A finite difference method (FDM) solving the coupled partial differential equations governing three-dimensional (3D) motions of a towed underwater cable has been implemented in a combined ensemble Kalman filter (EnKF) and ensemble Kalman smoother (EnKS), as a new approach to combined state and parameter estimation for towed underwater cables. A simulation study of the method applied to a seismic streamer has been performed. Cable state variables as well as model parameters are estimated. Parameters estimated are crossline ocean current varying with time as well as cable tangential drag coefficient. The presented results indicate that the method is able to estimate state as well as parameters for seismic streamers.

References

References
1.
Polydorides
,
N.
,
Storteig
,
E.
, and
Lionheart
,
W.
,
2008
, “
Forward and Inverse Problems in Towed Cable Hydrodynamics
,”
Ocean Eng.
,
35
(
14
), pp.
1429
1438
.
2.
Solheim
,
P.
,
2013
, “
Method for Determining Correction Under Steering of a Point on a Towed Object Towards a Goal Position
,” Tromsø, Norway, U.S. Patent No.
8,606,440
.https://www.google.com/patents/US8606440
3.
Türkyilmaz
,
Y.
,
2004
, “
Modeling and Control of Towed Seismic Cables
,”
Ph.D. thesis
, Norwegian University of Science and Technology, Trondheim, Norway.https://brage.bibsys.no/xmlui/handle/11250/228790
4.
Howell
,
C. T.
,
1991
, “
Numerical Analysis of 2-D Nonlinear Cable Equations With Applications to Low-Tension Problems
,”
First International Offshore and Polar Engineering Conference
, Edinburgh, UK, Aug. 11–16, SPE Paper No.
ISOPE-I-91-092
https://www.onepetro.org/conference-paper/ISOPE-I-91-092.
5.
Burgess
,
J. J.
,
1991
, “
Modelling of Undersea Cable Installation With a Finite Difference Method
,”
First International Offshore and Polar Engineering Conference
, Edinburgh, UK, Aug. 11–16, SPE Paper No.
ISOPE-I-91-095
.https://www.onepetro.org/conference-paper/ISOPE-I-91-095
6.
Neto
,
A. G.
,
2016
, “
Dynamics of Offshore Risers Using a Geometrically-Exact Beam Model With Hydro-Dynamic Loads and Contact With the Seabed
,”
Eng. Struct.
,
125
, pp.
438
454
.
7.
Ablow
,
C. M.
, and
Schechter
,
S.
,
1983
, “
Numerical Simulation of Undersea Cable Dynamics
,”
Ocean Eng.
,
10
(
6
), pp.
443
457
.
8.
Milinazzo
,
F.
,
Wilkie
,
M.
, and
Latchman
,
S. A.
,
1987
, “
An Efficient Algorithm for Simulating the Dynamics of Towed Cable Systems
,”
Ocean Eng.
,
14
(
6
), pp.
513
526
.
9.
Sanders
,
J. V.
,
1982
, “
A Three-Dimensional Dynamic Analysis of a Towed System
,”
Ocean Eng.
,
9
(
5
), pp.
483
499
.
10.
Evensen
,
G.
,
1994
, “
Sequential Data Assimilation With a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics
,”
J. Geophys. Res.
,
99
(C
5
), pp.
10143
10162
.
11.
Evensen
,
G.
,
2009
,
Data Assimilation: The Ensemble Kalman Filter
,
Springer
,
Berlin
, Chap. 9.
12.
Evensen
,
G.
,
Hove
,
J.
,
Meisingset
,
H. C.
,
Reiso
,
E.
,
Seim
,
K. S.
, and
Espelid
,
Ø.
,
2007
, “
Using the EnKF for Assisted History Matching of a North Sea Reservoir Model
,”
SPE Reservoir Simulation Symposium
, Woodlands, TX, Feb. 26–28, SPE Paper No.
SPE-106184-MS
.
13.
White
,
F. M.
,
2011
,
Fluid Mechanics
,
7th ed.
,
McGraw-Hill
,
New York
, p.
578
.
14.
Faltinsen
,
O. M.
,
1990
,
Sea Loads on Ships and Offshore Structures
,
Cambridge University Press
,
Cambridge, UK
, p.
61
.
15.
Yang
,
N.
,
Jeng
,
D.-S.
, and
Zhou
,
X. L.
,
2013
, “
Tension Analysis of Submarine Cables During Laying Operations
,”
Open Civ. Eng. J.
,
7
(
1
), pp.
282
291
.
16.
Newman
,
J. N.
,
1977
,
Marine Hydrodynamics
,
The MIT Press
,
Cambridge, MA
, pp.
37
41
.
17.
Keller
,
H. B.
,
1970
, “
A New Difference Scheme for Parabolic Problems
,”
Numerical Solution of Partial Differential Equations
, Vol.
2
, Academic Press, New York, pp.
265
293
.
18.
Cebeci
,
T.
,
Shao
,
J. P.
,
Kafyeke
,
F.
, and
Laurendeau
,
E.
,
2005
,
Computational Fluid Dynamics for Engineers
,
Horizons Publishing
,
Long Beach, CA
, Chap. 4.
19.
Matlab
, 2014, “
The Language of Technical Computing
,” MathWorks, Natick, MA.
20.
Rispin
,
P.
,
1980
, “
Data Package No. 1 for Cable and Array Maneuvering
,” David W. Taylor Naval Ship Research and Development Center, Bethesda, MD.
21.
Evensen
,
G.
,
2009
, “
The Ensemble Kalman Filter for Combined State and Parameter Estimation
,”
IEEE Control Syst. Mag.
,
29
(
3
), pp.
83
104
.
22.
Grønnevik
,
R.
, and
Evensen
,
G.
,
2001
, “
Application of Ensemble-Based Techniques in Fish Stock Assessment
,”
Sarsia
,
86
(
6
), pp.
517
526
.
23.
Evensen
,
G.
,
2003
, “
The Ensemble Kalman Filter: Theoretical Formulation and Practical Implementation
,”
Ocean Dyn.
,
53
(
4
), pp.
343
367
.
24.
Brown
,
R. G.
, and
Hwang
,
P. Y. C.
,
1997
,
Introduction to Random Signals and Applied Kalman Filtering
,
Wiley
,
New York
, Chap. 5.
25.
Pedersen
,
E.
, and
Sørensen
,
A. J.
,
2001
, “
Modelling and Control of Towed Marine Seimic Streamer Cables
,”
IFAC Proc. Vol.
,
34
(
7
), pp.
89
94
.
26.
White
,
F. M.
,
1972
, “
An Analysis of Axisymmetric Turbulent Flow Past a Long Cylinder
,”
ASME J. Basic Eng.
,
94
(
1
), pp.
200
204
.
This content is only available via PDF.
You do not currently have access to this content.