The least-square support vector machine (LS-SVM) is used to estimate the dynamic parameters of a nonlinear marine vessel steering model in real-time. First, maneuvering tests are carried out based on a scaled free-running ship model. The parameters are estimated using standard LS-SVM and compared with the theoretical solutions. Then, an online version, a sequential least-square support vector machine, is derived and used to estimate the parameters of vessel steering in real-time. The results are compared with the values estimated by standard LS-SVM with batched training data. By comparison, a sequential least-square support vector machine can dynamically estimate the parameters successfully, and it can be used for designing a dynamic model-based controller of marine vessels.

References

References
1.
Sutulo
,
S.
,
Moreira
,
L.
, and
Guedes Soares
,
C.
,
2002
, “
Mathematical Models for Ship Path Prediction in Manoeuvring Simulation Systems
,”
Ocean Eng.
,
29
(
1
), pp.
1
19
.
2.
Perera
,
L. P.
,
Oliveira
,
P.
, and
Guedes Soares
,
C.
,
2015
, “
System Identification of Nonlinear Vessel Steering
,”
ASME J. Offshore Mech. Arct. Eng.
,
137
(
3
), p.
031302
.
3.
Revestido Herrero
,
E. E.
, and
Velasco González
,
F. J.
,
2012
, “
Two-Step Identification of Non-Linear Manoeuvring Models of Marine Vessels
,”
Ocean Eng.
,
53
, pp.
72
82
.
4.
van de Ven
,
P. W. J.
,
Johansen
,
T. A.
,
Sørensen
,
A. J.
,
Flanagan
,
C.
, and
Toal
,
D.
,
2007
, “
Neural Network Augmented Identification of Underwater Vehicle Models
,”
Control Eng. Pract.
,
15
(
6
), pp.
715
725
.
5.
Golding
,
B.
,
Ross
,
A.
, and
Fossen
,
T. I.
,
2006
, “
Identification of Nonlinear Viscous Damping for Marine Vessels
,”
14th IFAC Symposium on System Identification
,
Newcastle, Australia
,
Mar. 29–31
, pp.
332
337
.
6.
Ross
,
A.
,
Selvik
,
O.
,
Hassani
,
V.
,
Ringen
,
E.
, and
Fathi
,
D.
,
2015
, “
Identification of Nonlinear Manoeuvring Models for Marine Vessels Using Planar Motion Mechanism Tests
,”
ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering
,
Newfoundland, Canada
,
ASME
Paper No. V007T06A014.
7.
Hassani
,
V.
,
Fathi
,
D.
,
Ross
,
A.
,
Sprenger
,
F.
,
Selvik
,
Ø.
,
Berg
,
T. E. T. E.
,
Fathi
,
D.
,
Sprenger
,
F.
, and
Berg
,
T. E. T. E.
,
2015
, “
Time Domain Simulation Model for Research Vessel Gunnerus
,”
ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering
,
Newfoundland, Canada
,
ASME
Paper No. V007T06A013.
8.
Söderström
,
T.
,
2013
, “
Comparing Some Classes of Bias-Compensating Least Squares Methods
,”
Automatica
,
49
(
3
), pp.
840
845
.
9.
Sutulo
,
S.
, and
Guedes Soares
,
C.
,
2014
, “
An Algorithm for Offline Identification of Ship Manoeuvring Mathematical Models From Free-Running Tests
,”
Ocean Eng.
,
79
, pp.
10
25
.
10.
Sutulo
,
S.
, and
Guedes Soares
,
C.
,
2015
, “
Offline System Identification of Ship Manoeuvring Mathematical Models With a Global Optimization Algorithm
,”
MARSIM 2015
,
Newcastle, UK
,
Sept. 8–11
, pp.
28
43
.
11.
Xu
,
H. T.
,
Hinostroza
,
M. A.
, and
Guedes Soares
,
C.
,
2018
, “
Estimation of Hydrodynamic Coefficients of a Nonlinear Manoeuvring Mathematical Model With Free-Running Ship Model Tests
,”
Int. J. Marit. Eng.
,
160
(
A3
), pp.
A-213
A-226
.
12.
Xu
,
H. T.
, and
Guedes Soares
,
C.
,
2018
, “
An Optimized Energy-Efficient Path Following Algorithm for Underactuated Marine Surface Ship Model
,”
Int. J. Marit. Eng.
,
160
(
A4
), pp.
A-411
A-421
.
13.
Chen
,
T.
, and
Ljung
,
L.
,
2013
, “
Implementation of Algorithms for Tuning Parameters in Regularized Least Squares Problems in System Identification
,”
Automatica
,
49
(
7
), pp.
2213
2220
.
14.
Golub
,
G. H.
, and
Reinsch
,
C.
,
1970
, “
Singular Value Decomposition and Least Squares Solutions
,”
Numer. Math.
,
14
(
5
), pp.
403
420
.
15.
Xu
,
H.
,
Hassani
,
V.
, and
Guedes Soares
,
C.
,
2019
, “
Uncertainty Analysis of the Hydrodynamic Coefficients Estimation of a Nonlinear Manoeuvring Model Based on Planar Motion Mechanism Tests
,”
Ocean Eng.
,
173
, pp.
450
459
.
16.
Xu
,
H. T.
,
Hassani
,
V.
, and
Guedes Soares
,
C.
,
2018
, “
Parameters Estimation of Nonlinear Manoeuvring Model for Marine Surface Ship Based on PMM Tests
,”
ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering
,
Madrid, Spain
,
ASME
Paper No. V11BT12A010.
17.
Perera
,
L. P.
,
Oliveira
,
P.
, and
Guedes Soares
,
C.
,
2016
, “
System Identification of Vessel Steering With Unstructured Uncertainties by Persistent Excitation Maneuvers
,”
IEEE J. Ocean. Eng.
,
41
(
3
), pp.
515
528
.
18.
Fossen
,
T. I.
,
Sagatun
,
S. I.
, and
Sørensen
,
A. J.
,
1996
, “
Identification of Dynamically Positioned Ships
,”
Model. Identif. Control
,
17
(
2
), pp.
153
165
.
19.
Åström
,
K. J.
, and
Källström
,
C. G.
,
1976
, “
Identification of Ship Steering Dynamics
,”
Automatica
,
12
(
1
), pp.
9
22
.
20.
Luo
,
W. L.
, and
Zou
,
Z. J.
,
2009
, “
Parametric Identification of Ship Maneuvering Models by Using Support Vector Machines
,”
J. Ship Res.
,
53
(
1
), pp.
19
30
.
21.
Luo
,
W.
,
Guedes Soares
,
C.
, and
Zou
,
Z.
,
2016
, “
Parameter Identification of Ship Maneuvering Model Based on Support Vector Machines and Particle Swarm Optimization
,”
ASME J. Offshore Mech. Arct. Eng.
,
138
(
3
), p.
031101
.
22.
Vapnik
,
V. N.
,
1998
,
Statistical Learning Theory
,
Wiley
,
New York
.
23.
Xu
,
H. T.
, and
Guedes Soares
,
C.
,
2016
, “
Vector Field Path Following for Surface Marine Vessel and Parameter Identification Based on LS-SVM
,”
Ocean Eng.
,
113
, pp.
151
161
.
24.
Xu
,
H. T.
, and
Guedes Soares
,
C.
,
2016
, “Waypoint-Following for a Marine Surface Ship Model Based on Vector Field Guidance Law,”
Maritime Technology and Engineering 3
,
C.
Guedes Soares
, and
T. A.
Santos
, eds.,
Taylor & Francis Group
,
London
, pp.
409
418
.
25.
Cauwenberghs
,
G.
, and
Poggio
,
T.
,
2001
, “
Incremental and Decremental Support Vector Machine Learning
,”
Adv. Neural Inf. Process. Syst.
,
13
(
x
), pp.
409
415
.
26.
Guo
,
Z.
, and
Guan
,
X.
,
2014
, “
Nonlinear Generalized Predictive Control Based on Online Least Squares Support Vector Machines
,”
Nonlinear Dyn.
,
79
(
2
), pp.
1163
1168
.
27.
Tang
,
H. S.
,
Xue
,
S. T.
,
Chen
,
R.
, and
Sato
,
T.
,
2006
, “
Online Weighted LS-SVM for Hysteretic Structural System Identification
,”
Eng. Struct.
,
28
(
12
), pp.
1728
1735
.
28.
ITTC
,
2002
, “
Recommended Procedures and Guidelines: Free Running Model Tests
.”
29.
Abkowitz
,
M. A.
,
1980
, “
Measurement of Hydrodynamic Characteristics From Ship Maneuvering Trials by System Identification
,”
SNAME Trans.
,
88
, pp.
283
318
.
30.
Fossen
,
T. I.
,
2011
,
Handbook of Marine Craft Hydrodynamics and Motion Control
,
John Wiley & Sons, Ltd
,
Chichester
.
31.
Clarke
,
D.
,
2015
, “
A History of Ship Manoeuvrability Theory and Practice
,”
International Conference on Marine Simulation and Ship Manoeuvrability
,
Newcastle upon Tyne, UK
,
Sept. 8–11
, pp.
1
27
.
32.
Sutulo
,
S.
, and
Guedes Soares
,
C.
,
2011
, “Mathematical Models for Simulation of Manoeuvring Performance of Ships,”
Maritime Engineering and Technology
,
C.
Guedes Soares
,
Y.
Garbatov
,
N.
Fonseca
, and
A. P.
Teixeira
, eds.,
Taylor & Francis Group
,
London
, pp.
661
698
.
33.
Tzeng
,
C. Y.
, and
Chen
,
J. F.
,
1999
, “
Fundamental Properties of Linear Ship Steering Dynamic Models
,”
J. Mar. Sci. Technol.
,
7
(
2
), pp.
79
88
.
34.
Suykens
,
J. A. K.
,
Van Gestel
,
T.
,
De Brabanter
,
J.
,
De Moor
,
B.
, and
Vandewalle
,
J.
,
2002
,
Least Squares Support Vector Machines
,
World Scientific
,
Singapore
.
35.
Suykens
,
J. A. K.
, and
Vandewalle
,
J.
,
1999
, “
Least Squares Support Vector Machine Classifiers
,”
Neural Process. Lett.
,
9
(
3
), pp.
293
300
.
36.
Vapnik
,
V. N.
,
1995
,
The Nature of Statistical Learning Theory
, Vol.
8
, No.
6
,
Springer
,
New York
,
187
pp.
37.
Golub
,
G. H.
, and
Van Loan
,
C. F.
,
2013
,
Matrix Computations
,
Johns Hopkins University Press
,
Baltimore, MD
.
38.
Perera
,
L. P.
,
Ferrari
,
V.
,
Santos
,
F. P.
,
Hinostroza
,
M. A.
, and
Guedes Soares
,
C.
,
2015
, “
Experimental Evaluations on Ship Autonomous Navigation and Collision Avoidance by Intelligent Guidance
,”
IEEE J. Ocean. Eng.
,
40
(
2
), pp.
374
387
.
39.
Hinostroza
,
M. A.
,
Xu
,
H. T.
, and
Guedes Soares
,
C.
,
2018
, “Path-Planning and Path-Following Control System for Autonomous Surface Vessel,”
Maritime Transportation and Harvesting of Sea Resources
,
C.
Guedes Soares
, and
A. P.
Teixeira
, eds.,
Taylor & Francis Group
,
London
, pp.
991
998
.
40.
Clarke
,
D.
,
2003
, “
The Foundations of Steering and Manoeuvring
,”
Proceedings of the IFAC Conference on Manoeuvring and Control of Marine Craft
,
Girona, Spain
,
Sept. 7–19
, Plenary talk.
41.
Xu
,
H. T.
,
Hinostroza
,
M. A.
, and
Guedes Soares
,
C.
,
2017
, “A Hybrid Controller Design for Ship Autopilot Based on Free-Running Model Test,”
Maritime Transportation and Harvesting of Sea Resources
,
C.
Guedes Soares
, and
A. P.
Teixeira
, eds.,
Taylor & Francis Group
,
London
, pp.
1051
1059
.
42.
Journee
,
J. M. J.
,
1970
, “
A Simple Method for Determining the Manoeuvring Indices k and t From Zigzag Trial Data
,”
Transl. Rep.
,
267
, pp.
1
9
.
You do not currently have access to this content.