A regression-tree-based method for structural reliability assessment
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Structural reliability plays a pivotal role in structural engineering, providing a quantitative basis for assessing safety, serviceability, and risk. Traditionally, the evaluation of a survival probability is carried out either through Monte Carlo simulations, which can be extremely computationally demanding, or through path integral approaches that account for absorbing barriers. However, for damped oscillators, path integral techniques typically require the probability density function (PDF) of the state variables, i.e., bi-dimensional PDF, which significantly increases both the mathematical complexity of the problem and the associated computational cost. In this paper, a regression tree is specifically trained on a large dataset to estimate, within a fraction of a second, the survival probability of a damped oscillator at a given time instant when subjected to white noise excitation. The proposed method aims to retain the accuracy of reliability computations while drastically reducing runtime. The accuracy of the proposed method is validated by comparing its predictions against a Monte Carlo simulation, showing strong agreement and confirming the proposed approach as a fast and effective tool for structural reliability assessment.
