The present study focuses on reliability analysis of linear discretized structures with uncertain mass and stiffness parameters subjected to stationary Gaussian multi-correlated random excitation. Under the assumption that available information on the uncertain parameters is poor or incomplete, the interval model of uncertainty is adopted. The reliability function for the extreme value stress process is evaluated in the framework of the first-passage theory. Such a function turns out to have an interval nature due to the uncertainty affecting structural parameters. The aim of the analysis is the evaluation of the bounds of the interval reliability function which provide a range of structural performance useful for design purposes. To limit detrimental overestimation caused by the dependency phenomenon, a sensitivity-based procedure is applied. The main advantage of this approach is the capability of providing appropriate combinations of the endpoints of the uncertain parameters which yield accurate estimates of the bounds of the interval reliability function for the extreme value stress process as long as monotonic problems are dealt with. Two case studies are analyzed to demonstrate the accuracy and efficiency of the presented method.

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These approaches employ a machine learning based optimization strategy, the so-called Bayesian optimization, for evaluating the upper and lower bounds of a generic response variable over the set of possible responses obtained when each interval variable varies independently over its range. The lack of knowledge caused by not evaluating the response function for all the possible combinations of the interval variables is accounted for by developing a probabilistic description of the response variable itself by using a Gaussian Process regression model. An iterative procedure is developed for selecting a small number of simulations to be evaluated for updating this statistical model by using well-established acquisition functions and to assess the response bounds. In both approaches, an initial training dataset is defined. While one approach builds iteratively two distinct training datasets for evaluating separately the upper and lower bounds of the response variable, the other one builds iteratively a single training dataset. Consequently, the two approaches will produce different bound estimates at each iteration. The upper and lower response bounds are expressed as point estimates obtained from the mean function of the posterior distribution. Moreover, a confidence interval on each estimate is provided for effectively communicating to engineers when these estimates are obtained at a combination of the interval variables for which no deterministic simulation has been run. Finally, two metrics are proposed to define conditions for assessing if the predicted bound estimates can be considered satisfactory. The applicability of these two approaches is illustrated with two numerical applications, one focusing on vibration and the other on vibro-acoustics.

Reliability assessment of linear discretized structures with interval parameters subjected to stationary Gaussian multicorrelated random excitation is addressed. The interval reliability function for the extreme value stress process is evaluated under the Poisson assumption of independent up-crossing of a critical threshold. Within the interval framework, the range of stress-related quantities may be significantly overestimated as a consequence of the so-called dependency phenomenon, which arises due to the inability of the classical interval analysis to treat multiple occurrences of the same interval variables as dependent ones. To limit undesirable conservatism in the context of interval reliability analysis, a novel sensitivity-based procedure relying on a combination of the interval rational series expansion and the improved interval analysis via extra unitary interval is proposed. This procedure allows us to detect suitable combinations of the endpoints of the uncertain parameters which yield accurate estimates of the lower bound and upper bound of the interval reliability function for the extreme value stress process. Furthermore, sensitivity analysis enables to identify the most influential parameters on structural reliability. A numerical application is presented to demonstrate the accuracy and efficiency of the proposed method as well as its usefulness in view of decision-making in engineering practice.