Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 1

ANALYSIS METHODOLOGY OF VORTEX-INDUCED MOTIONS (VIM) ON A MONOCOLUMN PLATFORM APPLYING THE

HILBERT-HUANG TRANSFORM METHOD

june | 2010

Rodolfo T. Gonçalves

Guilherme R. Franzini

Guilherme F. Rosetti

André L. C. Fujarra

Kazuo Nishimoto

TPN – Numerical Offshore Tank

Department of Naval Architecture and Ocean

Engineering

Escola Politécnica – University of São Paulo

São Paulo, SP, Brazil

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 2

Introduction

• The VIV is usually studied for rigid and flexible cylinders with large aspect ratio (L/D), for example in a riser dynamic scenario;

• VIM is investigated for rigid cylinders with low aspect ratio, e.g. spar and MPSO (Monocolumn Production, Storage and Offloading System);

• The different behavior between the phenomena arises from the 3D effects, which are attributed to the low aspect ratio in the VIM;

• The existence of motions in both directions, in-line and transverse, gives rise to larger amplitude motions which can be the cause of decrease in the mooring and risers fatigue life.

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 3

Motivation

• Experimental time-histories that emerge from VIM investigations are non-linear and non-stationary;

• Usual spectral analysis methods, based on Fourier Transform, rely on the hypotheses of linear and stationary dynamics;

• A method developed to treat non-stationary signals that originate from non-linear systems was presented by (Huang, et al., 1998). It is referred to as Hilbert-Huang transform method (HHT).

• The work proposes to create an analysis methodology to improve the statistics characteristics of VIM signal using the HHT.

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 4

Hilbert-Huang Method

Time History

EMD

IMFs

Hilbert Transform

Hilbert Spectrum H (ω,t)

Marginal Spectrum

Instantaneous Energy Level Hilbert-Huang

Spectrum

Characteristic motion

amplitude

Characteristic motion

frequency

ω

E

t

E

t

ω H

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 5

• Time history of motions in the transverse and in-line directions

• There are few peaks in the signal (approximately 20 peaks in the transverse direction)

• Poor statistics characteristics in evaluating the characteristic amplitude in the transverse direction, i.e. mean of only 2 points in the case of 10% highest peaks

• In order to improve the statistics characteristics of these signals, the HHT was applied and its results are presented as follows

Time History

0 50 100 150 200 250 300-1

-0.5

0

0.5

1

Time [s]

y/D

Motion in the transverse direction

0 0.05 0.10

10

20

30

40

50

Frequency [Hz]

Ma

rgin

al S

pe

ctr

um

0 100 200 3000

1

2

3

4

5x 10

-3

Insta

nta

ne

ou

s E

ne

rgy

Time [s]

0 50 100 150 200 250 300-1.5

-1.4

-1.3

-1.2

-1.1

-1

Time [s]

x/D

Motion in the in-line direction

0 0.05 0.10

0.5

1

1.5

2

Frequency [Hz]

Ma

rgin

al S

pe

ctr

um

0 100 200 3000

0.2

0.4

0.6

0.8

1

1.2x 10

-4

Insta

nta

ne

ou

s E

ne

rgy

Time [s]

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 6

EMD and IMFs

• A finite set of ‘Intrinsic Mode Functions’ (IMFs) is obtained from the original signal through an ‘Empirical Mode Decomposition’ (EMD)

• Each IMF contain the energy in different time scales

-1

0

1

Sig

nal

Empirical Mode Decomposition

-1

0

1

Imf

1

-0.05

0

0.05

Imf

2

-0.05

0

0.05

Imf

3

0 50 100 150 200 2500

0.05

0.1

Time [s]

Mean

Tre

nd

-2

-1.5

-1

Sig

nal

Empirical Mode Decomposition

-1

0

1

Imf

1

-0.1

0

0.1

Imf

2

-0.05

0

0.05

Imf

3

-0.05

0

0.05

Imf

40 50 100 150 200 250

-1.3

-1.25

-1.2

Time [s]M

ean

Tre

nd

• The non-zero mean trend is derived from the non-stationary signal behavior

• The sum of IMFs represents the original signal

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 7

Hilbert-Huang Spectrum

• This frequency-time distribution of the amplitude is designated as the Hilbert spectrum

Time [s]

Fre

qu

en

cy [H

z]

Hilbert-Huang Spectrum

0 50 100 150 200 2500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Y/D

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time [s]

Fre

qu

en

cy [H

z]

Hilbert-Huang Spectrum

0 50 100 150 200 2500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

X/D

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

• The frequency time-trace for the motions in the transverse direction is very energetic, but presents small fluctuations around 0.35 Hz.

• The frequency time-trace for the motions in the in-line direction has large fluctuation due to the highly non-stationary nature of the VIM.

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 8

Marginal Spectrum

• The marginal spectrum offers a measure of total amplitude (or energy) contribution from each frequency value. It is similar a the Power Spectrum by FFT

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

15

20

25

30

35

40

45

50

Frequency [Hz]

Ma

rgin

al S

pe

ctr

um

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Frequency [Hz]

Ma

rgin

al S

pe

ctr

um

• The high energy level is comprised of a low width range of frequencies for the motions in the transverse direction, whereas the energy level is significant in a large width range for the motions in the in-line direction.

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 9

Intantaneous Energy Level

• The IE can be used to check the energy fluctuation over time, i.e. the amplitude modulation.

0 50 100 150 200 250 3000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

-3

Insta

nta

ne

ou

s E

ne

rgy

Time [s]0 50 100 150 200 250 300

0

0.2

0.4

0.6

0.8

1

1.2x 10

-4

Insta

nta

ne

ou

s E

ne

rgy

Time [s]

• The IE for the motions in the in-line direction is more irregular than the transverse direction ones. This fact confirms the high modulation amplitude present in the signal.

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 10

Characteristic Amplitudes

• The characteristic motion amplitude is evaluated applying the mean of the 10% largest amplitudes from H(ω,t).

• The characteristic motion frequency is the mean of the frequency related to the 10% largest amplitudes from H(ω,t).

0 2 4 6 8 10 12 14 160

0.2

0.4

0.6

0.8

1

Vr0

Y / D

Traditional AnalysisFujarra, et al. (2009)

HHT AnalysisGonçalves, et al. (2010)

0 2 4 6 8 10 12 14 160

0.05

0.1

0.15

0.2

Vr0

X / D

Traditional AnalysisFujarra, et al. (2009)

HHT AnalysisGonçalves, et al. (2010)

• The numbers of points to calculate the mean is proportional to the number of points in the signal time history, which provides a better statistics.

• The comparison between HHT and Traditional Analysis showed: • Small difference in the transverse

direction (around 2%) • Differences around 25% in the

in-line direction for Vr > 9.0

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 11

Conclusions

• The values of characteristic motion amplitudes showed to be more reliable owing to the large number of points to calculate the statistics using HHT.

• The comparison between traditional analysis (mean of the 10% highest peaks) and HHT analysis for VIM pointed out to larger differences observing the motion in the in-line direction. The difference is due to the non-stationary behavior of the VIM phenomenon (modulation in the amplitude and frequency).

Shanghai | China | june | 2010 29th International Conference on Ocean, Offshore and Arctic Engineering 12

THANKS

rodolfo_tg@tpn.usp.br