Sequential Design for the Efficient Estimation of Offshore Structure Failure Probability

Estimation of the failure probability of offshore structures exposed to extreme ocean environments is critical to their safe design and operation. The conditional density of the environment (CDE) quantifies regions of the space of long term environment responsible for extreme structural response. Moreover, the probability of structural failure is obtained by simply integrating the CDE over the environment space. In this work, two methodologies for estimation of the CDE and failure probability are considered. The first (IS-PT) combines parallel tempering MCMC (for CDE estimation) with important sampling (for eventual estimation of failure probability). The second (AGE) combines adaptive Gaussian emulation with Bayesian quadrature. We evaluate IS-PT and two variants of the AGE procedure in application to a simple synthetic structure with multimodal CDE, and a monopile structure exhibiting non-linear resonant response. IS-PT provides reliable results for both applications for lesser compute cost than naive integration. The AGE procedures require balancing exploration and exploitation of the environment space, using a typically-unknown weight parameter, lambda. When lambda is known, perhaps from prior engineering knowledge, AGE provides a further reduction in computational cost over IS-PT. However, when unknown, IS-PT is more reliable.