulation. To improve computational efficiency for the monitoring problem, a new state-space version of ISEE is developed that incorporates state-estimation and a newly-developed state-sampling technique. The computational efficiency of the proposed technique is demonstrated through two numerical examples that show that it is vastly superior to Monte Carlo simulation in estimating the first-passage probability. Moreover, the approach produces useful by-products, including estimates for the model state and the uncertain excitation.