A Transient Enhancement Method for Two-Stage Helicopter Gearbox Fault Diagnosis Based on ALE

doi:10.4236/jsip.2013.43B023

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Journal of Signal and Information Processing, 2013, 4, 132-137

doi:10.4236/jsip.2013.43B023 Published Online August 2013 (http://www.scirp.org/journal/jsip)

A Transient Enhancement Method for Two-Stage

Helicopter Gearbox Fault Diagnosis Based on ALE

Xiange Tian1, Tie Wang2, Zhi Chen2, Fengshou Gu1, Andrew Ball1

1Centre for Efficiency and Performance Engineering, University of Huddersfield, Huddersfield, UK; 2Department of Vehicle Engi-

neering, Taiyuan University of Technology Taiyuan, Shanxi Province, China.

Email: [email protected], [email protected]

Received April, 2013.

ABSTRACT

Periodical impulse component is one of typical fault characteristics in vibration signals from rotating machinery. How-

ever, this component is very small in the early stage of the fault and masked by various noises such as gear meshing

components modulated by shaft frequency, which make it difficult to extract accurately for fault detection. The adaptive

line enhancer (ALE) is an effective technique for separating sinusoidals from broad-band components of an input signal

for detecting the presence of sinusoids in white noise. In this paper, ALE is explored to suppress the periodical gear

meshing frequencies and enhance the fault feature impulses for more accurate fault diagnosis. The results obtained from

simulated and experimental vibration signals of a two stage helical gearbox prove that the ALE method is very effective

in reducing the periodical gear meshing noise and making the impulses in vibration very clear in the time-frequency

analysis. The results show a clear difference between the baseline and 30% tooth damage of a helical gear which has not

been detected successfully in author’s previous studies.

Keywords: Adaptive Filter; Adaptive Line Enhancement; Transient Enhancement; Fault Diagnosis

1. Introduction

Impulsive sound and vibration signals in machinery are

often caused by component impacts which are commonly

associated with component faults. It has long been rec-

ognized that the presence of a fault is often indicated by

the presence, or increase in, impulsive signal elements.

However, it tends to be difficult to make objective meas-

urements of impulsive signals because of the high levels

of background noise. The detection of these impulsive

signals is hampered by the presence of the signals asso-

ciated with the normal running of the machine, with the

consequence that the detection of the weak impulsive

signals, which are especially associated with incipient

faults, is difficult [1]. It is the ‘normal’ signals which

form the background noise environment against which

the detection of fault induced impulsive signals must be

conducted. To improve the precision of fault diagnosis, it

is valuable to enhance the impulsive signals by sup-

pressing this background noise prior to further process-

ing.

De-noising and extraction of such faulty signals are

very important for fault diagnostics, especially for early

fault detection, in which the fault features are often very

weak and embedded in noise. Therefore, it is necessary

to enhance the data reliability and improve the accuracy

of the signal analysis. After successful pre-processing the

signal has an increased Signal to Noise Ratio (SNR),

which makes it more amenable to one of a gamut of sig-

nal processing tools which can be used to characterize

the signal, including Auto-Regressive (AR) modeling,

kurtosis evaluation, cepstrum analysis, time-frequency

analysis and higher order spectra analysis [2].

The ALE was introduced in as a method of detecting a

periodic signal in an incoherent background or con-

versely of removing periodic interference from a

broad-band signal of interest [3]. This technique can be

used with any of the adaptive filters classified till now

and uses a delay in the input signal to cancel out the un-

necessary part in it and thus get the desired response.

Naoto Sasaoka etc. applied ALE to reduce the sinusoidal

noise in noise speech signal [4]. J. R. Mohammed etc.

presented one noise reduction system based on two stag-

es of operation with the first stage based on the ALE fil-

ters and the second stage on NLMS (Normalized Least

Mean Square) filter. The first stage reduces the sinusoi-

dal noise from the input signal and the second stage re-

duces the wideband noise [5]. S. K. Lee and P. R. White

exploits two stage ALE filter structures in series to re-

duce the level of background noise. The resulting en-

hanced signals are analyzed in the time-frequency do-

main to obtain simultaneous spectral and temporal in-

A Transient Enhancement Method for Two-Stage Helicopter Gearbox Fault Diagnosis Based on ALE 133

formation. The techniques developed are applied to the

diagnosis of faults within an internal combustion engine

and to data from an industrial gearbox [2].

In this paper, to reduce the stationary periodic gear

meshing noise in gearbox vibration signals, ALE algo-

rithm based on an adaptive LMS filter is examined for

early fault detection. In such a way, the periodical noise

is cancelled from the signal and impulses contain fault

information are highlighted to produce more reliable de-

tection and diagnosis results.

2. Theoretical Background

2.1. Introduction of adaptive line enhancer

Adaptive noise cancellation (ANC) is a procedure whe-

reby a primary signal containing two uncorrelated com-

ponents can be separated into those components by mak-

ing use of a reference signal containing only one of them.

The reference signal does not have to be identical to the

corresponding part of the primary signal, just related to it

by a linear transfer function. The ANC procedure adap-

tively finds that transfer function, and can thus subtract

the modified reference signal from the primary signal,

leaving the other component.

)(ny



)(nd

)(ne

)(nx

Figure 1. Block diagram of adaptive noise canceller.

A block diagram of an adaptive noise cancellation al-

gorithm is shown in Figure 1. is the primary inpu t

of the algorithm, ()dn

()

()yn

(dn

denotes the reference input to the

adaptive filter and then filtered by the adaptive filter to

produce an outputclosely resembling.

is subtracted from to produce the system output

known as error signal. The adaptive filter coeffi-

cients are updated according toand reference sig-

nal

()dn ()yn

)

(en)(en)

()

n, which help minimize residual error noise.

ALE is in fact a degenerate form of the ANC in that its

reference signal, instead of being derived separately,

consists of a delayed version of the primary signal. Ac-

cording to Widrow [6] ALE is an adaptive self-tuning

filter capable of separating the periodic and stochastic

components in a signal different from other ANCs with

multi-sensors. The ALE simply uses a single sensor and

is therefore easier and more cost-effective to implement

it in condition monitoring practice.

As shown in Figure 2, it is a simple variation of the

ANC. It requires only a single input signal. In this case

the reference signal is obtained by delaying the input

signal by a certain number of samples. The adaptive

filter then endeavors to predict the reference signal



()

()en

from the delayed samples. The result is that any

input components which are predictable over the delay

appear at the filter output, whilst the error signal

contains those components which are unpredictable

over the delay.

()yn

)(ny



)(nd

)(ne

)(nx



Figure 2. Block diagram of adaptive line enhancer.

The ALE becomes an interesting application in noise

reduction because of its simplicity and ease of imple-

mentation. However, to obtain th e best perfor mance in its

computational process, the optimal approach is to exe-

cute ALE on a better convergence rate of adaptive algo-

rithm with a less complex adaptive filter structure. Adap-

tive algorithm could realize based on transversal Finite

Impulse Response (FIR), recursive Infinite Impulse Re-

sponse (IIR), lattice and sub-band filters [1].

The most widely used adaptive filtering technique is a

version of the LMS algorithm, initially proposed by Wi-

drow and Hoff. The LMS is based on the steepest descent

method, a gradient search technique to determine filter

coefficients that minimize the mean square prediction of

a transversal filter. The NLMS converges faster than the

conventional LMS because it employs a variable step

size parameter aimed at minimizing the instantaneous

output error [7, 8]. NLMS algorithm can be summarized

as below.

The output of adaptive filter is

()() ()ynn nT

. (1)

While ()

nand are given in Equation (2) and

Equation (3) ()wn

() [()(1)]nxnxnL

x

 (2)

() [()()]

nwnwn



w (3)

The adaptive coefficients update formula can be ex-

A Transient Enhancement Method for Two-Stage Helicopter Gearbox Fault Diagnosis Based on ALE

134

pressed as

()( 1)()()

()

nn ne





 

ww x

()() ()endn yn

(4)

(5)

where the error signalis given by Equation (5),

()en



the step size parameter which controls the convergence

speed and the stability of the filter and



is a small con-

stant in order to prevent division by zero in case no input

signal is present.

2.2. Time Synchronous Average

In experimental vibration, there are high levels of ran-

dom noises which will affect the accuracy of fault diag-

nosis, especially random impulses which can confuse the

periodicity of fault impulses. In this study, time syn-

chronous aver age (TSA) technique is applied to supp ress

the random noises. TSA resamples the vibration data

synchronously according to the angle of rotation. When

taken over many machine cycles, this technique removes

background noise and nonsynchronous events such as

transients and meshing components from other gear

transmission stages) in the vibration signal. This tech-

nique is extremely useful where multiple shafts those are

operating at only slightly different speeds and in close

proximity to one another are being monitored. A refer-

ence signal (usually from a tachometer) is always needed.

However, it can be inefficient at reducing some tonal

components of the background noise, i.e., those that are

commensurate (or nearly commensurate) with the rota-

tional frequency.

Assuming a signal ()

n consists of a periodic signal

()

and a noisy component, the period of ()vn

nis 0 whose corresponding frequency isT0

, thus

the signal can be expressed [9].

()() ()

nxnvn (6)

The synchronou s av er age of the signal()

nby using TSA

can be expressed as

()( )

nxt







iT (7)

where

is the number of the average segments, is

the averaged signal. ()yn

3. Signal Processing Methods

3.1. Denoising Scheme

The principle of the ALE [10] used to reduce sinusoids

will be described in this section based on the block dia-

gram given in Figure 2.

The primary input and reference input signals of the

system are given by

() () ()dn snn





 (8)

()()()(xn dnsnn)





 

)

(9)

where (

nis the fault impulse signal, ()n



represents

the sinusoidal noise and



is time delay factor. Since the

short time duration of impulses, the autocorrelation of

impulses fades as



increases. On the other hand, the

delayed sinusoidal noise(n)



 is correlated with()n



Thus, when the adaptive filter stable, ()n



may be esti-

mated by the output of adaptive filterand the im-

pulse components in error signalare enhanced com-

paring with desired signal.

()yn

()en

()dn

()() ()

() ()

() () ()

endn yn

dn n

nnn













(10)

The cost function of NLMS algorithm is defined as







 



() () ()

()2()(() ())

() ()

Esnn yn

EsnEsnnyn

Enyn







 





()() ()Ee nEdnyn







(11)

Since the fault signal is uncorrelated with noise,





()(()())0nnyn





. Then, Equation (11) becomes









2()()() ()Ee nEsnEnyn









[()]Ee n

(12)

Minimize is equivalent to minimize

. Therefore, the convergence of algo-

rithm will causeto be the minimum mean-square

estimation of

)]n()yn

()n

[() (Eny







There are three important parameters in ALE, the step

size



, the length of filter and the number of delay sam-

ples.



is the step size parameter controlling the conver-

gence rate within its suitable range. The step size value

affects the convergence behavior of an LMS filter; a too

low value of



leads to extremely long convergence time

of the algorithm, whereas a too high value of



causes

the algorithm to diverge, thus degrading the error per-

formance of the adaptive filter. Therefore, choosing a

suitable value for the step size is necessary when imple-

menting the LMS algorithm as an adaptive filter.

The periodic nature of the impulsive signal lays open

the possibility that the first stage of the scheme will iden-

tify them with the narrowband components and in doing

so attenuate them. To avoid such an eventuality care over

the choice of the parametersand must be exercised.

From reference [5], the length of filter must satisfy the

condition in Equation (14), where

L

Tis the period of the

A Transient Enhancement Method for Two-Stage Helicopter Gearbox Fault Diagnosis Based on ALE 135

signal. 2

LT (14)

3.2. Parameters Selection Method

In this part, the selection method of ALE parameters ap-

plied in this paper is introduced.

05 10 15 20

Delay factor

Kurto s is v alue

L=16

05 10 15 20

Delay factor

Kurto s is v alue

L=32

05 10 15 20

Delay factor

Kurtosis v alue

L=64

05 10 15 20

Delay factor

Kurtosis v alue

L=128

0.05

0.1

0.3

0.5

0.7

0.9

Figure 3. Kurtosis values under varies parameters.

Figure 4. Time-frequency analysis results.

Kurtosis is used in engineering for detection of fault

symptoms because it is sensitive to sharp variant struc-

tures, such as impulses. The bigger the impulse in signal,

the larger the kurtosis is. The kurtosis value comparison

of signals after ALE processing based on different pa-

rameter sets are shown in Figure 3. The green line indi-

cates the kurtosis value of signal before ALE processing.

Different line colors and style represent different



val-

ues, L indicates the length of adaptive filter and delay

factor is



From Figure 3, it is obvious that kurtosis values are

increased after ALE. To compare the impulse enhance-

ment effects, the parameter sets which corresponding to

maximum kurtosis under each L is selected for compari-

son. Then, the signals are analyzed in time-frequency

domain.

Figure 4 illustrates the time-frequency analysis com-

parison between original signal and signals after ALE

based on four different parameter sets. Figure 4(a) plots

the original signal and Figures 4(b)-(e) give out the ALE

results while the parameters are selected by maximum

kurtosis criteria in Figure 3 under the four filter length

16, 32, 64 and 128, separately. It can be seen that the

main periodic components at 1500Hz and 2500Hz are

reduced greatly after ALE and the other components

which are smaller can be observed clearly. It is obviously

that the result in Figure 4(e), which corresponds to the

maximum kurtosis value parameter set in Figure 3, can

reveal the nonstationary components better than other

three parameter sets. So the kurtosis maximization crite-

rion is applied to choose ALE parameters in the follow-

ing machine fault diagnosis.

4. Signal Processing Results

The practical gearbox experimental vibration signals

collected when the gearbox operated under five different

loads and four cases (Healthy, 30% tooth break, 60%

tooth break and 100% tooth break).

00.05 0.10.15 0.2

-1

Tim e(s)

A cceleration(m /s

)

Baseline

00.05 0.10.15 0.2

-1

Tim e(s)

Acceleration(m/s

)

30% Damage

00.05 0.10.15 0.2

-1

Tim e(s)

Acceleration(m/s

)

60% Damage

00.05 0.10.15 0.2

-1

Tim e(s)

Acceleration(m/s

)

100% Damage

Figure 5. Raw vibration signal in time domain.

A Transient Enhancement Method for Two-Stage Helicopter Gearbox Fault Diagnosis Based on ALE

136

00.05 0.10.15 0.2

-0. 5

0.5

Time(s)

Acceleration(m/s2)

Baseline

00.05 0.10.15 0.2

-0. 5

0.5

Time(s)

Accel eration(m /s2)

30% Damage

00.05 0.10.15 0.2

-0. 5

0.5

Time(s)

Acceleration(m/s2)

60% Damage

00.05 0.10.15 0.2

-0. 5

0.5

Time(s)

Acceleration(m/s2)

100% Damage

Figure 6. TSA vibration signal in time domain.

Figure 5 gives out the raw vibration data for four cas-

es under load 3, where the baseline is the healthy case.

Figure 6 shows the TSA results of the vibration signals

given out in Fig. 3 for five revolutions of the input shaft.

It can be seen that the impulse components of the vibra-

tion signals are highlighted for all the test conditions.

TSA signals show much clearer indication of the 60%

and 100% tooth damage compared with the baseline and

30% tooth damage. However the signals between the

baseline and 30% tooth damage cannot be observed with

noticeable differences.

To evaluate the denoise effect of ALE algorithm, Fig-

ure 7 and Figure 8 give out the time-frequency analysis

results comparison , take the signal under the 4th load as

example, signals under other loads have similar per-

formance.

As shown in Figure 8, there are several periodical

modulation frequencies generated by rotation of machine

and can be seen as background noise at about 1500Hz,

3000Hz and 4500Hz. The purpose of ALE is to remove

these frequencies. The TSA signals also contain impulse

components which are short duration and periodical con-

tents for certain frequencies which are spread over the

time direction. These components carry the fault infor-

mation of gearbox tooth break damage. Figure 8 shows

the results after the ALE processing. It can be seen that

the modulation frequencies are reduced significantly. The

results show that ALE is effective in reducing sinusoids

and extract impulses from wide band periodical noises.

For a detailed comparison, two common feature pa-

rameters: root mean square (RMS) and kurtosis are cal-

culated from the TSA vibration signals ALE errors sig-

nals. As shown in Figure 9(a), RMS is not able to sepa-

rate the four cases over different loads. Comparing with

the baseline and 30% tooth damage, in Figure 9(b), the

kurtosis values of 60% tooth damage and 100% tooth

damage is clearly separated from the other two cases

except the first load. However, the difference between

the baseline and 30% tooth damage is not very obvious

for fault separation. Figure 9(c) and Figure 9(d) illus-

trate the RMS and kurtosis value comparison from the

error signal which is the signal after ALE denoising

processing. From the RMS value comparison of error

signal, there are differences between all loads except the

first and all four fault cases which gives out clear differ-

ence compared with TSA signal. The kurtosis value of

error signal is much higher than that of TSA signal, when

means the proportion of impulses is enhanced. But the

difference between kurtosis values of different fault cases

is not so clearly as the RMS value of error signal.

Figure 7. TSA vibration signals in time-frequency domain.

Figure 8. Signals after ALE in time-frequency domain.

A Transient Enhancement Method for Two-Stage Helicopter Gearbox Fault Diagnosis Based on ALE

137

12345

0. 02

0. 03

0. 04

0. 05

0. 06

Load inde x

RM S valu e

(a) RMS of TSA Si gnal

Baseline

30% Dam age

60% Dam age

100% Dam age

12345

Load inde x

Kurtosis value

(b) Kurt osis of TSA Si gnal

12345

0. 01

0. 02

0. 03

0. 04

0. 05

Load inde x

RM S value

(c ) RMS of E rror S i gnal

12345

Load inde x

Kurtosis v alue

(d) K urtosis o f Erro r S i gn al

Figure 9. RMS and kurtosis value comparison of TSA and

error signal (L = 20, mu = 0.075, Δ = 12).

1 2 3 45

0. 02

0. 03

0. 04

0. 05

0. 06

Load index

RMS value

(a) RMS of TSA Signal

Baseline

30% Damage

60% Damage

100% Damage

12 34 5

Load index

Kurtosis value

(b) K urto si s of TSA Si g nal

1 2 3 45

0. 01

0. 02

0. 03

0. 04

0. 05

Load index

RMS value

12 34 5

Load index

Kurtosis value

(d) K urtosi s of E rro r S i gn al

Figure 10. RMS and kurtosis value comparison of TSA and

error signal (L = 32, mu = 0.0375, Δ = 60).

Figure 10 illustrates the results obtained from another

set of ALE parameters, the results for 30% tooth damage

is worse, while for higher severity faults the results is

better.

5. Conclusions

In this study, ALE has been examined for the fault detec-

tion and diagnosis of a two stage helical gearbox based

on noisy vibration signals. TSA is used to suppress the

random noise firstly and then ALE is to reduce the con-

tinuous meshing components, which allows impulsive

features shown by the time-frequency analysis represen-

tations to be highlighted effectively. In this way, the in-

cipient tooth damage fault can be detected clearly.

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