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Advances in Adaptive Data AnalysisVol. 4, Nos. 1 & 2 (2012) 1250005 (14pages)c World Scientific Publishing Company

DOI:10.1142/S1793536912500057

BUILT-IN TEST SIGNAL FEATURE EXTRACTION

METHOD BASED ON HILBERTHUANG TRANSFORM

MIAO ZHANG, YI SHEN, XIAO-LEI ZHANG,ZHI-BO WANG and YE ZHANG

Department of Control Science and Engineering,

Harbin Institute of Technology, 150001, [email protected]@hit.edu.cn

Received 30 March 2011Revised 7 March 2012

Accepted 26 April 2012Published 30 August 2012

This work proposes a feature extraction method from HilbertHuang-transform- orHHT-based data analysis of built-in test (BIT) signals, which are sampled on-site andwithout reference signals for fault diagnosis. The proposed method fully utilizes self-

adaptation of the HHT method in characterizing the envelope amplitude and instanta-neous frequency for the intrinsic mode function (IMF), so as to single out the featureswith most irregular characteristics. Simulations are carried out on steering gear feedbackvoltage signal of target drone aircraft, and the extracted features show great potentialfor the improvement in built-in fault diagnosis.

Keywords : HilbertHuang transform; built-in test; feature extraction; intrinsic modefunction; empirical mode decomposition.

1. Introduction

The built-in test (BIT) technology is an important way to improve the capability ofsystem testing and diagnosis, and it has played an important role in protecting the

operational readiness of electromechanical systems and improving maintenance effi-

ciency [Drees and Young (2002)]. However, the diagnosis method of traditional BIT

technology is too simple, and its ability of using diagnostic information is also lim-

ited because of the difficulty of adaptive feature extraction. Therefore, problems in

application such as the poor performance of fault detection and isolation, underre-

ported rate, and high false-alarm rate severely restrict the BIT system performance

into full play [Hwang et al. (2010)].

Feature extraction is usually an important part of fault classification and diag-nosis, and it extracts the features with the following condition: the properties or

values of different samples from the same class should be very close, whereas the

properties or values of samples from different classes should have a greater difference

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M. Zhang et al.

[Duan and He (2007)]. In addition, this stage needs to extract the most discrimi-

nating features that are invariant for transformations whose class information is not

related [Wang et al.(2007)]. In most cases, the BIT system processes nonstationary

and nonlinear data; therefore, we consider using HilbertHuang transform (HHT),

which has expertise in the area of data processing to design the feature extractionprogram, thus supporting BIT system to achieve a low underreported rate and a

high accuracy of fault diagnosis [Tang et al. (2010)].

The HHT method, published by Norden E. Huang of NASA in 1998, is an

adaptive nonstationary and nonlinear signal analysis method, including empirical

mode decomposition (EMD) and Hilbert transform (HT) [Huang et al. (1998)]. HT

operates signals by convolution with the function 1/t, resulting in local properties

ofx(t), as the following equation:

y(t) =H{x(t)}= 1

CPV

x()t

d =x(t) 1t

, (1)

where CPVis Cauchy principle value. We can get the following equation from the

view of frequency domain:

Y(f) =jX(f) sgn(f) =

jX(f), f >0

0, f= 0

jX(f), f 0

X(f), f= 0

0, f


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Built-in Test Signal Feature Extraction Method Based on HHT

The instantaneous frequency definition ofx(t) is as follows:

f(t) = 1

2(t) =

1

2

d

dt(t) (8)

If we calculate the instantaneous frequency of an actual signal with the above equa-tion directly, misjudgment could be caused by the bias component and multifre-

quency components, resulting in a large difference compared with the instantaneous

frequency of original signal. Therefore, if we want to use the HT to obtain mean-

ingful instantaneous frequency, then appropriate processing of the signal must be

made first. Therefore, we should filter out the local bias component and match

the average local symmetry to zero before making sense of the signal spectrum

analysis.

EMD is an important step in the HHT algorithm. Unlike the traditional methods

that use fixed shape windows as decomposition basis functions, that basis functions

of EMD are extracted from the signals, namely, intrinsic mode functions (IMFs),

which must meet the following two characteristics:

(1) Throughout the function, the number of extreme points and the number of zero

points should be either equal or differ by 1 and,

(2) At any time, the local mean of envelope defined by the local maximum envelopes

should be 0.

EMD will decompose a signal into a sum of a finite number of IMFs as well as the

residue, and the IMF makes the follow-up HT analysis meaningful by construct-

ing the analytic function to calculate the instantaneous frequency [Kopsinis and

McLaughlin (2009)].

The signal decomposition process in the HHT is driven by the signal itself with

full self-adaptation, and the IMF component signals can be realized physically,

which is in line with the actual situation of the objective world. The HHT is con-

sidered to be not only a powerful self-adaptive method of solving nonstationary and

nonlinear signals but also a major breakthrough in linear and steady-state spec-trum analyses based on Fourier transformation in recent years; therefore, it has

been widely applied.

In order to solve the problem that it is difficult to extract features adaptively

for nonstationary and nonlinear data in previous programs, this paper proposes

a BIT-signal feature extraction method based on HHT. In this paper, the HHT is

used to extract features adaptively with some algorithms and improve the diagnosis

accuracy in the follow-up BITs, which could make the difference between normal

signal and fault signal more distinguishable.

In Sec. 2, a new feature extraction method suitable for BIT signal is derived fromthe HHT, which consists of both EMD and HT. Section 3 presents the simulation

results and discussion, and Sec. 4 concludes this paper.

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2. Methodology

This paper proposes a BIT-signal feature extraction method based on HHT. The

purpose of this paper is achieved as follows: using an EMD algorithm to decompose

the BIT-sampled signal into its first-order IMF (IMF1) and residual function, then

carrying out the HT on IMF1 to search the feature, and determining the starting

and ending time of potential failure feature; finally, intercepting the correspond-

ing characteristics of the signal out from the original signal. The flowchart of this

method is shown in Fig. 1, which is divided into five steps:

Step 1: EMD

The input signal is decomposed by the EMD algorithm, and then the IMF and

residue, denoted as IMF1 and RES, are obtained. Only one IMF is obtained from

the EMD process, which is described as follows:

(a) Input signal x(t), t= 1, 2, . . . , N ;

(b) Screening process initialization:k = 1,hk1(t) =x(t), wherehk1(t) is (k 1)

times screening of the residual function during the IMF decomposition;

(c) Implementation of screening procedures: first, using the cubic spline function,

find out the upper and lower envelopes ofhk(t); second, obtain the average of

the upper and lower envelopes mk1(t); finally, do hk(t) =hk1(t)mk1(t);

Step 1Empirical Mode Decomposition

1st Intrinsic Mode Function Residue

EnvelopeAmplitude

1st Order Differential

Hilbert Transform

InstantaneousFrequency

Frequency

Differential

Estimation for Feature

Location

Feature Extraction

Step 2

Step 3

Step 4

Step 5

Fig. 1. The flowchart of BIT signal feature extraction method based on HHT.

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(d) Judge whether hk(t) satisfies the conditions of IMF; make decision according

to standard deviation (SD) by calculating HSD = (hk1(t)hk(t))2/h2k1(t).

IfHSD is less than 0.25, then the IMF component c(t) =hk(t) and continue to

step 5, otherwise, k= k + 1, and return to step 3;

(e) The residue (RES) can be calculated by r(t) =x(t)c(t);(f) By now, the input signalx(t) consists of the IMF1 and the RES, which can be

shown as:x(t) =c(t) +r(t).

Step 2: HT

Through the HT, we can get the amplitude and instantaneous frequency.

At the beginning, according to Eq. (1), we obtain the discrete convolution of

IMF1:c(t), t= 1, 2, . . . , N . Then, the analytic signal ofc(t) is known asc(t) +jy(t).

The envelope of the signal a(t) can be calculated according to Eq. (6).

Finally, calculate the phase(t) and instantaneous frequencyf(t) of the analyticsignal as Eqs. (7) and (8).

After these steps, we prepare the obtained amplitude a(t) and instantaneous

frequencyf(t) for the next step.

Step 3: First-order difference

Calculate the first-order differential of the instantaneous frequency of IMF1, or

f(t).

In order to describe the variation of the instantaneous frequency of IMF1, cal-

culate f(t) by the following equation:f(t) =f(t+ 1)f(t). (9)

Step 4: Integrated estimation for feature location

Determine the characteristic position of time generally and also the set of

appearance time of the potential failure.

Generally, the original sampling signals of BIT do not contain the original

model, which can be seen as nonstationary, nonlinear signal, and the IMF1 of the

input signal not only contains the false alarm and noise signal but also reflects the

high-frequency components of fault signal, and the amplitude somewhat decreases;therefore, the diagnosis of faults directly from IMF1 is not ideal, but use HT on

the IMF1; from its amplitude and instantaneous frequency, we can determine the

potential fault signal occurring time.

At first, calculate the absolute value of the first-order difference of the instan-

taneous of IMF1, or g(t):

g(t) =|f(t)|. (10)

Because there is a process of striking envelope curve in the process of EMD, it is

likely to exit end effect in the application. Therefore, it is necessary to shield offthe first and the end 10% data, and these data are excluded from the set of feature

times by means of 0.1N < t 0.9N. The data that are less than the average value

ing(t) will be removed. While calculating the difference oft, the data int and t + 1

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are used; the instant t+ 1 should be contained in the set of feature time, ifg(t) is

not less than the average. In addition, some selected features, whose amplitude is

less than the average in a(t), will also be excluded. At last, the set of feature time

is given as Eq. (11) where the criterion is obtained empirically as follows:

=

t

g(t) g or g (t1) g

a(t) a, 0.1N < t 0.9N

. (11)

For further explanation about Eq. (11), this empirical criterion is designed to filter

out the original features (or suspected fault times) with a certain rate of change

in instantaneous frequency, so g(t) g is chosen incipiently. Experimental results

showed that if we only use this, a lot of false-alarm signal features (usually with

small amplitude) were also selected out; therefore, we added a(t) a to avoid

choosing the false alarm features. Besides, fault diagnosis expert system generallyrequires that the BIT signal has at least five consecutive times as a valid input data;

therefore, many features with high rate of change in instantaneous frequency are

thrown away due to not meeting the length requirement, which results in higher

missed detection rate; therefore, we adopt g(t) g or g(t 1) g instead of

g(t) g to obtain more suspected fault features with required consecutive times.

Moreover, we utilize 0.1N < t 0.9Nto avoid the EMD end effect problem.

Step 5: Final features generation

The final features are generated based on the original signal. As the generated

features should enter the BIT system for faults diagnosis, only these features owing

a certain length or dimension are meaningful. In practical application, we can delete

continuous time sequence of which the total length is less than 5 (including noncon-

tinuous single time point) from the set of feature time , then we could obtain a

new set of feature time consisting one or more pieces of continuous composition, and

the total length of each time sequence is greater than or equal to 5; the final feature

signal is intercepted in accordance with on the input signal, i.e., x(t), t .

The proposed feature extraction method at least has the following two

advantages:

(1) The proposed method processes the BIT signals by means of HHT, which con-

tains two steps, namely, EMD and HT. The fault features are generated from

the original signals by analyzing the instantaneous amplitude and frequency.

The presented approach is more adaptive and flexible than the other feature

extraction methods.

(2) The proposed method essentially adopts a reduction strategy directly targeted

for the raw data rather than a data transformation strategy. It not only makes

feature signals retain the original physical meaning of the raw data but also

makes the follow-up BITs able to accumulate diagnosis data and update the

fault diagnosis database, which is convenient for the application of decision-

making or higher-level analysis.

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3. Experimental Results

To indicate the specific implementation of proposed feature extraction method, we

use the target drone aircrafts steering gear feedback voltage signals sampled by its

BIT system as an example. Target drone aircraft is a major type of air target, which

can also be used as bait for enemy targets. It is a kind of Unmanned Aerial Vehicle

that has lifting surface and relies on the autopilot and radio systems for motor

control. This experimental example signal gets interception from the steering gear

feedback voltages while the target drone aircraft performs some provisions self-check

tasks [Liu and Lin (2007)]. Five sections of original data are selected both in normal

condition and in fault condition, and the initial position calibration is carried out

for all of the 10 sections of original data. The interference action is added at time

70 0.1 s to the target drone aircraft, and it results in two different effects: voltage

drop is more uniform in normal mode, whereas voltage drop completes after a sharpdrop and recover in fault mode. The BIT system uses SD to detect the abnormal

phenomenon of the sharp drop and recovery.

The experiment selects five sections of the original data in both normal and

fault conditions as input data and performs the following steps separately, which are

exactly the same. Take one section of data as an example, the actual implementation

is as follows:

First, the EMD is carried out on the input data to obtain the IMF1 and the

RES function.

Second, HT is carried out on IMF1 to obtain its amplitude and instantaneousfrequency. Equation (1) is used to carry out the discrete convolution of c(t) and

obtain the HHTy(t) on IMF1. Then, Eq. (6) is used to get the envelope amplitude

a(t) of the analytic signalc(t)+jy(t). Further, Eqs. (7) and (8) are used to calculate

the phase angle(t) and the instantaneous frequency f(t) of the analytic signal.

Third, Eq. (9) is used to calculate the first-order difference f(t) of IMF1s

instantaneous frequency.

Fourth, determine the location of the features, i.e., identify the set of moments

when potential fault features occur. Equation (10) is used to calculate the absolute

value g(t) of the first-order difference of IMF1s instantaneous frequency. Then,Eq. (11) is used to identify the set of feature time .

Finally, generate the final feature based on the original signal. Remove consecu-

tive time sequences (include nonconsecutive single point of time) whose total length

is less than 5 from the set of feature time to get a new set of feature moments

(consists of one or more segments of continuous feature time sequences, and

the total length of each segment should be more than or equal to 5), and the

final feature signals are intercepted in accordance with on the input signals, i.e.,

x(t), t .

Next, the efficiency of the method of extracting features is analyzed and verified

in both normal condition and fault condition. The feedback voltage of steering

gear in the normal condition showed in Fig. 2 is transformed to the IMF1 showed

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10 20 30 40 60 70 80 90

0

1

2

3

4

Sampling time sequence [0.1s]

Feedbackvoltage[V]

Fig. 2. Steering gear feedback voltage in normal condition.

10 20 30 40 60 70 80 90-0.2

0

0.2

0.4


Feedbackvoltage

IMF1[V]

Fig. 3. IMF1 arising from steering gear feedback voltage after EMD in normal condition.

10 20 30 40 60 70 80 900

0.2

0.4


IMF1amplitude[V]

Fig. 4. Magnitude of IMF1 in normal condition.

10 20 30 40 60 70 80 900

1

2


IMF1instantaneous

frequency

Fig. 5. Instantaneous frequency of IMF1 in normal condition.

10 20 30 40 60 70 80 900

0.5

1


IMF1differential

absolute[V/s]

Fig. 6. Absolute value of the first-order differential of instantaneous frequency of IMF1 in normalcondition.

in Fig. 3 after the process of EMD. Then, HT is carried out on IMF1 to get itsamplitude and instantaneous frequency as shown in Figs. 4 and 5. And then, the

first-order difference of IMF1s instantaneous frequency is obtained and its absolute

value is also calculated as shown in Fig. 6. After removing the moment when the

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10 20 30 40 60 70 80 900

0.5

1


IMF1selected

differential

absolute[V/s]

Fig. 7. Absolute value of the first-order differential of instantaneous frequency of IMF1 afterfiltering in normal condition.

10 20 30 40 60 70 80 900

1


feedbackvoltage

featurelocation

Fig. 8. Feature location of steering gear feedback voltage in normal condition.

absolute value and amplitude is less than the average number, we can obtain the

time sequences, which are shown in Fig. 7. Finally, by removing consecutive time

sequences whose total length is less than 5, we can get the feature time sequences

as shown in Fig. 8, and the signal segments matching the feature time location of

the original signal are the final features we extract.

In the same way, after carrying out all the steps of the method proposed in thispaper on the feedback voltage of steering gear in the fault condition as shown in

Fig. 9, we can obtain the results as shown in Figs. 1015.

It is difficult to visually evaluate the effect of feature extraction from the final

feature location. Therefore, we can remain the features physical meaning of the

10 20 30 40 60 70 80 900

1

2

3

4


Feed

back

volta

ge[V]

Fig. 9. Steering gear feedback voltage in fault condition.

10 20 30 40 60 70 80 90-0.5

0

0.5

1


Fee

dbackvoltage

IMF1[V]

Fig. 10. IMF1 arising from steering gear feedback voltage after EMD in fault condition.

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10 20 30 40 60 70 80 900

0.5

1


IMF1amplitude[V]

Fig. 11. Magnitude of IMF1 in fault condition.

10 20 30 40 60 70 80 900

1

2

3


IMF1instantaneous

frequency[V]

Fig. 12. Instantaneous frequency of IMF1 in fault condition.

10 20 30 40 60 70 80 900

0.5

1

1.5


IMF1differential

absolute[V/s]

Fig. 13. Absolute value of the first-order differential of instantaneous frequency of IMF1 in fault

condition.

10 20 30 40 60 70 80 900

0.5

1

1.5


IMF1selected

differential

absolute[V/s]

Fig. 14. Absolute value of the first-order differential of instantaneous frequency of IMF1 afterfiltering in fault condition.

10 20 30 40 60 70 80 900

1


feedbackvoltage

featurelocation

Fig. 15. Feature location of steering gear feedback voltage in fault condition.

BIT system and use the SD to evaluate the obtained limited suspicious featuresperformance. The results are showed in Table 1. Indexes 15 are from the feed-

back voltage of steering gear in the normal condition and are showed in Fig. 16,

whereas indexes 610 are from the feedback voltage of steering gear in the fault

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Table 1. Diagnosis results for feature extraction on steering gearfeedback voltage BIT signals.

Sequence Feature time set Standard deviation Level

1 {57, 58, . . . , 65, 66} {57, 58, . . . , 65, 66} Normal

2 {56, 57, . . . , 62, 63} {56, 57, . . . , 62, 63} Normal3 {56, 57, 58, 59, 60} {56, 57, 58, 59, 60} Normal

4 {57, 58, . . . , 62, 63} {57, 58, . . . , 62, 63} Normal

5 {40, 41, 42, 43, 44} {40, 41, 42, 43, 44} Normal

{56, 57, . . . , 63, 64} {56, 57, . . . , 63, 64}

6 {67, 68, . . . , 77, 78} {67, 68, . . . , 77, 78} Fault

7 {66, 67, . . . , 77, 78} {66, 67, . . . , 77, 78} Fault

8 {67, 68, . . . , 77, 78} {67, 68, . . . , 77, 78} Fault

9 {67, 68, . . . , 76, 77} {67, 68, . . . , 76, 77} Fault

10 {67, 68, . . . , 76, 77} {67, 68, . . . , 76, 77} Fault

0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedback

voltage[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedback

voltage[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedb

ack

voltage

[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedback

voltage[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4


Feedback

voltage[V]

(1)

(2)

(3)

(4)

(5)

Fig. 16. Original sample data of the feedback voltage of steering gear numbered from 1 to 5 innormal condition.

condition and are showed in Fig. 17. The entire data is measured through repeated

experiments in the same operational instruction condition, and the final feature

location is showed in Figs. 18 and 19. It should be noted that we get two segments

of consecutive feature time sequences from the data of index 5; therefore, we should

calculate the two segments of data, respectively, to obtain the SDs, but we only

use the larger value of them in diagnosis. SD values reflect the disperse degree offeatures, and a fault can be diagnosed if the value is too large. From the result

of Table 1, the SDs of indexes 15 are less than 0.4V (SD is 0.3320V); how-

ever, the SDs of indexes 610 are more than 0.6 V (SD is 0.7431 V). The former,

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0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedback

voltage[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedb

ack

voltag

e[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedback

voltage[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4

Feedback

voltage[V]

0 10 20 30 40 50 60 70 80 90 1000

2

4


Feedb

ack

voltage[V]

(6)

(7)

(8)

(9)

(10)

Fig. 17. Original sample data of the feedback voltage of steering gear numbered from 6 to 10 infault condition.

0 10 20 30 40 50 60 70 80 90 1000

1

feature

location

0 10 20 30 40 50 60 70 80 90 1000

1

feature

location

0 10 20 30 40 50 60 70 80 90 1000

1

feature

location

0 10 20 30 40 50 60 70 80 90 1000

1

feature

location

0 10 20 30 40 50 60 70 80 90 1000

1


feature

location

(1)

(2)

(3)

(4)

(5)

Fig. 18. Feature location of the feedback voltage of steering gear numbered from 1 to 5 in normalcondition.

corresponding to the real situations, are normal, whereas the latter are faulty. Itis so clear that with the help of the feature extraction method proposed in this

paper, we can obtain not only the greater diagnostic margin but also the higher

efficiency.

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0 10 20 30 40 50 60 70 80 90 1000

1

feature

location

0 10 20 30 40 50 60 70 80 90 1000

1

feature

loca

tion

0 10 20 30 40 50 60 70 80 90 1000

1

feature

location

0 10 20 30 40 50 60 70 80 90 1000

1

feature

location

0 10 20 30 40 50 60 70 80 90 1000

1


feature

loc

ation

(6)

(7)

(8)

(9)

(10)

Fig. 19. Feature location of the feedback voltage of steering gear numbered from 6 to 10 in faultcondition.

4. Conclusions

In this paper, we have proposed a BIT-signal feature extraction method based on

HHT. The proposed method essentially adopts a reduction strategy that is directly

targeted for the raw data, rather than a data transformation strategy. Since thefault features are generated from the original signals by analyzing the envelope

amplitude and instantaneous frequency of IMF, this approach is more adaptive

and flexible than other feature extraction methods. Simulations are carried out on

steering gear feedback voltage signal of target drone aircraft, and the extracted

features show great potential for the improvement in the built-in fault diagnosis.

Acknowledgments

This work was financially supported by the Fundamental Research Funds for theCentral universities (HIT.NSRIF.201160, HIT.KLOF.2010017) and China Postdoc-

toral Science Foundation (20110491067).

References

Drees, R. and Young, N. (2002). Built-in test in support system maintenance. IEEEInstrum. Meas. Mag., 5(3): 2529.

Duan, C. D. and He, Z. J. (2007). Fault feature extraction method using the lifting wavelettransform and its applications. J. Vib. Shock, 26(2): 1013.

Huang, N. E., Shen, Z., Long, S. R. et al. (1998). The empirical mode decomposition andthe Hilbert spectrum for nonlinear and nonstationary time series analysis. Proc. R.Soc. London, 454(1971): 903995.

Hwang, I., Kim, S., Kim, Y. and Seah, C. E. (2010). A survey of fault detection, isolation,and reconfiguration methods. IEEE Trans. Control Syst. Technol., 18(3): 636653.

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Kopsinis, Y. and McLaughlin, S. (2009). Development of EMD-based denoising methodsinspired by wavelet thresholding. IEEE Trans. Signal Process., 57(4): 13511362.

Liu, Z. and Lin, H. (2007). Research on intelligent built-in test fault diagnosis of more-electric aircraft electrical power system.Binggong Xuebao/Acta Armamentarii, 28(11):13571362.

Tang, B. P., Jiang, Y. H. and Zhang, X. C. (2010). Feature extraction method of rollingbearing fault based on singular value decomposition-morphology filter and empiricalmode decomposition. J. Mech. Eng., 46(5): 3742.

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