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A Small Leak Detection Method Based on VMD Adaptive De-Noising and Ambiguity Correlation Classification Intended for Natural Gas Pipelines Qiyang Xiao 1 , Jian Li 1, *, Zhiliang Bai 1 , Jiedi Sun 2 , Nan Zhou 1 and Zhoumo Zeng 1 1

2

*

State Key Laboratory of Precision Measurement Technology and Instrument, Tianjin University, Tianjin 300072, China; [email protected] (Q.X.); [email protected] (Z.B.); [email protected] (N.Z.); [email protected] (Z.Z.) School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China; [email protected] Correspondence: [email protected]; Tel.: +86-1313-2122-397; Fax: +86-22-2740-2366

Academic Editor: Vittorio M. N. Passaro Received: 26 October 2016; Accepted: 8 December 2016; Published: 13 December 2016

Abstract: In this study, a small leak detection method based on variational mode decomposition (VMD) and ambiguity correlation classification (ACC) is proposed. The signals acquired from sensors were decomposed using the VMD, and numerous components were obtained. According to the probability density function (PDF), an adaptive de-noising algorithm based on VMD is proposed for noise component processing and de-noised components reconstruction. Furthermore, the ambiguity function image was employed for analysis of the reconstructed signals. Based on the correlation coefficient, ACC is proposed to detect the small leak of pipeline. The analysis of pipeline leakage signals, using 1 mm and 2 mm leaks, has shown that proposed detection method can detect a small leak accurately and effectively. Moreover, the experimental results have shown that the proposed method achieved better performances than support vector machine (SVM) and back propagation neural network (BP) methods. Keywords: pipeline small leakage detection; variational mode decomposition; adaptive de-noising method; ambiguity correlation classification

1. Introduction Due to increasing demands for natural gas, gas pipeline construction has developed rapidly. However, for a variety of natural and artificial reasons small leakage accidents happen occasionally in pipelines, which cause tremendous economic losses and casualties [1,2]. In order to provide for the safe operation of pipelines, small leak detection in pipelines should be studied [3,4]. Nowadays, pipeline leak detectors mainly determine the occurrence of leaking accidents based on delivery pressure and flow rate changes, which are influenced by various factors, such as transporting materials and transporting conditions [5,6]. When a leak occurs, there is an air-structure coupling between the high-velocity escaping gas and the tube wall surrounding the leak location, thereby causing stress waves that propagate along the body of the pipe on both sides of the leak hole. This phenomenon is known as stress wave emission and is considered to be a general acoustic emission. The acoustic emission (AE) technique realizes dynamic non-destruction testing according to AE source characteristics (e.g., defect type, size and position), which has advantages of high sensitivity and all-weather real-time detection [7–9]. Therefore, in this paper the AE technique was used for small leak detection in natural gas pipelines. The complicated surrounding environment, big noise disturbances and non-stationary characteristics of collected signals in small pipeline leaks, require a signal de-noising method in Sensors 2016, 16, 2116; doi:10.3390/s16122116

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order to extract the weak signal characteristics [10]. Traditional de-noising methods are based on noise frequency removal by a filter. However, this method has obvious limitations for signals with wideband noise, non-stationary signals and short-time transient signals [11,12]. The wavelet threshold de-noising method is superior to traditional de-noising methods, but it still cannot provide an ideal effect because of overlapping frequencies in the wavelet decomposition and the difficult selection of an accurate threshold [13,14]. Empirical mode decomposition (EMD) can reduce vibration signal noise, but EMD still has some theoretical problems, such as inadequate enveloping, over-enveloping, and mode mixing [15]. Vibrational mode decomposition (VMD) is a new non-stationary signal processing method proposed in 2014 [16]. VMD determines the frequency center and bandwidth of decomposed components by iteratively searching for the optimal solution for the variation mode, thus enabling an adaptive decomposition of the non-stationary signals [17]. Compared to EMD recursive “screening”, VMD decomposes signals into non-recursion and variation modes, and controls the convergences condition. Therefore, it can effectively eliminate the mode mixing in the decomposition process [18,19]. With respect to the non-stationary signals collected by sensors, this paper proposes the VMD adaptive de-noising method to process collected signals, extract noiseless component and eliminate noise disturbances. Conventional pattern recognition methods, like the back propagation neural network (BP) and support vector machine (SVM), are widely applied in the non-destructive testing field. Riahi et al. distinguished signals of different corrosion stages by a BP neural network in the acoustic emission testing of a tank bottom [20]. Qu et al. classified three anomalous events of pipelines (leaking, digging and walking) using SVM and realized a pipeline leak detection method [21]. Nevertheless, the BP neural network has the disadvantages of abundant parameter settings, slow convergence and easily getting caught in a local minimum, which restricts its diagnosis accuracy and wide applicability [22]. Compared to the BP neural network, the SVM generalization performance has been improved greatly, but it requires artificial assignment of kernel functions and kernel function parameters, thus restricting SVM applications significantly. Ambiguity function is a traditional time-frequency analysis tool that has an important role in non-stationary signal analysis and processing theory. In addition, it has been widely used in radar signal analysis and processing, optical information processing, etc. [23]. However, the ambiguity function has problems with cross terms and difficulties extracting signal time-frequency characteristics. In order to solve these problems, the ambiguity correlation classifier (ACC) is constructed based on the correlation coefficient, which can reduce the computational load and avoid disturbances from cross terms, without parameter setting. ACC recognizes different signal types according to internal relationships of eigenvalues and provides a method for small leak detection in pipelines. In this paper, a pipeline leak detection method based on VMD and ACC is proposed for small leakage accidents in natural gas pipelines. Firstly, the collected signals were decomposed by VMD and the adaptive de-noising method was proposed for the de-noising process. Afterwards, noiseless components were reconstructed and de-noising signals were obtained. Finally, according to the signal ambiguity characteristics, ACC was proposed to train and test different types of reconstructed signals. Experimental results demonstrated that this method can detect small pipeline leak accidents accurately. The paper is organized as follows: in Section 2, the proposed adaptive de-noising method based on VMD is described, and a simulation is presented in order to illustrate the proposed method. In Section 3, the ambiguity correlation classifier for pipe leakage detection is presented. In Section 4, the small leakage detection method is explained. The proposed leakage-detection scheme is experimentally validated, and compared with BP and SVM methods in Section 5. Lastly, brief conclusions are given in Section 6. 2. VMD Adaptive De-Noising Method 2.1. Variational Mode Decomposition Variational mode decomposition is a new self-adaptive signal processing method, which was proposed by Dragomiretskiy in 2014 [16]. This method achieves self-adaptive signal decomposition

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through construction and solution of variational problems [17]. The VMD algorithm transfers the signal decomposition process to the variational framework. Hence, the VMD decomposition process is an optimal-solution processing for a constrained variational process. For constrained-variation problems, the augmented Lagrange function is introduced to transform the constrained variation problem into an unconstrained variation problem. In order to obtain an optimal solution, the alternate direction method of multipliers (ADMM) is used to calculate the saddle point of the augmented Lagrange function, which is the optimal solution of the constrained-variation equation [18]. The saddle-point problem is solved by the alternate renewal of components and Lagrange multiplier, i.e., by solving the optimal-solution problem of the variational problem. The VMD algorithm continuously updates the modes in the frequency domain, and finally transforms them to the time domain through the Fourier inversion transformation. The specific algorithm is as follows: n o _1 (1) Initialize uˆ 1k , ωk1 , λ , and n = 0. λ is the Lagrange multiplier, {uk } = {u1 , . . . , uk }

(2) (3)

represents K components set after decomposition, and {ωk } = {ω1 , . . . , ωk } represents the center frequencies set of components after decomposition. n = n + 1, execute the whole loop. Execute innermost loop, k = 1 : k, uk and ωk are renewed according to uˆ nk +1 and ωkn+1 : n

uˆ nk +1

o

fˆ(ω ) − ∑ uˆ in+1 (ω ) − ∑ uˆ in (ω ) + (λˆ n (ω )/2)

=

i k

1 + 2α(ω − ωkn )2 ωkn+1

2 R ∞ n+1 ˆ ω u ( ω ) dω 0 k = R 2 ∞ n +1 ˆ (ω ) dω 0 uk

(1)

(2)

where α is the penalty parameter, f (t) represents the signal, and real part of {uˆ k (ω )} conducting Fourier inversion is {uk (t)}. _ n +1

(4)

Renew λ according to λ

(ω ) for ω ≥ 0.

λˆ n+1 (ω ) = λˆ n (ω ) + τ [ fˆ(ω ) − ∑ uˆ nk +1 (ω )]

(3)

k

(5)

where τ is the update parameter of the Lagrangian multiplier. 2 2 If ∑ kuˆ n+1 − uˆ n k / uˆ n ≤ ε , end the whole loop, output the k modal components uk , otherwise, k

k

k 2

k 2

repeat steps from Equation (2) to Equation (4). 2.2. VMD-Based Noise Adaptive Removal Approach Signals collected by sensors often contain noise interference, which weakens the leakage characteristics. In order to extract the characteristic information accurately, components after VMD have to be de-noised, which increases the signal-to-noise ratio (SNR). Currently, most studies divide components after VMD into noise components and noiseless components. They eliminate noise components and reconstruct noiseless components to realize a de-noising process [24]. Sun et al. presented a multi-wavelet block threshold method to remove the noise components [25]. Kang et al. effectively eliminated high-level noise by exploiting a soft–threshold with adaptively estimated positive and negative noise levels from the time domain AE signal [14,26]. As it is well known, an amplitude is a signal characteristic, so noise information could be gained by amplitude analysis. Probability density function (PDF) means that the probability of some random vibration signal amplitude is within certain range [27]. Therefore, the PDF can be used to distinguish the noise signals. Hence, an adaptive

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de-noising method was proposed in this paper by combing VMD and PDF, which was used for signals processing and de-noising signals acquisition. Specific steps of the algorithm are: (1)

For any data {xi , i = 1, . . . , n}, calculate its PDF fˆh (x): x − xi 1 n k( ) fˆh ( x ) = nh i∑ h =1

(2)

(3)

(4)

where k(•) presents the Gaussian kernels function and h is the bandwidth. To prevent overlarge of variance and deviation h is often determined 0.15 times of the prediction confidence interval of variable x. Calculate PDFs of the original signal x (t) and component uk (t) after VMD: P = PDF ( X (t))

(5)

Qk = PDF (uk (t))

(6)

where p and Q are PDFs, and K is the number of decomposed components. Calculate distance (L(k)) between two PDFs: L(k) = dist( PDF ( x (t)), PDF (uk (t)))

(7)

L(ks ) = k P − Q k2 + R∞ = ( P(z) − Q(z))2 dz

(8)

−∞

(4)

Choose noiseless component according to the distance: Nth = argmax{ L(k )}

(9)

1≤ k ≤ K

It can be concluded from Equation (9) that Nth − 1 components are noiseless components and the rest of them are noise components. 2.3. Algorithm Simulation In order to verify the algorithm effectiveness, a simulation signal is used. The simulation signal was composed of frequency-modulated and amplitude-modulated signals and random white noises. The corresponding mathematical expressions are: x1 (t) = [1 + 0.3cos(10πt)]sin[200πt + sin(15πt)]

(10)

x2 (t) = cos[60πt + sin(10πt)]

(11)

x (t) = x1 (t) + x2 (t) + 0.4randn

(12)

t = [0, 0.4]

(13)

After VMD of the simulation signal, PDFs of decomposed components and the original signal were calculated. VMD results are shown in Figure 1 and the distance between two PDF is shown in Figure 2. In Figure 2, the PDF of U3 has the largest distance of the original signal. Therefore, previous two components were chosen as the noiseless components. According to Figure 1, two previous components are noiseless components and the third component is the noise component. The obtained results show that the VMD adaptive de-noising method can eliminate noise interference effectively and obtain noiseless signals.

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U2U2

2 2 0 0 -2 -2 0 0

U3U3

1 1 0 0 -1 -1 0 0

t/s t/s Figure 1. VMD results of the simulated signal. Figure 1. 1. VMD results results of of the the simulated simulated signal. signal. Figure VMD

PDF distance PDF distance

15 15

10 10

5 5

0 0U1 U1

U2 U2

U3 U3

U components U components Figure 2. PDF distance between U components and the original signal. Figure 2. PDF distance between U components and the original signal. Figure 2. PDF distance between U components and the original signal.

In Figure 2, the PDF of U3 has the largest distance of the original signal. Therefore, previous two In Figure 2, the PDF of U3 has the largest distance of the original signal. Therefore, previous two components were chosen as the SNR noiseless components. According to Figure 1, two EMD previous Mean error square (MES) are often used to evaluate de-noising effect and components were chosen as and the noiseless components. According to Figure 1, [28]. two previous components are for noiseless components and the third component is the noise component. The VMD were used de-nosing process, and obtained results are listed in Table 1. components are noiseless components and the third component is the noise component. The obtained results show that the VMD adaptive de-noising method can eliminate noise interference obtained results show that the VMD adaptive de-noising method can eliminate noise interference 1. MSE and SNR of simulated signals. effectively and obtain noiselessTable signals. effectively and obtain noiseless signals. Mean error square (MES) and SNR are often used to evaluate de-noising effect [28]. EMD and Mean error square (MES) andSimulated SNR are Signals often used to evaluate de-noising effect [28]. EMD and SNR 1. VMD were used for Method de-nosing process, and obtained resultsMSE are listed in Table VMD were used for de-nosing process, and obtained results are listed in Table 1. VMD EMD

Before de-noising 0.0463 After de-noising 0.004signals. Table 1. MSE and SNR of simulated Table After 1. MSE and SNR of simulated signals. de-noising 0.0234

13.4451 24.0253 17.5643

Method Method

Simulated Signals MSE SNR Simulated Signals MSE SNR Before de-noising 0.0463 13.4451 de-noisingsignal 0.0463 13.4451 A higher SNR andVMD a smaller MES Before after de-noised indicate a better de-noising effect. As it After de-noising 0.004 24.0253 VMD After de-noising 0.004 24.0253 can be seen in Table 1, EMD effects due to mode mixing, EMD has poor de-noising After de-noising 0.0234 17.5643while VMD achieves After de-noising 0.0234 signals 17.5643 good de-noising effectsEMD since it can decompose non-stationary effectively and acquire the

correct components. A higher SNR and a smaller MES after de-noised signal indicate a better de-noising effect. As it A higher SNR and a smaller MES after de-noised signal indicate a better de-noising effect. As it can be seen in Table 1, EMD has poor de-noising effects due to mode mixing, while VMD achieves can be seen in Table 1, EMD has poor de-noising effects due to mode mixing, while VMD achieves good de-noising effects since it can decompose non-stationary signals effectively and acquire the good de-noising effects since it can decompose non-stationary signals effectively and acquire the correct components. correct components.

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3. Ambiguity Correlation Classifier 3.1. Ambiguity Correlation Theory As a non-stationary signal analysis method, the ambiguity function has been widely used due to its advantages in delay-frequency shift plane analysis [23]. Like Cohen’s time-frequency distribution, the ambiguity function suffers from a serious cross terms interference in signal analysis and has a heavy computational load. Interference disturbs effective analysis and signal explanation, as well as component parameters extractions, thus causing difficult extraction of the time-frequency signal characteristics. Hence, there must be an internal relationship between eigenvalues of different signal types. Such an internal relationship varies significantly among different types. Correlation coefficients can be used as the internal relationship measure. Different absolute values of correlation coefficients indicate different correlation degrees between signal eigenvalues [29]. According to that, the ambiguity correlation method was proposed in order to avoid interference from cross terms and to reduce the computation load of a time-frequency analysis. Specific steps are as follows: (1)

Calculate ambiguity function of signal x(t): A(τ, θ ) =

1 2π

Z

r x (t, τ )e jθt dt

r x (t, τ ) = x (t + τ/2) x ∗ (t − τ/2)

(2)

τ0 ,θ0

∞ Z ∞

−∞ −∞

A x (τ, θ ) Ay (τ − τ0 , θ − θ0 )dτdθ

τ ,θ

ρ xy (τ, θ ) = R0 0 R 1 R∞ R∞ ∞ ∞ [ −∞ −∞ A2x (τ, θ )dτdθ −∞ −∞ A2y (τ, θ )dτdθ ] 2

(17)

Select correlation coefficient when τ = 0 or θ = 0: R ∞ R∞ max −∞ −∞ A x (0, θ ) Ay (0 − τ0 , θ − θ0 )dτdθ τ ,θ

ρ xy (0, θ ) = R0 0 R 1 R∞ R∞ ∞ ∞ [ −∞ −∞ A2x (0, θ )dτdθ −∞ −∞ A2y (0, θ )dτdθ ] 2 R ∞ R∞ max −∞ −∞ A x (τ, 0) Ay (τ − τ0 , 0 − θ0 )dτdθ τ ,θ

ρ xy (τ, 0) = R0 0 R 1 R∞ R∞ ∞ ∞ [ −∞ −∞ A2x (τ, 0)dτdθ −∞ −∞ A2y (τ, 0)dτdθ ] 2 (5)

(16)

In Equation (16), R xy (τ, θ ) is the correlation function. Calculate normalized correlation coefficient ρ xy (τ, θ ): R ∞ R∞ max −∞ −∞ A x (τ, θ ) Ay (τ − τ0 , θ − θ0 )dτdθ

(4)

(15)

where r x (t, τ ) is the autocorrelation function of signals, A(τ, θ ) is the ambiguity function of signal x(t). Calculate the correlation function of ambiguity function images of signals x(t) and y(t): Z R xy (τ, θ ) = max

(3)

(14)

(18)

(19)

Calculate the ambiguity correlation coefficient ρ: s ρ=

ρ2xy (0, θ ) + ρ2xy (τ, 0) 2

(20)

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Providing the reliable theoretical basis and method to build the identification system based on the ambiguity correlation coefficient of leakage signals. Sensors 2016, 16, 2116

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3.2. Basic Principle of Classifier 3.2. Basic Principle of Classifier

The ambiguity correlation classifier (ACC) represents a one-to-one classifier. ACC has advantages The ambiguityload correlation classifier (ACC) a types one-to-one classifier. has by of low computational and no parameter setting.represents Firstly, two of signals were ACC processed advantages of low computational load and no parameter setting. Firstly, two types of signals were the VMD-based adaptive de-noising method in order to get the de-noised signals. Ambiguity functions processedsignals by the A VMD-based adaptive de-noising method in calculated. order to getThe thecorrelation de-noised signals. of de-noised and B, as well as the test signal C, were coefficient, Ambiguity functions of de-noised signals A and B, as well as the test signal C, were calculated. The I, between the ambiguity function of A and the ambiguity function of C was calculated. Similarly, correlation coefficient, I, between the ambiguity function of A and the ambiguity function of C was the correlation coefficient, II, between the ambiguity function of B and the ambiguity function of C calculated. Similarly, the correlation coefficient, II, between the ambiguity function of B and the was calculated. Afterwards, I and II were compared. In the case that I > II, then C is equal to A; ambiguity function of C was calculated. Afterwards, I and II were compared. In the case that I > II, otherwise, C is equal to B. If A is a de-noised signal of a 1 mm leak, B is de-the noised signal of the then C is equal to A; otherwise, C is equal to B. If A is a de-noised signal of a 1 mm leak, B is de-the non-leak situation, C is an unknown signal. they aresignal. input Next into ACC to identify, and C can noised signal of and the non-leak situation, and C isNext an unknown they are input into ACC to be determined to be a 1 mm leakage signal or no leakage signal. If C is neither a 1 mm leakage signal identify, and C can be determined to be a 1 mm leakage signal or no leakage signal. If C is neither a 1 nor a non-leak signal, thennor C continues be classified as described Theas principle ofabove. the ambiguity mm leakage signal a non-leaktosignal, then C continues to beabove. classified described The correlation is showncorrelation in Figure classifier 3. principleclassifier of the ambiguity is shown in Figure 3.

Figure 3. 3. ACC ACC flowchart. Figure flowchart.

4. Small Leak Detection Method

4. Small Leak Detection Method

The small leak detection method based on VMD and ACC can eliminate noise interference, The small leak detection methodfrom based on VMD and ACC can eliminate noise extract characteristic components weak and input reconstructed signals intointerference, the classifierextract in characteristic components from weak and reconstructed signals into the classifier in order order to realize a small leak detection. Theinput flowchart of this detection method is shown in Figure 4. to realize a small leak detection. The flowchart of this detection method is shown in Figure 4. Specific Specific steps are as follows:

steps are as follows: (1) (2) (3) (4)

(1) Collect experimental data by sensors and get series of U components of collected data from VMD. Collect experimental data by sensors and get series of U components of collected data from VMD. (2) Select noiseless componentsaccording according to to VMD VMD adaptive method. Select noiseless components adaptivede-noising de-noising method. (3) Reconstruct chosen noiseless components and input using the ACC. Reconstruct chosen noiseless components and input using the ACC. (4) Collect several groups of data for training and testing, and realize the pipeline small leak Collect several groups of data for training and testing, and realize the pipeline small detection.

leak detection.

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Figure 4. Flowchart of the small leakage detection method. Figure4.4.Flowchart Flowchart of of the small Figure small leakage leakagedetection detectionmethod. method.

5. Experimental Results and Analysis 5. Experimental Resultsand andAnalysis Analysis 5. Experimental Results 5.1. Experimental Apparatus and Instrumentations Experimental Apparatusand andInstrumentations Instrumentations 5.1.5.1. Experimental Apparatus The experimental of sensors, sensors,data dataacquisition acquisitioncards, cards, bearing pipelines The experimentalsetup setupwas wascomposed composed bearing pipelines andand The experimental setup was composedofof sensors, data acquisition cards, bearing pipelines computer. The pipe was a seamless steel pipe with an outer diameter of 108 mm and wall thickness TheThe pipepipe was awas seamless steel pipe with an with outer an diameter 108 mm of and wall thickness andcomputer. computer. a seamless steel pipe outer of diameter 108 mm and wall of 4.5 mm; and the leak testing was implemented basedon on11mm mmand and2 2mm mm holes. Under of 4.5 mm; and the leak testing was implemented based holes. Under thethe testtest thickness of 4.5 mm; and the leak testing was implemented based on 1 mm and 2 mm holes. Under pressure of of 1.0–2.0 conductedatataaflow flowrate rateofof3.13.1 m/s through internal pressure 1.0–2.0MPa, MPa,pipeline pipelinedeflation deflation was was conducted m/s through internal the test pressure of 1.0–2.0 MPa, pipeline deflation was conducted at a flow rate of 3.1 m/s through decompression. piezoelectric acceleration accelerationtransducers transducers used were decompression.The Thesensitivities sensitivities of of the the YD-82 YD-82 piezoelectric used were internal decompression. The2sensitivities of the YD-82 piezoelectric acceleration transducers used 2 2 2 2 22 2 2 2 2 the pC/ms pC/ms pC/ms pC/ms 167.2 165.8 160.4 , 189 and frequency response is from 0 0 pC/ms pC/ms pC/ms pC/ms 167.2 165.8 , ,160.4 189 and frequency response is isfrom were 167.2 pC/ms 165.8 pC/ms , 160.4 pC/ms , 189 pC/ms andthe the frequency response from KHz 10 KHz. Theoutput outputwas was converted the charge amplifier. Experimental tototo 1010 KHz. The voltage signal by the charge amplifier. Experimental 0KHz KHz KHz. The output wasconverted convertedtotoaavoltage voltagesignal signalby by the charge amplifier. Experimental data were collected by a NI USB-6259 data acquisition card at a rate of 5 Ks/s. The experimental data were werecollected collectedbybya NI a NI USB-6259 data acquisition at a of rate of 5 Ks/s. The experimental data USB-6259 data acquisition cardcard at a rate 5 Ks/s. The experimental setup setup is shown setup is shown inin Figure is shown in Figure 5.Figure5.5.

Figure 5. Experiment system schematic.

Figure 5. Experiment system schematic. Using the experimental platform, 1 mm leak signals, 2 mm leak signals and the signals under normal (non-leak)platform, were collected, are presented in Figure Usingconditions the experimental 1 mm and leakthey signals, 2 mm leak signals6.and the signals under

Using the experimental platform, 1 mm leak signals, 2 mm leak signals and the signals under normal conditions (non-leak) (non-leak) were were collected, collected, and and they they are are presented presentedin inFigure Figure6.6. normal conditions


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Figure 6. Signals collected by sensors. Figure6.6.Signals Signals collected collected by Figure by sensors. sensors.

U7 U7

U6 U6

U5 U5

U4 U4

U3 U3

U2 U2

U1 U1

5.2.5.2. Acoustic Emission Signal Acoustic Emission SignalDe-Noising De-Noising 5.2. Acoustic Emission Signal De-Noising The signal collected by one sensor under 11 mm leak was taken as an an example. example.The Theobtained obtained The signal collected sensor under mm taken The signal collected byby oneone sensor under 1 mm leakleak waswas taken as anasexample. The obtained VMD VMD results of that signal are shown in Figure 7. VMD results of that signal are shown in Figure 7. results of that signal are shown in Figure 7.

0

0

200 200

400 400

600 600

800 1000 1200 800 Sample 1000 dots 1200

1400 1400

1600 1600

1800 1800

2000 2000

Sample dots

Figure 7. VMD results of a 1 mm leak signal. Figure Figure 7. 7. VMD VMD results results of of aa 11 mm mm leak leak signal. signal.

Moreover, the signal components after VMD were processed by VMD adaptive de-noising Moreover, the signalcomponents components after VMD were processed VMD adaptive method. The the distances between theafter probability density function ofbythe original signalde-noising and the Moreover, signal VMD were processed by VMD adaptive de-noising method. method. The density distances the density probability density of theand original signal and the probability function of components were calculated (Figure signal 8). The distances between thebetween probability function of thefunction original the probability density probability density function of components were calculated (Figure 8). function of components were calculated (Figure 8).

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PDFdistance distance PDF

200 200

150 150

100 100

50 50

0 0U1 U1

U2 U2

U3 U3

U4 U4

U5 U5

U U components components

U6 U6

U7 U7

Figure Figure 8. 8. PDF PDF distance distance between between U U components components and and the the 11 mm mm leak leak signal. signal.

Frequencyshifts shifts frequency frequencyshifts shifts Frequency Frequencyshifts shifts Frequency

As density function of U can be be seen seen in in Figure Figure 8, 8, the the probability probability density density function function of of U U555 has has the the largest largest distance distance of of the the As it it can original signal. Therefore, the first four components were chosen as the noiseless components and original signal. signal. Therefore, Therefore,the thefirst firstfour fourcomponents components were chosen as the noiseless components and were chosen as the noiseless components and the the were as noise The first components were the remaining remaining three were chosen chosen as the the noise components. components. The first four four were components were remaining three three were chosen as the noise components. The first four components reconstructed, reconstructed, forming a reconstruction signal. Ambiguity function of the reconstructed signal reconstructed, forming a signal. reconstruction signal. Ambiguity of thesignal reconstructed signal was was forming a reconstruction Ambiguity function of the function reconstructed was calculated and calculated and the result is presented in Figure 9. calculated the result is presented in Figure 9. the result isand presented in Figure 9.

1mm 1mm leak leak signal signal

-3

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Non-leak Non-leak signal signal

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2mm 2mm leak leak signal signal

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-3 -3

-2 -2

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0 0

Time Time delay delay

1 1

Figure 9. Ambiguity Ambiguity function images images of de-noised de-noised signals. Figure Figure 9. 9. Ambiguity function function images of of de-noised signals. signals.

In have similar delays and frequency shifts, so Figure 9, 9, the theambiguity ambiguityfunctions functionsof threesignals signals have similar delays and frequency shifts, In Figure Figure 9, the ambiguity functions ofofthree three signals have similar delays and frequency shifts, so they could not be distinguished effectively. As a result, the ACC was proposed for extraction so they could distinguished effectively.AsAsa aresult, result,the theACC ACCwas was proposed proposed for for extraction extraction of they could notnot bebe distinguished effectively. of these three realization of small leak detection in pipelines. signals’ characteristics and realization of small leak detection in pipelines. these three realization of small leak detection in pipelines. 5.3. 5.3. Small Small Leakage Leakage Detection Detection with with ACC ACC

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5.3. Small Leakage Detection with ACC For comparison purposes, mean values and standard deviations (SD) of the ambiguity correlation coefficients of de-noised signals based on VMD and EMD were calculated, and the obtained values are presented in Tables 2 and 3, respectively. Sensors 2016, 16, 2116

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Table 2. Mean values and SD of ambiguity correlation coefficients using EMD method.

For comparison purposes, mean values and standard deviations (SD) of the ambiguity correlation coefficients of de-noised signals1#based on VMD2#and EMD were3#calculated, and the Data Group in Tables 2 and 3, respectively. obtained values are presented 1 mm Leak

Non-Leak

2 mm Leak

value 0.4074 correlation 0.3664 0.3042 2. Meanmean values and SD of ambiguity coefficients using EMD method. 1Table mm leak SD 0.0530 0.0629 0.0969 1#

2# 3# 0.2415 0.3650 Non-Leak 2 mm Leak 0.0340 0.0534 0.3664 0.3042 1 mm leak 0.0629 0.0969 0.2789 mean value SD 0.30420.0530 0.3650 2 mm leak mean value0.09690.3664 0.2415 0.3650 0.0452 SD 0.0534 Non-leak SD 0.0629 0.0340 0.0534 mean value 0.3042 0.3650 0.2789 2 mm leak Table 3. Mean values and SD ofSD ambiguity0.0969 correlation 0.0534 coefficients 0.0452 using VMD method. Group meanData value 0.3664 1 mm Leak SD 0.06290.4074 mean value

Non-leak

1# 2# 3# method Table 3. Mean values and SD of ambiguity correlation coefficients using VMD Data Group 1 mm Leak Non-Leak 2 mm Leak 1# 2# 3# Data Group mean value 0.7447 0.3134 0.1025 1 mm Leak Non-Leak 2 mm Leak 1 mm leak SD mean value0.07170.7447 0.1164 0.3134 0.1025 0.0969 1 mm leak 0.1164 0.0969 0.0685 mean value SD 0.31340.0717 0.8407 Non-leak SD mean value0.11640.3134 0.0240 0.8407 0.0685 0.0534 Non-leak SD 0.1164 0.0240 0.0534 mean value 0.1025 0.0685 0.2253 2 mm leak 0.0685 0.2253 0.0452 SD mean value0.09690.1025 0.0534 2 mm leak SD 0.0969 0.0534 0.0452

According to to results presented and According results presentedininTable Table2,2,EMD EMDcould couldnot notacquire acquire accurate accurate components components and eliminate noise interference due to the mode-mixing effect, resulting in a poor differentiation of mean eliminate noise interference due to the mode-mixing effect, resulting in a poor differentiation of values and SD ofand the SD ambiguity correlationcorrelation coefficient. Thus, it isThus, impossible to recognize different mean values of the ambiguity coefficient. it is impossible to recognize pipeline conditions. On the other hand, the VMD adaptive de-noising method can extract natural different pipeline conditions. On the other hand, the VMD adaptive de-noising method can extract modes of vibration separate components accurately. Therefore, the mean SD natural modes of and vibration andnoise separate noise components accurately. Therefore, thevalues mean and values of the correlation coefficients could becould distinguished clearly.clearly. Further comparison was andambiguity SD of the ambiguity correlation coefficients be distinguished Further comparison obtained by normal curves ofcurves the correlation coefficients’ mean values and SD, presented was obtained by distribution normal distribution of the correlation coefficients’ mean values and SD, in Tables 2 and and the obtained results are shown Figures 11, respectively. presented in 3, Tables 2 and 3, and the obtained resultsinare shown10 inand Figures 10 and 11, respectively. 8

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Figure 10. Normal distribution curves based on EMD: (a) for 1# case; (b) for 2# case; and Figure 10. Normal distribution on(a) EMD: for(b) 1#for case; (b) and for (c) 2# for case; and Figure 10.case. Normal distribution curvescurves based based on EMD: for 1#(a) case; 2# case; 3# case. (c) for 3# (c) for 3# case.

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Comparing the results presented in Figures 10 and 11, it can be concluded that the normal Comparing the results presented in Figures 10 and 11, it can be concluded that the normal Comparing the results presented in Figures 10 and degree 11, it can concluded that of the distribution curves can intuitively present the correlation and be recognition degree thenormal three distribution curves can intuitively present the correlation degree and recognition degree of the three distribution curves can intuitively present the correlation degree and recognition degree of the three

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signals Using the the EMD-based EMD-based de-noising signals in in the the ambiguity ambiguity domain. domain. Using de-noising method, method, the the normal normal distribution distribution curves could not be distinguished clearly because of the EMD mode mixing phenomenon, curves could not be distinguished clearly because of the EMD mode mixing phenomenon, while while the the VMD VMD can can eliminate eliminate the the mode mode mixing mixing effectively effectively in in the the decomposition decomposition process, process, thus, thus, the the VMD-based VMD-based de-nosing de-nosing method method can can distinguish distinguish the the three three states states of of the the signals signals and and the the normal normal distribution distribution curves. curves. Thirty groups of data were chosen for training and testing, of which twenty groups were used for Thirty groups of data were chosen for training and testing, of which twenty groups were used training, and ten were used testing. SVM, BP and ambiguity for training, andgroups ten groups werefor used for Three testing.classifiers, Three classifiers, SVM, BP and correlation ambiguity classifier, were used for data training and testing. Test results are shown in Figure 12.in Figure 12. correlation classifier, were used for data training and testing. Test results are shown 3

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(c) Figure 12. Classification of test figure: (a) obtained by ACC; (b) obtained by BP; and (c) obtained by SVM. Figure 12. Classification of test figure: (a) obtained by ACC; (b) obtained by BP; and (c) obtained by SVM.

In Figure 12, the training times of SVM, BP and ambiguity correlation classifier are 15 s, 25 s and 6 s, respectively. Compared to SVM and BP, the ambiguity correlation classifier achieves better In Figure 12, the training times of SVM, BP and ambiguity correlation classifier are 15 s, classification effect and requires a shorter training time, which is caused by the absence of parameter 25 s and 6 s, respectively. Compared to SVM and BP, the ambiguity correlation classifier achieves setting and the small computational load. Test accuracies of these three classifiers for 60 groups of better classification effect and requires a shorter training time, which is caused by the absence of data, wherein 40 were used for training and 20 were used for testing, are presented in Figure 13. parameter setting and the small computational load. Test accuracies of these three classifiers for As it can be seen in Figure 13, all three classifiers can distinguish the different conditions of 60 groups of data, wherein 40 were used for training and 20 were used for testing, are presented in pipelines, but compared to BP and SVM, the proposed classifier achieves the highest mean Figure 13. recognition rate and realizes the best small leak detection in pipelines, because of its small computational load and no parameter setting.

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100

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(c) Figure 13. 13. Test Test accuracy accuracy of of classifiers: classifiers: (a) (a) for for 11 mm mm leak; leak; (b) (b) for for non-leak; non-leak; and and (c) (c) for for 22 mm mm leak. leak. Figure

5.4. Discussion As it can be seen in Figure 13, all three classifiers can distinguish the different conditions of The experimental indicate proposed method can effectively detect small leaks in pipelines, but comparedresults to BP and SVM,that thethe proposed classifier achieves the highest mean recognition noisy environments. This improvement is due to the proposed VMD adaptive de-noising and rate and realizes the best small leak detection in pipelines, because of its small computational loadACC and approach. Compared no parameter setting. to the recursive “screening” mode of the EMD, VMD can non-recursively decompose a multi-component signals into a number of components and control the decomposition 5.4. Discussionconditions reasonably. Hence, the VMD adaptive de-noised method can effectively convergence eliminate the mode-mixing phenomenon with noise method immunity. to its nodetect parameter The experimental results indicate that thegood proposed canDue effectively smallsetting leaks and small computational load, the ACC method achieves better classification effects and shorter in noisy environments. This improvement is due to the proposed VMD adaptive de-noising and training times than the BP or methods.“screening” Despite themode advantages offered by the scheme ACC approach. Compared to SVM the recursive of the EMD, VMD canproposed non-recursively for effectively detecting small leaks in natural gas pipelines, it has however certain The decompose a multi-component signals into a number of components and control thelimitations. decomposition penalty parameters and number of components in the VMD decomposition process need to be convergence conditions reasonably. Hence, the VMD adaptive de-noised method can effectively prioritized, hence, our future research will focus on investigating how to adaptively set the eliminate the mode-mixing phenomenon with good noise immunity. Due to its no parameter setting parameters of the VMD method. and small computational load, the ACC method achieves better classification effects and shorter training times than the BP or SVM methods. Despite the advantages offered by the proposed scheme for 6. Conclusions effectively detecting small leaks in natural gas pipelines, it has however certain limitations. The penalty parameters number of components the VMD decomposition process need and to beweak prioritized, Due to and the complicated surroundinginenvironment, large noise disturbances, signals hence, focus on investigating howsignals to adaptively set the parameters of the duringour thefuture small research leakage will of pipelines, pipeline-leakage have unobvious characteristics. VMD method. A small leak detection method based on VMD and ACC is proposed in this paper. For the non-stationary signals with strong noise, the VMD adaptive de-noising method is proposed according to the signal probability density function in order to process the signal and to acquire the

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6. Conclusions Due to the complicated surrounding environment, large noise disturbances, and weak signals during the small leakage of pipelines, pipeline-leakage signals have unobvious characteristics. A small leak detection method based on VMD and ACC is proposed in this paper. For the non-stationary signals with strong noise, the VMD adaptive de-noising method is proposed according to the signal probability density function in order to process the signal and to acquire the noiseless components. Noiseless components were then reconstructed successfully, forming the de-noised signals. Furthermore, in order to overcome the problems of traditional classifiers, such as heavy computational load and abundant parameter settings, the ambiguity correlation classifier is proposed for training and testing of the reconstructed signals. According to obtained experimental results, the proposed method can detect small pipeline leakages and achieve a higher mean detection rate than the classical SVM and BP methods. Acknowledgments: The authors gratefully acknowledge the support provides for this research by the National Natural Science Foundation Project of China (No. 61374219), a grant from Natural Science Foundation Project of Hebei province (No. E2016203223), Tianjin Research Program of Application Foundation and Advanced Technology (No. 14JCZDJC32300), Specialized research fund for the doctoral program of higher education (20130032130001), National Key Research and Development Program (2016YFC0802103). Author Contributions: Qiyang Xiao and Jian Li conceived and designed the experiments; Zhiliang Bai and Jiedi Sun performed the experiments and analyzed the data; Zhoumo Zeng and Nan Zhou provided guidance and recommendations for this research. Jian Li contributed to the contents and writing of this manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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