Estimation of first-passage probability under stochastic wind excitations by active-learning-based heteroscedastic Gaussian process

In the processes for designing and assessing structural systems, it is essential to evaluate their reliability against stochastic loads caused by natural or human-made hazards, e.g., wind loads, earthquakes, and collisions. The first-passage probability is a crucial measure of a system's reliability under such conditions. However, the first-passage probability estimation generally requires repetitive dynamic simulations and thus may result in high computational cost. This paper proposes a new active-learning-based surrogate method that efficiently estimates the first-passage probability under stochastic wind excitations to address the computational issue. The proposed method introduces an alternative formulation using the conditional distribution of the maximum response given time-invariant uncertain parameters to handle the high dimensionality of stochastic excitation sequences. The method employs the Gaussian-process-based surrogate model with heteroscedastic noises to fit the distribution parameter functions considering uncertainties arising from the structural system and the environmental loads. In addition, an adaptive training process of surrogates is introduced to identify the best experimental designs achieving efficient convergence. The numerical examples of an eight-story building and a transmission tower demonstrate that the proposed method can produce accurate estimation results with fewer structural simulations than existing methods.