NORPIE 2004 Trondheim, 14 June

NORPIE 2004Trondheim, 14 June

Automatic bearing fault classification combining statistical classification and fuzzy logic

Tuomo Lindh

Jero Ahola

Petr Spatenka

Anna-Lena Rautiainen

www.lut.fi

Rotor10 %

Stator37 %Bearing

41 %

Others12 %

Introduction to fault classification

Neural networks, unsupervised Kohonen’s maps, supervised BPStatistical classification, Mahalanobis distance, Support vector MachinesHidden Markov chains,Fuzzy logicAdaptive, model based methods and many others

Deterministic Stochastic, probabilisticknown parameters Pattern classificationparameter estimation neural networksrule based inference statistical methodsfuzzy logicMathematical modelling

Why probabilistic and deterministic ?

• Statistical pattern classification

• search patterns of features

• compare with known prototypes of faults

• Deterministic calculation, rules

• calculates the magnitudes

• estimates the risk of fault classification

• calculates the quality of features• avoid known pit falls (classification method, behaviour of machines etc.)

Appearance of cyclic bearing faults in motor frame vibration

Time

Fre

quen

cy

0 0.02 0.04 0.06 0.08 0.1 0.120

2000

4000

6000

8000

10000

12000

14000

16000

Time

Fre

quen

cy

0 0.02 0.04 0.06 0.08 0.1 0.120

2000

4000

6000

8000

10000

12000

14000

16000

)()(*)()()()()( ,, tnthtxtxtxtxtyj

jnmi

imtpbeme

Wang (1998), Lindh (2002)

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

7

8

9

features

pro

toty

pe

ve

cto

r v

alu

e

0 100 200 300 400 500 6000

1

2

3

4

5

6x 10

-3

f [Hz]

0 2 4 6 8 10 12 14 160

2

4

6

8x 10

-3

Outerrace

Innerrace

rollingelement

cage

testvector

features

Statistical classification

n

lll mxmx

nc

1kk,ii,ik 1

1

yx1

xyyx2 mm'mm Cr

Minimum distance classifier

0 100 200 300 400 500 600

0

1

2

3

4

5

6x 10

-3

f [Hz]

expected bearing pass frequencies *

rotational side band frequencies o

other maximum value x

Fuzzy logic, the fault size estimation

0 100 200 300 400 500 6000

1

2

3

4

5

6x 10

-3

f [Hz]

expected bearing pass frequencies *

rotational side band frequencies o

other maximum value x

Fuzzy logic, the probability of the fault

uses the results of the

statistical classification as input

Fault classifier

Feature extractionEnvelope spectrumformation

Signal Statistical distancecalculation

Minimum distanceclassifier

Feature extraction

Fuzzy logics

Classificationdata

Result

RMS, peaks, etc.

Results

0 100 200 300 400 500 6000

1

2

3

4

5

6x 10

-3

f [Hz]

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6x 10

-3

Outerrace

Innerrace

rollingelement cage

testvector

features

0 100 200 300 400 500 6000

1

2

3

4

5

6x 10

-3

f [Hz]

0 2 4 6 8 10 12 14 160

1

2

3

4x 10

-3

Outerrace

Innerrace

rollingelement

cage

testvector

features

Results

Classification results using 16- dimensional feature space covering all four fault types.

The bold cases are selected with the minimum distance classifier.

healthy outer race inner race ball spin cagehealthy 0.6981 1.3607 2.7905 1.6052 2.3892outer race 5.3817 1.2018 7.0394 8.7226 7.5465inner race 2.9616 3.2331 1.0653 2.7675 2.7684ball spin 6.5451 5.3318 8.2085 1.0579 6.7352cage 0.7758 1.4425 0.8656 1.7417 0.1666

Results

Classification results using four dimensional feature space. The distance between test vector and any fault prototypes are calculated separately. The bold cases are selected with the minimum distance classifier.

test data distance to outer race inner race ball spin cagehealthy healthy 0.1767 0.148 0.1107 0.138

broken 0.781 4.235 1.2339 1.3203outer race healthy 3.9542 0.2946 0.2454 0.2164

broken 0.0394 6.5133 1.4492 1.4779inner race healthy 0.556 2.4608 0.441 2.0332

broken 1.385 0.3182 1.6345 2.656ball spin healthy 0.2327 0.3109 4.4202 0.1176

broken 0.9328 4.1784 0.2219 1.7265cage healthy 0.2827 0.3915 0.2275 4.0238

broken 1.0563 5.0148 1.7709 0.073

Results

Fault degreetest data outer race inner race ball spin cage

healthy 0.18 0.17 0.17 0.18outer race 0.47 0.42 0.18 0.10inner race 0.03 0.36 0.03 0.32ball spin 0.18 0.17 0.50 0.18cage 0.18 0.16 0.17 0.50

Classification results using simple fuzzy logic for the determination of fault degree

Results

Classification results using fuzzy logic that estimates the fault degree as well as the probability of the faults. Action can be formed with fuzzy logic or multiplication of the fields of table of previous slide with the probabilities of this table. The actions are selected with trigger levels.

test data outer race inner race ball spin cage outer race inner race ball spin cagehealthy 0.18 0.17 0.16 0.17 0.03 0.03 0.03 0.03outer race 0.49 0.3 0.3 0.2 0.23 0.13 0.05 0.02inner race 0.32 0.35 0.17 0.16 0.01 0.13 0.01 0.05ball spin 0.32 0.17 0.17 0.16 0.06 0.03 0.09 0.03cage 0.32 0.17 0.16 0.58 0.06 0.03 0.03 0.29

Fault probability Action

Conclusions

The method where the Mahalanobis distance based statistical classification results were used as one input in fuzzy logic was introduced.

This input and other qualitative features of the spectrum were taken into account in the fuzzy logic which evaluated the probability of a certain fault. The other fuzzy logic evaluated the degree of certain fault and by combining the outputs of these logics, the final suggestion of the state and required action were given.

What?