We combine an averaging procedure with a Hilbert transform-based algorithm for parameter estimation of a nonlinear ocean system roll model. System backbone curves obtained from data are compared to those obtained analytically and are found to be accurate. Sensitivity of the results is tested by introducing random noise to a nonlinear model describing roll response of a small fishing boat. An example field calibration test of a small semisubmersible exhibiting nonlinear damping is also considered.

1.
Bass
D. W.
, and
Haddara
M. R.
,
1988
, “
Nonlinear Models of Ship Roll Damping
,”
International Shipbuilding Progress
, Vol.
35
, pp.
5
24
.
2.
Bendat, J. S., and Piersol, A. G., 1986, Random Data—Analysis and Measurement Procedures, John Wiley & Sons, New York, NY.
3.
Bikdash
M.
,
Balachandran
B.
, and
Nayfeh
A. H.
,
1994
, “
Melnikov Analysis for a Ship with a General Roll-Damping Model
,”
Nonlinear Dynamics
, Vol.
6
, pp.
101
124
.
4.
Bitner-Gregerson
E. M.
, and
Gran
S.
,
1983
, “
Local Properties of Sea Waves Derived from a Wave Record
,”
Applied Ocean Research
, Vol.
5
, pp.
210
214
.
5.
Cardo
A.
,
Francescutto
A.
, and
Nabergoj
R.
,
1982
, “
On Damping Models in Free and Forced Rolling Motion
,”
Ocean Engineering
, Vol.
9
, pp.
295
307
.
6.
Chakrabarti, S. K., 1990 Nonlinear Methods in Offshore Engineering, Elsevier, Amsterdam, Holland.
7.
Coulon, F., 1986 Signal Theory and Processing, Arthech House.
8.
Falzarano
J. M.
,
Shaw
S. W.
, and
Troesh
A. W.
,
1992
, “
Application of Global Methods for Analyzing Dynamical Systems to Ships Rolling Motion and Capsizing
,”
International Journal of Bifurcation and Chaos
, Vol.
2
, pp.
101
115
.
9.
Feldman
M.
,
1994
, “
Nonlinear System Vibration Analysis Using the Hilbert Transform: Free Vibration
,”
Mechanical Systems and Signal Processing
, Vol.
2
, pp.
119
227
.
10.
Flower
J. O.
, and
Sabati Aljaff
W. A. K.
,
1980
, “
Krylov-Bogoliubov’s Solution to Decaying Nonlinear Oscillations in Marine Systems
,”
International Shipbuilding Progress
, Vol.
27
, pp.
225
230
.
11.
Froude, W. 1955, The Papers of William Froude, Inst. of Naval Architects, London, U.K.
12.
Gottlieb
O.
,
Feldman
M.
, and
Yim
S. C. S.
,
1996
, “
Parameter Identification of Nonlinear Ocean Mooring Systems Using the Hilbert Transform
,”
ASME JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING
, Vol.
118
, Feb., pp.
29
36
.
13.
Haddara
M. R.
, and
Bennett
P.
,
1989
, “
A Study of Angle Dependence of Roll Damping Moment
,”
Ocean Engineering
, Vol.
16
, pp.
411
427
.
14.
Haddara
M. R.
, and
Cumming
D.
,
1992
, “
Experimental Investigation into the Physics of Roll Damping
,”
International Shipbuilding Progress
, Vol.
39
, pp.
323
343
.
15.
Hsieh
S. R.
,
Troesh
A.
, and
Shaw
S. W.
,
1994
, “
A Nonlinear Method for Predicting Vessel Capsizing in Random Beam Seas
,”
Proceedings, Royal Society A
, Vol.
446
, pp.
195
211
.
16.
Hudspeth, R. T., and Medina, J. R., 1988, “Wave Group Analysis by the Hilbert Transform,” ASCE Proceedings, 21st Coastal Engineering Conference, Spain, pp. 884–898.
17.
Jiang, C., and Troesh, A. W., 1995, “Roll Motion Modeling: Parameter Determination and their Effects on Ship Nonlinear Stability,” preprint.
18.
Mathisen
J. B.
and
Price
W. G.
,
1984
, “
Estimation of Ship Roll Damping Coefficients
,”
Trans. RINA
, Vol.
127
, pp.
295
307
.
19.
Meirovitch, L., 1970, Methods of Analytical Dynamics, McGraw-Hill, New York, NY.
20.
Mitra, S. K., and Kaiser, J. F., 1993, Handbook for Digital Signal Processing, Wiley-Interscience, New York, NY.
21.
Nayfeh
A. H.
, and
Sanchez
N. E.
,
1988
, “
Stability and Complicated Rolling Response of Ships in Regular Beam Seas
,”
International Shipbuilding Progress
, Vol.
37
, pp.
331
352
.
22.
Newman, J. N., 1977, Marine Hydrodynamics, MIT Press, Cambridge, U.K.
23.
Roberts
J. B.
,
1985
, “
Estimation of Nonlinear Ship Roll Damping from Free-Decay Data
,”
Journal of Ship Research
, Vol.
29
, pp.
127
138
.
24.
Sanders, J. A., and Verhulst, F., 1985, Averaging Methods in Nonlinear Dynamics, Springer, New York, NY.
25.
Sarpkaya, T., and Isaacson, M. 1981, Mechanics of Wave Forces on Offshore Structures, Van Nostrand-Reinhold, New York, NY.
26.
Shields, D. R., and Zueck, R. F., 1988, Offshore Tech. Conference, Houston, TX, Paper No. 5454.
27.
Thompson
J. M. T.
,
Rainey
R. C. T.
, and
Soliman
M. S.
,
1990
, “
Ship Stability Criteria Based on Chaotic Transients from Incursive Fractals
,”
Proceedings Royal Society A
, Vol.
332
, pp.
149
167
.
28.
Tomlinson
G. R.
,
1987
, “
Developments in the Use of the Hilbert Transform for Detecting and Quantifying Nonlinearity Associated with Frequency
,”
Mechanical Systems and Signal Processing
, Vol.
1
, pp.
151
171
.
29.
Virgin
L.
1987
, “
The Nonlinear Rolling Response of a Vessel Including Chaotic Motions Leading to Capsize in Regular Seas
,”
Applied Ocean Research
, Vol.
5
, pp.
210
214
.
30.
Wang, H. T., and Teng, C. C., 1994, “Nonlinear Aspects of the Motion Behavior of Directional Wave Buoys,” ASME Proceedings, 13th International Conference of OMAE, Houston, TX, Vol. I, pp. 11–18.
31.
Wiggins, S., 1990, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York, NY.
32.
Witz
J. A.
,
Ablett
C. B.
, and
Harrison
J. H.
,
1989
, “
Roll Response of Semi-submersibles with Nonlinear Restoring Moment Characteristics
,”
Applied Ocean Research
, Vol.
11
, pp.
153
166
.
33.
Wright
J. H. G.
, and
Marshfield
W. B.
1979
, “
Ship Roll Response and Capsize Behavior in Beam Seas
,”
Trans. RINA
, Vol.
122
, pp.
129
148
.
This content is only available via PDF.
You do not currently have access to this content.