Research On Prediction Of Planing Craft Motion Based On Grey System Theory

Planing craft is widely used because of its advantages such as flexible, low cost, lowroutine maintenance cost. To design an effective automatic control system of planing craft, aprediction model should be built to predict its motion attitude real-timely and precisely.While sailing in wave, the complexity of the actual wave condition the complexity of themotion of the planing craft. The motion usually is the superposition of several kinds ofsimple motion, that is to say, there are coupling influences among the each degree offreedom to a certain extent. This makes it quite difficult to predict the motion attitude ofplaning craft accurately. Meanwhile, because of the characteristics such as high speed andrandom, it is unrealistic to build a model to predict the motion of planing craft by using amass of original data and hard to get a good predictive effect. According to thecharacteristics of the motion of planing craft, and combined with the advantages of greysystem such as not high demand for the original data and high precision for predicting, amethod to predict the motion attitude of planing craft by using the MGM(1,N) model in greysystem theory was proposed by this paper.Firstly, the grey characteristics of planing craft motion system were analyzed, includingthe relationship among the each degree of freedom, and the grey characteristics of thefactors such as wave that affect the motion of planing craft. This makes a foundation for theapplication of grey system theory in the prediction of planing craft motion. Besides, SinceMGM(1,N) model was proposed, it has been applied in many areas, therefore, this paperresearch on the theoretical system of MGM(1,N) model. The basic form of MGM(1,N)model, the definition of parameter matrix, the proof of the theory are given, which lay agood foundation for the subsequent theory research.Secondly, according to the characteristics of planing craft motion attitude and thepriority principle of new information in grey system theory, this paper proposes therecurrence formula of MGM(1,N) model’s parameter matrix after a group and a batch ofdata was newly added. Because of the characteristics such as high speed and randomness,the predicting accuracy and time are limited by predicting the motion attitude of planing craft using the huge original data to build a MGM(1,N) model. Therefore, to prolongpredicting time and improve predicting accuracy, the newly acquired data should becombined with the former data to update the parameter matrix of MGM(1,N) model.Simultaneously, because of the characteristic of grey system is that the more original datamay lead to a worse predicting effect, the prior data should be eliminated after the new datais added into the model. Based on the theory of block matrix, this paper proposes therecurrence formula of the parameter matrix of MGM(1,N) model after a group and a batchof data is newly added, named recurrence MGM(1,N) model.Thirdly, this paper applies recurrence MGM(1,N) model into the prediction of motionattitude of planing craft. Based on a large number of motion attitude data of planing craftsailing in the environment of wave tank is acquired, and the numerical simulation test iscarried out. The results of numerical simulation test show that using recurrence MGM(1,N)model to predict planing motion attitude is feasible and can get a good prediction effect. Sothe method proposed by this paper can reflect the planing craft motion mechanismsuccessfully, and had rational and effective functions of analyzing trend and forecasting.Finally, the stability analysis method of the motion system of planing craft is proposedby using the Lyapunov stability theory.