# Roll motion parameter identification using response in random waves

Wu, Xia (1992) Roll motion parameter identification using response in random waves. Masters thesis, Memorial University of Newfoundland.

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## Abstract

The concept of the random decrement has been used successfully in the damping identification of linear systems. The formulation of the random decrement existing in the literature is based on the assumptions that the dynamic system is linear, time invariant and subjected to Gaussian, white noise excitation. Thus, the principle of superposition can be used in formulating the equation for the random decrement. -- In this study, the concept of the random decrement is extended to nonlinear systems. Using the Fokker-Plank Equation approach, it can be shown that the random decrement formed by calculating the expected value of a stationary random rolling process satisfies the differential equation governing the free roll motion. It is also shown that, the autocorrelation function for the stationary nonlinear roll motion excited by a zero mean, Gaussian, white noise random process, satisfies a linearized free roll equation. Thus the random decrement and the autocorrelation function curves can be used for identifying the parameters in the nonlinear equation of free roll motion. -- The validity, accuracy and reliability of the Random Decrement Technique in determining the parameters of the nonlinear equation for roll motion are investigated in this study. The technique is applied to roll motion obtained from: 1) computer simulation by using a fourth order Runge Kutta routine; 2) experiments of three ship models rolling in a towing tank; 3) full scale tests on a real fishing vessel. A method for evaluating the parameters in the nonlinear roll equation from free roll decay, the random decrement and the autocorrelation function is developed and presented in this study. This method is based on the theory of equivalent linearization. The application of the method provides accurate estimation for the parameters from both simulated and measured data. -- It is shown that the random decrement and the autocorrelation function curves extracted from a history of nonlinear roll response to random excitation closely resemble the measured free roll decay curve. The predicted natural frequency obtained by either the random decrement or autocorrelation function method can be used to determine the value of the metacentric height for a ship rolling under the action of unknown random excitations. The damping coefficients estimated by either method are used to generate free roll decay curve which agrees well with the measured free roll decay curve. -- This method does not rely on a model experiment and does not require the measurement of wave height. In addition, roll response of a ship can be easily measured with the ship underway. It is expected that the method would be particularly useful for assessing roll stability of a ship sailing in a realistic sea.

Item Type: Thesis (Masters) http://research.library.mun.ca/id/eprint/5409 5409 Bibliography: leaves 85-89. Engineering and Applied Science, Faculty of 1992 Submission Stability of ships; Ships--Hydrodynamics