Uncertainty quantification in the dynamic analysis of offshore structures
Consideration for uncertainty is critical in problems associated with structural dynamics, especially in the offshore environment. Deterministic solutions are often insufficient to achieve confidence in computational results and for use in design. In uncertainty quantification (UQ) for problems dealing with many random or stochastic sources, surrogate models are often developed to reduce costs associated with running a "truth" model to verify response levels associated with low probability. Polynomial chaos expansion (PCE) is one approach used in developing such surrogate models. However, conventional PCE relies on parametric families to define the polynomials for expansion. Also, for high-dimensional problems, PCE can be inefficient if appropriate dimension reduction is not employed. Arbitrary PCE (aPCE) approaches, based on Gram-Schmidt orthogonalization, can be used to define polynomials in terms of the uncertain variables and offers a non-parametric option for UQ. An aPCE approach that can systematically account for multivariate stochasticity is developed in this study. Dimension reduction can aid in developing computationally efficient surrogate models; in this study, a gradient-based active subspace approach that identifies dominant influences on a model output's variability is employed for dimension reduction. Both aPCE and active-subspace dimension reduction are employed in studies that are focused on the dynamics of offshore structures and on low-probability events of interest.
This dissertation represents a collection of four papers that deal with PCE surrogate modeling and dimension reduction. Each paper, representing a separate chapter, contributes to the development of accurate and efficient UQ approaches for offshore structure dynamics problems involving various sources of uncertainty. We demonstrate the proposed approaches in different applications: I. estimation of fatigue damage in a marine riser due to vortex-induced vibration; II. prediction of the long-term extreme response of a moored floating structure; III. surrogate model development for structural reliability analysis; and IV. dimension reduction in the extreme response prediction of offshore structures.