MECHANICAL AND AERONAUTICAL ENGINEERING AND SHIPBUILDING 23
Model identification of the
manoeuvring ship
G. V A N LEEUWEN
Shipbuilding Laboratory
Subdepartment of Naood Architecture Delft University of Technology Mekelweg 2
Delft-2208, The Netherlands
Delft Progr. Rep., Series C: Mechamcal and aeronautical engineering and shipbuilding, 1 (1973) pp. 23-24. A short review is given, of the various aspects of the model-identification problem ofthe manoemting ship. Attention is paid to the mathematical models and to the role of the restricted accuracy of the fiiU-scale measurements. Finally some data concerning the present investigation are given.
Eiitro^ictiim
From a certain point of view, a close connec-tion exists between the model-identificaconnec-tion and the idea to represent a system by a minimum number of constants. As far as concems the manoeuvring ship, Nomoto's well-known T.K. model may serve as an example of characterizing the ship's manoeu-vring properties in a rough manner.
In thé course of time, other applicatio>ns for mathematical m o t ^ were fouiûi, in particular to predict the system's behaviour under various conditions. As a consequence, a variety of matiiematical model forms are developed, each having its own field of appli-cation.
In general, the determination of tiie unknown parametö;s also vïuiés with the particular properties of the models. If free running model tests or fuü scale manoeuvres are used to find these parameters, the model-identification technique is applied, while at the same time this technique serves tp j u d ^ the si^ificance of the adopted terms in such models. IN^fliHiiatical modeb
The d^erences between the various kinds of models concern in the first place the number of ^erential equations. If only predictions of small course changes-are of interest, apart from integrating the yaw rate, the model consists of one eqoation, describing the yaw-rate only. Such modds are often in use for autopilot research, for instance. In generd, only smaU difiicailties will be met in finding a suitable id<»itificatibn technique in this case, When 1 ^ ^ values of the yaw rate occur, also the speed-reduction beicomes iniportant. hi those cases a second diffi^ntial equatipn, describing the forward speed, should be added while both yaw-rate and speed aû-e the
varia-ble of both the differentia equations. As a omsequence, the identification procedure will be more comphcated in this case.
For real-time simula.tipn piu-ppses the mathe-matical model should desoribe the drift- or sway velocity additionaUy, which rneans tlü-ee coupled non-linear differential equations, while a rather advanced identification techni-que is needed in this case. Moreover, a critical chpice ofthe required manoeuvres is necessary. For this purpose an investigation on the distribution of information over the parts of Üie various kmds of manoeuvres in use now, seems to be useful. Conceming the choice of a mathematical model, suitable to prpvide accurate descriptions of an extended range of manoeuvres, it is noted that at least two basically differrait model types are available for this purpose.
The first kind primarily describes a great number of hydrödyhamic efiects, such as side forces due to a drift- or rudder angle etc. Each term in these mo<^s represents such a hydrodynamic effect and, if suffirait effects are retained, these models fit the purpose; The principle property of the second kind of models is just to describe the relations between the relevant state variables, as yaw-rate, sway-velodty, rudder angle and the forward speed. Consequently the termis in it need not neces-sarily be tbe sanie as those in the first kind models. In general the number of terms in the first kind will be some dozens, while the num-ber of tiie second kind is mucJi smaller. Restiictioiis
In principle, it is possible to find all of the hychodynamic effeats, just mentioned, by ^lalyzmg the results of full-scale- or free running model tests, using identification-, or rather, optimization-techniques. The main
24 1 (1973) DELFT PROGRESS REPORT problem* however, is the restricted accuracy
of this kmd of information: Systematical errors as well as noise, make a comiderable part of the information unrecognizable as sudi. This means, that the terms in the mathe-matici model, which could be considered responsible ifpr this part of tiie infórnmtion, can probably not be identified.
In this resped, consid^able restrictions are due to the inaccurate and contradictory infprmation whidi is often obtained froni longitudinal speed measurements.
Unfortunatdy, a correct prediction of for-ward speed is extremely important to obtain useful {»redictions pf heading- and drift a n ^ because of the strong cross-coupîÉing effect between these variables and the for-ward speed. Though this phenomenon was already known, it was ^own very clearly, when predicting a number bf mahoeuSres, using the results of extended PMM-tests with a tanker model: Small changes of the resis-tance-thrust balance bad a considerable effect upon.aii variables, much more as had corre-sponding changes of other quantities in the system. This is (tescribed in more detail in reSnrence 1, concemmg these tests.
Identification tedunqn^
tihe general prmt^le of these techniques is based upon ttie improvement of an initially estimated set of unknown parameters, using the differences between the predicted and tfae observed values Of the variables which are of mterest. The way in whidi tfa^e differences are handled to obtain the improvonent, is the main feature of the optimization tedüiique. As there are many pf such tediniques, an important st^ in the: i(tentifica.tion procédure is the choice of the right optimization techni-que. Another choice has to be made and that is conceming the way in which the above men-tioned 'differences' are defined. An attr^tive procedure is tp use the values of the variables at a restrkted number of sigjiificant points of time. For instance, when using zig-zag test resists, the: moments m which the course has reached its maxiniüm, are to be considered
as such^. Altemative points of time, or com-binations of two or more significant promts of time, are possible. When turning circle tests are involved, one could, for instance, take samples after each 60 degree of tum.
This 'discrete-points' proœdure may demand some preparative work, but the advantage is that the infiuence of disturbances and noise is eliminated fpr the most psut by fitting the data coached on a basis of trae. Of coiirse this procedure dóes not apply when random output of the system has to be used for its identification, as might be the case wheal identifying the ships course-keeping prpperties only.
The invest^tfons
Using the '(^screte-points' procedure, some results have already been obtained at the identification of a tanker, simulated by a sixty-ccN^cient model.
It was assumed that the behaviour of this simulated ship could be described by a thirteen coeffident non-linear model, with an overall accuracy of about ten percent. The manoeuvres used for this identification, consist of seven modified zig-zag manoeuvres and fourteen turning circles. The stationary characteristics df the original model showed a considera.ble asymmetrical behaviour, whidi hampered the
solution of the problem.
Using a tiial-and-error method and a rather intuitive procedure of improving the set of imknown parameters, an overall accuracy of eight per pent in the prediction of the rnanoeu-yres was obtained.
t o solVe the set of differential equations a digital Computerprogramme was used. A. second and rnore systematic atternpt to solve the identification problem of the manoeuvring ship was started just a few months ago, using a hybrid computer and a random-search optimization technique.
1. G. v M Leeuwen and J.M.J..Joimiée'Precfaction of ship manoeuvrability' (TNO report I58S, March 1972).
