DDDAS: A Framework for the Dynamic Data-Driven Fault Diagnosis of Wind

Turbine Systems

CMMI – 0540132 (Texas A&M University) PI: Yu Ding (IE) CMMI – 0540278 (University of Connecticut) PI: Jiong Tang (ME)Students: Eunshin Byon, Chiwoo Park (TAMU)

Yi Lu, Xin Wang (UConn)Starting date: June 2006 (36-month project)

Background

• Wind energyPollution free, fastest growing energy sourceEnough wind energy in the U.S. to produce three times as much electricity as the U.S. uses now

• Current situation and costToday wind generates less than 0.5% of US electricityClass 6 sites (average wind speeds of 6.7 m/s at 10 m height) can market electricity at 3 to 4 c/kWh – can compete with traditional energy source after tax credit (1.7c/kWh); New class 6 sites becoming less availableCurrent emphasis is on Class 4 sites (5.8 m/s at 10 m height) that cover large area - 20 times the developable wind resource of Class 6 sites; cost at 5 to 6 c/kWh – goal is to reduce cost to 3c/kWh

• Major hurdleHigh maintenance cost and failure caused down time

Wind Turbine System

wind turbine component

crew member

up to 70 m

ground vehicle

na b

Z1 3

LKJ

FA

n a n

Z 2 1

nP 1

Z 1 1 nZ W 1

2 2Z

1 2ZP 1Z

GE

C D

H I

2 3Z n

Z W 2

B

2.47 2.64 3.90 2.81x x x = 71.77

• Extremely complicated systemBlades up to 70m longMany gear stages to speed up

• Operate under non-steady condition• Operate in remote area• Maintenance

Mobilization of crane $60,000Crew of 12 in 3 day $15,000

• Failure…• Low speed wind turbine has longer

blades and more complex gearbox

Challenges and Current Limitation in Wind Turbine Health Monitoring

• Need a highly sensitive, robust, and autonomous health monitoring system

Reduce maintenance costReduce failure-caused down time Reduce false alarms

• ChallengesExtreme complexity of the systemNon-steady operation and large uncertainty/noise

• Existing methods and limitationSensory system is fixed and incomplete (only recording gearbox vibration signals – black-box in airplane)Non-dynamic and non-robust signal processing and feature extractionModeling approach is rigid – pure mechanistic models or neural network

Dynamic Data-Driven Framework for Wind Turbine Diagnosis

• Re-configurable sensory network: fixed sensors and wireless/mobile sensors• Data-driven pre-processing modules: adaptive feature extraction and sensor

anomaly removal• Multi-level models, incorporating historical data and on-line signals into

modeling/prediction• Dynamic interrogation strategy: action taken according to current conditions

Data from wired sensors Adaptive wavelets

for feature extraction Robust methods for sensor self-diagnosis

An influence coefficient network MART model

Pr(fault)

Low risk

High risk with no fault ID

High risk with fault ID

Scheduled local interrogation

Whole-system local interrogation

Narrowed area local interrogation

Data from wireless sensors or mobile acoustics sensors Local damage

propagation model

A lumped parameter vibration model Historical data

Confidence about damage prediction

Not confident

Get more sensing data confident

Maintenance decision & action

Upd

ate

the

pred

ictiv

e m

odel

(Dynamic interrogation strategy)

A global hybrid predictive model Robust, feature-oriented pre-processing

Blade Local Detection: Wave propagation Based Approach

• Lamb waveselastic guided waves propagating in a solid layer with free boundarieshighly sensitive to local discontinuities – compared to global, vibration based methods conveniently generated and sensed by piezoelectric transducers embedded in wind turbine blades – in situ damage detection

• Damage detection systemundamaged blade

damaged blade: mode conversion, phase change, frequency shift, etc.

wave propagation patterns have noticeable difference, but subject to noise/uncertainty in wind turbine operations

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UndamagedDamaged

Time (μs)

Current Practices

How to differentiate damaged signals from healthy signals?• Feature extraction and de-noising

time-domain analysis or spectral analysis (Fourier transform)joint time-frequency analysis (continuous/discrete wavelet transforms). Haar, Daubechies, Mexican hat, Gabor, Morlet: choice of wavelets is not always clearde-noising: local and/or global averaging, filtering

• Decision makinguncertainty/variation/noise addressed through root-mean-square deviation (RMSD) , mean absolute percentage deviation (MAPD), covariance (Cov) and correlation coefficient (CC)

Current practice limitationsad hoc methods requiring human interpretation/intervention – no systematic way of dealing with noise/uncertaintydecision making is not quantitative – confidence level?

Blade Local Interrogation: New Approach

• Objective – develop a robust and quantitative approach for blade local interrogation using piezo transducers

• Integrated methodology – three inter-related componentsadaptive harmonic wavelet transform (AHWT)

data-driven feature extractionprincipal component analysis (PCA) based truncation procedure

feature highlighting and denoisinghandle multiple signals when embedded into AHWT

Hotelling’s T2 analysiseliminate outliers from the baselineconfidence level-based decision making under PCA based feature highlighting

• Method is generic – can be directly extended to data-driven monitoring of gearbox transient vibration

New Approach Overview

{wmnk}1

{wmnk}5

Baseline signals, L = 5 AHWT basis

Wavelet coefficients

Minimum total entropy

Common wavelet basis {wmnk}u

(Subgrouping, K=3)

larger than UCL1 ?

Remove corresponding baseline signal Yes

Test signal

{wmnk}2

{wmnk}3

{wmnk}4

No

larger than UCL2 ?

Yes NoDamaged Undamaged

PCA denoising

Hotelling’s T2

Hotelling’s T2

Robust Signal Processing and Local Decision Making

Feature Extraction

Feature Highlighting Denoising

QuantitativeDecision

Making

Adaptive Harmonic Wavelet Transform

• Harmonic wavelet transformeach level (m, n) corresponds to one frequency range (m2π, n2π).

easy interpretation - signal analysis is carried out in specific frequency bands associated with known physical meaningsflexibility in selecting level parameters m and ncomputational efficiency - coefficients can be calculated using FFT

• Adaptive harmonic wavelet transform (Liu, 2003)treat each selection as a partition of

1 2 2( ) ( )2

0 otherwise

kin m

mnk

e m nW n m

ωπ ω π

ω π−

−⎧

≤ ≤⎪= −⎨⎪⎩

exp 2 ( ) exp 2 ( )( ) ( )

( ) 2mnk mn

k kin t im tk n m n mw t w t

n m n m i t

π π

π

⎡ ⎤ ⎡ ⎤− − −⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦= − =− −

{ }0 0 1 1 1 1( , ), ( , ), , ( , )L Lm n m n m n− −…{0,1, , }fNΩ = …

Data-Driven Feature Extraction

Shannon entropy-based algorithm

search a (e.g. binary) partition tree for the best wavelet basis, giving sparsest representationof the signal

• Improved AHWT for multi-signal applicationssince AHWT is data-driven, multiple signals

from the same healthy blade may lead to different ‘best’ wavelet basestotal Shannon entropy

select the common wavelet basis for the baseline dataset

( ) logj jj

H p p= −∑x

1 2( ) ( ) ( ) ( )l LH H H H= + + +A a a a{ }mnk uw

arg min ( )ll

u H= A

2 2where /j jp x= x

Feature Extraction Example

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Volta

ge (m

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624

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uenc

y (k

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Time (μs)(b)

Leve

l

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4

3

2

1

(c) Time (μs)

Scal

e

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17

33

49

65

81

97

113

128

(d)

noisefeaturenoise

feature?

AHWT versus discrete/continuous Daubechies 4

Sample signal AHWT map

Discrete DB4 map

Continuous DB4 map

{wmnk}1

{wmnk}5

Baseline signals, L = 5 AHWT basis

Wavelet coefficients

Minimum total entropy

Common wavelet basis {wmnk}u

(Subgrouping, K=3)

larger than UCL1 ?

Remove corresponding baseline signal Yes

Test signal

{wmnk}2

{wmnk}3

{wmnk}4

No

larger than UCL2 ?

Yes NoDamaged Undamaged

PCA denoising

Hotelling’s T2

Hotelling’s T2

New Approach Overview

Robust Signal Processing and Local Decision Making

Feature Highlighting and De-Nosing

• Principal component analysis (PCA)transforms a number of correlated variables into a reduced vector spaceimplemented by singular value decomposition (SVD)

• Denoising by PCA truncationthe first principal component (PC) accounts for major variation, and each succeeding PC explains as much of the remaining variability as possiblenoise can be reduced by eliminating the information not contained in the first few principal components percentage truncation threshold ET%

0

1 1

min

. . %rk K

j jj j

rk rk

s t ETλ λ= =

=

>∑ ∑

Features are further highlighted in the joint time-frequency domain.

{wmnk}1

{wmnk}5

Baseline signals, L = 5 AHWT basis

Wavelet coefficients

Minimum total entropy

Common wavelet basis {wmnk}u

(Subgrouping, K=3)

larger than UCL1 ?

Remove corresponding baseline signal Yes

Test signal

{wmnk}2

{wmnk}3

{wmnk}4

No

larger than UCL2 ?

Yes NoDamaged Undamaged

PCA denoising

Hotelling’s T2

Hotelling’s T2

New Approach Overview

Robust Signal Processing and Local Decision Making

Quantitative Decision Making

• Hotelling’s T2 analysis – deal with normal variation under multiple baseline measurements

Phase I: baseline self-checking

T2 follows the F-distributionPhase I upper control limit:

purify the baseline dataset by eliminating outliersPhase II: decision making for damage detection

Phase II upper control limit – updated due to new on-line measurement

If any calculated T2 value exceeds UCL2, we may conclude that, at the confidence level of (1-α)%, the analyzed structure is in damaged stateIf a signal is normal, it will be added to the baseline

2 -1ˆˆ ˆ ˆ ˆl l lT = T(x -μ)C (x -μ)

21

, ,( 1) ( , )( )K L

K LUCL F K L KL L Kα α

−= −

−

2, ,

( 1)( 1) ( , )( )K L

K L LUCL F K L KL L Kα α− +

= −−

Lamb Wave Propagation

• Analytical solutions under idealized boundary conditionswave equations

dispersive equations

strain output

2 22

l2 2

2 22

t2 2

0 (longitudinal)

0 (transverse)

kx z

kx z

ϕ ϕ ϕ

ψ ψ ψ

⎧∂ ∂+ + =⎪⎪ ∂ ∂

⎨∂ ∂⎪ + + =⎪ ∂ ∂⎩

( )

12 2 2 2 2

22 2 2

tan 1 4 10

tan 2 1

d

d

ζ ζ ζ ξ ζ

ξ ζ ζ

±⎛ ⎞− − −⎜ ⎟+ =⎜ ⎟− −⎝ ⎠

0 50 100 150 200 250 300

1

2

3

4

5

6

Frequency (kHz)V

eloc

ity (k

m/s

)

GroupPhaseS0

A0

( )

( )

s

s

a

a

2s s t s s

x 1 2

2a a t a a

1 2

cosh( )cosh( )1( , ) | ( )e e'

sinh( )sinh( )1 ( )e e'

ik x ik tz d

k k

ik x ik t

k k

k s k s d q dx t Y Y

s

k s k s d q dY Y

a

ω

ω

πε ω

μ

πω

μ

+∞− Δ

==−∞

+∞− Δ

=−∞

⎧ ⎫⎪ ⎪= − Δ⎨ ⎬Δ⎪ ⎪⎩ ⎭

⎧ ⎫⎪ ⎪+ + Δ⎨ ⎬Δ⎪ ⎪⎩ ⎭

∑ ∑

∑ ∑

Dynamic Analysis

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AnalyticalNumericalExperimental

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AnalyticalNumericalExperimental

(a)

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1AnalyticalNumericalExperimental

Time (μs)(b)

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itude

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0.2

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Frequency (kHz)

Scal

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eak

ampl

itude

S0

A0

Healthy structure response study

Symmetric and Antisymmetric amplitudes versus frequency

under 50 kHz excitation under 90 kHz excitation under 130 kHz excitation

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Frequency (kHz)

Peak

am

plitu

de ra

tio (S

0/A0)

Local Detection Demonstration

Damage is clearly detected in the T2 chart!

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Sens

or o

utpu

t (m

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BaselineTest

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Freq

uenc

y (k

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Time (μs)(b)

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Freq

uenc

y (k

Hz)

Time (μs)(c) 5 10 15 20 250

50

100

150

200

250

Subgroup

T2 v

alue

UndamagedDamaged

(d)

UCL2

sensor signals(90 kHz excitation)

AHWT map: baseline signal

AHWT map: test signal (damaged)

T2 chart: detection results

Detection Sensitivity under Different Excitation Frequency

• Center frequency of the excitation signal

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50

100

150

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250

Subgroup

T2va

lue

50 kHz90 kHz115 kHz130 kHz

UCL2

01 2( ) sin( )[1 cos( )] 2

tf t tTπω= −

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Frequency (kHz)Pe

ak a

mpl

itude

ratio

(A0/S

0)

Detection results under different center frequencies

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Scal

ed p

eak

ampl

itude

S0

A0

Detection Sensitivity Relative to Crack Size

Detection sensitivity with respect to crack depth and width

5 10 15 20 250

50

100

150

200

250

Subgroup

T2va

lue

w = 0.4 mmw = 0.8 mmw = 1.2 mmw = 1.6 mm

UCL2

5 10 15 20 250

50

100

150

200

250

300

350

400

Subgroup

T2va

lue

h/2d = 16.7%h/2d = 22.2%h/2d = 27.8%h/2d = 33.3%h/2d = 44.4%

UCL2

Major factor to the detection sensitivity is the crack depth, when the crack width is small compared to the wavelength.

On-going Work

• Set up a laboratory test bed of wind turbine with coupled gearbox and rotating blades

• Data-driven local detection approach applied to gearbox vibration monitoring

• Develop dynamic and hybrid models of blade-gearbox system• Develop dynamic interrogation strategy

PC with dSPACE boardLow-pass filters

Power amplifiers

DC motor controller

DC PM drive motor

DC PM load motor

Resistive load

Accelerometer and acoustic sensor signals

Piezoelectric sensor signals Signal analyzer Power amplifiers

Piezoelectric actuator

Blade

Thanks

DDDAS will enable the autonomous diagnosis of wind turbines that operate under non-steady condition with variation/uncertainty