Illustrative Examples, Two Different Machine Data

Illustrative Examples

• Machine Vibration

Moderate

Strong

Knock region

White Noise, Background Noise

0 2000 4000 6000 8000 10000 12000 140000

0.5

1

1.5

2

PS

D B

KG

No

ise

Freq Hz

0 50 100 150 200 250 300 350 400 450 500-0.2

-0.15

-0.1

-0.05

0

Eve

nt-

fre

e S

egm

ent

s

0 500 1000 1500 2000 2500 3000 3500-2

-1

0

1

2

Cy

cle

Dat

a

Acceleration Data, Single Cylinder Engine, Knock Condition

Background Noise Removal

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10

De

nois

ed

Signal with Backgroung Noise Removed

0 500 1000 1500 2000 2500 3000 3500-10

-5

0

5

10Cylinder Head Vibrations, Original and Denoised, Cycle #1

Ori

gin

al

Wavelet DecompositionMultiresolution

Wavelet Coefficients andDenoising

Residual( Noise Component)

Denoising, Another Example

Thresholded coefficients

Leve

l nu

mbe

r

1000 2000 3000

5

4

3

2

1

1000 2000 3000

-5

0

5

10

Original and de-noised signals

Original coefficients

Leve

l nu

mbe

r

1000 2000 3000

5

4

3

2

1

-5

0

5

d5

Original details coefficients

-5

0

5

d4

-5

0

5

d3

-5

0

5

d2

1000 2000 3000

-10

0

10

d1

Two Stage Denoising of Signals

0 100 200 300-2

-1

0

1

2No Knock Cycle #11

Ori

gin

al

0 100 200 300-2

-1

0

1

2

Den

Sta

ge

1

0 100 200 300-1

-0.5

0

0.5

1

1.5

Den

Sta

ge

2

0 100 200 300-4

-2

0

2

4

0 100 200 300-4

-2

0

2

4

0 100 200 300-4

-2

0

2

4

6 Hard Knock, Cycle #7

Signal component at WP No.38: a) Severe Faulty Condition, b), Mild Fault (b), Fault-free Condition (c).

WP node 38

-0.5

0

0.5

-0.5

0

0.5

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950

-0.5

0

0.5

Sample point

Denoised Signal, WP Node

0 100 200 300-2

-1

0

1

2

Ori

gin

al

No Knock Cycle #6

0 100 200 300-1

-0.5

0

0.5

1

Den

Sta

ge

1

0 100 200 300-0.2

-0.1

0

0.1

0.2

Den

Sta

ge

2

0 100 200 300-2

-1

0

1

2D

en S

tag

e 2

0 100 200 300-4

-2

0

2

4

Den

Sta

ge

1

0 100 200 300-4

-2

0

2

4

Ori

gin

al

Hard Knock Cycle #7

Illustration of Sparsity of Wavelet Coeffs

0 10 20 30-10

0

10

Cy

cle

# 8

0 100 200 300-5

0

5

Mild

Kn

ock

0 100 200 300-1

0

1N

o K

no

ckSignal at High Freq.Band #36

0 100 200 300-5

0

5

Ha

rd K

no

ck

0 10 20 30-10

0

10

20

Cyc

le #

1

0 10 20 30-5

0

5

Cyc

le #

6

Coeffs

Variability of Cyclic Signals

Illustration of Variablity, Spectral Variability, 16 cycles

0 2000 4000 6000 8000 10000 12000 140000

200

4001

6 c

yc

les

Spectrum of Mclean Data, Cyl Head vibration, full cycle

0 2000 4000 6000 8000 10000 12000 140000

200

400

me

an

0 2000 4000 6000 8000 10000 12000 140000

50

100

std

0 2000 4000 6000 8000 10000 12000 140000

0.5

1

std/

me

an

Freq Hz

Spectrum of the vibration signal and its denoised version

Variability in Cyclic Runs

• Variation of vibrations in three consecutive cycles

Original Denoised

Analysis in Coefficient Domain