Time dependent reliability: a time series point of view

Resumo

Engineering problems where material properties deteriorate over time or in cases of random loading

modelled as a random process, the evaluation of the probability of structural failure generates a significant compu-
tational cost, mainly because it is a time-variant reliability problem. Stochastic problems, in which the probability

of failure is time-dependent, shows to be interesting to know about the computational cost and accuracy of the

method disponible in the literature to evaluate the reliability. The assessment of time-dependent reliability prob-
lems is still a challenging task. Besides the difficulty to characterize a problem from real-world data, most of known

solutions rely on approximations suitable only for specific cases or on burdensome simulation approaches. This
is due to the difficulty in working with general stochastic processes, particularly for situations of non-ergodicity.
A time-series model is a particular case of stochastic process that operates in continuous state space and discrete
time set. Such models can be used to represent a wide range of random phenomena that spans through time,
usually with simpler formulation. They are also relatively simple to build from data tables, which are usually all
the information available about time-dependent behavior of random engineering systems. Thus, this work makes
a comparison of the application between the expansion optimal linear estimation (EOLE) method and time-series
model (e.g. ARMA), used to evaluate the time-dependent failure probability, presenting the computational cost
and the accuracy of the results obtained, and details about the solutions are addressed.