PER method for Fault detection of a planetary gear under variable speed conditions

1. Seoul National University
Positive Energy Residual (PER) Based
Planetary Gears Fault Detection Method
Under Variable Speed Conditions
Presenter: Jungho Park
PhD Candidate in Seoul National University
Visiting Researcher in University of Alberta
System Health & Risk Management Laboratory
Department of Mechanical & Aerospace Engineering
Seoul National University

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Seoul National University
Edmonton
Seoul
Location
Mechanical engineering department

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Seoul National University
Professor
Associate
professor
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professor
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professor
Total
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Under-
graduate
M.A Ph.D. Total
16,511 7,882 3,709 28,102
Under-graduate Graduate Professional Graduate
16 Colleges with
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College & School (As of April, 2017 )
Full-time faculty (As of April, 2018; Unit: Persons)
Students (As of April, 2018; Unit: Persons)

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Biography
Education
 B.S. Seoul National University, Aug. 12’
 Ph. D. Seoul National University, Aug. 19’ (Expected)
Experience
 Korean Army, Apr. 2009 – Feb. 2011
 Intern at Samsung Heavy Industries, Dec. 11’ – Feb. 12’
Research interest
 Model-based fault diagnosis of a planetary gear
 Fault detection of a planetary gear under variable speed conditions
Publication
 8 Journal papers (2 first author), 1 in revision
 Research assistant at PARC, Jul. 17’ – Nov. 17’

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CONTENTS
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Introduction1
PER (Positive Energy Residual) method2
Case study: Simulation & Experiment3
Conclusion4

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Introduction
http://www.youtube.com/watch?v=u8QEqtvt_IA
Sun gearCarrier
Ring gear
Planet gear
 Planetary gear: Ring, sun, planet and carrier
 Multiple planets could share the heavy loads
 Applications : wind turbine, helicopters, etc.
 Economic loss and casualties from unexpected failures
Fault Detection of a Planetary Gear
Various methods have been developed for fault detection of the planetary gears

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Introduction
*Randall, R. B. "A new method of modeling gear faults." Journal of mechanical design 104.2 (1982): 259-267.
Normal
Fault
Distributed
 Usually based on vibration (acceleration) signals
 Time-domain signals could be covered with noise
 Fault detection by side-band behaviors in frequency domain
Previous Methods for Gear Fault Detection*
Many fault detection methods have been developed
based on frequency-domain
Local

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Limitation of the Previous Methods
Introduction
Distributed Local
*Randall, R. B. "A new method of modeling gear faults." Journal of mechanical design 104.2 (1982): 259-267.
 Variable speed conditions in real-world applications
 Frequency-domain based methods are not available
Normal in Variable speed
Fault in Variable speed
Need for fault detection methods which can
also be applied to variable speed conditions

9. Seoul National University
PER (Positive Energy Residual)
method
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PER (Positive Energy Residual) method
Review of the Techniques – (1) Wavelet Transform
 Wavelet transform (WT): Represent transient signals in the time-frequency domain
 Adaptive in resolution: High time resolution in high frequency &
Low time resolution in low frequency
 Good performance in extracting transient signals from contraction of wavelet
 Widely used for fault detection in combination with machine learning (ML)
Limitations of WT in fault detection under variable speeds :
Need stationary conditions used with the machine learning (ML)
𝑊𝑇 𝑎, 𝑏
= 𝑥 𝑡 𝜓(
𝑡 − 𝑏
𝑎
)𝑑𝑡
∞
−∞
Time-domain signals
Wavelet TransformTime-domain
Wavelet

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PER (Positive Energy Residual) method
Review of the Techniques – (2) Gaussian Process
 Gaussian process (GP): Represent statistical properties of the non-linear signals in the
continuous domain using Gaussian distribution
 Could be used for regression using observed signals
 Prediction results will be based on mean and standard deviation
Could statistically represent non-linear behaviors of wavelet coefficients
from variable speed conditions
Gaussian process regression model
𝑌 𝑡 ~ 𝐺𝑃(𝑚 𝑡 , 𝑘 𝑡, 𝑡′
)
Observation
𝒟 = (𝑡, 𝑓 𝑡 )
Prediction
𝒚 𝐧𝐞𝐰|𝒟 ~ 𝒩(𝑚 𝒕 𝒏𝒆𝒘|𝒟 , 𝜎new
2
𝒕 𝒏𝒆𝒘|𝒟 )
𝒕 𝒏𝒆𝒘
Mean
Std.
Obs.

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Procedures for the PER Method – (1)
PER (Positive Energy Residual) method
Normal
Fault
Normal
Fault
Wavelet Coeff.
① Measurement
of vibration signals
② Wavelet
coefficients
Wavelet
transform
 Could represent time-varying behaviors of
vibration signals
 Could extract transient behaviors from
peaks in the signals

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Procedures for the PER Method – (1)
PER (Positive Energy Residual) method
Normal
Fault
Normal
Fault
Wavelet Coeff.
③ Marginalized
wavelet
coefficients
② Wavelet
coefficients
Marginalize
 Transformation of 3-D data to 2-D data
 More efficient for signal processing

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Procedures for the PER Method – (2)
PER (Positive Energy Residual) method
 Could represent statistical behaviors of non-
linear wavelet coefficients
 Predicted mean values represent the effects
of variable speed condition
③ Marginalized
wavelet
coefficients
GP
regression
④ Predicted
statistical
properties
Gaussian
process
regression
Normal
Fault
Normal
Fault

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Procedures for the PER Method – (2)
PER (Positive Energy Residual) method
GP
regression
④ Predicted
statistical
properties
⑤ Energy
residual (ER) =
Wavelet coeff.
- mean
Normal
Fault
Normal
Fault
 The effects of variable speed conditions could
be minimized while leaving faulty information
Subtract mean
values

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Procedures for the PER Method – (3)
PER (Positive Energy Residual) method
 Faulty behaviors exist only in a positive direction
 Take the positive portions of ER to enhance fault
sensitivity
⑤ Energy
residual (ER) =
Wavelet coeff.
- mean
Normal
Fault
⑥ Positive
energy residual
(PER)
Take positive
portions
Normal
Fault
Calculate
kurtosis

17. Seoul National University
Flowchart
PER (Positive Energy Residual) method
>Threshold
Yes No
Faulty state Normal state
Step 1: Wavelet transform & Marginalize
Step 2: Gaussian process (GP) regression
Marginalized
wavelet coefficients, 𝑤𝑡
Step 3: Calculate energy residual (ER)
Predicted mean, m
Step 5: Calculate kurtosis of PER
ER = 𝑤𝑡 − 𝑚
Step 4: Calculate positive portions
in ER (PER)
PER
Testing vibration signals
Calculate ratio of kurtosis between
training normal and testing data
Kurtosis of PER from training
normal data
Kurtosis of PER from training
fault data

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Case study:
Simulation & Experiment
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Case Study: Simulation
Accelerometer
*Inalpolat, Murat, and A. Kahraman. "A theoretical and experimental investigation of modulation sidebands of planetary gear sets."
Journal of Sound and Vibration 323.3 (2009): 677-696.
A Simulation Model of the Planetary Gear*
 Acceleration signals considering vibration modulation
 Variable speed condition : -300(t-3)2+2800 RPM
 Different amplitudes according to rotating speed
 Assumption of planet gear fault (4 levels)

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Case Study: Simulation
Simulated Vibration Signal
Normal
Fault 1
Fault 2
Fault 3
Fault 4

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Case Study: Simulation
Demonstration of the proposed method using kurtosis at each step

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Case Study: Simulation
Result
Ratios of Kurtosis btw. Normal and Faults
F1/N F2/N F3/N F4/N
WT 1.0132 1.1010 1.2622 1.4640
ER 1.0341 1.1232 1.3099 1.6046
PER 1.5186 3.6843 6.0268 7.6211
Fault/Normal

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Case Study: Experiment
20 sec.
A Planetary Gear in a 2kW Wind Turbine Simulator
 5 levels of fault in a planet gear (M=1.5)
(Semi-circle shapes with D=0.25, 0.75, 1.25mm)
 Variable speed: Sinusoidal curve (T=20 sec.)
 Torque: 2Nm, Temp: 60°C
D=0.25 D=0.75 D=1.25

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Case Study: Experiment
Experimental Vibration Signal
2018/7/31
Measured vibration signals of planetary gears at each fault level
Normal
Fault 1
Fault 2
Fault 3

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Case Study: Experiment
Demonstration of the proposed method using kurtosis at each step

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Case Study: Simulation Model
Ratios of Kurtosis btw. Normal and Faults
(5 times of 20 seconds data averaged)
F1/N F2/N F3/N
WT 1.0464 1.0627 3.5783
ER 1.0915 1.0806 3.7216
PER 1.2106 1.1177 4.3372

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Conclusion
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 Development of a PER method for a planetary gear fault detection under
variable speed conditions
 Employment of wavelet transform (WT) and a Gaussian process (GP)
 Derivation of energy residual (ER) by subtracting predicted mean values of
GP from marginalized wavelet coefficients
 Kurtosis from positive portions of energy residual, ER (PER)
 We demonstrated the performance using simulation and experiment
Conclusions
 Application of the proposed method to various variable speed conditions
 Application of the proposed method to various rotating machinery (bearing, motor, etc.)
Future Works
Conclusion

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THANK YOU
FOR LISTENING
2018/7/31 - 29 -

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Back-up
F1/N F2/N F3/N F4/N F5/N
PER
(Variable)
1.13 1.43 1.25 1.91 5.89
Kurtosis
(Const.)
1.06 1.11 1.05 1.24 1.87
Constant speed: Kurtosis
Variable speed: PER
D=0.25 D=0.5 D=0.75
D=1 D=1.25