Modified controlling GM(1,1) model for pitch motion using the transformation of triangle function

In this paper, the simulation of ship pitch is studied. There existed time series, period graph method, neural networks and GM(1,1) of grey system theory to be used to study the motion of ship. A system model is constructed for ship pitch using grey system theory. Not alike GM(1,1), a new method is proposed to handle the residual GM(1,1) of pitch series using the inverse transformation of triangle function. Noticing the multivaluedness of inverse trigonometric function, a monotone increasing series is obtained from the error of pitch prediction with the transformation. Finally, according to the fact that GM(1,1) can simulate the monotone series very well, the GM(1,1) model is constructed for the error series of GM(1,1) model. The numerical results imply that the method is better than residual GM(1,1) model.