This document discusses using time-frequency and wavelet analysis to assess turbulence/rotor interactions. It analyzes turbine response data using techniques like the continuous wavelet transform and multiresolution decomposition to better understand how transient turbulent events excite turbine modal responses and influence loading. The analyses show that coherent turbulent structures containing a range of frequencies can excite a broadband aeroelastic response in turbines. Load peaks often occur when constituent modal responses are in phase. The first and second symmetric and asymmetric rotor modes appear most susceptible to excitation from turbulent eddies with space scales less than a quarter of the rotor diameter.
Using time frequency and wavelet analysis to assess turbulence-rotor interactions, 19th asme wind symposium, jan 11, 2000
1. 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
2. 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.
3. 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.
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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
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What Turbulence Characteristics
Influence the Loading Spectrum?
Alternating stress
0 10 20 30 40 50
Alternatingcycles/hour
10-3
10-2
10-1
100
101
102
103
104
Region of
Greatest
Spectral
Variability
Extreme Loading
Events, Fatigue
Damage
High Loading Tail
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Previously We Have
Shown That . . .
Alternating stress
0 10 20 30 40 50
Alternatingcycles/hour
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
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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'
8. January 11, 2000 19th ASME Wind Energy Symposium 8
Conventional Power Spectrum of
Blade Flapwise Load Time History
Frequency (Hz)
0.1 1 10
Rootflapload(kNm)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
-5
0
5
10
15
20
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?
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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)
10. 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
11. January 11, 2000 19th ASME Wind Energy Symposium 11
Wavelet Definitions
dt
s
bt
s
tfbsW
−
= ∫
∞
∞−
ψ
1
)(),(
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,
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Morlet Analyzing Wavelet
(used for continuous wavelet transform analysis)
Wavelet Function Fourier Transform Magnitude
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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
Scalecenterfrequencyandbandwidth(Hz)
0.06
0.08
0.2
0.4
0.6
0.8
2
4
6
8
20
40
0.1
1
10
center frequency
bandwidth
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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
0.8
1.0
1.2
1.5
3.0
5.0
10.0
2.0
Frequency(Hz)
Scales
15. January 11, 2000 19th ASME Wind Energy Symposium 15
8th Order Symmlet Analyzing Wavelet
Frequency Response Magnitude
(used for multiresolution analysis)
17. 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 . . .
18. 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
19. January 11, 2000 19th ASME Wind Energy Symposium 19
Multiresolution Analysis Detail
Frequency Band Ranges
Detail
Band
Cyclic
Frequency
Range (Hz)
Known Characteristic Modal Responses within Band
B1 7.5 - 15.0 Rotor 2nd
flapwise bending; 2nd
asymmetric flapwise bending
B2 3.75 - 7.5 Rotor 1st
lag bending; 2nd
asymmetric lag bending
B3 1.875 - 3.75 Rotor 1st
symmetric flapwise bending, 1st
1st
/2nd
asymmetric flap
bending; tower fore/aft and side/side asymmetric bending
B4 0.938 - 1.875 Tower 1st
fore/aft and side/side bending
B5 0.469 - 0.938 1-P
B6 0.234 - 0.469
Detail
Band
Cyclic
Frequency
Range (Hz)
Known Characteristic Modal Responses within Band
B1 15.0 - 30.0 Rotor 1st
/2nd
torsion bending; 3rd
symmetric lag bending
B2 7.5 - 15.0 Flexbeam 2nd
flap bending; blade shell 4th
flap bending
B3 3.75 - 7.5 Rotor 3rd
symmetric and asymmetric bending; 2nd
asymmetric lag
bending; blade shell 2nd
flap bending
B4 1.875 - 3.75 Rotor 2nd
asymmetric flap bending; blade shell 1st
flap bending
B5 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-P
B7 0.234 - 0.469 Rotor 1st
symmetric flap bending
Rigid (Micon 65) Turbine
Flexible (Wind Eagle) Turbine
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Rigid Turbine Response to
Turbulent Flow Excitation
60 sec record First 20-sec detail of record
CWT of Reynolds stresses
and root flapwise loads
21. 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
0.8
1.0
1.2
1.5
3.0
5.0
10.0
2.0
22. 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
23. 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
