Analytical and computational methods for non-Gaussian reliability analysis of nonlinear systems operating in stochastic environments
Author(s)
Guth, Stephen Carrol![Thumbnail](/bitstream/handle/1721.1/152670/guth-sguth-phd-meche-2023-thesis.pdf.jpg?sequence=3&isAllowed=y)
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Advisor
Sapsis, Themistoklis P.
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Statistical problems arise in many areas of ocean engineering, such as ship seakeeping, structural reliability, and design, and can be caused both by uncertainty in materials and construction, and by the inherently stochastic nature of random waves. Due to the dynamical nonlinearity of these systems, the statistical response is typically non-Gaussian with highly non-trivial distribution tails, making the problem of risk analysis a very hard one. However, accurate estimates of responses and loads are important, both to avoid catastrophic failures like capsize or hull breach, but also to make long term plans such as maintenance schedules, fatigue calculations, and route selections. These statistics are especially important during the design phase, when the statistical performance of different hull configurations or structure designs is an important factor in choosing the final design. Further, the most important events to accurately estimate are also often the most difficult: extreme events that live in the unlikely tails of statistical distributions.
Traditional direct experiments and simulations, which have trouble accounting for these types of random parameters or random forcing, typically must be repeated many times in order to characterize statistical results engineers are interested in. Unfortunately, this “iron law of Monte Carlo techniques" quickly leads to economically infeasible requirements on the number of experiment or simulation repeats, especially requirements for resolving distribution tails and the likelihood of rare events. These costs are bad enough when evaluating a single hull configuration, but become ruinous when comparing the performance of different hull choices in all but the most restricted conditions. In this thesis, we develop a set of analytical and computational techniques to replace expensive long time Monte Carlo simulations with more economical carefully designed short time simulations combined with analytical formulas.
This thesis is divided into four parts. In the first part, we develop a theory for designing stochastic wave-structure interaction simulations. This theory is designed to reduce simulation costs by replacing long time steady state simulations with short time wave-episode simulations, without sacrificing the fidelity of the statistical calculations, i.e. with theoretical guarantees for statistical convergence. In the second part, we apply ideas of data-driven reduced order modeling to the pairs of wave-episodes and associated responses, and demonstrate how we can recover accurate statistics with data from only a small number of simulations. Importantly, we use machine learning techniques well suited to learning from the parametrized wave-episodes, and well suited to recovering statistical quantities. In the third part, we develop ideas based on active learning and optimal experimental design to further improve on data efficiency by using intermediate simulation results to improve upon later experiment parameters. These active learning techniques are based upon high quality uncertainty quantification in order to choose experimental designs that target regions of design space with two properties: regions with low model certainty, and regions that are likely contributors to tail risks. In the final part, we analytically examine the effects of intermittent random loads on material fatigue lifetimes according to the Serebrinksy-Ortiz fatigue model. The analytical predictions for fatigue lifetime statistics have important differences compared to the traditional linear models, e.g. the rainflow counting algorithm, especially in the long tail of early failure risks in the presence of intermittent extreme event loads, and make direct use of the statistics calculated in the first three parts.
The four parts of this thesis fit together, first by calculating the statistical responses and loads of nonlinear ocean systems subjected to given sea conditions, and then by exploring the fatigue effects of those known statistical loads. In particular, each part of this thesis takes especial care to resolve the distribution tails of statistical quantities of interest. Extreme events, whether rogue waves or slamming loads, can have a disproportionate impact on the performance of naval vessels and marine structures, and so the techniques presented in this thesis are carefully designed to maximize accurate resolution of non-Gaussian tail risks, without multiplying simulation costs and data requirements endlessly. Looking forward, the natural next step is to apply these techniques to tow tank experiments, where costs are highest and data the most reliable. The application of these techniques will naturally lead to risk averse design and optimization, with orders of magnitude lower cost for data acquisition and avoidance of over-engineering.
Date issued
2023-09Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringPublisher
Massachusetts Institute of Technology