Fault Feature Extraction Method of Rotor Vibration Signals Based

on Blind Source Separation and Wavelet Transform

Feng Miao

and Ruzhi Feng

School of Physical and Electrical Information, Luoyang Normal University, Luoyang 471022, China

Henan Mechanical and Electrical Vocational College, Zhengzhou 451191, China

miaofeng3699@163.com,229042106@qq.com

Keywords: Fault feature extraction, Wavelet De-noising, Blind source separation, Rotor.

Abstract: In this paper, a new fault feature extraction method is presented based on wavelet transform and blind

source separation. At first, wavelet transform is employed to de-noise measured signals to remove the

process noise. Then blind source separation based on second order statistics is used to extract blind source

signals of the process. The simulation and experiment testing results show the proposed method that

compare with other method based on blind source analysis directly with process information can effectively

extract the quantitative feature extraction. Finally，the signals of rotor vibration with noise interference

were separated successfully using the proposed method.

1 INTRODUCTION

Blind source separation (BSS) means that the

observation signal can be used to recover the

independent component process of the source signal

according to the statistical characteristics of the

input source signal without knowing the source

signal and the transmission channel parameters. In

recent years, BBS has become a very popular signal

processing technology. Since Zeng and Li(2002,

2003) proposed a class method of neural blind

source separation, the blind source signal separation

method has made a number of fruitful research, in

the field of communications, voice and biomedical

rapid development and promotion.

The vibration signal of the mechanical

equipment is an important information source for

fault identification and diagnosis, and the vibration

signal is often mixed with several signals, which

brings difficulties to the feature recognition and

diagnosis. The study of blind source signal

separation method provides the conditions for the

separation of vibration signals and fault feature

recognition. In the mechanical fault diagnosis

system, the signal obtained by the sensor is

inevitably disturbed by different types of unknown

noise. In the unknown general noise environment,

the separation effect of BSS-based mechanical

source signal is often poor if the influence of noise is

neglected (Miao, 2014; Lei, 2011; Hu, 2003; Yu,

2005). Therefore, the influence of noise must be

taken into account in BSS-based mechanical fault

diagnosis. In this paper, combined with wavelet

filtering and BSS, the wavelet filter is used to de-

noise the test signal, and then the second order

statistic of the signal is used to separate the blind

source signal, and the simulation and experimental

study are carried out.

2 THE LIKELIHOOD OF THE

BSS MODEL WITH NOISE

MIXING

In the model of linear instantaneous mixing with

noise, the relationship between the unknown source

signal and the observed signal can be described as

the form (Huang, 2008; Ye, 2010) of the equation

(1)

() () ()yt Ast nt=+

(1)

Where

( ) [ ( ), ( ),..., ( )]

is the

M-dimensional random observation vector in the

case of noise,

( ) [ ( ), ( ),..., ( )]

st s t s t s t=

the N-dimensional source signal, the components

114

Miao, F. and Feng, R.

Fault Feature Extraction Method of Rotor Vibration Signals Based on Blind Source Separation and Wavelet Transform.

In 3rd International Conference on Electromechanical Control Technology and Transportation (ICECTT 2018), pages 114-118

ISBN: 978-989-758-312-4

()

st in the source signal are assumed to be

statistically independent,

( ) [ ( ), ( ),..., ( )]

nt n t n t n t= is the M-

dimensional additive observation noise, and

N≥ , A is a mixed matrix of an unknown

N× ,In this case, the purpose of blind source

separation is to find an

N× full rank separation

matrix B, so that the estimated source signal vector

between the various components as independent as

possible, such as Figure 1 shows. In the figure, the

output signal

'( )st is the estimation result of the

source signal

()

. It is defined as

'( ) ( ) ( ) ( )s t By t BAs t Bn t== +

(2)

Obviously, if the noise item

()nt in equation (2)

is not Gaussian noise, then its appearance makes the

estimation of separation matrix B become a biased

estimate.

However, even if B obtains an exact estimate of

S, the

()

nt in Eq. (2) also increases the variance

of the source estimate S. Therefore, in the strong

noise environment, if you want to improve the

separation performance, the first need for effective

de-noising method for signal de-noising.

Fig.1 Model of blind source separation with noise

3 THE METHOD OF BLIND

SOURCE SEPARATION BASED

ON WAVELET

3.1 The principle of wavelet de-noising

Wavelet transform can simultaneously analyze the

local characteristics of the signal in the time domain

and frequency domain. The continuous wavelet

transform of the square integrable function

() ( )

tLR∈ is defined as (Li, 2005)

(,) () ( )

(), ()

WT a b

tdt

ft t

∞

−∞

−

=< >

∫

The kernel function

() ( )

ψψ

−

= of

the wavelet transform is the result of the time shift

()t

and scale scaling

of the parent wavelet

and

,<>

is the inner product operation. The basic

idea of wavelet transform is to use a family of

functions to represent or approximate a signal. The

family function is called the wavelet function

system. It is through a wavelet function of the

expansion and translation, to produce its "wavelet"

to form.

3.2 The method of blind source

separation based on wavelet

In BSS-based mechanical fault diagnosis, people

often on the test signal directly blind source signal

separation, while ignoring the impact of noise, the

separation effect is often poor (Miao, 2014). In order

to eliminate the pollution of the noise signal and

improve the effect of the blind source separation

method, before the separation of the mixed signal

vector

( ) [ ( ), ( ),..., ( )]

observed in

the noisy case, it is necessary to de-noise with the

wavelet method and then blind source signal

separation. For wavelet de-noising - BSS method.

This process can be expressed as Figure 2.

In this method, there are two important

processes: wavelet de-noising pretreatment, blind

source separation process. In (Li, 2005), these

wavelet de-noising methods are compared. The

corresponding wavelet de-noising method can be

selected according to need. Here the wavelet soft

threshold de-noising method for pre-processing.

For the blind source separation process, at

present, there are many effective linear or nonlinear

BSS algorithms, such as JADE, Informax, MISEP,

FastICA algorithm. Since the JADE algorithm

(Huang, 2008) is robust and usually obtains a more

stable source estimation result, the JADE algorithm

is chosen.

Fig.2 Wavelet de-noising-BSS method

Fault Feature Extraction Method of Rotor Vibration Signals Based on Blind Source Separation and Wavelet Transform

115

4 SIMULATIONS AND

EXPERIMENTAL RESULTS

4.1 Simulation

Using matlab to generate two simulation signals, as

shown in Figure 3; the mixed matrix is randomly

selected to obtain its mixed signal, and two separate

signals are obtained by BBS separation without

adding noise, as shown in Fig4. The separation

results may also vary in amplitude and order due to

the possibility of proportional distortion and order

reversal in the matrix of weights used in the

separation. It can be seen in Figure 4, the separation

signal sequence and the source signal is consistent,

the separation signal to retain the dynamic

characteristics of the source signal, but in varying

degrees of varying degrees of amplification.

However, this is the result of the ideal without

noise or noise pollution is very small case. But in

reality the impact of noise is inevitable, then the

effect of the classic BBS method will be affected. In

the observation signal to add a certain degree of

white noise, and then BBS separation, separation of

signals and shown in Figure 5, the separation signal

and the original signal is very different, the

separation effect is poor.

Fig.3 Original signals

Fig.4 Separated signals in non-noisy mixtures

Therefore, characteristic signal separation in case

of noisy interference, we must consider the impact

of noise. Here the wavelet de-noising-BSS method is

used, in which the de-noising step uses soft

threshold wavelet de-noising, and the separation

result is shown in Fig6. It can be seen that although

there are some errors in the separation effect, the

overall separation effect is still ideal.

Fig.5 Separated signals in noisy mixtures

(no de-noising process)

Fig.6 Separated signals in noisy mixtures

(P.S.-soft shrinkage)

4.2 Experimental analysis

The test rotor system is shown in Fig7. For the set

test system, two sensors are provided: an eddy

current sensor 9 is mounted in the vertical direction

of the mass disk I; a non-contact eddy current

displacement sensor 10 is mounted in the vertical

direction of the right side of the coupling. Rotor

speed of 3800r / min, sampling frequency of 5kHZ,

sampling points of 1024. Signal acquisition and

recording using a computer-based dynamic signal

acquisition and analysis system.

Figure 8 is the noise source signal without noise

separation, and Figure 9 is the vibration source

signal separated by noise reduction. Corresponding

to Fig. 8 and Fig. 9, it can be seen that the

combination of wavelet de-noising and blind source

separation can separate the vibrating source well.

0 100 200 300 400 500 600 700 800 900 1000

-1

-0.5

0.5

s'1

0 100 200 300 400 500 600 700 800 900 1000

-1

-0.5

0.5

s'2

0 100 200 300 400 500 600 700 800 900 1000

-2

s'1

0 100 200 300 400 500 600 700 800 900 1000

-2

s'2

0 100 200 300 400 500 600 700 800 900 1000

-1

-0.5

0.5

s'1

0 100 200 300 400 500 600 700 800 900 1000

-1

-0.5

0.5

s'2

0 100 200 300 400 500 600 700 800 900 1000

-1

-0.5

0.5

0 100 200 300 400 500 600 700 800 900 1000

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-0.5

0.5

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Specific analysis of the results of the following

aspects:

Fig.7 Rotor system and sensor position

Fig.8 Power spectrums of mixed signals from two sensors

Fig.9 Power spectrums of vibration signals after separation

(1) From the spectrum of the two sensor

acquisition signals in Fig. 8, it can be clearly seen

that the non-stationary intrinsic vibration signal of

the rotor is submerged in a number of impulsive

noise generated by the modulator in response to the

frequency distribution of the rotor Band, the

frequency distribution of the two stacked together.

From the perspective of the strength of the signal

component, the strong impulse noise occupies the

main signal component status in the signal. Thus, the

vibration signal is a mixed signal subjected to strong

impulse noise and other random interference.

(2) It can also be seen in Fig. 8 that several fault

characteristic frequencies of the acquisition signal

are aliased on each power spectrum due to the

propagation of the structural vibration, and it is

difficult to determine which faults exist. It is

difficult to accurately diagnose the fault in the event

of an unknown failure.

(3) After the wavelet de-noising and blind source

separation, the power spectrum shown in Fig. 9 is

better separated from the fault characteristic. The

power spectrum of each sensor signal after

separation is basically only showing a fault feature.

Figure 9 (a) shows only the rubbing characteristics,

and Figure 9 (b) shows only the misalignment

feature. Figure 9 (a) and Figure 9 (b), although both

are multiplier, but Figure 9 (b) 2 times the frequency

is significantly greater than 1 octave. This

distinguishes between rupture and misalignment.

(4) The results of wavelet de-noising and blind

source separation clearly eliminate the influence of

strong impulse noise and other random interference

signals in Fig.

5 CONCLUSIONS

In BSS-based mechanical source separation, the

resulting measurement signal is often contaminated

by process noise, the useful signal is buried in the

noise. In this paper, we first use the wavelet function

to de-noise the measurement signal, and then use the

second-order statistics of the signal to separate the

blind source signal. By simulation As a result, it can

be seen that in the case of strong background noise

mixing, the separation of the mechanical source

signal without direct noise removal is often not well

separated because the noise can also be regarded as a

source signal. Finally, the proposed method is

applied to the actual rotor vibration source

separation, although there are some errors in the

separation effect, but the overall separation effect is

still ideal. Simulation and experimental results show

that the blind source signal separation based on

wavelet de-noising is more effective to extract the

essential signal characteristics of rotor vibration

fault than the direct blind source separation.

0 50 100 150 200 250 300 350 400

500

1000

1500

2000

(a)The eddy current sensor 9 samples the power spectrum of the signal(f/Hz)

FFT Am plitude/m m

0 50 100 150 200 250 300 350 400

500

1000

1500

2000

(b)The eddy current sensor 10 samples the power spectrum of the signal(f/Hz)

FFT Am plitude/mm

0 50 100 150 200 250 300 350 400 450 500

100

150

200

(a)The eddy current sensor 9 samples the power spectrum of the signal(f/Hz)

FFT Am plitude/m m

0 50 100 150 200 250 300 350 400 450 500

100

150

(b)The eddy current sensor 10 samples the power spectrum of the signal(f/Hz)

FFT Am plitude/m m

Fault Feature Extraction Method of Rotor Vibration Signals Based on Blind Source Separation and Wavelet Transform

117

ACKNOWLEDGEMENTS

The research described in this paper was supported

by Foundation of He’nan Educational Committee

(16A470021) and key scientific and technological

project of Henan Province (172102210097).

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