Failure Probability Prediction for Offshore Floating Structures Using Machine Learning

Accurately estimating the failure probability is crucial in designing civil infrastructure systems, such as floating offshore platforms for oil and gas processing/production, to ensure their safe operation throughout their service periods. However, as a system becomes complex, the evaluation of a limit state function may involve the use of an external computer solver, resulting in a significant computational burden to perform Monte Carlo simulations (MCS). Moreover, the high-dimensionality of the limit state function may limit efficient sampling of input variables due to the “curse of dimensionality.” To address these issues, an efficient machine learning framework is proposed, combining polynomial chaos expansion (PCE) and active subspace. This will enable the accurate and efficient evaluation of the failure probability of an offshore structure, which typically involves a large number of uncertain parameters. Unlike conventional PCE schemes that use the original random variable space or the auxiliary variable space for building a surrogate model, the proposed method utilizes a reduced-dimension space to circumvent the “curse of dimensionality.” An appropriate coordinate transformation is first sought so that most of the variability of a limit state function can be accounted for. Next, a PCE surrogate limit state function is constructed on the derived low-dimensional “active subspace.” The Gram-Schmidt orthogonalization process is used for making basis polynomial functions, which is particularly effective when input random parameters do not follow the Askey scheme and/or when a dependence structure between the input parameters exists. Therefore, a nonlinear iso-probabilistic transformation, which makes the convergence of a surrogate to the true model difficult, is not required, unlike traditional PCE. Numerical examples, including limit state functions related to structural dynamics problems, are presented to illustrate the advantages of the proposed method in estimating failure probabilities for complex structural systems. Specifically, the method exhibits significantly improved efficiency in estimating the failure probability of an offshore floating structure without compromising accuracy as compared to traditional PCE and MCS.