Abstract

Gaussian process regression (GPR) is a commonly used approach for establishing the nonparametric models of ship maneuvering motion, and its performance depends on the selection of the kernel function. However, no single kernel function can be universally applied to all nonparametric models of ship maneuvering motion, which may compromise the robustness of GPR. To address this issue, an adaptive ensemble of multi-kernel GPRs based on heuristic model screening (AEGPR-HMS) is proposed in this paper. In the proposed method, four kernel functions are involved in constructing the ensemble model. The HMS method is introduced to determine the weights of individual-based GPR models, which can be adaptively assigned according to the baseline GPR model. To determine the hyper-parameters of these kernel functions, the genetic algorithm is also employed to compute the optimal values. The KVLCC2 tanker provided by the SIMMAN 2008 workshop is used to validate the performance of the proposed method. The results demonstrate that the AEGPR-HMS is an efficient and robust method for nonparametric modeling of ship maneuvering motion.

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References

1.
Sutulo
,
S.
, and
Guedes Soares
,
C.
,
2014
, “
An Algorithm for Offline Identification of Ship Maneuvering Mathematical Models From Free Running Tests
,”
Ocean Eng.
,
79
, pp.
10
25
.
2.
Mei
,
T.
,
Liu
,
Y.
,
Ruiz
,
M. T.
,
Lataire
,
E.
,
Vantorre
,
M.
,
Chen
,
C.
, and
Zou
,
Z.
,
2021
, “
A Hybrid Method for Predicting Ship Maneuverability in Regular Waves
,”
ASME J. Offshore Mech. Arct. Eng.
,
143
(
2
), p.
021203
.
3.
He
,
H. W.
,
Wang
,
Z. H.
,
Zou
,
Z. J.
, and
Liu
,
Y.
,
2022
, “
Nonparametric Modeling of Ship Maneuvering Motion Based on Self-Designed Fully Connected Neural Network
,”
Ocean Eng.
,
251
(
3
), p.
111113
.
4.
Ouyang
,
Z.-L.
, and
Zou
,
Z.-J.
,
2021
, “
Nonparametric Modeling of Ship Maneuvering Motion Based on Gaussian Process Regression Optimized by Genetic Algorithm
,”
Ocean Eng.
,
238
, p.
109699
.
5.
Abkowitz
,
M. A.
,
1964
,
Lectures on Ship Hydrodynamics – Steering and Maneuvering
,
Hydro & Aerodynamic Laboratory
.
6.
Ogawa
,
A.
, and
Kasai
,
H.
,
1978
, “
On The Mathematical Model of Maneuvering Motion of Ships
,”
Int. Shipbuild. Prog.
,
25
(
292
), pp.
306
319
.
7.
Selvam
,
R. P.
,
Bhattacharyya
,
S. K.
, and
Haddara
,
M. R.
,
2005
, “
A Frequency Domain System Identification Method for Linear Ship Maneuvering
,”
Int. Shipbuild. Prog.
,
52
(
1
), pp.
5
27
.
8.
Weilin
,
L.
,
Tieshan
,
L.
, and
Zaojian
,
Z.
,
2009
, “
Parametric Identifiability in Modeling of Ship Maneuvering Motion
,”
J. Dalian Marit. Univ.
,
35
(
4
), pp.
1
3
.
9.
Yoon
,
H. K.
, and
Rhee
,
K. P.
,
2003
, “
Identification of Hydrodynamic Coefficients in Ship Maneuvering Equations of Motion by Estimation-Before-Modeling Technique
,”
Ocean Eng.
,
30
(
18
), pp.
2379
2404
.
10.
Jian-Chuan
,
Y.
,
Zao-Jian
,
Z.
, and
Feng
,
X.
,
2015
, “
Parametric Identification of Abkowitz Model for Ship Maneuvering Motion by Using Partial Least Squares Regression
,”
ASME J. Offshore Mech. Arct. Eng.
,
137
(
3
), p.
031301
.
11.
Perera
,
L. P.
,
Oliveira
,
P.
, and
Guedes Soares
,
C.
,
2011
, “
Dynamic Parameter Estimation of a Nonlinear Vessel Steering Model for Ocean Navigation
,”
30th International Conference on Ocean, Offshore and Arctic Engineering
,
Rotterdam, Netherlands
,
June 19–24
, pp.
881
888
.
12.
Luo
,
W. L.
, and
Li
,
X. Y.
,
2017
, “
Measures to Diminish the Parameter Drift in the Modeling of Ship Maneuvering Using System Identification
,”
Appl. Ocean Res.
,
67
, pp.
9
20
.
13.
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
.
14.
Rudin
,
C.
, and
Radin
,
J.
,
2019
, “
Why Are We Using Black Box Models in AI When We Don’t Need To? A Lesson From an Explainable AI Competition
,”
Harvard Data Sci. Rev.
,
1
(
2
), pp.
1
9
.
15.
Xue
,
Y.
,
Liu
,
Y. J.
,
Xue
,
G.
, and
Chen
,
G.
,
2021
, “
Identification and Prediction of Ship Maneuvering Motion Based on a Gaussian Process With Uncertainty Propagation
,”
J. Marine Sci. Eng.
,
9
(
8
), p.
804
.
16.
Xue
,
Y.
,
Liu
,
Y.
,
Ji
,
C.
,
Xue
,
G.
, and
Huang
,
S.
,
2020
, “
System Identification of Ship Dynamic Model Based on Gaussian Process Regression With Input Noise
,”
Ocean Eng.
,
216
, p.
107862
.
17.
Li
,
Z. H.
,
Yang
,
H.
,
Chao
,
S.
, and
Zi
,
Y. P.
,
2022
, “
Recurrent Neural Networks for Nonparametric Modeling of Ship Maneuvering Motion
,”
Int. J. Naval Archit. Ocean Eng.
,
14
, pp.
1
15
.
18.
Bai
,
W.
,
Ren
,
J.
, and
Li
,
T.
,
2019
, “
Genetic Optimization-Based Locally Weighted Learning Identification Modeling of Ship Maneuvering With Full Scale Trial
,”
Fut. Gener. Comput. Syst.
,
93
, pp.
1036
1045
.
19.
Jiang
,
L.
,
Shang
,
X.
,
Jin
,
B.
,
Zhang
,
Z.
, and
Zhang
,
W.
,
2024
, “
Black-Box Modeling of Ship Maneuvering Motion Using Multi-Output Least-Squares Support Vector Regression Based on Optimal Mixed Kernel Function
,”
Ocean Eng.
,
293
, p.
116663
.
20.
Wang
,
Z.
,
Xu
,
H.
,
Xia
,
L.
,
Zou
,
Z.
, and
Soares
,
C. G.
,
2020
, “
Kernel-Based Support Vector Regression for Nonparametric Modeling of Ship Maneuvering Motion
,”
Ocean Eng.
,
216
, p.
107994
.
21.
Zhang
,
Y.-Y.
,
Wang
,
Z.-H.
, and
Zou
,
Z.-J.
,
2022
, “
Black-Box Modeling of Ship Maneuvering Motion Based on Multi-Output Nu-Support Vector Regression With Random Excitation Signal
,”
Ocean Eng.
,
257
(
4
), p.
111279
.
22.
Rasmussen
,
C. E.
,
2004
, “
Gaussian Processes in Machine Learning
,”
Mach. Learn.
,
3176
, pp.
63
71
.
23.
Guan
,
Y.
,
Li
,
D.
,
Xue
,
S.
, and
Xi
,
Y.
,
2021
, “
Feature-Fusion-Kernel-Based Gaussian Process Model for Probabilistic Long-Term Load Forecasting
,”
Neurocomputing
,
426
, pp.
174
184
.
24.
Stoddard
,
J. G.
,
Birpoutsoukis
,
G.
,
Schoukens
,
J.
, and
Welsh
,
J. S.
,
2019
, “
Gaussian Process Regression for the Estimation of Generalized Frequency Response Functions
,”
Automatica
,
106
, pp.
161
167
.
25.
Ariza Ramire
,
W.
,
Leong
,
Z. Q.
,
Nguyen
,
H.
, and
Jayasinghe
,
S. G.
,
2018
, “
Nonparametric Dynamic System Identification of Ships Using Multi-Output Gaussian Processes
,”
Ocean Eng.
,
166
, pp.
26
36
.
26.
Zhang
,
Z.
, and
Ren
,
J.
,
2021
, “
Locally Weighted Non-Parametric Modeling of Ship Maneuvering Motion Based on Sparse Gaussian Process
,”
J. Marin. Sci. Eng.
,
9
(
6
), p.
606
.
27.
Ouyang
,
Z.-L.
,
Zou
,
Z.-J.
, and
Zou
,
L.
,
2023
, “
Adaptive Hybrid-Kernel Function Based Gaussian Process Regression for Nonparametric Modeling of Ship Maneuvering Motion
,”
Ocean Eng.
,
268
, p.
113373
.
28.
Liu
,
S.-Y.
,
Ouyang
,
Z.-L.
,
Chen
,
G.
,
Zhou
,
X.
, and
Zou
,
Z.-J.
,
2023
, “
Black-Box Modeling of Ship Maneuvering Motion Based on Gaussian Process Regression With Wavelet Threshold Denoising
,”
Ocean Eng.
,
271
, p.
113765
.
29.
Lim
,
D.
,
Ong
,
Y. S.
,
Jin
,
Y. C.
, and
Sendhoff
,
B.
,
2007
, “
A Study on Metamodeling Techniques, Ensembles, and Multi-Surrogates in Evolutionary Computation
,”
Annual Conference of Genetic and Evolutionary Computation Conference
,
London, UK
,
July 7
, pp.
1288
1295
.
30.
Viana
,
F. A. C.
,
Haftka
,
R. T.
, and
Steffen
,
V.
,
2009
, “
Multiple Surrogates: How Cross-Validation Errors Can Help Us to Obtain the Best Predictor
,”
Struct. Multidiscipl. Optim.
,
39
(
4
), pp.
439
457
.
31.
Stromberg
,
N.
,
2021
, “
Comparison of Optimal Linear, Affine and Convex Combinations of Metamodels
,”
Eng. Optim.
,
53
(
4
), pp.
702
718
.
32.
Acar
,
E.
,
2010
, “
Various Approaches for Constructing an Ensemble of Metamodels Using Local Measures
,”
Struct. Multidiscipl. Optim.
,
42
(
6
), pp.
879
896
.
33.
Liu
,
H. T.
,
Xu
,
S. L.
,
Wang
,
X. F.
,
Meng
,
J. G.
, and
Yang
,
S. H.
,
2016
, “
Optimal Weighted Pointwise Ensemble of Radial Basis Functions With Different Basis Functions
,”
Am. Inst. Aeronaut. Astronaut.
,
54
(
10
), pp.
3117
3133
.
34.
Lai
,
X. N.
,
Pang
,
Y.
,
Zhang
,
S.
,
Sun
,
W.
, and
Song
,
X. G.
,
2022
, “
An Adaptive Ensemble of Surrogate Models Based on Heuristic Model Screening
,”
Struct. Multidiscipl. Optim.
,
65
(
12
), p.
21
.
35.
Stern
,
F.
,
Agdrup
,
K.
,
Kim
,
S. Y.
, et al
,
2011
, “
Experience from SIMMAN 2008 —The First Workshop on Verification and Validation of Ship Maneuvering Simulation Methods.
J. Ship Res
,
55(2)
, pp.
135
147
.
36.
Fossen
,
T. I.
,
2021
,
Handbook of Marine Craft Hydrodynamics and Motion Control
,
Wiley
.
37.
Cheng
,
K.
, and
Lu
,
Z.
,
2020
, “
Structural Reliability Analysis Based on Ensemble Learning of Surrogate Models
,”
Struct. Saf.
,
83
, p.
101905
.
38.
Wang
,
Z. C.
,
Xia
,
H.
,
Peng
,
B. S.
,
Yang
,
B.
,
Zhu
,
S. M.
,
Zhang
,
J. Y.
, and
AnnorNyarko
,
M.
,
2021
, “
A Multi-Stage Hybrid Fault Diagnosis Approach for Operating Conditions of Nuclear Power Plant
,”
Ann. Nucl. Energy
,
153
, p.
10
.
39.
Helma
,
S.
,
2016
, “
A Scaling Procedure for Modern Propeller Designs
,”
Ocean Eng.
,
120
, pp.
165
174
.
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