Extreme value methods for the estimation of offshore structure failure probability

Speers, Matthew and Tawn, Jonathan and Jonathan, Philip and Randell, David (2026) Extreme value methods for the estimation of offshore structure failure probability. PhD thesis, Lancaster University.

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Abstract

Estimation of the failure probability of offshore structures exposed to extreme ocean environments is critical to their safe design and operation. This estimation must consider the joint extremal behaviour of the metocean environment surrounding the structure, and the physical interaction between the environment and the structure. This thesis uses multivariate conditional extreme value models for the joint metocean environment, coupled with simulation from physically-based models for short-term wave variability and wave-structure interaction. Using this forward approach, we can capture the uncertainty and short-term variability in each stage of estimation. Existing approaches for offshore structure design, such as environmental contour methods, do not account for this short-term variability in the ocean environment. They make simplifying assumptions about the wave-structure interaction to avoid the need for simulation from physically-based models, since this simulation can be computational infeasible in practice. We demonstrate that these assumptions are not valid for all structural scenarios, making structural risk assessment with these contour methods unreliable. We develop two alternative methods for the estimation of structural failure probability when full forward simulation is infeasible. These consist of an efficient sampling technique that combines importance sampling and parallel tempering Markov-chain Monte-Carlo, and a Gaussian emulator for the physical model with associated utility function for active learning. Each of these approaches outperform a standard Monte-Carlo sampling method for representative structural scenarios. When using the conditional extreme value model, it is required to select a threshold in one ‘conditioning variable’, such that any data with conditioning variable above the threshold is used for inference. Care must be taken when choosing this threshold to best balance the associated bias-variance trade-off. Our method for automatic threshold selection allows for optimised use of the observed data. We demonstrate the benefits of our method when estimating joint extreme probabilities and model parameters over existing methods.