Damping Structure Selection in Nonlinear Ship Manoeuvring Models Tristan Perez *,** El´ıas Revestido-Herrero *** * School of Engineering, Discipline of Mechanics and Mechatronics, The University of Newcastle, Callaghan NSW 2308, AUSTRALIA, ** Centre for Ships and Ocean Structures (CeSOS), Norwegian University of Science and Technology (NTNU), Trondheim, NORWAY *** Dept. of Electronic Technology, Systems Engineering, and Automatic Control, University of Cantabria, Spain, Abstract: This paper presents the application of a statistical method for model structure selection of lift-drag and viscous damping components in ship manoeuvring models. The damping model is posed as a family of linear stochastic models, which is postulated based on previous work in the literature. Then a nested test of hypothesis problem is considered. The testing reduces to a recursive comparison of two competing models, for which optimal tests in the Neyman sense exist. The method yields a preferred model structure and its initial parameter estimates. Alternatively, the method can give a reduced set of likely models. Using simulated data we study how the selection method performs when there is both uncorrelated and correlated noise in the measurements. The first case is related to instrumentation noise, whereas the second case is related to spurious wave-induced motion often present during sea trials. We then consider the model structure selection of a modern high-speed trimaran ferry from full scale trial data. Keywords: System Identification, Regression Analysis, Ship Dynamics, Hypothesis Testing. 1. INTRODUCTION The increasing requirement for accuracy of manoeuvring models in ship building contractual agreements is favour- ing more and more the use of system identification (ITTC, 2005). The use of computational fluid dynamics and hy- drostatic computations based on the hull shape allows one to predict the value of the mass and restoring terms in a ship model with adequate accuracy (Perez and Fossen, 2006). Due to the complex phenomenon associated with damping forces, however, it is difficult to obtain reliable models without using experimental data. Different parametric model structures have been proposed in the past for the damping terms. Most of these model structures stem either from Taylor expansions (Abkowitz, 1964) or a combination of physical effects like circulation and cross-flow drag principles (Fedyaevsky and Sobolev, 1964). A recent discussion of model structures can be found in Clarke (2003), which motivated the re-apraisal based on physical insight found in Ross (2008). Modelling of ship manoeuvring based on physical considerations may easily result in over parameterised models since the modelling approach involves the use of force superposition and expansions or related approximations of the different effects. This approach leads to some parameterisations to be preferred over their competing counterparts (Blanke and Knudsen, 2006). Thus, given experimental results, there is a set of potential models whose relative merit needs to be assessed. This paper presents the application of a statistical method for model structure selection of damping components in ship manoeuvring models. The damping model is posed as a classical (statistical) linear model (a linear model with deterministic regressors and uncorrelated model un- certainty or measurement noise). A family of such models is postulated based on previous work of Ross (2008). Then, a nested test of hypothesis problem is considered to select a preferred model structure within the postulated family. The testing is approached using stepwise regression. Deci- sions about model structure are based on statistical tests that rely upon the assumptions related to the classical linear model. These assumptions hold only approximately for the ship damping model since the regressors are a function of the velocity measurements and therefore noisy. Furthermore, model uncertainty may be correlated due wave-induced motion. As discussed by Silvey (1975), with a practical problem of this kind, one can opt to look, and hope, for an optimal method that adhere more closely to the conditions, or abandon the idea of optimality in favour of intuitive appeal and apply a method that would still lead to acceptable solutions. The latter is the approach followed in this paper. Using simulated data, we test the robustness of the method to the case of noisy regressors with both correlated and uncorrelated noise characteristic 8th IFAC Conference on Control Applications in Marine Systems Rostock-Warnemünde, Germany September 15-17, 2010 978-3-902661-88-3/10/$20.00 © 2010 IFAC 73 10.3182/20100915-3-DE-3008.00053