On the Order of Polynomial Regression Models for Manoeuvring Forces

The paper is investigating certain aspects of polynomial regression models used for representation of hydrodynamic forces acting on a ship performing normal (moderate) manoeuvres. A unique polynomial model of increased order developed by Oltmann, Sharma and Wolf at the end of 70s on the basis of high-precision model tests was taken as a primary one. The model was used to generate sample sets of responses which were further approximated with simpler third-order polynomial models presented here as secondary regressions. The structure of the secondary models was chosen using the stepwise forward regression procedure and the coefficients were further estimated by the least-square algorithm. The resulting model turned out to be much more economical in terms of the number of regressors and estimated parameters and does not include regressors of higher order and acceleration-velocity cross-coupling terms present in the primary model. At the same time, comparisons of the force/moment responses, zigzag manoeuvre time histories and of the spiral curves demonstrated that no tangible loss of accuracy can be traced. The conclusion is made that no terms of the order higher than three should enter polynomial models used in ship manoeuvring. Copyright ©2012 IFAC