The Prediction Of Nonlinear Ship Motion Based On Multi-Varble Grey Model MGM(1, N)

Disturbed by wave, the six-degree-freedom motion will be created when ship sails in head sea. Because of the complexity of wave, the ship motion is very complex, and six degree-freedom motions are coupled with each other to consist of a complex nonlinear system. In practice, the forecasting for its nonlinear motion is significant, but the nonlinearity and randomicity of the motion make it complex and difficult to research theoretically. People usually built up the equation of motion by calculating the forces acting on ship in the hydromechanical perspective, or work out the frequency response functions by model experiments to do the prediction for ship nonlinear motion. But each kind of method is based on the hypothesis of either linearity or doing weak nonlinearity processing locally, so there still are many problems when characterizing the ship nonlinear motion is taken into consideration. Therefore, it is very valuable to build up a nonlinear system model for ship motion and do prediction on real time.In this paper, by the characteristic analysis of the experimental data from pool experiment and the grey and nonlinear character of the ship motion system, on the basis of the sufficient research of the grey dynamic model, the grey MGM(1,3) model is applied to describe the nonlinear ship motion system after the Range Transformation is applied for data proceeding. And the prediction of coupled heave-pitch motion is got from the model. The Multi-Varible Grey Model MGM(1, n) is a system model characterizing the mutual influences of the parameters by differential equations, which can simulate and predict the trend of parameters effectively without much prior information. The introduction of the Range Transformation makes the complex motion data fit for the mechanism of the MGM(1,n) model, which makes a good preparation for the prediction. Furthermore, the requirement of MGM(1, n) model for the original data is researched, and a relative theorem is given.Finally, the simulating and predicting condition of the model is shown based on the different sea condition and developing trend character of motion data. From the whole numerical experiment results and analysis, the model for nonlinear ship motion prediction proposed in this paper is feasible, and the simulating and predicting condition is ideal.