Toward quantifying uncertainties in the performance and design of offshore structures
Creators: name: Liu, Jinsong
Publisher: name: The University of Texas at Austin
Year: 2021
Subjects: Reliability analysis
Surrogate modeling
Polynomial chaos expansion (PCE)
Offshore structures

description: Accurate modeling and prediction of the long-term extreme response of offshore structures is of importance in their design. To ensure the operational safety of offshore systems over their service life, it must be verified that extreme load levels do not exceed the design resistance or capacity. A rational approach to formulate this problem is based on probabilistic design, which must account for uncertainties in the system and the environment in a direct manner. The most straightforward way to address this problem is by means of Monte Carlo Simulation (MCS) wherein all the sources of uncertainty are accounted for random sampling. However, due to the slow convergence rate of MCS and cost associated with response computations for each sample for dynamic systems, this method is not preferred in practice. This is especially true when dealing with low target probabilities of failure. To address noted challenges associated with the use of MCS, this study adopts the use of less expensive surrogate models that are representative of the original “truth” system that must be developed by means of a limited number of samples. Once established, MCS can be used with the surrogate model to assess any Quantity of Interest (QoI), such as a T-year return period load (for critical offshore systems, 50-100 year return periods are often of interest). For the surrogate models in this work, we apply the widely used Polynomial Chaos Expansion (PCE) method that seeks to represent the QoI original system, M(x), in terms of orthogonal polynomials that depend on a weight function f(x), defined by the probability distribution of all the underlying random variables. There are two key steps involved in building an accurate PCE surrogate model—first, one needs appropriate samples of the true system response for specified inputs and, then, one must estimate the polynomial expansion coefficients of the surrogate model using these sampled values. The accuracy of the PCE surrogate model developed in this manner depends not only on the number of evaluated samples but also on the specific locations of samples in the selected set. For engineering problems that are complex and for which the true response is expensive to evaluate, the number of samples used should be minimized. To this end, we explore advanced sampling approaches to extract as much information as possible regarding the true system by means of a limited number of samples. Specifically, instead of using simple MCS random samples, we will use optimal designs (D- and S-optimal designs, specifically) that offer an ‘optimal’ sample of small size from the domain of the input variables. Using these samples, then, Least-Angle Regression (LAR) is employed to build efficient “sparse” PCE models that improve the stability and accuracy of model prediction relative to ordinary PCE. To address the reliability problem where one is interested in rare events associated with very low probabilities of exceedance (or occurrence), a sequential sampling scheme is used with “exploration” samples that first span the entire domain of the variables; this is then followed by additional “exploitation” samples that seek to improve the accuracy of the surrogate model over-identified local domains of interest. Finally, a novel Christoffel Least Squares (CLS) approach is formulated and used to further reduce the required number of samples for accurate and stable PCE surrogate models. CLS relies on alternative but consistent distributions and associated orthogonal polynomial families for sampling that when used with appropriate weight functions lead to theoretically more efficient samples and are easily adapted in the PCE model building.