Research Projects

A highly nonlinear characteristic is strongly involved in the ship hydrodynamics models. It is necessary that the dynamic stability of ships in the realistic sea is dependent on their rolling motion and therefore the investigation of ships’ roll dynamics is most crucial, unlike other degrees of freedom of ship motion. For this purpose, it is generally required to investigate ship roll damping for accurate and efficient prediction of its response to various loading environments and the development of control strategies: this is essential for the design of ship-shaped structures. However, determining the roll damping is difficult because of its strong nonlinearity. In ship hydrodynamics, roll motion is without a doubt one of the most important and dangerous effects of waves on ships. The case of a ship that, in the presence of a regular forcing term, has lost the equilibrium of her upright position, and hence is in critical condition, has attracted the attention of researchers dealing with nonlinear dynamics due to the inherent peculiarities of the unsymmetrical oscillation. It is essential to study and compute the maximum rolling amplitudes of ships in regular and irregular beam seas taking into consideration the effects of the nonlinearities. For small roll motions, the rolling response of a ship can be adequately modelled by nonlinear, fractional, and stochastic differential equations. However, as the amplitude of oscillation is increased, non-linear effects come into account. There are several forms of fractional-type differential equations (ODEs and PDEs) arising in ship dynamics have been proposed, and there has been significant interest in developing approximation algorithms for their numerical solutions. The chaotic motion of ship roll in stochastic beam seas, which is regarded as a bounded noise will be investigated in detail. The stochastic Melnikov approach will be applied to the model and the criterion for the chaos in the mean-square sense will be derived. This project aims to develop machine-learning-based wavelet algorithms (both discrete and continuous wavelet algorithms) to predict accurate hydrodynamics parameters for selected non-linear, fractional, and stochastic ship hydrodynamics models. Discrete and continuous wavelets transform algorithms are relatively new and an emerging area in applied mathematical research. As a powerful tool, wavelets have been extensively used in signal processing, image compression, numerical analysis, and many other areas. Wavelets permit the accurate representation of a variety of functions and operators. To the best of our knowledge until now there are no rigorous machine learning-based continuous wavelet algorithms have been reported for the mathematical models of delay-differential, nonlinear, fractional order, and stochastic differential equations arising in ship hydrodynamics.