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Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering

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Gas pressure regulators are widely applied in natural gas pipeline networks, correspondingly, establishing an efficient fault diagnosis approach of regulators plays a critical role in optimizing the safety and reliability of pipeline network systems. In our paper, considering that the outlet pressure signals of gas regulators are nonstationary and nonlinear, we propose a fault diagnosis approach combining a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and fuzzy c-means (FCM) clustering to classify three typical faults of gas regulators. First, we propose to apply the CEEMDAN approach for decomposing intrinsic mode functions (IMFs). Then feature vectors of the typical faults are established by Hilbert marginal spectrum (HMS) of IMFs. Finally, we adopt cluster centers and feature clustering algorithm to distinguish the types of faults. The experimental results indicate the high performance of the present fault diagnosis approach. The membership degrees of test samples obtained from the CEEMDAN algorithm are optimized to be within 0.9 to 1.
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Fault Diagnosis of Gas Pressure
Regulators Based on CEEMDAN and
Feature Clustering
SHEN TIAN1, XIAOYU BIAN2, ZHIPENG TANG2, KUAN YANG2, LEI LI2
1Graduate School of Zhengzhou University, Zhengzhou 450001, Henan, China
2School of Physics and Engineering, Zhengzhou University, Zhengzhou 450001, Henan, China
Corresponding author: Lei Li (lilei@zzu.edu.cn)
ABSTRACT Gas pressure regulators are widely applied in natural gas pipeline networks, correspondingly,
establishing an efficient fault diagnosis approach of regulators plays a critical role in optimizing the safety
and reliability of pipeline network systems. In our paper, considering that the outlet pressure signals of gas
regulators are nonstationary and nonlinear, we propose a fault diagnosis approach combining a complete
ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and fuzzy c-means (FCM)
clustering to classify three typical faults of gas regulators. First, we propose to apply the CEEMDAN
approach for decomposing intrinsic mode functions (IMFs). Then feature vectors of the typical faults
are established by Hilbert marginal spectrum (HMS) of IMFs. Finally, we adopt cluster centers and
feature clustering algorithm to distinguish the types of faults. The experimental results indicate the high
performance of the present fault diagnosis approach. The membership degrees of test samples obtained
from the CEEMDAN algorithm are optimized to be within 0.9 to 1.
INDEX TERMS Gas pressure regulators, fault diagnosis, CEEMDAN, feature extraction, spectral analysis,
fuzzy c-means clustering
I. INTRODUCTION
Pressure regulators are designed to maintain constant out-
put pressure regardless of the variations in the upstream
pressure or the downstream flow [1]. These control valves are
widely applied in the fields of industries and household, such
as aircraft [2], aerospace [3], vehicle [4], mining [5], etc. In
cooking and heating fields [6], the compressed natural gas,
regulated by a series of pressure regulators, eventually goes
to household supply systems at a lower pressure. Any fault of
a gas pressure regulator in this chain may lead to the leakage
of explosive gas, causing economic losses and residential
casualties [7]–[8]. Therefore, an effective fault detection
and identification approach for gas pressure regulators has
become an urgent problem to be solved [9]–[14].
In low-pressure gas pipeline networks, the stability of
outlet pressure is one of the most important parameters that
reflects the performance of a gas regulator. Depending on
its maximum allowable operating pressure (MAOP), we can
define three types of networks: high, middle and low pressure
gas networks [15]. The pressure value of low-pressure net-
works which eventually goes to household supply systems
ranges from 20 kPa down to 2 kPa [16]. When a faulty
regulator is operating, its outlet pressure signal, which fluc-
tuates abnormally, is rich in state information. Most common
faults in a pilot-operated gas pressure regulator shown in
Fig. 1 include three types: high frequency surge, low outlet
pressure at peak hours, and high closing pressure at night
[17]. The schematic outlet pressure signals of a healthy and
three faulty regulators are shown in Fig. 2, and the reasons of
typical faults are summarized in Table 1. In the stage of signal
processing, the signals gathered from gas regulators usually
show nonlinearity and nonstationarity due to the variety of
interference factors and unstable conditions in a pipeline
[14]. Hence, a thorough solution for outlet pressure signal
processing is crucial to fault diagnosis of gas regulators.
In the literature, fault diagnosis has been shown to be
performed through various algorithms, i.e., fast Fourier trans-
form (FFT) [18]–[20], short-time Fourier transform (STFT)
[21]–[23], wavelet transform (WT) and wavelet packet de-
composition (WPD) [24] –[26], empirical mode decomposi-
tion (EMD) [27]–[29], and Hilbert-Huang transform (HHT)
[30]–[32]. These strategies can be successfully applied to the
fault diagnosis in certain scenarios, but with limitations. The
FFT has an advantage of a higher extraction efficiency than
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S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
FIGURE 1. Experimental platform: A pilot-operated gas regulator in
regulating box.
FIGURE 2. The outlet pressure signal from (a) a healthy regulator, (b) a
regulator with surge, (c) a regulator with low outlet pressure, and (d) a
regulator with high closing pressure. (The features of the original
time-varying waveforms above are schematic and optimized.)
all other methods, but it performs poorly in nonlinear and
nonstationary conditions. The STFT has adopted its decom-
position method from global to local, which is used on non-
stationary signal processing; however, it shows inefficiency
in multi-resolution analysis and nonlinearity conditions. The
wavelet-based techniques have improved the loss of infor-
mation and the resolution limitations introduced by Fourier
analysis; however, desired wavelet requires a strict design
of filters for the diverse fault types, and thus any improper
selection of the basis function can affect the analysis results
[33, 47].
As an ideal time-frequency analysis approach, EMD ex-
hibits a better performance in analyzing amplitude-frequency
modulated (AM-FM) and multicomponent signals. Com-
pared with traditional FFT and WT, the data driven method
of the EMD does not require designated assumptions behind
a fundamental model and is suitable for both nonlinear and
TABLE 1. Typical faults and reasons
Types Reasons
1) the stem of regulator rubs against its
Surge guide hole
2) the support bracket of regulator rubs
against other parts
1) the port of pilot is clogged
2) the spring stiffness of regulator is reduced
Low outlet (material fatigue)
pressure at 3) the gas filter contains impurities
midday peak (upstream problem)
4) the actual flow rate of regulator is higher
than the rated (improper selection of regulator)
5) inpropriate inlet pressure (upstream problem)
High closing 1) the sealing part is aged or damaged
pressure at 2) the valve gasket contains impurities which
night lead to gas leakage
3) the pliot is not working
nonstationary signals. Meanwhile, the EMD decomposes a
signal into approximative monocomponents called instinct
mode functions (IMFs). Some of these IMFs are sensitive
and relevant to specific faults, thus making the EMD ideal
for fault feature extraction of a system. Moreover, the HHT
method [34] is an advanced method which combines the self-
adaptive EMD algorithm and the Hilbert transform (HT) in
order to produce a time-frequency distribution of amplitude
called Hilbert spectrum (HS). So far, the EMD has been
applied in many cases, but its application in gas pressure
regulation is rarely reported.
Although the EMD displays decent performance in diverse
fields, its drawbacks in separating close modes cannot be
ignored. As a dyadic filter bank [35], the EMD suffers from
sampling rate issues and insufficient performance in noisy
industrial environments, which have hindered its application
in fault diagnosis. A vital drawback of the EMD method is
the presence of oscillations of very different amplitudes in a
mode, or very similar ones in different modes, termed "mode
mixing" [36]. To alleviate this problem, several methods
were proposed [37]–[40]. These methods, however, can only
reduce mode mixing to some extent due to different attempts
of signal mixed with noise generating different decompo-
sition results. Some of the methods lead to a significant
residual noise while others increase the decomposition level
[41]. Therefore, these algorithms can hardly be applied in
diagnostic schemes for gas regulators.
In this paper, we proposed an automatic diagnostic frame-
work for gas pressure regulators, which is for the most
part manual and inaccurate nowadays. Utilizing a complete
ensemble EMD with adaptive noise (CEEMDAN) to extract
weak features from pressure signals, a holistic diagnosis
approach is applied based on CEEMDAN and feature cluster-
ing. First, to alleviate mode mixing and improve diagnostic
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S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
accuracy of results, the CEEMDAN algorithm is utilized;
then IMFs are computed based on a unique residue [42].
Second, we collect a finite number of IMFs, which contain
the fault features of a gas regulator, to reconstruct a feature
vector based on Hilbert marginal spectrum (HMS). Third,
we use feature vectors to construct faulty sample centers
by a fuzzy c-means (FCM) clustering method [43]. Finally,
the fault diagnosis method is verified by collected data from
residential gas regulators.
The remaining parts of our paper are organized as follows:
Section II introduces the CEEMDAN algorithm and FCM
clustering. Section III gives a full account of experiment
results and analysis aiming at one healthy pressure regulator
and three faulty pressure regulators as we adopt the tradition-
al and CEEMDAN algorithms to diagnose the outlet pressure
of gas regulator respectively. Finally, the FCM clustering is
used to classify the fault types. Conclusions are drawn in the
last section.
II. METHOD
A. EMPIRICAL MODE DECOMPOSITION AND MODE
MIXING
Empirical mode decomposition is a self-adaptive algorithm
that was first proposed by Huang et al. in [34]. It can
decompose the original signals into a series of IMFs and a
residue function. Suppose the original signal is x(n), in EMD
x(n)can be written as:
x(n) =
K
X
k=1
I MF k(n) + r(n)(1)
where Kdenotes the number of decomposed IMFs; I MF k
denotes the kth IMF; and r(n)is the residue of the signal
x(n).
The realization of EMD algorithm consists of four steps:
extract local maximum and minimum of a signal, interpolate
extremum points to generate lower and upper envelopes,
calculate the mean of the upper and lower envelopes, judge
whether the difference between the signal x(n) and the mean
of envelope is an IMF, and sift and iterate. Moreover, each
IMF must satisfy two conditions:
1) The numbers of local extremum points and zero cross-
ings must be equal or differ by one.
2) The local mean of the upper and lower envelopes is
zero.
Although the EMD method has proven to be efficient
for signal processing, the drawbacks are obvious, such as
end effect, sampling rate issue, mode mixing, etc. [44]. If
mode mixing occurs, an IMF component no longer has a
physical significance by itself, suggesting falsely that there
may be different physical processes represented in a mode
[45]. An improved method which can decompose IMFs with
a narrower frequency spectrum is thus in need.
B. COMPLETE ENSEMBLE EMPIRICAL MODE
DECOMPOSITION WITH ADAPTIVE NOISE
Aiming at the mode mixing phenomenon, Torres et al. [42]
recently proposed a method called CEEMDAN. Given a
signal x(n), this algorithm defines an operator Ej(·)which
produces the jth mode decomposed by the EMD. Because
adding the white Gaussian noise at each stage of the decom-
position directly will lead to incomplete decomposition with
residual noise, in this approach, a particular noise Ej(ωi(n))
is added to extract the jth IMF component. The steps of the
CEEMDAN algorithm are described as follows:
1) Add ε0ωi(n)to the original signal x(n)to obtain
realization X(n) = x(n) + ε0ωi(n), where ωi(n)
denotes the ith added white noise with N(0,1), and
εkis the kth signal-to-noise ratio (SNR) coefficient.
Decompose by EMD Irealizations X(n)to obtain the
first IMFs and calculate the mean value by
^
I MF 1(n) = 1
I
I
X
i=1
I MF i
1(n) = IMF1(n)
2) Then calculate the first residue: r1(n) = x(n)
^
I MF 1(n). By adding ε1E1[ωi(n)] to the first residue
r1(n), we can obtain the realizations r1(n) +
ε1E1[ωi(n)],i= 1,2...I.
3) Decompose realizations r1(n) + ε1E1[ωi(n)] Itimes,
compute the mean value and then obtain the second
IMF:
^
I MF 2(n) = 1
I
I
X
i=1
E1{r1(n) + ε1E1[ωi(n)]}
4) For k= 2,3...K, calculate the kth residue: rk(n) =
rk1
^
I MF k(n), decompose the realizations rk(n) +
εkEk[ωi(n)],i= 1,2...I, and then the (k+ 1)th IMF
can be defined as:
^
I MF k+1 (n) = 1
I
I
X
i=1
E1{rk(n) + εkEk[ωi(n)]}
5) Repeat Step 4 for next kuntil rk(n)cannot be decom-
posed. The final residue is :
R(n) = x(n)
K
X
k=1
^
I MF k
Therefore, the original signal is written as:
x(n) =
K
X
k=1
^
I MF k+R(n)
Although the single experiment may certainly produce very
noisy results, the added Ej(ωi(n)) can cancel out each other
in the ensemble mean of enough experiments. The ensemble
mean is regarded as the true IMF.
The εkcoefficients enable us to choose the SNR at each
phase. To determine the parameter settings of the CEEM-
DAN, the noise amplitude needs to be reduced when the gas
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S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
pressure signal is dominated by high-frequency components.
When the gas pressure signal is dominated by low-frequency
components, the amplitude of added noise should be in-
creased [46]. To alleviate mode mixing and reduce errors,
we can increase the ensemble number to a few hundred and
the error caused by the added white noise can be reduced to
a very small extent or even negligible. Therefore, we used
the CEEMDAN with an ensemble number of 500, and the
amplitude of noise was 0.2 times standard deviation of the
pressure signal.
C. MODIFIED HILBERT–HUANG TRANSFORM AND
FEATURE VECTOR
The traditional HHT consists of two parts: the EMD and
Hilbert spectrum analysis (HSA). The almost monocompo-
nent IMFs decomposed by EMD provide a proper method
for the instantaneous frequency analysis of complex signals.
Applying the Hilbert transform to each IMF, we obtain a
time-frequency-energy distribution, called Hilbert spectrum.
Nevertheless, an IMF can cease to have physical meaning by
itself due to the mode mixing originated from the EMD. Thus
obtained Hilbert spectrum cannot reveal the signal features
accurately. To solve this problem, we used CEEMDAN in-
stead of EMD to decompose the original signal.
After applying the CEEMDAN algorithm on a signal, a set
of IMFs with different feature scales is obtained. Suppose the
ith IMF is ci, the Hilbert transform is defined in the following
equation:
di(t) = 1
πZ
−∞
ci(τ)
tτ(2)
Combining ciand di, an analytic signal can be expressed
as:
zi(t) = ci(t) + jdi(t) = ai(t)ej θi(t)
ai(t) = pc2
i(t) + d2
i(t)
θi(t) = arctan di(t)
ci(t)
(3)
where ai(t)denotes the instantaneous amplitude (IA) and
θi(t)is the instantaneous phase.
If the signal x(t) is monocomponent, the instantaneous
frequency (IF) can be expressed as:
ωi(t) = i(t)
dt (4)
With definitions above, the original signal x(t)can be
written as:
x(t) = Re
n
X
i=1
ai(t)ejRωi(t)dt (5)
where Redenotes the real part. According to the Equation
(5), the Hilbert spectrum can be defined as:
H(ω, t) = Re
n
X
i=1
ai(t)ejRωi(t)dt (6)
According to Equation (6), the Hilbert marginal spectrum
is written as:
h(ω) = ZT
0
H(ω, t)dt (7)
where Tdenotes the sampling time period. Then according to
Equation (7), the total energy of the original signal is defined
as:
E=Z
0
h(ω)(8)
The Hilbert marginal spectrum can describe the frequency-
energy distribution of a pressure signal. In order to analyze
these fault features precisely, we divided the HMS further
into five frequency bands. The energy of each frequency band
is defined as:
Ej=Zbj
aj
|h(ω)|(j= 1,2· · ·5) (9)
where Ejdenotes the energy of jth frequency band, ajand
bjare the lower and upper limits of jth frequency band
respectively. With these definitions, we can establish a feature
vector Vof an outlet pressure signal as:
V= [E1/E, E2/E · · · E5/E](10)
E=
5
X
i=1
Ei(11)
D. FUZZY C-MEANS AND CLUSTER CENTER
The FCM algorithm, which was proposed by Bezdek et al.
[43], is a fuzzy analysis method focused on evaluating the
centroids of multiple clusters and the activation levels of data
modes. Based on a large number of experiments, we found
that a gas regulator may have multiple faults in its life cycle,
and each fault has a unique clustering structure. Thus, we
used the FCM algorithm to identify the types of faults in
diagnostic schemes.
The FCM algorithm is based on an objective function,
which can be written as:
J(U, Z) = PC
i=1 Pn
j=1(µij )m(dij )2
i(1...t...C)
j(1...k...n)
(12)
where U,Z,n, and mdenote the membership matrix, cluster
center, the number of samples, and the weight index (also
known as smoothing factor which is 2 in most cases), re-
spectly. In this paper, we chose random values to initialize
a prototype (cluster center) of samples.
The goal of fuzzy c-means clustering is to compute a group
of center vectors to minimize the objective function, which
can be defined as:
min {J(U, Z)}=
n
X
j=1
min {
C
X
i=1
(µij )m(dij )2}(13)
In this definition, the membership degree µij satisfies the
following relationship:
C
X
i=1
µij = 1 (14)
where Cdenotes the number of the categories. dij, the degree
of distortion between the jth sample point and the ith cluster
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S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
center, is generally expressed by the distance between two
vectors:
d2
ij =kxjzik2(15)
where xjdenotes the sample point and zidenotes cluster
center.
With these definitions and according to Equation (14), we
can use Lagrange method to calculate membership degrees.
Suppose the Lagrange function is:
F=
C
X
i=1
(µij )m(dij )2+λ(
C
X
i=1
µij 1) (16)
where λis a parameter. Suppose F
∂λ =PC
i=1 µij 1=0,
∂F
∂µtk = [m(µtk )m1(dtk )2λ] = 0. We can obtain the
following equation:
µtk =λ
m(dtk)2
1
m1
=λ
m
1
m11
(dtk)2
1
m1
(17)
Bring Equation (17) into PC
i=1 µik = 1, the following
equation can be obtained:
C
X
i=1
µik =λ
m
1
m1(C
X
i=1
[1
(dik)2])
1
m1
= 1 (18)
and the equation in (18) can be written as:
λ
m
1
m1
=1
nPC
i=1[1
(dik)2]o
1
m1
(19)
Then bring Equation (19) into Equation (17), the µtk can be
obtained:
µtk =1
PC
i=1[dtk
dik ]2
m1
(20)
According to the membership degree µtk, we can obtain
the membership matrix U. For the iteration of updating the
prototype, suppose ∂J (U,Z)
∂zi= 0, we can obtain the following
equation:
∂J (U, Z )
∂zi
=
n
X
k=1
(µik)m2[(xkzi)]T(xkzi)
∂zi
=
n
X
k=1
(µik)m[4(xkzi)]
=4[
n
X
k=1
(µik)m(xkzi)]
=4[
n
X
k=1
(µik)mxk
n
X
k=1
(µik)mzi]=0
(21)
Then, the prototype (cluster center) can be updated as:
zi=Pn
k=1(µik )mxk
Pn
k=1(µik )m(22)
Repeat Equations (13)–(22) until the zicoincides with the
centroid of a cluster. The final ziis regarded as the standard
cluster center, and we can thus obtain the corresponding
membership degrees of samples.
E. DIAGNOSTIC SCHEME BASED ON CEEMDAN AND
FCM
The diagnostic scheme for gas regulators consists of two
parts: building parameters and diagnostic verification, which
are as follows:
1) Calculate total energy Eof healthy regulators by
CEEMDAN, HSA and statistical analyze, and then set
a healthy threshold.
2) Analyze faulty samples to establish a cluster center for
each of the three typical faults by our method.
3) Input testing signal x(t). First, calculate its energy
and confirm if value exceeds the threshold. If not, this
regulator is healthy.
4) If yes, this regulator is faulty. Then extract its IMFs by
CEEMDAN, calculate feature vector Vby HMS and
identify membership degree by FCM.
The diagnostic scheme for gas regulators based on CEEM-
DAN and FCM is shown in Fig. 3.
FIGURE 3. Flowchart of the diagnostic scheme for gas regulators.
III. EXPERIMENT RESULTS AND ANALYSIS
A. EXPERIMENTAL PLATFORM
The approach proposed above was verified in a gas regulating
box as shown in Fig. 1. This platform consisted of a pilot-
operated regulator (RTZ-/0.6 AQ, made by Hebei Anxin Co.,
Ltd.), a gas filter, an inlet pressure valve, an outlet pressure
valve, and other auxiliary devices.
In identical running conditions, we mainly researched four
gas regulators: a regulator with a deformed stem (surge sim-
ulation), a regulator with clogged ports (low outlet pressure
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S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
FIGURE 4. The results from a regulator with surge: (a) IMFs based on the EMD, and (b) Hilbert marginal spectra of IMFs.
FIGURE 5. The results from a regulator with surge: (a) IMFs based on the CEEMDAN, and (b) Hilbert marginal spectra of IMFs.
simulation), a regulator with damaged sealing rings (high
closing pressure simulation), and a healthy regulator. We
replaced the tested regulator after each group of experiments.
The rated running pressure of tested regulators was 2500 Pa,
and the inlet pressure was maintained at 20 kPa by upstream
regulators. In the regulating box, we installed a wireless
pressure monitoring terminal which enabled us to derive
sufficient outlet pressure data. For each regulator, similar
experiments were conducted and each set of data collection
lasted for 2 days. All pressure data from regulators were
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S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
FIGURE 6. Spectra of IMFs 1 to 5 obtained by (a) the EMD, and (b) the
CEEMDAN.
recorded at 15-minute intervals, totalling 96 pressure values
in one day. In order to display experimental results clearly, all
frequency domains of figures in next sections ranging from 1
to 2500 were normalized (α·f,α= 4.6×106).
B. FEATURE EXTRACTION BASED ON CEEMDAN
After the pressure signal was collected, the EMD was applied
to decompose the signal into a set of IMFs. The CEEMDAN
with a noise amplitude of 0.2 and an ensemble size of 500
was applied on the same signal, respectly. Figs. 4(a) and 5(a)
illustrate the decomposed IMF components from a regulator
with surge. Meanwhile, Figs. 4(b) and 5(b) describe the
corresponding frequency-amplitude (energy) distribution of
these IMFs, which is also known as the Hilbert marginal
spectrum. By comparing Fig. 4(a) and Fig. 5(a), it is obvious
that the CEEMDAN decomposed this faulty signal thorough-
ly into more monocomponents. Moreover, in Fig. 5(b), each
IMF occupied almost a unique frequency band in HMS.
Hence, the CEEMDAN algorithm was verified effective for
fault feature extraction.
In order to observe the influence of mode mixing, the
Hilbert marginal spectrum of IMFs 1 to 5 were obtained by
EMD and CEEMDAN, as shown in Fig. 6. We discovered
that the lines of spectra based on CEEMDAN were less
overlapped than those by EMD. Fig. 5(b) displays a clear-
er separation of frequency distribution between each IMF,
which indicates that CEEMDAN can alleviate mode mixing
well enough for further analysis.
C. FEATURE VECTOR BASED ON HILBERT SPECTRUM
ANALYSIS
After the IMFs were obtained, the system energy of a reg-
ulator was calculated to identify the severity of faults, and
necessary parameters including healthy threshold, feature
vectors were computed.
First, according to Equations (2)–(7), Fig. 7 shows the
obtained Hilbert spectrum of a signal from a healthy regulator
and three defective regulators. The xaxis of 4 corresponding
marginal spectra ranges from 0 to 3.398, which corresponds
to the logarithmic value of normalized frequency from 1 to
2500. Any fluctuation of the original signal will produce a
local energy peak in time domain of the Hilbert spectrum.
By Fig. 7, we found the features of time-frequency-energy
distribution as follows:
1) The energy distribution of the signals from healthy
regulators is more stable than those from the faulty
ones.
2) In high frequency bands, the energy of a regulator with
surge is even larger than the other two types of faults.
3) The energy of regulators with the other two types of
faults mainly distributed in lower frequency bands, but
the energy is much distinct in Fig. 7(c).
Second, according to Equation (8), the total energy of each
operating state can be calculated based on their marginal
spectra. As shown in Fig. 7, we found that the energy value of
a healthy system is far below other defective ones and this is
consistent with the energy distribution in Hilbert spectrum.
Therefore, there should be a healthy threshold which can
identify the severity of a fault. In this paper, we computed this
threshold by 51 data sets from a healthy pressure regulator.
The method to acquire each data set is the same as mentioned
in Experimental Platform section. The normalized threshold
7.7646 in Fig. 8 is the average of data plus three times
standard deviation. By this threshold, we could pick healthy
signals out of an unknown signal pool.
For the defective signals, the key parameter to distinguish
the fault types was its feature vector. The yaxis of the
HMS was divided into five frequency bands to calculate
the local energy component Ei. As shown in Fig. 7, the
normalized frequency band from 1 to 500 in every Hilbert
spectra included massive energy, so it was divided into two
bands. As a result, these normalized frequency bands vary
in the range of 1–253, 254–508, 509–1021, 1022–1533,
and 1534–2500. Then according to Equations (8)–(10), the
energy ratios were calculated to build the feature vectors.
For gas regulators monitored in this experiment, the feature
vectors of three typical faults are shown in Fig. 9. It can be
seen that the energy ratios of high frequencies E1/E,E2/E,
E3/E,E4/E are higher for a regulator with surge (see Fig.
9). In comparison, the energy ratio of low frequency E5/E
is significantly greater for regulators with other two faults.
Based on the above analysis, the distinct differences among
vectors indicate that they are able to represent corresponding
faults.
VOLUME 4, 2016 7
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10.1109/ACCESS.2019.2941497, IEEE Access
S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
FIGURE 7. The HS and corresponding HMS of a signal from (a) healthy, (b) surge, (c) low outlet pressure, and (d) high closing pressure regulator.
FIGURE 8. Energy of signals from a healthy and three typical faulty gas
regulators. (Normalized energy = E/α,α= 4.6×106)
FIGURE 9. The feature vector of a signal from (a) a regulator with surge,
(b) a regulator with low outlet pressure, and (c) a regulator with high
closing pressure.
8VOLUME 4, 2016
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/ACCESS.2019.2941497, IEEE Access
S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
TABLE 2. The standard cluster center of FCM algorithm based on the EMD.
E1E2E3E4E5
Surge 0.0867 0.0661 0.1461 0.2480 0.4530
Low Outlet Pressure 0.0273 0.0141 0.0393 0.0780 0.8412
High Closing Pressure 0.0382 0.0230 0.0659 0.1905 0.6823
TABLE 3. The standard cluster center of FCM algorithm based on the CEEMDAN.
E1E2E3E4E5
Surge 0.1685 0.0840 0.1829 0.1480 0.4166
Low Outlet Pressure 0.0390 0.0156 0.0393 0.0718 0.8343
High Closing Pressure 0.0595 0.0284 0.0852 0.1579 0.6689
TABLE 4. The membership matrix of the test samples from the EMD after FCM.
Diagnosis Results Test Samples
Surge Low Outlet Pressure High Closing Pressure
Cluster Surge 0.882 0.771 0.921 0.843 0.020 0.042 0.023 0.042 0.554 0.039 0.038 0.035
Center Low 0.025 0.052 0.020 0.037 0.834 0.309 0.894 0.309 0.072 0.351 0.557 0.197
High 0.093 0.177 0.059 0.120 0.147 0.649 0.083 0.649 0.347 0.610 0.405 0.768
TABLE 5. The membership matrix of the test samples from the CEEMDAN after FCM.
Diagnosis Results Test Samples
Surge Low Outlet Pressure High Closing Pressure
Cluster Surge 0.955 0.977 0.967 0.965 0.006 0.001 0.010 0.001 0.009 0.008 0.004 0.002
Center Low 0.012 0.007 0.010 0.010 0.957 0.993 0.945 0.992 0.019 0.026 0.012 0.005
High 0.033 0.016 0.023 0.026 0.038 0.006 0.045 0.007 0.972 0.966 0.984 0.994
D. FAULT DIAGNOSIS BASED ON FCM CLUSTERING
As described in Experimental Platform section, three groups
of experiments – a regulator with surge fault, a regulator
with low outlet pressure, and a regulator with high closing
pressure – were conducted to classify the fault types. The
data sampling interval for each experimental group was 15
minutes and a data collection procedure lasted for two days.
Each experimental group consisted of two phases: building
standard cluster centers of a typical fault, and computing the
membership degrees of test samples.
The goal of Phase 1 was to build 3 standard cluster centers
of typical faults. The sampling procedure was repeated 8
times to obtain a total of 8 data sets for each experimental
group. Thus for 8 data sets, the number of feature vectors is
24. Then, the FCM clustering method was used to calculate
a cluster center for each cluster of feature vectors, and these
cluster centers were set as the standard cluster centers. To
verify the stability of our method, we also applied the EMD
on the same data sets as comparison groups. Tables 2 and 3
present the standard cluster centers of FCM algorithm based
on the EMD and the CEEMDAN.
The goal of Phase 2 was to compute the membership de-
grees of test samples. To classify the fault type of an unknown
signal, we repeated the sampling procedure to collect another
18 more data sets. Then, we calculated the feature vectors
of these data sets, and obtained their membership degrees
with standard cluster centers. A part of the diagnosis results
are shown in Tables 4 and 5. In Table 4, false classification
results are presented. Two samples with low outlet pressure
were classified as ones with high closing pressure. Another
two samples with high closing pressure were classified as one
with surge, and one with low outlet pressure. In Table 5, by
contrast, we can observe that the diagnostic results based on
the CEEMDAN algorithm is relatively ideal.
To validate the diagnostic accuracy of proposed approach,
we used identical data sets to conduct two more groups of ex-
periments based on STFT with Hamming window function,
and WT using a db4 mother wavelet. The whole diagnosis
results of 18 data sets (54 test samples) based on STFT,
WT, EMD, and CEEMDAN are shown in Fig. 10. It can be
VOLUME 4, 2016 9
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/ACCESS.2019.2941497, IEEE Access
S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
FIGURE 10. The stability of diagnosis results based on STFT, WT, EMD, and CEEMDAN.
seen that the diagnostic accuracy calculated by the STFT,
WT and EMD algorithms are unstable. Some membership
degrees are significantly low, and false diagnosis results often
occur: eleven errors in STFT, nine errors in WT, and seven
errors in EMD. Hence, the fault diagnosis accuracy of STFT,
WT, and EMD is 79.6%, 83.3%, and 87.0%respectively. By
contrast, for the CEEMDAN algorithm, all the samples are
classified into three categories correctly, and the membership
degree of test samples ranges between 0.9 to 1. Overall, the
proposed diagnostic method has been proved to be effective
by experimental results.
IV. CONCLUSION
In this paper, a novel fault diagnosis approach for gas pres-
sure regulators based on CEEMDAN and feature clustering
is proposed. The CEEMDAN algorithm was used to extract
fault features of a regulator. In comparison with the EMD,
the CEEMDAN was able to alleviate the mode mixing signif-
icantly. Hence, we can obtain a more accurate Hilbert spec-
trum to reflect fault information distibution. Then, FCM was
usd to classify diverse types of faults. Experimental results
indicate that the proposed method can achieve diagnostic
results with a higher degree of accuracy.
The currently proposed fault diagnosis approach for gas
pressure regulators is competent for further application.
When the parameters or structures of gas regulator are
changed, accurate diagnosis results may not be obtained.
Even so, the proposed method is capable of diagnosing more
fault types effectively if requisite parameters mentioned in
this paper are known. However, compound faults in sin-
gle regulators are not taken into account in this paper. In
future research, an improved approach which can identify
compound faults on single gas pressure regulators will be
considered.
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SHEN TIAN received the B.E. degree from
North China Electric Power University, Beijng,
China, in 2012, and the Master degree in Busi-
ness Administration from Zhengzhou University,
in 2018. From 2013, he worked as a project man-
ager in Research & Development Center, Hanwei
Electronics Group Corporation, Zhengzhou, Chi-
na. His current research interests include sensor
application and signal processing.
XIAOYU BIAN is pursuing the bachelor’s degree
in electrical engineering in Zhengzhou university,
Zhengzhou, China. His current research interests
include array signal processing, machine learning
and computer vision.
ZHIPENG TANG received the B.E. degree in
electronic engineering from Zhengzhou Univer-
sity, Zhengzhou, China, in 2018. He is pursuing
the master’s degree in electrical engineering in
Zhengzhou university. His current research in-
terests include array signal processing, machine
learning and computer vision.
KUAN YANG received the B.S. degree in elec-
trical engineering from the Zhengzhou University,
Zhengzhou, China, in 2017, where he is currently
pursuing the master’s degree with instrumentation
engineering. His current research interests include
array signal processing, machine learning, holo-
graphic imaging and computational imaging.
VOLUME 4, 2016 11
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/ACCESS.2019.2941497, IEEE Access
S. Tian et al.: Fault Diagnosis of Gas Pressure Regulators Based on CEEMDAN and Feature Clustering
LEI LI received the B.S. degree in electronic engi-
neering from Zhengzhou University, Zhengzhou,
China, in 2004 and the Ph.D. degree in electron-
ic engineering from the Institute of Acoustics,
Chinese Academy of Sciences, in 2009. He is
currently an Associate Professor in the School of
Physics and Engineering at Zhengzhou Univer-
sity. His current research interests include array
signal processing, machine learning and computer
vision.
12 VOLUME 4, 2016
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