The Updating MGM (1,n) Model And Its Application In Ship Motion Prediction

The ship, especially the aircraft carrier plays the dominant role in the marine stuff affairs. And the prediction of the aircraft carrier motions in the sea has significance to the takeoff and landing of the battle plane. The high accuracy and long time of predicted result will promote the safety and enhance the battle effectiveness of the plane greatly.The Grey System Theory is a method to deal with the incomplete information system in Control Theory. It initializes the data to draw the useful information, and does the simulation, control and prediction to the system via differential equations. Because of the less requirements to data and the feasibility, the Grey System Theory has been broadly used in many fields.Because of the complexity of different conditions in the sea, the ship motions have a lot of random characters and undetermined factors. Those characters, factors and the mutual affects among them are analysed and their grey properties are pointed out. They are the bases of the application of the Grey System Theory in ship motion prediction of heave and pitch.In this paper, the MGM(1,n), a predicting model in Grey System Theory, is introduced into the prediction of the ship motion. It predicts the ship motion system consists of pitch, heave and wave. According to the characteristics of the ship motions data obtained from the laboratory experiment, the Range Transformation is applied on the data to unify the affection in the data. The whole solving process is presented in detail and the coefficients are chosen via the thought of discrete integration and the though of least square. After studying the shortages of the MGM(1,n) Model and the requirements of new information by the Grey System, the updating mechanism is introduced into the MGM(1,n) model and the Updating MGM(1,n) Model is proposed to apply in the prediction of ship motion system. With the changing of the coefficients, the Updating MGM(1,n) Model reflects the mutual influences between the elements in system and the changing tendency of the system online. Finally, a good result shows that the average prediction time can last 4-5 seconds within the error of 20%, at least a period. The longest time is around 8 seconds, which may consist two periods.In the numerical experiment analysis, some different groups of data are used to predict. And from.the analysis, the main influences to the error are got. They are the waves with nonlinearly changing and the coupling influences among the two motions of degree. In addition, the relationship between the data chosen and the predicted time in acceptable error is discussed in the paper. The insufficient data has no enough information to depict the characters of the original data, which makes the error increased. The relationship between the system updating coefficients in each updating process and the calculating time in quantum is studied, and its influence to real time predicting. The Lypnov stability of the model and the relationship between the element varying and the output of the system are discuessed. At last the model prolongs the predicted time within acceptable error rationally.