Abstract

The behavior of a nonlinear dynamic system under arbitrary excitation can be represented by the Volterra series if the Volterra kernels of different orders are known. This study presents a methodology for a direct estimation of the Volterra kernel coefficients up to the second-order using prepared data obtained by running a time-domain analysis of the system of interest. To avoid potential problems during kernel estimation, the Volterra kernel is expanded into a polynomial series using the Laguerre polynomials, and the coefficients of the Laguerre polynomials are then estimated using a least-square method. A nonlinear oscillator with a quadratic stiffness term is introduced, and the methodology is applied to check the applicability and accuracy. The methodology is applied to a more realistic engineering problem of a simplified riser under irregular wave excitation.

References

References
1.
Wray
,
J.
, and
Green
,
G. G. R.
,
1994
, “
Calculation of the Volterra Kernels of Nonlinear Dynamic System Using an Artificial Neural Network
,”
Biol. Cybern.
,
71
(
3
), pp.
187
195
. 10.1007/BF00202758
2.
Marmarelis
,
V. Z.
, and
Zhao
,
X.
,
1997
, “
Volterra Models and Three-Layer Perceptrons
,”
IEEE Trans. Neural Networks
,
8
(
6
), pp.
1421
1433
. 10.1109/72.641465
3.
Worden
,
K.
,
Billings
,
S. A.
,
Stansby
,
P. K.
, and
Tomlinson
,
G. R.
,
1994
, “
Identification of Nonlinear Wave Forces
,”
J. Fluid. Struct.
,
8
(
1
), pp.
19
71
. 10.1006/jfls.1994.1002
4.
Chance
,
J. E.
,
Worden
,
K.
, and
Tomlinson
,
G. R.
,
1998
, “
Frequency Domain Analysis of NARX Neural Networks
,”
J. Sound Vib.
,
213
(
5
), pp.
915
941
. 10.1006/jsvi.1998.1539
5.
Birpoutsoukis
,
G.
, and
Schoukens
,
J.
,
2015
, “
Nonparametric Volterra Kernel Estimation Using Regularization
,”
International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings
,
IEEE
,
Pisa
, Italy, pp.
222
227
.
6.
Israelsen
,
B. W.
, and
Dale
,
A. S.
,
2014
, “
Alche Spring Meeting and Global Congress on Process Safety
,”
Alche Spring Meeting and Global Congress on Process Safety
,
New Orleans, LA
,
Mar. 30–Apr. 3
.
7.
Mazaheri
,
S.
, and
Downie
,
M. J.
,
2004
, “
Response-Based Method for Determining the Extreme Behavior of Floating Offshore Platforms
,”
Ocean Eng.
,
32
(
3–4
), pp.
363
393
. 10.1016/j.oceaneng.2004.08.004
8.
Rodrigues
,
M. V.
,
Correa
,
F. N.
, and
Jacob
,
B. P.
,
2007
, “
Implicit Domain Decomposition Methods for Coupled Analysis of Offshore Platform
,”
Commun. Numer. Meth. Eng.
,
23
(
6
), pp.
599
621
. 10.1002/cnm.945
9.
Yasseri
,
S. F.
,
Bahai
,
H.
,
Bazargan
,
H.
, and
Aminzadeh
,
A.
,
2010
, “
Prediction of Safe Sea-State Using Finite Element Method and Artificial Neural Network
,”
Ocean Eng.
,
37
(
2–3
), pp.
200
207
. 10.1016/j.oceaneng.2009.11.006
10.
Vazquez-Hernandez
,
A. O.
,
Ellwanger
,
G. B.
, and
Sagrilo
,
L. V. S.
,
2011
, “
Long-Term Response Analysis of FPSO Mooring Systems
,”
Appl. Ocean Res.
,
33
(
4
), pp.
375
383
. 10.1016/j.apor.2011.05.003
11.
Pina
,
A. C.
,
Pina
,
A. A.
,
Albrecht
,
C. H.
,
Lima
,
B. S. L. P.
, and
Jacob
,
B. P.
,
2013
, “
ANN-Based Surrogate Models for the Analysis of Mooring Lines and Risers
,”
Appl. Ocean Res.
,
41
, pp.
76
86
. 10.1016/j.apor.2013.03.003
12.
Pina
,
A. C.
,
Albrecht
,
C. H.
,
Lima
,
B. S. L. P.
, and
Jacob
,
B. P.
,
2014
, “
Wavelet Network Meta-Models for the Analysis of Slender Offshore Structures
,”
Eng. Struct.
,
68
, pp.
71
84
. 10.1016/j.engstruct.2014.02.039
13.
Pina
,
A. C.
,
Monteiro
,
B. F.
,
Albrecht
,
C. H.
,
Lima
,
B. S. L. P.
, and
Jacob
,
B. P.
,
2014
, “
ANN and Wavelet Network Meta-Models for the Coupled Analysis of Floating Production Systems
,”
Appl. Ocean Res.
,
48
, pp.
21
32
. 10.1016/j.apor.2014.07.009
14.
Chri1stiansen
,
N. H.
,
Voie
,
P. E. T.
,
Høgsberg
,
J.
, and
Sødahl
,
N.
,
2013
, “
Efficient Mooring Line Fatigue Analysis Using a Hybrid Method Time Domain Simulation Scheme
,”
Proceedings for the ASME 32nd International Conference on Ocean, Offshore and Arctic Engineering
,
Nantes, France
,
June 9–14
.
15.
Kim
,
Y.
,
Kim
,
J. H.
, and
Kim
,
Y.
,
2014
, “
Time Series Prediction of Nonlinear Ship Structural Responses in Irregular Seaways Using a Third-Order Volterra Model
,”
J. Fluid. Struct.
,
49
, pp.
322
337
. 10.1016/j.jfluidstructs.2014.04.019
16.
Kim
,
Y.
,
2015
, “
Finite Memory Quadratic Volterra Model for the Response Prediction of a Slender Marine Structure Under a Morison Load
,”
J. Fluid. Struct.
,
56
, pp.
75
88
. 10.1016/j.jfluidstructs.2015.05.003
17.
Schetzen
,
M.
,
1980
,
The Volterra and Wiener Theories of Nonlinear Systems
,
Wiley-Interscience Publication
,
Hoboken, NJ
.
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