
24
conventional system identification methods, such as
least squares method (LS), maximum likelihood
method(ML)andextendedKalmanfilter(EKF),have
been successfully applied to estimate the ship‐
maneuveringmodel.Forinstance,Xuetal.(Xuetal.
2014)incorporatedLSwithintegralsamplestructure
and Euler method to identify the
linear
hydrodynamic model in the horizontal plane of an
underwatervehicleusingsimulateddata.Åstromand
Kållstrom(Åstrom&Kållstrom1976) appliedMLto
determine steering dynamics of a freighter and a
tanker using free steering experiments on full‐scale
ships.Shi et al.(Shi et al. 2009) tackled
identification
ofanon‐linearshipmaneuveringmodel
basedonEKF.ThismethodwasalsousedbyPerera
et al. (Perera et al. 2015) to identify the stochastic
parameters of a nonlinear ocean vessel steering
model. In recent years, a variety of novel methods
basedonthemodernartificialintelligenttechnology,
such
as the artificial neural network (ANN), genetic
algorithm(GA)andsupportvectormachines(SVM),
have been used successfully in the parameter
identification of the ship maneuvering model. ANN
wasusedbyRajeshandBhattacharyya(Rajeshetal.
2008)todealwithsystemidentificationofanonlinear
maneuvering model for large
tankers. Sutulo and
Guedes Soares (Sutulo & Guedes Soares 2014)
developed an identification method based on the
classic genetic algorithm to estimate a mathematical
model describing the ship maneuverability by using
simulation data corrupted by the white noise of
various levels. Comparatively, SVM directs at finite
samples, which requires no initial
estimation of
parametersbuthas goodgeneralizationperformances
andglobaloptimal(Luo&Cai2014).In2009,Luoand
Zou (Luo & Zou 2009) firstly successively applied
SVM to identify hydrodynamic derivatives of
Abkowitz model from the free‐running model test,
and predicted zigzag tests using the regressive
Abkowitzmodel.
Otherstudiescanbefoundfromthe
research group guided by Zou (Zhang et al. 2013 &
Zhangetal.2011&Xuetal.2012&Wangetal.2013)
andreferencestherein.
Insuch a variety of identification methods, some
are developed to on‐line identify time‐varying
coefficients,
for instance, recursive least square
method (RLS) algorithm and least mean squares
(LMS) algorithm (Ljung 2002). Since the change of
current weather and ship loading conditions can
cause parameter variations of ship maneuvering
models, the well‐known RLS with an advantage of
simple construction is used in this paper to
identify
parametersofshipmaneuveringmodels.
As well known, the identification results of RLS
aresensitivetotheinitialvaluesofparameters(Zhang
et al. 2013). Hence, this contribution aims at
conqueringsuchdrawbackofRLS bybenefitingfrom
applying firstly SVM which is a kind of batch
identification technique and
requires no initial
estimation of the parameters, to provide RLS initial
values. Additionally, this paper makes an effort to
analyze the choice of the training sample number
applied for SVM to identify initial values of ship
maneuveringmodels.
The data for learning and validation of
identificationprocedureareobtainedfrom
simulation
ofshipmaneuveringmodelscombinedwithexisting
particulars. For consideration of real navigation
situationinfluencedbydifferentdisturbances,suchas
wind,waveandcurrents,thesimulationtestdataare
corrupted by non‐correlated white noise, i.e.,
Gaussian white noise. Then, two different filters,
namely,Waveletfilters(Barford1992)andEmpirical
Mode Decomposition (EMD) algorithm (Wang et al.
2014)areusedtoomitnegativeinfluenceofexternal
disturbancesonidentificationresults.
Thepaperisorganizedasfollows.Insection2,the
mathematical model of ship maneuvering is
described.The identification methods including RLS
and SVM are introduced in section 3. The
implementation of ship maneuvering models’
identification is conducted and the identification
results are analyzed in section 4. Finally, the
conclusionoftheworkissummarizedinsection5.
2 THEMATHEMATICALMODELOFSHIP
MANEUVERING
Ship dynamics are complex due to nonlinear and
coupling characteristics. At present, three types of
mathematical
model of ship maneuvering are
common. MMG model is modular model separately
describing rudder effects and propeller effects.
Abkowitz model is whole‐ship model regarding
influences on the ship as the whole using Taylor
seriesexpansion.Theresponsemodel,particularly,is
theNomotomodels (Fossen2011).In thisstudy, the
problem of determining ship steering dynamics is
focused from the point of view of parameter
identification.Assumingthattheshipforwardspeed
is constant (
0
u
), the steering dynamics of a surface
shipcanbedescribedas(Åstrom&Kållstrom1976)
0
0
001
0
0
010 0
mY mx Y
vGr
v
mx N I N r
Gv zr
YYm Y
vr
v
NNmx r N
vr G
(1)
where
m
isthenon‐dimensionalmassoftheship;
G
isthenon‐dimensionallongitudecoordinateofthe
ship’s center of gravity;
I
z
is the non‐dimensional
inertia moment about
z
‐axis;
v
,
r
are non‐
dimensionalsmallperturba tionsrespectively;
v
isthe
non‐dimensionalswaylinearvelocity;
,
r
arenon‐
dimensional yaw rate;
is the non‐dimensional
heading angle;
is the rudder angle;
Y
v
,
Y
r
,
Y
,
Y
v
,
Y
r
arerespectivehydrodynamiccoefficientsof
theswaymotion;
v
,
r
,
,
v
,
r
arerespective
hydrodynamiccoefficientsoftheyawmotion,and
,
2
vL
v
U
2
,
2
rL
r
U
,
U
,
v
v
U
,
rL
r
U
,
22
Uuv
o
.
The normalized equations of motion, i.e., Eq.(1),
areeasilyconverted tostandardstatespacenotation