On The Grey Prediction Method And Its Application In Watercraft Motion Modeling And Prediction

There are a large number of nonlinear systems in practice,so the study of nonlinear systems and prediction method are very important. By research on the watercraft motions,the author analyses the grey characteristics of ship motions,then construct a new prediction model-Grey Prediction Model. In this paper,the author make the stability analysis and error analysis to the new model,and make the numerical experiment with real data of ship motion.Because of complexity in sea,ship motion have the random property,hi this paper,the grey characteristics of the factors which influence the motion of ship is studied,and the system of ship motion is found to be a Grey System. It is a foundation of constructing the Grey Model for ship 6-motions using Grey System Theory. This paper includes1. The author revised the original data by data generation. GM(1,1) is suitable for the monotone series very well,however,it is not effective for oscillation series,and the prediction time is so short(l-2 second). Therefore,the modified transformation of triangle function is proposed for the oscillation series,and the monotone series can be obtained.2. Two models-1-order Grey Model and 2-order Grey Model are studied,and results imply that the original 1-order Grey Model and 2-order Grey Model are not suitable for forecasting the ship motions. Some 1-order methods such as GM(1,1),Residual Model and Period Model make the predicting data have the monotone property,so they can not be applied to predict the oscillation series of ship motions. In this paper,the author propose a new GM(1,1) model for oscillation series using the Transformation of Triangle Function,and change them to be the monotone series,then constructe GM(1,1) model for simulating prediction of original given data.3. Research on GM(2,1) model,the author find that there is no law to choose the initial value of GM(2,1) Model. In this paper,the author propose a method to solve the problem using the Method of Minimum Squares,and then get the system response equation of the new GM(2,1). It can decrease the big error of original GM(2,1) Model.4. The smooth condition for discrete series is studied,and some mistakes about the white exponential law is pointed out. The author proposes the modified condition of white exponential law which makes the data to apply the GM model.5. Real motion data is used for numerical experiments. First,the authorstudies and compares several grey models-GM(1,1),Residual Model,PeriodModel,GM(1,1) with inverse Transformation of Triangle Function,GM(2,1) and modified GM(2,1),then choose GM( 1,1) with Transformation of Triangle Function to be the prediction model for ship motions. Second,the author proves the transformation of parallel translation can make discrete data more smooth,so can revise prediction error. The numerical results imply that the prediction model can forecast the developing tend of real data,and make the prediction data fit well with the original data. In error of 0.2 degree,the model can predict 8-17 seconds for the ship motion. It also proves that the model is good. By the analysis of system parameter,the author find that the prediction model is stable.