Title page for ETD etd-05202009-211838


Type of Document Master's Thesis
Author Story, William Robert
URN etd-05202009-211838
Title Application of Lyapunov Exponents to Strange Attractors and Intact & Damaged Ship Stability
Degree Master of Science
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
McCue-Weil, Leigh S. Committee Chair
Brown, Alan J. Committee Member
Neu, Wayne L. Committee Member
Keywords
  • Lyapunov
  • Stability
  • Ship
  • nonlinear
  • dynamics
Date of Defense 2009-04-29
Availability unrestricted
Abstract
The threat of capsize in unpredictable seas has been a risk to vessels, sailors, and cargo since the beginning of a seafaring culture. The event is a nonlinear, chaotic phenomenon that is highly sensitive to initial conditions and difficult to repeatedly predict. In extreme sea states most ships depend on an operating envelope, relying on the operator’s detailed knowledge of headings and maneuvers to reduce the risk of capsize. While in some cases this mitigates this risk, the nonlinear nature of the event precludes any certainty of dynamic vessel stability.

This research presents the use of Lyapunov exponents, a quantity that measures the rate of trajectory separation in phase space, to predict capsize events for both intact and damaged stability cases. The algorithm searches backwards in ship motion time histories to gather neighboring points for each instant in time, and then calculates the exponent to measure the stretching of nearby orbits. By measuring the periods between exponent maxima, the lead-time between period spike and extreme motion event can be calculated. The neighbor-searching algorithm is also used to predict these events, and in many cases proves to be the superior method for prediction.

In addition to the ship stability research, the Lyapunov exponents are used in conjunction with bifurcation analysis to determine regions of stable behavior in strange attractors when the system parameters are varied. The boundaries of stability are important for algorithm validation, where these transitions between stable and unstable behavior must be accounted for.

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