ALTERNATIVE METHODS FOR THE IDENTIFICATION OF HYDRODYNAMIC COEFFICIENTS FROM STANDARD MANOEUVRES
Michele Viviani (FINCANTIERI Naval Vessel Business Unit, Genova/Italy)
Roberta Depascale (CETENA S.p.A., Genova/Italy)
Luca Sebastiani (CETENA S.p.A., Genova/Italy)
Carlo Podenzana Bonvino (Università di Genova DINAV, Genova/Italy)
Roberto Dattola (MARISTAT/SPMM, Roma/Italy)
Massimo Soave (MARISTAT/CEIMM, Roma/Italy)
The problem of ship manoeuvrability has increasingly grown in consideration in the last decade, both for merchant and naval ships. With regards to merchant ships, the adoption by IMO of the RESOLUTION A.751(18) in 1993  established minimum manoeuvrability standards to grant safety for all seagoing ships. With regards to naval ships, a strong interest has been manifested by NATO NG6, which established a Specialist Team in naval ship manoeuvrability with the aim of developing, at last, a standardised criteria. The work of this ST resulted in a first Working Paper  and a subsequent ANEP will be probably published by the end of the present year with a set of preliminary criteria. An estimation of ship manoeuvrability is strongly related to the accuracy in the determination of the hydrodynamic coefficients which specify the mathematical model of ship manoeuvring used in the existing prediction tools. These coefficients are usually estimated, in a preliminary stage of design, from regression formulas based on existing model-test data , which may lead to inaccurate predictions for non-conventional vessels or ships exceeding the parametric range of the experimental data base. The aim of the work presented in this paper is the development of a method to identify the hydrodynamic coefficients starting from standard experimental results in order to be able to extract data from the wide experimental data-base available (sea and model-tests trials); two different procedure for the identification of the hydrodynamic coefficients will be presented, with the comparison of their merits and shortcomings.
1. INTRODUCTION TO THE METHODS
The first method analysed, developed by CETENA and Fincantieri, is the application of optimization algorithms in order to find the coefficients from the main parameters of typical manoeuvres, using the simulation program for surface ships SIMSUP   developed by CETENA linked with the program of numerical optimization FRONTIER  developed by EnginSoft.
The second method analysed, developed inside a PhD project by the University of Genoa, is the application of filtering techniques to time histories of the same standard manoeuvres analysed using optimization techniques, as it was done in  and  where the authors used Extended Kalman Filter analyzing ZigZag and Turning Circle manoeuvres. In this case, in order to apply filtering techniques a simulator similar to SIMSUP has been developed in MATLAB environment.
It has to be noted that one of the aims of the studies carried on is to obtain values for the hydrodynamic coefficients from the usual standard manoeuvres, and in particular from ZigZag and Turning Circle manoeuvres, because the success of such a procedure would allow to extract data from the experimental data-base of more than 400 ships developed by CETENA in many years of experimental trials. This is the reason which prevented from analysing different possible trials, as it has been done in some recent works .
It has to be noted, finally, that since this study is aimed especially to investigate the feasibility of the two methods, for simplicity the roll motion, which is usually considered in manoeuvrability problems, has been neglected, considering only surge, sway and yaw motions. This assumption should not affect greatly the results since the manoeuvres analysed have been chosen in the low Froude number range, with consequent low roll motions.
In the following table 1 the main dimensions of the ship utilized for this analysis are reported in non-dimensional forms.
Table 1 Main dimension of the ship utilized
The speed range analyzed correspond to Froude numbers in the range 0.15÷0.20.
2. PROGRAM UTILIZED
Before explaining the two different procedures used, in the following paragraphs a description of software utilized (simulation programs, optimization program and filters) is reported.
2.1 Simulation Programs
The simulation program SIMSUP, developed by CETENA has been adopted for the identification study using optimization techniques. The program allows to perform manoeuvrability simulations for surface ships with four degrees of freedom (surge, sway, yaw and roll) under the action of propulsion and steering system and taking into account also the influence of environment (i.e. wind, sea, current, shallow water). This program has a specific calculation module which, on the basis of the characteristics of the ship, by means of statistical regression formulae developed by SSPA  on a great number of hulls tested at the PMM, permits to determine the hydrodynamic derivative coefficients. A similar simulator has been developed in MATLAB environment to be coupled with some filters. This simulator, with respect to SIMSUP program, uses a simplified representation of the propulsion system and of the mathematical model of manoeuvring but these differences are considered negligible in the analysis of the feasibility of the two methods. In both the programs the mathematical model used is one of the possible alternatives of the well-known model derived from the motion equations:
) = X
) = Y (1)
+ur) = N
where X, Y, N are forces and moment due to the hydrodynamic effect on the hull and to the propeller and rudder actions. In particular, the forces and moment acting on the hull and generated by the rudder are expressed using an expansion in Taylor series of second and third order respectively  corrected in order to take into account some effects, such as the interaction between propeller and rudder, in accordance with SSPA mathematical model.
The resulting equations utilized are therefore as follows:
where in general:
u surge velocity
v sway velocity
r yaw velocity
d=δ rudder angle
de=δe encounter rudder angle
n load coefficient
nr number of rudders
L ship length
R ship resistance
T propeller thrust
T(x) local draft
CD(x) cross-flow drag coefficient
Yrud total rudder force
Irud lever arm of the rudder force
Yvmodv = Yv|v|
Yvmodr = Yv|r|
Yrmodr = Yr|r|
and where Ytd, Ytddd, Yntd and Yntddd are used to take into account the interaction between rudder and propeller together with cc2 and kr. Finally it has to be noted that the coefficients Yur, Yuv, Nur and Nuv are considered as part of their correspondent linear terms Yr, Yv, Nr and Nv.
The employed mathematical model was validated through an extensive theoretical-experimental correlation analysis for single  and twin-screw ships with one or two rudders  (for conventional merchant ship hull forms).
2.2 Optimization program
FRONTIER is a commercial software for multi-objective optimization developed by EnginSoft, Trieste, which can be used as a platform for the management of all calculations associated with an optimization process. It manipulates the input files used to execute outside software tools in batch-mode, launches the programs in a concerted manner and scans the output files produced during each run for desired data (for instance the current value of an objective function). FRONTIER, therefore, allows to perform iteratively and automatically a series of calculations using different programs (in this case SIMSUP), in order to evaluate an objective function to be minimized or maximized by means of different optimization algorithms (e.g. Genetic Algorithms, Gradient search).
As already mentioned, some filters have been coupled to the simulator developed in MATLAB environment. These filters have not been developed directly by the authors, but they are part of a toolbox developed by the Technical University of Denmark  and have been used within a PhD project by the University of Genoa. These filters are well described in , their major characteristic is that they make use of an interpolation formula for derivation of state estimators for nonlinear systems instead of Taylor approximations as it is for other existing filters, such as the Extended Kalman Filter. In this study, in particular, the second order filter (DD2) was used in order to consider the non-linearities of the equations adopted to represent the ship system.