Abstract

The primary aim of structural dynamics is to describe how structures behave under time-dependent loading conditions. Dynamic loads, such as those from wind, waves, or earthquakes, often involve significant uncertainty. One approach to address this uncertainty is through stochastic processes, which capture both the randomness and time-varying nature of dynamic loads [5]. Although this method provides a powerful analytical tool, it also introduces complexities for practical design. With stochastic dynamic loads, the structural response becomes a stochastic process, requiring the uncertainty in the response to be accurately described using appropriate probabilistic descriptors [3,4]. Among these descriptors, the first excursion probability is particularly useful. It quantifies the likelihood that structural responses exceed a set threshold within the duration of the stochastic load [5]. However, estimating this probability is challenging due to the high dimensionality of the problem (resulting from the time discretization of the stochastic load) and the associated time dependences. Simulation methods offer a potential solution, as they are generally insensitive to problem dimensionality and naturally account for dependences.

Within this context, the lecture explores recent advances in estimating first excursion probabilities for structural systems subjected to stochastic loads. The discussion focuses on a specific problem class – linear structural responses under Gaussian stochastic loads. Key areas of focus include:

· Reliability analysis and its sensitivity, where sensitivity refers to how the first excursion probability changes with variations in structural properties [6,7].

· Optimal structural design under stochastic loading conditions [2].

· Addressing epistemic uncertainty, which arises from factors such as incomplete knowledge [1].

Both theoretical and practical aspects of applying simulation methods to solve first excursion probability problems are covered. Case studies are presented to demonstrate the effectiveness and practical use of the discussed tools.