January 11, 2000 19th ASME Wind Energy Symposium 1

N.D. Kelley R.M. Osgood

National Wind Technology Center National Renewable Energy Laboratory

J.T. Bialasiewicz A. Jakubowski

Department of Electrical Engineering University of Colorado at Denver

Using Time-Frequency and Wavelet Analysis to Assess Turbulence/Rotor

Interactions

January 11, 2000 19th ASME Wind Energy Symposium 2

Background

We need to understand the turbulence/rotor interaction in both the time and frequency domains.

The high-stress events seen in turbine rotors are non-stationary and typically last only a few seconds.

Conventional spectral decomposition of the turbulent wind field (excitation) and associated rotor loading (response) is inadequate because of the transient nature of these events.

Previous work has shown that large loading events are often associated with the ingestion of coherent turbulence structures by turbine rotors.

January 11, 2000 19th ASME Wind Energy Symposium 3

Study Objectives

We wish to identify analysis tools that will allow us to: – Describe spectral characteristics of turbulent structures

that produce large aeroelastic responses – Obtain the spectral characteristics of rotor aeroelastic

responses from short, transient events that produce large loading peaks.

Use this information to understand the atmospheric conditions that produce such events in order to identify and numerically simulate them.

January 11, 2000 19th ASME Wind Energy Symposium 4

Approach

Identify suitable techniques to allow us to obtain frequency domain information from short-period loading events

Evaluate the applicability of various Time-Frequency analytical tools to allow us to perform “local” analyses of transient events using – Windowed or Short-Time Fourier Transforms – Wavelet Transforms

Use both observed and simulated inflow and turbine response data for the evaluation

January 11, 2000 19th ASME Wind Energy Symposium 5

What Turbulence Characteristics Influence the Loading Spectrum?

Alternating stress0 10 20 30 40 50

Alte

rnat

ing

cycl

es/h

our

10-3

10-2

10-1

100

101

102

103

104

Region of Greatest Spectral Variability

Extreme Loading Events, Fatigue Damage

High Loading Tail

January 11, 2000 19th ASME Wind Energy Symposium 6

Previously We Have Shown That . . .

Alternating stress0 10 20 30 40 50

Alte

rnat

ing

cycl

es/h

our

10-3

10-2

10-1

100

101

102

103

104

Bulk Inflow Parameters Influence Slope of High Loading Tail: Vertical Stability

Hub-Height Friction Velocity, u*

Instantaneous Inflow Parameters That Influence Individual Loading Events:

Turbulent Reynolds Stresses

u’w’ (u*)2 u’v’ v’w’

High Loading Tail

January 11, 2000 19th ASME Wind Energy Symposium 7

Example of Relationship Between Observed Flapwise Load Excursions and

Hub Turbulent Reynolds Stresses

Hub Reynolds stress components

Time (s)0 25 50 75 100 125 150

(m/s

)2

-40

-20

0

20

40

Zero-mean root flapwise bending

kNm

-10

-5

0

5

10

u'w'u'v'v'w'

January 11, 2000 19th ASME Wind Energy Symposium 8

Conventional Power Spectrum of Blade Flapwise Load Time History

Frequency (Hz)0.1 1 10

Roo

t fla

p lo

ad (k

Nm

)2 /Hz

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Zero-mean flapwise loads

Time (s)0 10 20 30 40 50 60

kNm

-15-10-505

101520

1-P

• Excellent frequency resolution or localization (0.1 Hz)

• Very poor time resolution or localization (60 secs)

But what is the spectral distribution for these transient event peaks?

January 11, 2000 19th ASME Wind Energy Symposium 9

Linear Time-Frequency Analysis Tools Evaluated

Energy Density – Spectrogram (obtained using the Windowed

or Short-Time Fourier Transform) – Scalogram (obtained using wavelet transform)

Wavelet Transforms – Continuous (CWT) – Discrete (DWT) (Multiresolution analysis)

January 11, 2000 19th ASME Wind Energy Symposium 10

Technique Comparisons

time

time time

Time Domain Analysis Frequency Domain Analysis

Short-Time Fourier Analysis Wavelet Analysis

Excellent time resolution, no frequency resolution

Excellent frequency resolution, no time resolution

Moderate time resolution, moderate frequency resolution

Good time resolution at high frequencies, poor at low frequencies. Poor frequency resolution at high frequencies, good at low frequencies.

Energy min max

January 11, 2000 19th ASME Wind Energy Symposium 11

Wavelet Definitions

dts

bts

tfbsW

−

= ∫∞

∞−

ψ1)(),(

Continuous Wavelet Transform of Signal f(t)

where ( )tψ is the wavelet function, s = scale, b = translation

Discrete Wavelet Transform of Signal f(n)

)2(2)(),(),( 2/ kngnfjiWbsW jj

Zn

−== −−

∈∑

where Njs j ∈= ,2 and Nkkb j ∈= ,2

dyadic scale dyadic translation

)(ng is the wavelet function,

January 11, 2000 19th ASME Wind Energy Symposium 12

Morlet Analyzing Wavelet (used for continuous wavelet transform analysis)

Wavelet Function Fourier Transform Magnitude

January 11, 2000 19th ASME Wind Energy Symposium 13

Scale-to-Frequency Conversion/Bandwidth for Morlet

Wavelet at 240 samples/sec

CWT Scale (s)6 8 15 20 30 40 60 80 150 200 300 40010 100

Scal

e ce

nter

freq

uenc

y an

d ba

ndw

idth

(Hz)

0.060.08

0.2

0.4

0.60.8

2

4

68

20

40

0.1

1

10

center frequencybandwidth

January 11, 2000 19th ASME Wind Energy Symposium 14

Continuous Wavelet Transform Example

Wind Eagle Turbine Blade Shell Flapping Signal

data sample number (time)

min - dynamic stress energy - max

1-P (0.93 Hz)

0.4

0.5

0.7

0.6

0.81.01.21.5

3.05.0

10.0

2.0

Frequency (Hz) Sc

ale

s

January 11, 2000 19th ASME Wind Energy Symposium 15

8th Order Symmlet Analyzing Wavelet Frequency Response Magnitude

(used for multiresolution analysis)

January 11, 2000 19th ASME Wind Energy Symposium 16

Multiresolution Decomposition Example

(discrete wavelet transform) kN

m

Observed Micon 65 Root Edge Signal

time (sec)

8-16 Hz band: 2nd flap, 2nd asym flap, tower 2nd fore/aft, tower 2nd side/side

Residual signal < 0.5 Hz

4-8 Hz band: Rotor 1st edge, 2nd asym 1st edge

2-4 Hz band: Rotor 1st/2nd asym 1st flap, 1st flap(non-rot), tower 1st fore/aft asym

1-2 Hz band: Tower 1st fore/aft, side/side

0.5-1 Hz band: 1-P, (gravity load)

January 11, 2000 19th ASME Wind Energy Symposium 17

Specifically We Have Found

At least for constant speed rotors, Windowed Fourier transforms do not appear to provide more information than is available from the wavelet transforms.

The use of both continuous and discrete wavelet transforms allows us to partition turbulent energy scales and rotor dynamic responses.

We now present an overview of our results . . .

January 11, 2000 19th ASME Wind Energy Symposium 18

Time Series and Wavelet Analyses Presentation Format

Hub-height horizontal wind speed

Hub-height Reynolds stresses

Root flapwise-bending load

Time Histories

Continuous Wavelet Transform Coefficients of

Root Flapwise-Bending Signal

Discrete Wavelet Transform Detail Frequency Bands of

Root Flapwise-Bending Signal (Multiresolution Analysis)

Time

January 11, 2000 19th ASME Wind Energy Symposium 19

Multiresolution Analysis Detail Frequency Band Ranges

DetailBand

CyclicFrequencyRange (Hz)

Known Characteristic Modal Responses within Band

B1 7.5 - 15.0 Rotor 2nd flapwise bending; 2nd asymmetric flapwise bendingB2 3.75 - 7.5 Rotor 1st lag bending; 2nd asymmetric lag bendingB3 1.875 - 3.75 Rotor 1st symmetric flapwise bending, 1st 1st/2nd asymmetric flap

bending; tower fore/aft and side/side asymmetric bendingB4 0.938 - 1.875 Tower 1st fore/aft and side/side bendingB5 0.469 - 0.938 1-PB6 0.234 - 0.469

DetailBand

CyclicFrequencyRange (Hz)

Known Characteristic Modal Responses within Band

B1 15.0 - 30.0 Rotor 1st/2nd torsion bending; 3rd symmetric lag bendingB2 7.5 - 15.0 Flexbeam 2nd flap bending; blade shell 4th flap bendingB3 3.75 - 7.5 Rotor 3rd symmetric and asymmetric bending; 2nd asymmetric lag

bending; blade shell 2nd flap bendingB4 1.875 - 3.75 Rotor 2nd asymmetric flap bending; blade shell 1st flap bendingB5 0.938 - 1.875 Rotor 1st asymmetric flap bending; rotor 2nd symmetric flap bending;

tower 1st/2nd fore/aft and side/side bending; drive train 1st bending;blade shell 1st flap bending

B6 0.469 - 0.938 Rotor 1st asymmetric lag bending; 1-PB7 0.234 - 0.469 Rotor 1st symmetric flap bending

Rigid (Micon 65) Turbine

Flexible (Wind Eagle) Turbine

January 11, 2000 19th ASME Wind Energy Symposium 20

Rigid Turbine Response to Turbulent Flow Excitation

60 sec record First 20-sec detail of record CWT of Reynolds stresses

and root flapwise loads

January 11, 2000 19th ASME Wind Energy Symposium 21

Flexible Turbine Response to Turbulent Flow Excitation

60 sec record First 20-sec detail of record CWT of Reynolds stresses

and root flapwise loads

0.4

0.5

0.7

0.6

0.81.01.21.5

3.05.0

10.0

2.0

January 11, 2000 19th ASME Wind Energy Symposium 22

Simulated Response of Flexible Turbine to Turbulence Excitation

20-sec record Comparison of inflow and aeroelastic parameters in fixed and rotating space

January 11, 2000 19th ASME Wind Energy Symposium 23

Conclusions

A coherent turbulent structure contains a wide range of phase-related frequencies (turbulent eddy wavelengths) that excite a broadband aeroelastic response in turbine rotors and support structures

Multiresolution analysis shows that load peaks occur when the constituent modal responses occur in phase or unison

The first and second symmetric and asymmetric rotor modes appear to be most susceptible to such excitation

Coherent turbulent eddies, whose space scales are less than a quarter of the rotor diameter, play a major role in developing peak load responses