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Leak location of pipelines based on characteristic entropy
Accepted Manuscript Leak location of pipelines based on characteristic entropy Lei Ni, Juncheng Jiang, Yong Pan, Zhirong Wang PII:
S0950-4230(14)00056-4
DOI:
10.1016/j.jlp.2014.04.004
Reference:
JLPP 2755
To appear in:
Journal of Loss Prevention in the Process Industries
Received Date: 14 January 2014 Revised Date:
24 March 2014
Accepted Date: 15 April 2014
Please cite this article as: Ni, L., Jiang, J., Pan, Y., Wang, Z., Leak location of pipelines based on characteristic entropy, Journal of Loss Prevention in the Process Industries (2014), doi: 10.1016/ j.jlp.2014.04.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Leak location of pipelines based on characteristic entropy Lei Ni, Juncheng Jiang1 , Yong Pan, Zhirong Wang Jiangsu Key Laboratory of Urban and Industrial Safety, College of Urban Construction and Safety Engineering, Nanjing Tech University, Nanjing, 210009, China
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Abstract: The leakage of oil/gas pipelines is one of the major factors to influence the safe operation of pipelines. So it is significant to detect and locate the exact pipeline leakage. A novel leak location method based on characteristic entropy is proposed to extract the input feature vectors. In this approach, the combination of wavelet packet and information entropy is called “wavelet packet characteristic entropy” (WP-CE). The combination of empirical mode decomposition and information entropy is called “empirical mode decomposition characteristic entropy” (EMD-CE). Both pressure signal and flow signal of low noise and high noise of pipeline leakage are decomposed to extract the characteristic entropy. The location of pipeline leak is determined by the combination of the characteristic entropy as the input vector and particle swarm optimization and support vector machine method (PSO-SVM). The results of proposed leak location method are compared with those of PSO-SVM based on physical parameters. Under the condition of high noise, the results of proposed leak location method are better than those of PSO-SVM based on physical parameters. Keywords: leak location; pipeline; characteristic entropy; wavelet packet; empirical mode decomposition
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1. Introduction Pipeline transportation has been widely used in every walk of life because of its special merits in transporting liquid, gas, slurry. However, more and more serious leak problems have not only affected the natural run but also made huge loss to human life and wealth. Currently, some methods and systems for pipeline leak detection have been developed. Ostapkowicz, P(Ostapkowicz 2014) presented an improved method based on negative pressure wave detection which used median filtering of the calculating deviations of pressure signals. Yang, J(Yang et al. 2013) extracted the sound signal of pipe and presented the neural-network approach for identification of pipeline leakage. Srirangarajan (Srirangarajan et al. 2013) used multiscale wavelet method to detect and locate pipe burst events in water distribution system. L. Molina-Espinosa.(Molina-Espinosa, Cazarez-Candia and Verde-Rodarte et al. 2013) established the transient model of an incompressible flow of pipes with leaks. The finite differences technique was used to resolve the model. Ayed Lazhar (Lazhar, Hadj-Taïeb et al. 2013) studied a single viscoelastic pipe by the transient analysis and the viscoelastic factor was considered by a generalized KelvinVoigt model. He also considered the presence of the two leaks in a pipe. In the above methods of pipeline leak location, intelligent algorithm and pattern recognition was one of the main methods. In this method, the extraction of input vector was very important. Salvatore Belsito (Belsito et al. 1998)proposed a leak-detection method based on artificial neural networks (ANN), which can detect and locate leak down to 1% of flow rates. This method could compensate for the operational variations and prevent spurious alarms by combining with adequate preprocessing of those data. The input feature vectors of this method were inlet and outlet flow rate, and the fluid pressures. Henrique(Da Silva et al. 2005)used fuzzy system to classify the running mode and identify the operational transients. The fuzzy system could identify the leakage better because of adjusted thresholds. It 1 corresponding author: JunchengJiang. E-mail address: [email protected]. Postal address: Mail box 13, No. 200 North Zhongshan Road, Nanjing Tech University, Nanjing, 210009, China. 1
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was adequate to evaluate a small-scale LPG pipeline monitoring case. The input feature vectors of this method were transient measured through average volumetric flow (Transqm) and transient measured through the origin–destination differential pressure variation (Transdp). But it was difficult to determine the thresholds of the input feature vectors. The Interactive Self-organizing Data Analysis Technique Algorithm (ISODATA) method was used to classify the normal pipeline and abnormal pipeline by Hu Jinqiu(Jinqiu et al. 2007). The abnormal pressure waves of pipeline leakage were detected by pressure transducers. Ten features extracted from samples are mean, effective value, peak value, root amplitude, mean square, root-mean-square, variance, and skewness in time-domain, peak amplitude and corresponding frequency point infrequency-domain. J. Izquierdo (Izquierdo et al. 2007) proposed a neuro-fuzzy approach to detect the pipeline leakage. The flow rate and piezometric heads of pipeline were extracted to the input feature vectors. WojciechTylman (Tylman, Kolczyński and Anders 2010)proposed a leak-detection method based on neural networks and Bayesian network to detect leaks of dielectric fluid in underground high-pressure and fluid-filled (HPFF) cables. The input feature vectors of this method were pressure, temperature and electric value. C.A. Laurentys (Laurentys et al. 2011) proposed a leak-detection method based on expert system. The input vectors of this method were flow, pressure and temperature. Santosh Kumar Mandal (Mandal, Chan and Tiwari et al. 2012) proposed a novel leak-detection method based on rough set theory and support vector machine (SVM). The input vectors were the normalized pressure and flow rate. Corneliu T.C. Arsene (Arsene, Gabrys and Al-Dabass et al. 2012)proposed a leak-detection method based on neural networks and graphs theory. The input vectors were head and flow. According to above analyses, the artificial neural network had practical limitations for small numbers of samples. The hyper-parameters of SVM were determined through experiences. At the same time, the pressure and flow rate of pipeline were chosen as the most used input vectors. They had definite physical meaning. In fact, the signal of pipeline leakage was an unsteady signal and easy to be interfered by its ambient noise. Besides, the correlation between input feature vectors and output values was poorer. In order to solve these problems, in this research, the input vectors of pressure and flow of pipeline leakage are extracted by information entropy (Cui et al. 2009). The information entropy combined with wavelet packet (WP) forms the wavelet packet characteristic entropy(Bokoski and Juricic 2012) (WP-CE). While the information entropy combined with empirical mode decomposition (EMD) forms the empirical mode decomposition characteristic entropy(Huang, Hu and Geng 2011) (EMD-CE).The methods of particle swarm optimization and support vector machine (PSO-SVM) (Ni, Jiang and Pan 2013)are employed as the location method in the system, which can recognize the different locations along with a pipeline effectively. The remainder of this paper is organized as follows: In Section 2, overview of WP, WP-CE, EMD EMD-CE and PSO-SVM algorithms is presented. Section 3 is the simulation study of pipeline leakage. Section 4 is the analysis of the performance of applied algorithms. Section 5 is the conclusions. 2 Basic theory 2.1 Wavelet packet Wavelet analysis can be used in multi-resolution analysis of time domain and frequency domain because of its good sense of localization. But the resolution of wavelet analysis is very poor when frequency is high. Wavelet packet decomposition can make multi-layer division for the frequency band of the fault signal and then can be further decomposed high frequency part of signal, which makes it more accurate in signal analysis. Wavelet packet transform can decompose signals into different frequency bands to choose adaptive frequency bands to overcome the disadvantages of wavelet transform (Qu et al. 2010). 2
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Fig.1 Schematic of three layer wavelet packet decomposition Wavelet packet decomposition has the following relationships: S=AAA3+DAA3+ADA3+DDA3+AAD3+DAD3+ADD3+DDD3. Wavelet packet decomposition can decompose the press and flow signal of pipeline leakage with the following recursion.
(1)
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u (t ) = 2 ∑ h(k )u (2t − k ) n 2n k u 2 n −1 (t ) = 2 ∑ g (k )u n (2t − k ) k Where, h(k) is high-pass filter and g(k) is low pass filter.
2.2 Wavelet packet characteristic entropy (WP-CE) Signal is decomposed into j layer wavelet packet coefficients. S(j,k) is wavelet packet decomposition sequence. K=0~2j-1. The wavelet packet decomposition of signal is regarded as a division of signal. The measure of the division of signal (Bokoski and Juricic 2012) is defined as:
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(i ) (i ) = NS F j k ∑ S F j k (i ) i
ε
( j ,k )
(2)
( , )
=1
( , )
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Where, SF(j,k)(i) is fourier transform value of S(j,k)(i). N is original signal length. According to the basic theory of entropy, wavelet packet characteristic entropy is defined as: N
H j , k = −∑ ε i =1
j ,k
(i ) log ε
j ,k
(i )
(k = 0 ~ 2 − 1) j
(3)
Hj,k is the j layer and the k-th wavelet packet characteristic entropy of signal. 2.3 Empirical mode decomposition EMD (Wu and Huang 2004; Yu, YuDejie and Cheng 2006), an adaptive method to decompose any data into a set of intrinsic mode function (IMF) components, is considered to be a breakthrough in the field of signal analysis in recent years. EMD is ideally suitable for analyzing data from non-stationary and nonlinear processes, while the non-stationary of press signal in pipeline leakage is obvious. So the EMD method can grasp the information of the signal characteristics more accurately and efficiently. Essentially, EMD algorithm is a numerical algorithm in which time-domain signal is decomposed by the frequency scale. The fluctuations of different scales or tendency are decomposed to produce a series of intrinsic mode functions with different characteristic scales. An intrinsic mode function (IMF) is a function which should meet the following conditions simultaneously (Huang et al. 1998): 3
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h j (t )−h j −1(t ) 2 h j (t )
2
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SD = ∑
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(1)In the whole data set, the number of extrema must be either equal to that of zero crossings, or at most differ in one. ; (2) At any point, the mean value of the envelope whether it is defined by the local maxima or the local minima must be zero. Under the above assumptions, IMF can be filtered out by EMD by the following steps: 1) Variables should be given initial value: r0(t)=x(t), i=1; 2) Extract the i-th IMF component: a) Set initial value of variables: h0(t)=ri(t), j=1; b) All local maxima and minima of hj-1(t) are confirmed; c) Local maxima and minima of hj-1(t) is interpolated using the cubic spline function and formed both Upper and lower envelopes line. d) Calculate the average of the upper and lower envelopes line, mj-1(t); e) Calculate the difference: hj(t)=hj-1(t)-mj-1(t); f) The standard deviation (SD) is used to judge each screening results:
i =0
(4)
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A typical value for SD can be set between 0.2 and 0.3. If SD satisfies the condition, stop counting and imfi(t)=hj(t), Otherwise, enter a loop computing from (B) and j=j+1 until SD is between 0.2 and 0.3. 3) ri(t)=ri-1(t)-imfi(t); 4) The sifting process is repeated until all, or the required numbers of IMFs, are extracted from the signal. In the first case the sifting process is terminated when the residual rn(t) of the sifting process has less than 3 extrema. The original signal x(t) can be expressed as a sum of extracted imfi(t) and the residual of the sifting process rn(t): n
x(t ) = ∑ imf (t ) + r n (t ) i
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2.4 Empirical mode decomposition characteristic entropy (EMD-CE) Signal is decomposed into several IMFs (IMF(a)).a=0-M, and M is the number of IMF. The IMF is regarded as a division of signal. The measure of the division of signal is defined as(Huang, Hu and Geng 2011):
IMF (i ) ε (i ) = ∑ IMF (i )
(6)
F (a )
N
(a )
i =1
F (a )
Where, IMFF(a)(i) is i-th fourier transform value of IMF(a)(i). N is original signal length. According to the basic theory of entropy, empirical mode decomposition characteristic entropy is defined as:
= −∑ ε a (i ) log ε a (i ) N
H
a
i =1
4
(a = 0 − M )
(7)
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Ha is the empirical mode decomposition characteristic entropy of the a-th IMF. 2.5 The extraction of the wavelet packet characteristic entropy of pipeline leakage signal The wavelet packet entropy of pressure signal and flow signal is extracted as follows: (1) Signal decomposition: The signal is decomposed into three layers wavelet coefficients. (2) Signal reconstruction: The sequence of eight frequency bands is reconstructed. The sequence of wavelet packet reconstruction of pressure signal and traffic signal is get. Each reconstruction signal contains the original signal from low to high frequency information without information redundancy and omissions. (3) The wavelet packet characteristic entropy vectors of signal: the wavelet packet entropy of pressure signal and flow signal is extracted by equations (2) and (3) and then construct the feature vectors (T). T=[HP(3 0),HP 3,1 ,HP 3,2 ,HP 3,3 ,HP 3,4 ,HP 3,5 ,HP 3,6 ,HP 3,7 ,HF(3 0),HF 3,1 ,HF 3,2 ,HF 3,3 , HF 3,4 ,HF 3,5 ,HF 3,6 ,HF 3,7 ].Because the higher characteristic of wavelet packet entropy is inconvenient. So, the eigenvectors are normalized.
∑7 H 3,j j = 0
1/2
H =
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Vector “T” is the normalized wavelet packet feature vector:
(8)
H H H H H H H H T ' = 3, 0 , 3,1 , 3, 2 , 3,3 , 3, 4 , 3,5 , 3, 6 , 3, 7 H H H H H H H H
(9)
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2.6 The extraction of the empirical mode decomposition characteristic entropy of pipeline leakage signal (1) Signal decomposition: The signal is decomposed into a sum of IMFs; (2) The empirical mode decomposition characteristic entropy vectors of signal: the EMD-CE of pressure signal and flow signal is extracted by equations (6) and (7) and then construct the feature vectors (T). T=[imfHP1, imfHP2, imfHP3,...,imfHPn,imfHF1,imfHF2, imfHF3,... ,imfHFm]. Because the higher characteristic of EMD-CE is inconvenient. So, the eigenvectors are normalized.
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1/2
(10)
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Vector “T” is the normalized wavelet packet feature vector:
T ' = imfH 1 ,imfH 2 ,imfH 3 ,...,imfH n H H H H
(11)
2.7 PSO-SVM method (1)Support vector machine (SVM) The support vector machine(Burges 1998) (SVM), which is based on structural risk minimization criterion to obtain a minimum actual risk, is a new machine learning algorithms. Its topology is determined by the support vector, and can overcome the defects of that of neural network method. SVM performs well in solving the practical problems of small and medium-sized sample, non-linear, high dimension and local minima points. (2)Algorithm of particle swarm optimization (Navalertporn and Afzulpurkar 2011) A group of random particles are initialized, and x and v denote the position and velocity of any particle respectively in the search space. Xi represents the position of the i-th particle in the D-dimensional search 5
ACCEPTED MANUSCRIPT space, while Vi represents the velocity of i-th particle in the D-dimensional search space. The best particle in the search space is recorded and represented as Pi=(pi1,pi2,…,piD) while the best particle in the group is recorded and represented as Pg=(pg1,pg2,….,pgD). Particle’s position and velocity are updated by the best particles according to the following equations. Repeat the front steps until the number of iterations reaches the predetermined value. id
= Ψ
v
id
+
c r (p 1
1
x
id
id
=
−
x
)+ c
x
id
id
+ v id
2
r (p 2
gd
−
x
id
)
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v
(12) (13)
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Where c1 and c2 are two acceleration constants regulating the relative velocities with respect to the best global and local positions.Ψ is the inertia weight (3)Parameter optimization method of SVM based on PSO The three major hyper-parameters C, σ and ε in SVM are optimized by PSO. The training process is described as follows(Ni, Jiang and Pan 2013): 1) Set up parameters of PSO for PSO–SVM. For PSO, set up the number of particle, maximum number of iterations, two acceleration constants (c1, c2) and inertia weight(Ψ). Initialize the velocity and position for each particle comprised of the hyper-parameters C, σ and ε. 2) Set the best position(Pi) from the particle with the minimal fitness in the swarm. 3) Train an SVM regression model with the corresponding hyper-parameters based upon cross validation in each candidate particle. 4) Update the velocity and position of each particle by using Eqs.(12) and (13) 5) Check the stopping criterion. If the generations don’t reached at the maximal number, then return to Step (4). Otherwise go to next step. 6) Terminate the algorithm and give the optimal hyper-parameters.
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2.8 Model validation Model validation is of crucial importance to pipeline leakage modeling. The calibration and predictive capability of a model of pipeline leakage should be tested through model validation. The most widely used correlation coefficient (R) can provide a reliable indication of the fitness of the model. In the present study, it is employed to validate the calibration capability of a model of pipeline leakage. As for the validation of predictive capability of a model of pipeline leakage, two basic principles (internal validation and external validation) are existed. The cross-validation (CV) is one of the most often used methods for internal validation. A good CV result (Q2) often indicates a good robustness and high internal predictive ability of a QSPR model(Golbraikh and Tropsha 2002). The internal predictive capability of a model is evaluated by leave-one-out cross-validation (Q2LOO) on the training set, which is calculated with the following equation(Gramatica, Pilutti and Papa 2004): 2
∧ y − y ∑ i i − ∑ y i − y
training
Q
2 LOO
= 1−
i =1
2
training i =1
(14)
∧
Where, yi,
y i , and
are the experimental, predicted, and mean values of the samples for the 6
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∧ ∑ yi − yi − ∑ y i − y tr
prediction
Q
2 ext
= 1−
i =1
2
prediction
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i =1
∧
Where, yi and
yi
are the experimental and predicted values of the samples for the prediction set,
−
and
(15)
y tr is the mean experimental values of the samples for the training set.
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Root mean square (RMS) is also selected as one of the parameters using in the model validation. 3. Simulation study For the case evaluated here, the main simulation parameters are presented as follows: length of pipeline, L=55km; pipe diameter, D=0.3414m;density of liquid, ρ=832kg/m3;inlet pressure, P(int)=1700kpa; outlet pressure, P(out)=1007kpa; Medium velocity, V=224m3/h; acoustic velocity, a=1100m/s. Besides, pipeline is divided into 50 sections, which the length is 1.1km. The Boundary conditions include the leak rate dw =5% and constant inlet pressure and outlet flow. The simulation process and results can be seen in the references(Ni, Jiang and Pan 2013).The results are shown in Fig.2 and Fig.3. 3.1Pipeline leak location under the condition of low noise
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1020000 1010000
outpress
1000000 990000 980000
3# 11# 21# 31# 41# 49#
960000 950000 940000 930000
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press(pa)
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920000 910000 900000 890000 880000 0
200
400
600
800
times(s)
Fig.2 Outlet press of different leak location
7
1000
1200
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inlet flow 1.76
49# 1.74
41# 31#
1.73
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inlet flow(m/s)
1.75
21# 11#
1.72
3# 1.71
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times(s)
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1000
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5000 0 -5000
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outpress (pa)
10000 0 -10000
400
3,0
200
3,1
0 1100000 1000000 900000 10000 0 -10000
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Fig.3 Inlet flow of different leak location (1) PSO-SVM method based on WP-CE
time(s)
Fig.4 Db5 wavelet packet decomposition coefficients of pressure signal
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3,5
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0.000 -0.005 0.005 0 0.000 -0.005 0.005 0 0.000 -0.005 0.005 0 0.000 -0.005 0.002 0 0.000 -0.002 0
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1.80 1.75 1.70 0.02 0 0.00 -0.02 0 0.005 0.000 -0.005 0.005 0
3,0
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time(s)
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Fig.5 Db5 wavelet packet decomposition coefficients of flow signal The wavelet packet characteristics entropy of the signal is extracted by following the steps in section 2.3. Fig.4 and Fig.5 show the wavelet packet decomposition coefficients of pressure signal and flow signal respectively when the leakage of pipe located at 3# hole. Both pressure signal and flow signal are decomposed by db5 wavelet packet. Pipeline measurement signal mutation can be seen clearly from node (3, 1). According to the above analysis, the normalized wavelet packet characteristic entropy in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 is training set. The normalized wavelet packet characteristic entropy s in No.16, 21, 29 and 36 is test set. Then, the PSO algorithm is implemented to find the optimal hyper-parameters C, σ and ε for eigenvectors model by using 3-fold cross validation. At the same time, the leak locations of pipelines are determined by SVM. The related parameters of C, σ and ε for RBF kernel function are varied in the arbitrarily fixed ranges[0.1, 100], [0.01, 1000] and [0.00001, 1]. Swarm size S=30, inertia weight Ψ=0.9, acceleration constants c1=1.6 and c2=1.5, and maximum number of iterations fixed at 300.
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Fig.6 Convergence curve of PSO-SVM method based on WP-CE
10
training set prediction set
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-10
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The leak locations of literature value
Fig.7 Distribution of residuals
10
50
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training set prediction set
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30
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The leak locations of calculated values by WP-CE-PSO-SVM
50
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The leak locations of literature value
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Fig.8 The results of PSO-SVM method based on WP-CE
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The convergence process of PSO is shown in Fig.6. The convergence curve shows the best fitness for the training samples which are obtained from the minimal fitness of the swarm in each generation. Relying on the PSO algorithm, make C= 100, σ= 0.01 and ε= 0.01. The regression results of SVM are shown in Table 1 and Table 2. The WP-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit good performance of the training SVM in Fig.8. As shown in Fig.7, the residuals are randomly distributed on both sides of zero line, so the predicted model which is established by PSO-SVM can be considered to be steady reasonably. Table 1 WP-CE and predict value of outlet press
0)
0.0642 0.0676
HP
HP
HP
HP
HP
HP
3,1
3,2
3,3
3,4
3,5
3,6
3,7
EP
(3
HP
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HP
0.3775
0.3836
0.3904
0.3417
0.3727
0.3845
0.3876
Location of WP-CE
3.0101
Location of BPNN(Ni, Jiang and Pan 2013) 7.7478
The literature value(Ni, Jiang and Pan 2013) 3
0.369
0.3855
0.3846
0.3499
0.3769
0.3808
0.3915
9.1653
8.6628
6
0.3775
0.3845
0.3819
0.3473
0.3777
0.3821
0.3868
13.5961
9.9509
9
0.3762
0.3823
0.3879
0.344
0.3778
0.378
0.3905
13.3115
11.0977
11
0.3743
0.382
0.3875
0.3498
0.3776
0.3748
0.3909
15.2761
12.5525
13
0.0772
0.3703
0.3763
0.3888
0.3472
0.3793
0.3877
0.3866
18.1037
15.476
18
0.0768
0.377
0.3849
0.3871
0.3494
0.3717
0.3788
0.3877
18.9899
19.1199
19
0.0801
0.374
0.3831
0.3945
0.3527
0.3686
0.3783
0.3846
25.5031
20.9519
23
0.0758
0.3763
0.378
0.3882
0.3518
0.375
0.3814
0.3864
16.0101
28.6404
16
0.0791
0.366
0.3803
0.387
0.3527
0.3793
0.3869
0.384
22.0732
24.9947
21
0.0811
0.3905
0.3852
0.3814
0.3495
0.3757
0.3772
0.3763
27.2179
26.4761
29
0.0695 0.0733 0.075
11
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HF 0)
HF
HF
HF
HF
HF
HF
3,1
3,2
3,3
3,4
3,5
3,6
3,7
Location of WP-CE
BPNN(Ni, Jiang and Pan 2013)
The literature value(Ni, Jiang and Pan 2013)
0.3776
0.3812
0.3915
0.3477
0.3779
0.3802
0.3864
3.0101
7.7478
3
0.0362
0.378
0.3797
0.3886
0.3485
0.3754
0.3838
0.3885
9.1653
8.6628
6
0.0373
0.378
0.3842
0.3911
0.3414
0.3734
0.3852
0.3883
13.5961
9.9509
9
0.0377
0.3703
0.3861
0.3851
0.35
0.3775
0.3813
0.392
13.3115
11.0977
11
0.0376
0.3785
0.3855
0.3825
0.3477
0.3782
0.3827
0.3873
15.2761
12.5525
13
0.0385
0.3769
0.3835
0.3889
0.344
0.3784
0.3786
0.3915
18.1037
15.476
18
0.0384
0.3756
0.3833
0.3891
0.3496
0.375
0.3765
0.3931
18.9899
19.1199
19
0.0388
0.3724
0.3798
0.3929
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0.3782
0.386
0.0384
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0.3797
0.393
0.3442
0.3783
0.3861
0.039
0.3767
0.3835
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0.3441
0.3785
0.3785
0.0384
0.3778
0.38
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0.3487
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(3
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Location of
25.5031
20.9519
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0.3882
16.0101
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3.2 Pipeline leak location under the condition of high noise The previous research is conducted under the condition of low noise. But in actual situation, there are varying noises in output signal obtained from pipeline leakage including the environmental noise, the noise of fluid inside and the influence of the instrument itself. So in this section, Gaussian white noise is superimposed on the original low noise signal to simulate the actual signal in MATLAB. Signal superposition results are shown in the Fig.9 and Fig.10.
1040000
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Fig.10 Inlet flow with white noise
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(1) PSO - SVM method based on the physical parameters The final outlet press value and the value of maximum of inlet flow are extracted as eigenvectors from the above analysis. The location of leak hole is output value. The locations of leak holes in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 are training set. The locations of leak holes in No.16, 21, 29 and 36 are test set. Then, the PSO algorithm is implemented to find the optimal hyper-parameters C, σ and ε for eigenvectors model by using 3-fold cross validation. At the same time, the leak locations of pipelines are determined by SVM. The related parameters of C, σ and ε for RBF kernel function are varied in the arbitrarily fixed ranges[0.1, 100], [0.01, 1000] and [0.00001, 1]. Swarm size S=30, inertia weight Ψ=0.9, acceleration constants c1=1.6 and c2=1.5, and maximum number of iterations fixed at 300. 300
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The leak locations of literature value
training set prediction set
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The–leak–locations–of–calculated–values –by–PS0-SVM
Fig.12 Distribution of residual
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Fig.13 The results of PSO-SVM
The convergence process of PSO is shown in Fig.11. Relying on the PSO algorithm, C=2872.5, σ= 0.01 and ε=1.8552 are defined. The regression results of SVM are shown in Table 3 and Fig.13, and outlet press and inlet flow are two elements of an eigenvector. As shown in Fig.12, all four prediction sets are on the same side of the zero line, so the stability of the model is poorer.
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ACCEPTED MANUSCRIPT Table 3 PSO-SVM based on physical parameters Outlet press(pa)
Inlet flow(m/s)
The literature value(Ni, Jiang and Pan 2013)
Location of PSO-SVM
1 2 3 4 5 6 7 8 9
948687.7 962460.3 951595.6 943639.6 940361.6 927427.2 944024.8 899926.2 935368.8
1.7673 1.7674 1.7671 1.7683 1.7694 1.7694 1.7715 1.7708 1.7725
6 11 16 21 26 31 36 41 46
13.3365 9.9885 11.9510 19.0496 25.0281 28.7144 33.5005 42.8554 40.0903
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(2) PSO-SVM method based on WP-CE
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Fig.14 Db4 wavelet packet decomposition coefficients of pressure signal with white noise
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The–leak–locations–of–calculated–values– of–WP-CE-PSO-SVM
Fig.15 Db5 wavelet packet decomposition coefficients of flow signal with white noise The signal with white noise is extracted the wavelet packet characteristics entropy by following the steps in section 2.3. Fig.14 and Fig.15 show the wavelet packet decomposition coefficients of pressure signal and flow signal respectively when the leakage of pipe located at 3# hole. The choice of mother wavelet has an important influence on the results of the analysis. Pressure signal is decomposed by db4 wavelet packet and flow signal is decomposed by db5 wavelet packet. Pipeline measurement signal mutation can be seen clearly from node (3,1). The same as the low noise situation, the high noise signal of pipeline leakage is extracted by wavelet packet characteristic entropy and calculated by PSO-SVM.
training set prediction set
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Fig.16 The results of PSO-SVM method based onWP-CE 16
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training set prediction set
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residuals
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Relying on the PSO algorithm, C= 10000, σ= 2358.7 and ε= 2.9251 are made. The regression results of SVM are shown in Table 4 and Table 5. The WP-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit good performance of the training SVM in Fig.16. As shown in Fig.17, the residuals are randomly distributed on both sides of zero line, so the predicted model which is established by PSO-SVM can be considered to be steady reasonably. Table 4 pipeline leak location of outlet press with WP-CE HP
3,1
3,2
3,3
0.0777
0.3743
0.3718
0.0706
0.3728
WP-CE-
HP
HP
3,4
3,5
3,6
3,7
0.3906
0.3579
0.3777
0.3780
0.3866
6
8.9255
0.3894
0.3813
0.3440
0.3820
0.3806
0.3873
11
13.9250
0.3782
0.3896
0.3897
0.3571
0.3679
0.3692
0.3853
16
18.9253
0.3728
0.3834
0.3908
0.3543
0.3734
0.3769
0.3848
21
19.4951
0.3771
0.3825
0.3928
0.3493
0.3702
0.3820
0.3820
26
23.0746
0.3724
0.3782
0.3844
0.3563
0.3852
0.3732
0.3865
31
28.0751
0.0851
0.3751
0.3917
0.3874
0.3472
0.3705
0.3780
0.3845
36
33.0750
0.0874
0.3784
0.3749
0.3905
0.3396
0.3754
0.3810
0.3933
41
38.0748
0.0789
0.3759
0.3831
0.3918
0.3386
0.3720
0.3802
0.3932
46
43.0755
0)
0.0754 0.0787 0.0796 0.0809
HP
The literature
HP
(3
HP
EP
HP
AC C
HP
17
value(Ni, Jiang and Pan 2013)
PSO-SVM
ACCEPTED MANUSCRIPT
Table 5 pipeline leak location of inlet flow with WP-CE WP-CE-
HF
HF
HF
HF
HF
HF
3,1
3,2
3,3
3,4
3,5
3,6
3,7
0.0366
0.3757
0.3841
0.3878
0.3495
0.3743
0.3828
0.3883
6
8.9255
0.0382
0.3753
0.3888
0.3865
0.3463
0.3770
0.3800
0.3882
11
13.9250
0.0375
0.3773
0.3903
0.3858
0.3470
0.3755
0.3791
0.3872
16
18.9253
0.0376
0.3716
0.3804
0.3906
0.3433
0.3792
0.3801
0.3964
21
19.4951
0.0368
0.3802
0.3903
0.3893
0.3505
0.3730
0.3730
0.3861
26
23.0746
0.0390
0.3787
0.3799
0.3903
0.3496
0.3739
0.3820
0.3880
31
28.0751
0.0394
0.3764
0.3783
0.3868
0.3443
0.3845
0.3875
0.3840
36
33.0750
0.0384
0.3784
0.3769
0.3951
0.3401
0.3765
0.3832
0.0379
0.3780
0.3775
0.3850
0.3518
0.3738
0.3768
SC
The literature
HF
0)
200 200
IMF9 IMF10
41
38.0748
0.3994
46
43.0755
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Fig.18 The IMFs of pressure signal with white noise
18
PSO-SVM
0.3911
400
TE D
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EP
20000 0 -20000 0 20000 0 -20000 0 30000 0 -30000 0 20000 0 -20000 0 30000 0 -30000 0 20000 0 -20000 20000 0 0 -20000 20000 0 0 -20000 20000 0 0 -20000 20000 0 0 -20000 0
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IMF8
IMF7
IMF6
IMF5
IMF4
IMF3
IMF2
IMF1
(3) PSO-SVM method 0based on EMD-CE 200
Pan 2013)
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(3
value(Ni, Jiang and
M AN U
HF
IMF4
0.01 0.00 -0.01
IMF5
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IMF6
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IMF7
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Fig.19 The IMFs of flow signal with white noise The signal with white noise is extracted the IMFs by following the steps in section 2.4. Fig.18 and Fig.19 show the IMFs of pressure signal and flow signal respectively when the leakage of pipe located at 3# hole. The pressure signal has ten IMFs while the flow signal has eight. Firstly, the first eight IMFs of pressure signal and all the eight IMFs of flow signal are selected to extract the characteristic entropy by following the steps in section 2.6.The results are shown in table 6 and table 7.
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Table 6 EMD-CE of outlet press imfHP2
imfHP3
imfHP4
imfHP5
imfHP6
imfHP7
imfHP8
The leak locations of literature value(Ni, Jiang and Pan 2013)
0.4634
0.4222
0.3996
0.3668
0.3124
0.3002
0.2545
0.2457
6
0.5135
0.4287
0.3821
0.3416
0.3206
0.2593
0.2515
0.2379
11
0.4761
0.4132
0.3787
0.3559
0.3239
0.3006
0.2637
0.2602
16
0.4559
0.4359
0.3989
0.3723
0.3264
0.3068
0.2541
0.1976
21
0.4740
0.4348
0.4038
0.3673
0.2975
0.2838
0.2462
0.2423
26
0.4831
0.4261
0.3933
0.3380
0.2939
0.2966
0.2924
0.2370
31
0.4655
0.4281
0.3983
0.3714
0.3269
0.2965
0.2282
0.2379
36
0.4704
0.4322
0.4060
0.3609
0.3149
0.3020
0.2408
0.2202
41
0.4883
0.4578
0.4258
0.3932
0.2480
0.2383
0.2369
0.2041
46
M AN U
SC
imfHP1
imfHF2
imfHF3
imfHF4
imfHF5
imfHF6
imfHF7
imfHF8
The leak locations of literature value(Ni, Jiang and Pan 2013)
0.5459
0.4752
0.3934
0.3323
0.2955
0.2537
0.2010
0.1371
6
0.5479
0.4619
0.4023
0.3091
0.3007
0.2531
0.2291
0.1487
11
0.5441
0.4889
0.4390
0.3651
0.2549
0.2229
0.1484
0.0476
16
0.5878
0.4956
0.4000
0.3005
0.5007
0.4657
0.4228
0.3615
0.2729
0.2351
0.1616
0.0531
21
0.3107
0.2393
0.2263
0.1340
26
0.5552
0.4725
0.4146
0.3530
0.2632
0.2298
0.2188
0.0455
31
0.5221
0.4525
0.4022
0.3754
0.2678
0.2363
0.2168
0.2130
36
0.5527
0.4597
0.3941
0.3337
0.2615
0.2397
0.2210
0.2046
41
0.5428
0.4828
0.4405
0.3663
0.2581
0.1837
0.2046
0.0439
46
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EP
imfHF1
TE D
Table 7 EMD-CE of inlet flow
20
ACCEPTED MANUSCRIPT According to the above analysis, the normalized EMD-CE in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 is the training set. The normalized EMD-CE in No.16, 21, 29 and 36 is the test set. Relying on the PSO algorithm, C= 1000, σ=5.9814 and ε= 0.01 are made. The regression results of SVM are shown in Fig. 20. The EMD-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit bad performance of the training SVM in Fig.20.
RI PT
training set prediction set
50 45 40 35
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Fig. 20 the results of PSO-SVM method based on EMD-CE Second, all the IMFs of pressure signal and flow signal are selected to extract the characteristic entropy by following the steps in section 2.6. The results are shown in Table 8 and Table 9.
21
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Table 8 EMD-CE of outlet press
0.3827 0.3665 0.3605 0.3894 0.3921 0.3747 0.3787 0.3919 0.4205
imfHP4 0.3512 0.3276 0.3388 0.3634 0.3566 0.3220 0.3531 0.3484 0.3883
imfHP5 0.2991 0.3075 0.3084 0.3187 0.2889 0.2800 0.3108 0.3039 0.2449
imfHP6 0.2875 0.2487 0.2862 0.2995 0.2755 0.2825 0.2819 0.2915 0.2353
imfHP7
imfHP8
0.2437 0.2412 0.2511 0.2481 0.2391 0.2786 0.2170 0.2324 0.2339
0.2353 0.2282 0.2477 0.1929 0.2353 0.2258 0.2262 0.2125 0.2015
imfHP9
imfHP10
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0.4043 0.4112 0.3933 0.4255 0.4222 0.4059 0.4070 0.4172 0.4521
imfHP3
0.2203 0.2142 0.2240 0.1853 0.1932 0.2204 0.2267 0.1968 0.1144
SC
0.4438 0.4925 0.4532 0.4450 0.4602 0.4603 0.4425 0.4540 0.4821
imfHP2
M AN U
imfHP1
The leak locations of literature value(Ni, Jiang and Pan 2013)
0.1852 0.1848 0.2089 0.1132 0.1409 0.2095 0.2116 0.1720 0.1090
6 11 16 21 26 31 36 41 46
Table 9 EMD-CE of inlet flow imfHF2
imfHF3
imfHF4
imfHF5
0.5459 0.5479 0.5441 0.5878 0.5007 0.5552 0.5221 0.5527 0.5428
0.4752 0.4619 0.4889 0.4956 0.4657 0.4725 0.4525 0.4597 0.4828
0.3934 0.4023 0.4390 0.4000 0.4228 0.4146 0.4022 0.3941 0.4405
0.3323 0.3091 0.3651 0.3005 0.3615 0.3530 0.3754 0.3337 0.3663
0.2955 0.3007 0.2549 0.2729 0.3107 0.2632 0.2678 0.2615 0.2581
imfHF6
AC C
EP
TE D
imfHF1
0.2537 0.2531 0.2229 0.2351 0.2393 0.2298 0.2363 0.2397 0.1837
22
imfHF7
imfHF8
0.2010 0.2291 0.1484 0.1616 0.2263 0.2188 0.2168 0.2210 0.2046
0.1371 0.1487 0.0476 0.0531 0.1340 0.0455 0.2130 0.2046 0.0439
The leak locations of literature value(Ni, Jiang and Pan 2013) 6 11 16 21 26 31 36 41 46
ACCEPTED MANUSCRIPT
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training set prediction set
50
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The–leak–location–of–calculated–value –of–all–the–EMD-CE
According to the above analysis, the normalized EMD-CE in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 is the training set. The normalized EMD-CE in No.16, 21, 29 and 36 is the test set. Relying on the PSO algorithm, C= 1000, σ=31.2895 and ε= 2.5844 are made. The regression results of SVM are shown in Fig.21. The EMD-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit good performance of the training SVM in Fig.21.As shown in Fig. 22, the residuals are randomly distributed on both sides of zero line, so the predicted model which is established by PSO-SVM can be considered to be steady reasonably.
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Fig. 21 The results of PSO-SVM based on EMD-CE 10 8 6
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training set prediction set
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The leak locations of literature value
Fig.22 Distribution of residuals 4 Discussion The results of different pipeline leak positioning methods are processed. The correlation coefficients 23
ACCEPTED MANUSCRIPT of training set and test set, Cross validation (Q2LOO Q2ext) and RMS are calculated to show in the following table. Table 10 performance comparison with different methods Training set
Model
RMS
Rext
Q2ext
RMS
BPNN
0.9661
0.9299
3.8701
0.5023
0.1211
7.1561
PSO-SVM
0.9998
0.9996
0.2959
0.9999
0.9995
0.1721
PSO-SVM method based on WP-CE
0.9946
0.9826
1.9274
PSO-SVM
0.9511
0.9005
4.611
PSO-SVM method based on WP-CE
0.9948
0.9624
2.8326
PSO-SVM based on part of EMD-CE
0.7873
0.5835
9.4316
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LOO
PSO-SVM based on all the EMD-CE
0.99
0.9588
2.9675
0.9914
0.9814
1.0402
0.9869
0.7726
3.6401
0.9588
0.9046
2.3575
0.9638
0.8138
3.2932
0.974
0.8854
2.5843
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Q
Prediction set
M AN U
Low noise
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Under the condition of low noise, the results of PSO-SVM method based on the physical parameters are better than those of PSO-SVM method based on WP-CE from the Table 10 and are better than those of BPNN method. But when the noise is high, the results of PSO-SVM method based on WP-CE and PSO-SVM method based on all the EMD-CE are better than those of PSO-SVM method based on the physical parameters while the results of PSO-SVM method based on part of EMD-CE are worse than those of PSO-SVM method based on the physical parameters. Under the condition of low noise, the outlet pressure and inlet flow value of different leakage can be distinguished easily. WP-CE is a signal processing method. It is not obvious that the relationship between WP-CE and output value is linear or nonlinear. So, the correlation of PSO-SVM based on physical parameters is better than that of PSO-SVM method WP-CE. In fact, as a general machine learning method, the PSO-SVM is based on the structural risk minimization principle, which minimizes an upper bound of the generalization error rather than minimizes the training error. So, the PSO-SVM has better generalization performance than ANN. Moreover, compared with ANN, once corresponding parameters are specified, the solution of SVM is definite and reproducible, which is clearly superior to ANN. When the noise is high, considering of the difficulties to identify the outlet pressure and inlet flow, the results of PSO-SVM method based on physical parameters are poor. The high frequency noise of signal is separated by WP-CE. The matching degree of low frequency signal and the original signal is higher. EMD method is based on the local feature of the signal, and can decompose signal adaptively into several intrinsic mode functions (IMFs)according to its characteristic time scale. So the results of PSO-SVM method based on all the EMD-CE and PSO-SVM method based on WP-CE are better than those of PSO-SVM method based on physical parameters. Although the first several IMFs have described the characteristic of the signal basically, the correlation of PSO-SVM method based on part of EMD-CE is worse than that of PSO-SVM method based on all the EMD-CE. So, the results of PSO-SVM method based on part of the EMD-CE are worse than those of PSO-SVM method based on all the EMD-CE. 5 Conclusions Characteristics entropy is presented for the application of the pipeline leak detection. The characteristic entropy of pipeline leakage signal is extracted as the input vector. The location of the pipeline 24
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Nomenclatures u(t) Wavelet packet decomposition sequence h(k) High-pass filter g(k) Low pass filter S(j,k) Wavelet packet decomposition sequence SF(j,k)(i) Fourier transform value of S(j,k)(i) N Original signal length
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leakage is determined by the combination of characteristic entropy and PSO-SVM. The results of this method are compared with those of PSO-SVM method based on physical parameters. The condition of high noise is defined to simulate the condition of actual pipeline leakage. In this case, the results of PSO-SVM based on characteristics entropy are better than those of PSO-SVM based on physical parameters. In the characteristics entropy method, PSO-SVM method based on WP-CE needed to choose a suitable mother function of wavelet, but that based on EMD-CE don’t need. The results of PSO-SVM method based on WP-CE with the suitable mother function of wavelet are close to those of PSO-SVM method based on all the EMD-CE. Therefore, PSO-SVM method based on EMD-CE is more convenient. So, the leak location method of pipeline based on characteristic entropy is an effective method. It can improve the processing ability of pipeline leakage signal effectively. This method can also provide the fundamental input parameter for leak location of pipeline.
The j layer and the kth wavelet packet characteristic entropy of signal
(i )
The measure of the division of signal
Initial value of variables The residual of the sifting process ith fourier transform value of IMF(a)(i)
Ha
The empirical mode decomposition characteristic entropy of the a-th IMF The feature vectors of pressure signal The feature vectors of flow signal The normalized wavelet packet feature vector The position of the i-th particle The velocity of i-th particle The best particle in the search space The best particle in the group Acceleration constants Inertia weight Leave-one-out cross-validation on the training set Leave-one-out cross-validation on the prediction set
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Acknowledgements The authors are grateful for the support given by Jiangsu Graduate Scientific Innovation Projects (CXLX11_0380) and Jiangsu Natural Science Foundation of China (BK2007587).
References: 25
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►The characteristic entropy of pipeline leakage signal is extracted as the input vector. ►The characteristic entropy combines with PSO-SVM method. ►In high noise condition, the results of PSO-SVM based on characteristics entropy are better. ►PSO-SVM method based on EMD-CE is more convenient.
S0950-4230(14)00056-4
DOI:
10.1016/j.jlp.2014.04.004
Reference:
JLPP 2755
To appear in:
Journal of Loss Prevention in the Process Industries
Received Date: 14 January 2014 Revised Date:
24 March 2014
Accepted Date: 15 April 2014
Please cite this article as: Ni, L., Jiang, J., Pan, Y., Wang, Z., Leak location of pipelines based on characteristic entropy, Journal of Loss Prevention in the Process Industries (2014), doi: 10.1016/ j.jlp.2014.04.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Leak location of pipelines based on characteristic entropy Lei Ni, Juncheng Jiang1 , Yong Pan, Zhirong Wang Jiangsu Key Laboratory of Urban and Industrial Safety, College of Urban Construction and Safety Engineering, Nanjing Tech University, Nanjing, 210009, China
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Abstract: The leakage of oil/gas pipelines is one of the major factors to influence the safe operation of pipelines. So it is significant to detect and locate the exact pipeline leakage. A novel leak location method based on characteristic entropy is proposed to extract the input feature vectors. In this approach, the combination of wavelet packet and information entropy is called “wavelet packet characteristic entropy” (WP-CE). The combination of empirical mode decomposition and information entropy is called “empirical mode decomposition characteristic entropy” (EMD-CE). Both pressure signal and flow signal of low noise and high noise of pipeline leakage are decomposed to extract the characteristic entropy. The location of pipeline leak is determined by the combination of the characteristic entropy as the input vector and particle swarm optimization and support vector machine method (PSO-SVM). The results of proposed leak location method are compared with those of PSO-SVM based on physical parameters. Under the condition of high noise, the results of proposed leak location method are better than those of PSO-SVM based on physical parameters. Keywords: leak location; pipeline; characteristic entropy; wavelet packet; empirical mode decomposition
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1. Introduction Pipeline transportation has been widely used in every walk of life because of its special merits in transporting liquid, gas, slurry. However, more and more serious leak problems have not only affected the natural run but also made huge loss to human life and wealth. Currently, some methods and systems for pipeline leak detection have been developed. Ostapkowicz, P(Ostapkowicz 2014) presented an improved method based on negative pressure wave detection which used median filtering of the calculating deviations of pressure signals. Yang, J(Yang et al. 2013) extracted the sound signal of pipe and presented the neural-network approach for identification of pipeline leakage. Srirangarajan (Srirangarajan et al. 2013) used multiscale wavelet method to detect and locate pipe burst events in water distribution system. L. Molina-Espinosa.(Molina-Espinosa, Cazarez-Candia and Verde-Rodarte et al. 2013) established the transient model of an incompressible flow of pipes with leaks. The finite differences technique was used to resolve the model. Ayed Lazhar (Lazhar, Hadj-Taïeb et al. 2013) studied a single viscoelastic pipe by the transient analysis and the viscoelastic factor was considered by a generalized KelvinVoigt model. He also considered the presence of the two leaks in a pipe. In the above methods of pipeline leak location, intelligent algorithm and pattern recognition was one of the main methods. In this method, the extraction of input vector was very important. Salvatore Belsito (Belsito et al. 1998)proposed a leak-detection method based on artificial neural networks (ANN), which can detect and locate leak down to 1% of flow rates. This method could compensate for the operational variations and prevent spurious alarms by combining with adequate preprocessing of those data. The input feature vectors of this method were inlet and outlet flow rate, and the fluid pressures. Henrique(Da Silva et al. 2005)used fuzzy system to classify the running mode and identify the operational transients. The fuzzy system could identify the leakage better because of adjusted thresholds. It 1 corresponding author: JunchengJiang. E-mail address: [email protected]. Postal address: Mail box 13, No. 200 North Zhongshan Road, Nanjing Tech University, Nanjing, 210009, China. 1
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was adequate to evaluate a small-scale LPG pipeline monitoring case. The input feature vectors of this method were transient measured through average volumetric flow (Transqm) and transient measured through the origin–destination differential pressure variation (Transdp). But it was difficult to determine the thresholds of the input feature vectors. The Interactive Self-organizing Data Analysis Technique Algorithm (ISODATA) method was used to classify the normal pipeline and abnormal pipeline by Hu Jinqiu(Jinqiu et al. 2007). The abnormal pressure waves of pipeline leakage were detected by pressure transducers. Ten features extracted from samples are mean, effective value, peak value, root amplitude, mean square, root-mean-square, variance, and skewness in time-domain, peak amplitude and corresponding frequency point infrequency-domain. J. Izquierdo (Izquierdo et al. 2007) proposed a neuro-fuzzy approach to detect the pipeline leakage. The flow rate and piezometric heads of pipeline were extracted to the input feature vectors. WojciechTylman (Tylman, Kolczyński and Anders 2010)proposed a leak-detection method based on neural networks and Bayesian network to detect leaks of dielectric fluid in underground high-pressure and fluid-filled (HPFF) cables. The input feature vectors of this method were pressure, temperature and electric value. C.A. Laurentys (Laurentys et al. 2011) proposed a leak-detection method based on expert system. The input vectors of this method were flow, pressure and temperature. Santosh Kumar Mandal (Mandal, Chan and Tiwari et al. 2012) proposed a novel leak-detection method based on rough set theory and support vector machine (SVM). The input vectors were the normalized pressure and flow rate. Corneliu T.C. Arsene (Arsene, Gabrys and Al-Dabass et al. 2012)proposed a leak-detection method based on neural networks and graphs theory. The input vectors were head and flow. According to above analyses, the artificial neural network had practical limitations for small numbers of samples. The hyper-parameters of SVM were determined through experiences. At the same time, the pressure and flow rate of pipeline were chosen as the most used input vectors. They had definite physical meaning. In fact, the signal of pipeline leakage was an unsteady signal and easy to be interfered by its ambient noise. Besides, the correlation between input feature vectors and output values was poorer. In order to solve these problems, in this research, the input vectors of pressure and flow of pipeline leakage are extracted by information entropy (Cui et al. 2009). The information entropy combined with wavelet packet (WP) forms the wavelet packet characteristic entropy(Bokoski and Juricic 2012) (WP-CE). While the information entropy combined with empirical mode decomposition (EMD) forms the empirical mode decomposition characteristic entropy(Huang, Hu and Geng 2011) (EMD-CE).The methods of particle swarm optimization and support vector machine (PSO-SVM) (Ni, Jiang and Pan 2013)are employed as the location method in the system, which can recognize the different locations along with a pipeline effectively. The remainder of this paper is organized as follows: In Section 2, overview of WP, WP-CE, EMD EMD-CE and PSO-SVM algorithms is presented. Section 3 is the simulation study of pipeline leakage. Section 4 is the analysis of the performance of applied algorithms. Section 5 is the conclusions. 2 Basic theory 2.1 Wavelet packet Wavelet analysis can be used in multi-resolution analysis of time domain and frequency domain because of its good sense of localization. But the resolution of wavelet analysis is very poor when frequency is high. Wavelet packet decomposition can make multi-layer division for the frequency band of the fault signal and then can be further decomposed high frequency part of signal, which makes it more accurate in signal analysis. Wavelet packet transform can decompose signals into different frequency bands to choose adaptive frequency bands to overcome the disadvantages of wavelet transform (Qu et al. 2010). 2
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Fig.1 Schematic of three layer wavelet packet decomposition Wavelet packet decomposition has the following relationships: S=AAA3+DAA3+ADA3+DDA3+AAD3+DAD3+ADD3+DDD3. Wavelet packet decomposition can decompose the press and flow signal of pipeline leakage with the following recursion.
(1)
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u (t ) = 2 ∑ h(k )u (2t − k ) n 2n k u 2 n −1 (t ) = 2 ∑ g (k )u n (2t − k ) k Where, h(k) is high-pass filter and g(k) is low pass filter.
2.2 Wavelet packet characteristic entropy (WP-CE) Signal is decomposed into j layer wavelet packet coefficients. S(j,k) is wavelet packet decomposition sequence. K=0~2j-1. The wavelet packet decomposition of signal is regarded as a division of signal. The measure of the division of signal (Bokoski and Juricic 2012) is defined as:
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ε
( j ,k )
(2)
( , )
=1
( , )
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Where, SF(j,k)(i) is fourier transform value of S(j,k)(i). N is original signal length. According to the basic theory of entropy, wavelet packet characteristic entropy is defined as: N
H j , k = −∑ ε i =1
j ,k
(i ) log ε
j ,k
(i )
(k = 0 ~ 2 − 1) j
(3)
Hj,k is the j layer and the k-th wavelet packet characteristic entropy of signal. 2.3 Empirical mode decomposition EMD (Wu and Huang 2004; Yu, YuDejie and Cheng 2006), an adaptive method to decompose any data into a set of intrinsic mode function (IMF) components, is considered to be a breakthrough in the field of signal analysis in recent years. EMD is ideally suitable for analyzing data from non-stationary and nonlinear processes, while the non-stationary of press signal in pipeline leakage is obvious. So the EMD method can grasp the information of the signal characteristics more accurately and efficiently. Essentially, EMD algorithm is a numerical algorithm in which time-domain signal is decomposed by the frequency scale. The fluctuations of different scales or tendency are decomposed to produce a series of intrinsic mode functions with different characteristic scales. An intrinsic mode function (IMF) is a function which should meet the following conditions simultaneously (Huang et al. 1998): 3
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(1)In the whole data set, the number of extrema must be either equal to that of zero crossings, or at most differ in one. ; (2) At any point, the mean value of the envelope whether it is defined by the local maxima or the local minima must be zero. Under the above assumptions, IMF can be filtered out by EMD by the following steps: 1) Variables should be given initial value: r0(t)=x(t), i=1; 2) Extract the i-th IMF component: a) Set initial value of variables: h0(t)=ri(t), j=1; b) All local maxima and minima of hj-1(t) are confirmed; c) Local maxima and minima of hj-1(t) is interpolated using the cubic spline function and formed both Upper and lower envelopes line. d) Calculate the average of the upper and lower envelopes line, mj-1(t); e) Calculate the difference: hj(t)=hj-1(t)-mj-1(t); f) The standard deviation (SD) is used to judge each screening results:
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A typical value for SD can be set between 0.2 and 0.3. If SD satisfies the condition, stop counting and imfi(t)=hj(t), Otherwise, enter a loop computing from (B) and j=j+1 until SD is between 0.2 and 0.3. 3) ri(t)=ri-1(t)-imfi(t); 4) The sifting process is repeated until all, or the required numbers of IMFs, are extracted from the signal. In the first case the sifting process is terminated when the residual rn(t) of the sifting process has less than 3 extrema. The original signal x(t) can be expressed as a sum of extracted imfi(t) and the residual of the sifting process rn(t): n
x(t ) = ∑ imf (t ) + r n (t ) i
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2.4 Empirical mode decomposition characteristic entropy (EMD-CE) Signal is decomposed into several IMFs (IMF(a)).a=0-M, and M is the number of IMF. The IMF is regarded as a division of signal. The measure of the division of signal is defined as(Huang, Hu and Geng 2011):
IMF (i ) ε (i ) = ∑ IMF (i )
(6)
F (a )
N
(a )
i =1
F (a )
Where, IMFF(a)(i) is i-th fourier transform value of IMF(a)(i). N is original signal length. According to the basic theory of entropy, empirical mode decomposition characteristic entropy is defined as:
= −∑ ε a (i ) log ε a (i ) N
H
a
i =1
4
(a = 0 − M )
(7)
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Ha is the empirical mode decomposition characteristic entropy of the a-th IMF. 2.5 The extraction of the wavelet packet characteristic entropy of pipeline leakage signal The wavelet packet entropy of pressure signal and flow signal is extracted as follows: (1) Signal decomposition: The signal is decomposed into three layers wavelet coefficients. (2) Signal reconstruction: The sequence of eight frequency bands is reconstructed. The sequence of wavelet packet reconstruction of pressure signal and traffic signal is get. Each reconstruction signal contains the original signal from low to high frequency information without information redundancy and omissions. (3) The wavelet packet characteristic entropy vectors of signal: the wavelet packet entropy of pressure signal and flow signal is extracted by equations (2) and (3) and then construct the feature vectors (T). T=[HP(3 0),HP 3,1 ,HP 3,2 ,HP 3,3 ,HP 3,4 ,HP 3,5 ,HP 3,6 ,HP 3,7 ,HF(3 0),HF 3,1 ,HF 3,2 ,HF 3,3 , HF 3,4 ,HF 3,5 ,HF 3,6 ,HF 3,7 ].Because the higher characteristic of wavelet packet entropy is inconvenient. So, the eigenvectors are normalized.
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2.6 The extraction of the empirical mode decomposition characteristic entropy of pipeline leakage signal (1) Signal decomposition: The signal is decomposed into a sum of IMFs; (2) The empirical mode decomposition characteristic entropy vectors of signal: the EMD-CE of pressure signal and flow signal is extracted by equations (6) and (7) and then construct the feature vectors (T). T=[imfHP1, imfHP2, imfHP3,...,imfHPn,imfHF1,imfHF2, imfHF3,... ,imfHFm]. Because the higher characteristic of EMD-CE is inconvenient. So, the eigenvectors are normalized.
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T ' = imfH 1 ,imfH 2 ,imfH 3 ,...,imfH n H H H H
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2.7 PSO-SVM method (1)Support vector machine (SVM) The support vector machine(Burges 1998) (SVM), which is based on structural risk minimization criterion to obtain a minimum actual risk, is a new machine learning algorithms. Its topology is determined by the support vector, and can overcome the defects of that of neural network method. SVM performs well in solving the practical problems of small and medium-sized sample, non-linear, high dimension and local minima points. (2)Algorithm of particle swarm optimization (Navalertporn and Afzulpurkar 2011) A group of random particles are initialized, and x and v denote the position and velocity of any particle respectively in the search space. Xi represents the position of the i-th particle in the D-dimensional search 5
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= Ψ
v
id
+
c r (p 1
1
x
id
id
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−
x
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x
id
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Where c1 and c2 are two acceleration constants regulating the relative velocities with respect to the best global and local positions.Ψ is the inertia weight (3)Parameter optimization method of SVM based on PSO The three major hyper-parameters C, σ and ε in SVM are optimized by PSO. The training process is described as follows(Ni, Jiang and Pan 2013): 1) Set up parameters of PSO for PSO–SVM. For PSO, set up the number of particle, maximum number of iterations, two acceleration constants (c1, c2) and inertia weight(Ψ). Initialize the velocity and position for each particle comprised of the hyper-parameters C, σ and ε. 2) Set the best position(Pi) from the particle with the minimal fitness in the swarm. 3) Train an SVM regression model with the corresponding hyper-parameters based upon cross validation in each candidate particle. 4) Update the velocity and position of each particle by using Eqs.(12) and (13) 5) Check the stopping criterion. If the generations don’t reached at the maximal number, then return to Step (4). Otherwise go to next step. 6) Terminate the algorithm and give the optimal hyper-parameters.
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2.8 Model validation Model validation is of crucial importance to pipeline leakage modeling. The calibration and predictive capability of a model of pipeline leakage should be tested through model validation. The most widely used correlation coefficient (R) can provide a reliable indication of the fitness of the model. In the present study, it is employed to validate the calibration capability of a model of pipeline leakage. As for the validation of predictive capability of a model of pipeline leakage, two basic principles (internal validation and external validation) are existed. The cross-validation (CV) is one of the most often used methods for internal validation. A good CV result (Q2) often indicates a good robustness and high internal predictive ability of a QSPR model(Golbraikh and Tropsha 2002). The internal predictive capability of a model is evaluated by leave-one-out cross-validation (Q2LOO) on the training set, which is calculated with the following equation(Gramatica, Pilutti and Papa 2004): 2
∧ y − y ∑ i i − ∑ y i − y
training
Q
2 LOO
= 1−
i =1
2
training i =1
(14)
∧
Where, yi,
y i , and
are the experimental, predicted, and mean values of the samples for the 6
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∧ ∑ yi − yi − ∑ y i − y tr
prediction
Q
2 ext
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i =1
2
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Where, yi and
yi
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−
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(15)
y tr is the mean experimental values of the samples for the training set.
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Root mean square (RMS) is also selected as one of the parameters using in the model validation. 3. Simulation study For the case evaluated here, the main simulation parameters are presented as follows: length of pipeline, L=55km; pipe diameter, D=0.3414m;density of liquid, ρ=832kg/m3;inlet pressure, P(int)=1700kpa; outlet pressure, P(out)=1007kpa; Medium velocity, V=224m3/h; acoustic velocity, a=1100m/s. Besides, pipeline is divided into 50 sections, which the length is 1.1km. The Boundary conditions include the leak rate dw =5% and constant inlet pressure and outlet flow. The simulation process and results can be seen in the references(Ni, Jiang and Pan 2013).The results are shown in Fig.2 and Fig.3. 3.1Pipeline leak location under the condition of low noise
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1020000 1010000
outpress
1000000 990000 980000
3# 11# 21# 31# 41# 49#
960000 950000 940000 930000
AC C
press(pa)
EP
970000
920000 910000 900000 890000 880000 0
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times(s)
Fig.2 Outlet press of different leak location
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inlet flow 1.76
49# 1.74
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AC C
outpress (pa)
10000 0 -10000
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M AN U
Fig.3 Inlet flow of different leak location (1) PSO-SVM method based on WP-CE
time(s)
Fig.4 Db5 wavelet packet decomposition coefficients of pressure signal
8
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inlet flow(m/s)
1.80 1.75 1.70 0.02 0 0.00 -0.02 0 0.005 0.000 -0.005 0.005 0
3,0
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time(s)
AC C
EP
TE D
Fig.5 Db5 wavelet packet decomposition coefficients of flow signal The wavelet packet characteristics entropy of the signal is extracted by following the steps in section 2.3. Fig.4 and Fig.5 show the wavelet packet decomposition coefficients of pressure signal and flow signal respectively when the leakage of pipe located at 3# hole. Both pressure signal and flow signal are decomposed by db5 wavelet packet. Pipeline measurement signal mutation can be seen clearly from node (3, 1). According to the above analysis, the normalized wavelet packet characteristic entropy in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 is training set. The normalized wavelet packet characteristic entropy s in No.16, 21, 29 and 36 is test set. Then, the PSO algorithm is implemented to find the optimal hyper-parameters C, σ and ε for eigenvectors model by using 3-fold cross validation. At the same time, the leak locations of pipelines are determined by SVM. The related parameters of C, σ and ε for RBF kernel function are varied in the arbitrarily fixed ranges[0.1, 100], [0.01, 1000] and [0.00001, 1]. Swarm size S=30, inertia weight Ψ=0.9, acceleration constants c1=1.6 and c2=1.5, and maximum number of iterations fixed at 300.
9
SC
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ACCEPTED MANUSCRIPT
M AN U
Fig.6 Convergence curve of PSO-SVM method based on WP-CE
10
training set prediction set
8 6
2 0 -2 -4
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-6
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residuals
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-8
-10
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The leak locations of literature value
Fig.7 Distribution of residuals
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training set prediction set
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The leak locations of calculated values by WP-CE-PSO-SVM
50
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The leak locations of literature value
M AN U
Fig.8 The results of PSO-SVM method based on WP-CE
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The convergence process of PSO is shown in Fig.6. The convergence curve shows the best fitness for the training samples which are obtained from the minimal fitness of the swarm in each generation. Relying on the PSO algorithm, make C= 100, σ= 0.01 and ε= 0.01. The regression results of SVM are shown in Table 1 and Table 2. The WP-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit good performance of the training SVM in Fig.8. As shown in Fig.7, the residuals are randomly distributed on both sides of zero line, so the predicted model which is established by PSO-SVM can be considered to be steady reasonably. Table 1 WP-CE and predict value of outlet press
0)
0.0642 0.0676
HP
HP
HP
HP
HP
HP
3,1
3,2
3,3
3,4
3,5
3,6
3,7
EP
(3
HP
AC C
HP
0.3775
0.3836
0.3904
0.3417
0.3727
0.3845
0.3876
Location of WP-CE
3.0101
Location of BPNN(Ni, Jiang and Pan 2013) 7.7478
The literature value(Ni, Jiang and Pan 2013) 3
0.369
0.3855
0.3846
0.3499
0.3769
0.3808
0.3915
9.1653
8.6628
6
0.3775
0.3845
0.3819
0.3473
0.3777
0.3821
0.3868
13.5961
9.9509
9
0.3762
0.3823
0.3879
0.344
0.3778
0.378
0.3905
13.3115
11.0977
11
0.3743
0.382
0.3875
0.3498
0.3776
0.3748
0.3909
15.2761
12.5525
13
0.0772
0.3703
0.3763
0.3888
0.3472
0.3793
0.3877
0.3866
18.1037
15.476
18
0.0768
0.377
0.3849
0.3871
0.3494
0.3717
0.3788
0.3877
18.9899
19.1199
19
0.0801
0.374
0.3831
0.3945
0.3527
0.3686
0.3783
0.3846
25.5031
20.9519
23
0.0758
0.3763
0.378
0.3882
0.3518
0.375
0.3814
0.3864
16.0101
28.6404
16
0.0791
0.366
0.3803
0.387
0.3527
0.3793
0.3869
0.384
22.0732
24.9947
21
0.0811
0.3905
0.3852
0.3814
0.3495
0.3757
0.3772
0.3763
27.2179
26.4761
29
0.0695 0.0733 0.075
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ACCEPTED MANUSCRIPT Table 2 WP-CE and predict value of inlet flow
HF 0)
HF
HF
HF
HF
HF
HF
3,1
3,2
3,3
3,4
3,5
3,6
3,7
Location of WP-CE
BPNN(Ni, Jiang and Pan 2013)
The literature value(Ni, Jiang and Pan 2013)
0.3776
0.3812
0.3915
0.3477
0.3779
0.3802
0.3864
3.0101
7.7478
3
0.0362
0.378
0.3797
0.3886
0.3485
0.3754
0.3838
0.3885
9.1653
8.6628
6
0.0373
0.378
0.3842
0.3911
0.3414
0.3734
0.3852
0.3883
13.5961
9.9509
9
0.0377
0.3703
0.3861
0.3851
0.35
0.3775
0.3813
0.392
13.3115
11.0977
11
0.0376
0.3785
0.3855
0.3825
0.3477
0.3782
0.3827
0.3873
15.2761
12.5525
13
0.0385
0.3769
0.3835
0.3889
0.344
0.3784
0.3786
0.3915
18.1037
15.476
18
0.0384
0.3756
0.3833
0.3891
0.3496
0.375
0.3765
0.3931
18.9899
19.1199
19
0.0388
0.3724
0.3798
0.3929
0.3442
0.3782
0.386
0.0384
0.3723
0.3797
0.393
0.3442
0.3783
0.3861
0.039
0.3767
0.3835
0.3889
0.3441
0.3785
0.3785
0.0384
0.3778
0.38
0.3881
0.3487
RI PT
0.036
SC
(3
HF
Location of
25.5031
20.9519
23
0.3882
16.0101
28.6404
16
0.3915
22.0732
24.9947
21
27.2179
26.4761
29
M AN U
0.3881
0.3754
0.3837
0.3888
TE D
3.2 Pipeline leak location under the condition of high noise The previous research is conducted under the condition of low noise. But in actual situation, there are varying noises in output signal obtained from pipeline leakage including the environmental noise, the noise of fluid inside and the influence of the instrument itself. So in this section, Gaussian white noise is superimposed on the original low noise signal to simulate the actual signal in MATLAB. Signal superposition results are shown in the Fig.9 and Fig.10.
1040000
EP
1000000 980000
AC C
outlet–pressure pa
1020000
16 36 29 21
960000 940000 920000 900000 880000
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16 36 29 21
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inlet–flow(m/s)
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1.73 1.72 1.71 1.70
SC
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M AN U
Fig.10 Inlet flow with white noise
EP
TE D
(1) PSO - SVM method based on the physical parameters The final outlet press value and the value of maximum of inlet flow are extracted as eigenvectors from the above analysis. The location of leak hole is output value. The locations of leak holes in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 are training set. The locations of leak holes in No.16, 21, 29 and 36 are test set. Then, the PSO algorithm is implemented to find the optimal hyper-parameters C, σ and ε for eigenvectors model by using 3-fold cross validation. At the same time, the leak locations of pipelines are determined by SVM. The related parameters of C, σ and ε for RBF kernel function are varied in the arbitrarily fixed ranges[0.1, 100], [0.01, 1000] and [0.00001, 1]. Swarm size S=30, inertia weight Ψ=0.9, acceleration constants c1=1.6 and c2=1.5, and maximum number of iterations fixed at 300. 300
fitness
AC C
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fitness
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Generations 13
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ACCEPTED MANUSCRIPT Fig.11 Convergence curve training set prediction set
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residuals
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The leak locations of literature value
training set prediction set
50
TE D
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The–leak–locations–of–calculated–values –by–PS0-SVM
Fig.12 Distribution of residual
10
AC C
0
0
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40
50
The–leak–locations–of–literature–value
Fig.13 The results of PSO-SVM
The convergence process of PSO is shown in Fig.11. Relying on the PSO algorithm, C=2872.5, σ= 0.01 and ε=1.8552 are defined. The regression results of SVM are shown in Table 3 and Fig.13, and outlet press and inlet flow are two elements of an eigenvector. As shown in Fig.12, all four prediction sets are on the same side of the zero line, so the stability of the model is poorer.
14
ACCEPTED MANUSCRIPT Table 3 PSO-SVM based on physical parameters Outlet press(pa)
Inlet flow(m/s)
The literature value(Ni, Jiang and Pan 2013)
Location of PSO-SVM
1 2 3 4 5 6 7 8 9
948687.7 962460.3 951595.6 943639.6 940361.6 927427.2 944024.8 899926.2 935368.8
1.7673 1.7674 1.7671 1.7683 1.7694 1.7694 1.7715 1.7708 1.7725
6 11 16 21 26 31 36 41 46
13.3365 9.9885 11.9510 19.0496 25.0281 28.7144 33.5005 42.8554 40.0903
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3,0
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0
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20000 0 -20000
800
3,2
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600
3,3
0
EP
outpress (Pa)
50000 0 -50000
400
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0
1100000 1000000 900000
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(2) PSO-SVM method based on WP-CE
RI PT
Sample
time(s)
Fig.14 Db4 wavelet packet decomposition coefficients of pressure signal with white noise
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TE D
50
EP
The–leak–locations–of–calculated–values– of–WP-CE-PSO-SVM
Fig.15 Db5 wavelet packet decomposition coefficients of flow signal with white noise The signal with white noise is extracted the wavelet packet characteristics entropy by following the steps in section 2.3. Fig.14 and Fig.15 show the wavelet packet decomposition coefficients of pressure signal and flow signal respectively when the leakage of pipe located at 3# hole. The choice of mother wavelet has an important influence on the results of the analysis. Pressure signal is decomposed by db4 wavelet packet and flow signal is decomposed by db5 wavelet packet. Pipeline measurement signal mutation can be seen clearly from node (3,1). The same as the low noise situation, the high noise signal of pipeline leakage is extracted by wavelet packet characteristic entropy and calculated by PSO-SVM.
training set prediction set
AC C
40
30
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10
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40
The–leak–locations–of–literature–value
Fig.16 The results of PSO-SVM method based onWP-CE 16
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training set prediction set
2
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residuals
1
0
-1
-3 10
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-2
The–leak–locations–of–literature–value Fig.17 Distribution of residuals
TE D
Relying on the PSO algorithm, C= 10000, σ= 2358.7 and ε= 2.9251 are made. The regression results of SVM are shown in Table 4 and Table 5. The WP-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit good performance of the training SVM in Fig.16. As shown in Fig.17, the residuals are randomly distributed on both sides of zero line, so the predicted model which is established by PSO-SVM can be considered to be steady reasonably. Table 4 pipeline leak location of outlet press with WP-CE HP
3,1
3,2
3,3
0.0777
0.3743
0.3718
0.0706
0.3728
WP-CE-
HP
HP
3,4
3,5
3,6
3,7
0.3906
0.3579
0.3777
0.3780
0.3866
6
8.9255
0.3894
0.3813
0.3440
0.3820
0.3806
0.3873
11
13.9250
0.3782
0.3896
0.3897
0.3571
0.3679
0.3692
0.3853
16
18.9253
0.3728
0.3834
0.3908
0.3543
0.3734
0.3769
0.3848
21
19.4951
0.3771
0.3825
0.3928
0.3493
0.3702
0.3820
0.3820
26
23.0746
0.3724
0.3782
0.3844
0.3563
0.3852
0.3732
0.3865
31
28.0751
0.0851
0.3751
0.3917
0.3874
0.3472
0.3705
0.3780
0.3845
36
33.0750
0.0874
0.3784
0.3749
0.3905
0.3396
0.3754
0.3810
0.3933
41
38.0748
0.0789
0.3759
0.3831
0.3918
0.3386
0.3720
0.3802
0.3932
46
43.0755
0)
0.0754 0.0787 0.0796 0.0809
HP
The literature
HP
(3
HP
EP
HP
AC C
HP
17
value(Ni, Jiang and Pan 2013)
PSO-SVM
ACCEPTED MANUSCRIPT
Table 5 pipeline leak location of inlet flow with WP-CE WP-CE-
HF
HF
HF
HF
HF
HF
3,1
3,2
3,3
3,4
3,5
3,6
3,7
0.0366
0.3757
0.3841
0.3878
0.3495
0.3743
0.3828
0.3883
6
8.9255
0.0382
0.3753
0.3888
0.3865
0.3463
0.3770
0.3800
0.3882
11
13.9250
0.0375
0.3773
0.3903
0.3858
0.3470
0.3755
0.3791
0.3872
16
18.9253
0.0376
0.3716
0.3804
0.3906
0.3433
0.3792
0.3801
0.3964
21
19.4951
0.0368
0.3802
0.3903
0.3893
0.3505
0.3730
0.3730
0.3861
26
23.0746
0.0390
0.3787
0.3799
0.3903
0.3496
0.3739
0.3820
0.3880
31
28.0751
0.0394
0.3764
0.3783
0.3868
0.3443
0.3845
0.3875
0.3840
36
33.0750
0.0384
0.3784
0.3769
0.3951
0.3401
0.3765
0.3832
0.0379
0.3780
0.3775
0.3850
0.3518
0.3738
0.3768
SC
The literature
HF
0)
200 200
IMF9 IMF10
41
38.0748
0.3994
46
43.0755
600
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400
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800
1000
400
600
800
1000
400
600
800
1000
200
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800
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200
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200
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1000
I
time(s)
Fig.18 The IMFs of pressure signal with white noise
18
PSO-SVM
0.3911
400
TE D
200
EP
20000 0 -20000 0 20000 0 -20000 0 30000 0 -30000 0 20000 0 -20000 0 30000 0 -30000 0 20000 0 -20000 20000 0 0 -20000 20000 0 0 -20000 20000 0 0 -20000 20000 0 0 -20000 0
AC C
IMF8
IMF7
IMF6
IMF5
IMF4
IMF3
IMF2
IMF1
(3) PSO-SVM method 0based on EMD-CE 200
Pan 2013)
RI PT
(3
value(Ni, Jiang and
M AN U
HF
IMF4
0.01 0.00 -0.01
IMF5
0.02 0.00 -0.02
IMF6
0.05 0.00 -0.05
IMF7
0.05 0.00 -0.05 0.05 0.00 -0.05
400
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200
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IMF3
0.01 0.00 -0.01
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IMF2
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IMF1
0.01 0.00 -0.01
IMF8
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AC C
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TE D
Fig.19 The IMFs of flow signal with white noise The signal with white noise is extracted the IMFs by following the steps in section 2.4. Fig.18 and Fig.19 show the IMFs of pressure signal and flow signal respectively when the leakage of pipe located at 3# hole. The pressure signal has ten IMFs while the flow signal has eight. Firstly, the first eight IMFs of pressure signal and all the eight IMFs of flow signal are selected to extract the characteristic entropy by following the steps in section 2.6.The results are shown in table 6 and table 7.
19
ACCEPTED MANUSCRIPT
RI PT
Table 6 EMD-CE of outlet press imfHP2
imfHP3
imfHP4
imfHP5
imfHP6
imfHP7
imfHP8
The leak locations of literature value(Ni, Jiang and Pan 2013)
0.4634
0.4222
0.3996
0.3668
0.3124
0.3002
0.2545
0.2457
6
0.5135
0.4287
0.3821
0.3416
0.3206
0.2593
0.2515
0.2379
11
0.4761
0.4132
0.3787
0.3559
0.3239
0.3006
0.2637
0.2602
16
0.4559
0.4359
0.3989
0.3723
0.3264
0.3068
0.2541
0.1976
21
0.4740
0.4348
0.4038
0.3673
0.2975
0.2838
0.2462
0.2423
26
0.4831
0.4261
0.3933
0.3380
0.2939
0.2966
0.2924
0.2370
31
0.4655
0.4281
0.3983
0.3714
0.3269
0.2965
0.2282
0.2379
36
0.4704
0.4322
0.4060
0.3609
0.3149
0.3020
0.2408
0.2202
41
0.4883
0.4578
0.4258
0.3932
0.2480
0.2383
0.2369
0.2041
46
M AN U
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imfHP1
imfHF2
imfHF3
imfHF4
imfHF5
imfHF6
imfHF7
imfHF8
The leak locations of literature value(Ni, Jiang and Pan 2013)
0.5459
0.4752
0.3934
0.3323
0.2955
0.2537
0.2010
0.1371
6
0.5479
0.4619
0.4023
0.3091
0.3007
0.2531
0.2291
0.1487
11
0.5441
0.4889
0.4390
0.3651
0.2549
0.2229
0.1484
0.0476
16
0.5878
0.4956
0.4000
0.3005
0.5007
0.4657
0.4228
0.3615
0.2729
0.2351
0.1616
0.0531
21
0.3107
0.2393
0.2263
0.1340
26
0.5552
0.4725
0.4146
0.3530
0.2632
0.2298
0.2188
0.0455
31
0.5221
0.4525
0.4022
0.3754
0.2678
0.2363
0.2168
0.2130
36
0.5527
0.4597
0.3941
0.3337
0.2615
0.2397
0.2210
0.2046
41
0.5428
0.4828
0.4405
0.3663
0.2581
0.1837
0.2046
0.0439
46
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Table 7 EMD-CE of inlet flow
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ACCEPTED MANUSCRIPT According to the above analysis, the normalized EMD-CE in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 is the training set. The normalized EMD-CE in No.16, 21, 29 and 36 is the test set. Relying on the PSO algorithm, C= 1000, σ=5.9814 and ε= 0.01 are made. The regression results of SVM are shown in Fig. 20. The EMD-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit bad performance of the training SVM in Fig.20.
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Fig. 20 the results of PSO-SVM method based on EMD-CE Second, all the IMFs of pressure signal and flow signal are selected to extract the characteristic entropy by following the steps in section 2.6. The results are shown in Table 8 and Table 9.
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Table 8 EMD-CE of outlet press
0.3827 0.3665 0.3605 0.3894 0.3921 0.3747 0.3787 0.3919 0.4205
imfHP4 0.3512 0.3276 0.3388 0.3634 0.3566 0.3220 0.3531 0.3484 0.3883
imfHP5 0.2991 0.3075 0.3084 0.3187 0.2889 0.2800 0.3108 0.3039 0.2449
imfHP6 0.2875 0.2487 0.2862 0.2995 0.2755 0.2825 0.2819 0.2915 0.2353
imfHP7
imfHP8
0.2437 0.2412 0.2511 0.2481 0.2391 0.2786 0.2170 0.2324 0.2339
0.2353 0.2282 0.2477 0.1929 0.2353 0.2258 0.2262 0.2125 0.2015
imfHP9
imfHP10
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0.4043 0.4112 0.3933 0.4255 0.4222 0.4059 0.4070 0.4172 0.4521
imfHP3
0.2203 0.2142 0.2240 0.1853 0.1932 0.2204 0.2267 0.1968 0.1144
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0.4438 0.4925 0.4532 0.4450 0.4602 0.4603 0.4425 0.4540 0.4821
imfHP2
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0.1852 0.1848 0.2089 0.1132 0.1409 0.2095 0.2116 0.1720 0.1090
6 11 16 21 26 31 36 41 46
Table 9 EMD-CE of inlet flow imfHF2
imfHF3
imfHF4
imfHF5
0.5459 0.5479 0.5441 0.5878 0.5007 0.5552 0.5221 0.5527 0.5428
0.4752 0.4619 0.4889 0.4956 0.4657 0.4725 0.4525 0.4597 0.4828
0.3934 0.4023 0.4390 0.4000 0.4228 0.4146 0.4022 0.3941 0.4405
0.3323 0.3091 0.3651 0.3005 0.3615 0.3530 0.3754 0.3337 0.3663
0.2955 0.3007 0.2549 0.2729 0.3107 0.2632 0.2678 0.2615 0.2581
imfHF6
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0.2537 0.2531 0.2229 0.2351 0.2393 0.2298 0.2363 0.2397 0.1837
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imfHF7
imfHF8
0.2010 0.2291 0.1484 0.1616 0.2263 0.2188 0.2168 0.2210 0.2046
0.1371 0.1487 0.0476 0.0531 0.1340 0.0455 0.2130 0.2046 0.0439
The leak locations of literature value(Ni, Jiang and Pan 2013) 6 11 16 21 26 31 36 41 46
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According to the above analysis, the normalized EMD-CE in No.3, 6, 9, 11, 13, 18, 19, 23, 26, 31, 33, 39, 41, 43, 46 and 49 is the training set. The normalized EMD-CE in No.16, 21, 29 and 36 is the test set. Relying on the PSO algorithm, C= 1000, σ=31.2895 and ε= 2.5844 are made. The regression results of SVM are shown in Fig.21. The EMD-CE of outlet press and inlet flow is two elements of an eigenvector. The results of test exhibit good performance of the training SVM in Fig.21.As shown in Fig. 22, the residuals are randomly distributed on both sides of zero line, so the predicted model which is established by PSO-SVM can be considered to be steady reasonably.
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10
20
30
40
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The leak locations of literature value
Fig.22 Distribution of residuals 4 Discussion The results of different pipeline leak positioning methods are processed. The correlation coefficients 23
ACCEPTED MANUSCRIPT of training set and test set, Cross validation (Q2LOO Q2ext) and RMS are calculated to show in the following table. Table 10 performance comparison with different methods Training set
Model
RMS
Rext
Q2ext
RMS
BPNN
0.9661
0.9299
3.8701
0.5023
0.1211
7.1561
PSO-SVM
0.9998
0.9996
0.2959
0.9999
0.9995
0.1721
PSO-SVM method based on WP-CE
0.9946
0.9826
1.9274
PSO-SVM
0.9511
0.9005
4.611
PSO-SVM method based on WP-CE
0.9948
0.9624
2.8326
PSO-SVM based on part of EMD-CE
0.7873
0.5835
9.4316
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PSO-SVM based on all the EMD-CE
0.99
0.9588
2.9675
0.9914
0.9814
1.0402
0.9869
0.7726
3.6401
0.9588
0.9046
2.3575
0.9638
0.8138
3.2932
0.974
0.8854
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Under the condition of low noise, the results of PSO-SVM method based on the physical parameters are better than those of PSO-SVM method based on WP-CE from the Table 10 and are better than those of BPNN method. But when the noise is high, the results of PSO-SVM method based on WP-CE and PSO-SVM method based on all the EMD-CE are better than those of PSO-SVM method based on the physical parameters while the results of PSO-SVM method based on part of EMD-CE are worse than those of PSO-SVM method based on the physical parameters. Under the condition of low noise, the outlet pressure and inlet flow value of different leakage can be distinguished easily. WP-CE is a signal processing method. It is not obvious that the relationship between WP-CE and output value is linear or nonlinear. So, the correlation of PSO-SVM based on physical parameters is better than that of PSO-SVM method WP-CE. In fact, as a general machine learning method, the PSO-SVM is based on the structural risk minimization principle, which minimizes an upper bound of the generalization error rather than minimizes the training error. So, the PSO-SVM has better generalization performance than ANN. Moreover, compared with ANN, once corresponding parameters are specified, the solution of SVM is definite and reproducible, which is clearly superior to ANN. When the noise is high, considering of the difficulties to identify the outlet pressure and inlet flow, the results of PSO-SVM method based on physical parameters are poor. The high frequency noise of signal is separated by WP-CE. The matching degree of low frequency signal and the original signal is higher. EMD method is based on the local feature of the signal, and can decompose signal adaptively into several intrinsic mode functions (IMFs)according to its characteristic time scale. So the results of PSO-SVM method based on all the EMD-CE and PSO-SVM method based on WP-CE are better than those of PSO-SVM method based on physical parameters. Although the first several IMFs have described the characteristic of the signal basically, the correlation of PSO-SVM method based on part of EMD-CE is worse than that of PSO-SVM method based on all the EMD-CE. So, the results of PSO-SVM method based on part of the EMD-CE are worse than those of PSO-SVM method based on all the EMD-CE. 5 Conclusions Characteristics entropy is presented for the application of the pipeline leak detection. The characteristic entropy of pipeline leakage signal is extracted as the input vector. The location of the pipeline 24
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Hj,k ε
(j ,k )
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Nomenclatures u(t) Wavelet packet decomposition sequence h(k) High-pass filter g(k) Low pass filter S(j,k) Wavelet packet decomposition sequence SF(j,k)(i) Fourier transform value of S(j,k)(i) N Original signal length
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leakage is determined by the combination of characteristic entropy and PSO-SVM. The results of this method are compared with those of PSO-SVM method based on physical parameters. The condition of high noise is defined to simulate the condition of actual pipeline leakage. In this case, the results of PSO-SVM based on characteristics entropy are better than those of PSO-SVM based on physical parameters. In the characteristics entropy method, PSO-SVM method based on WP-CE needed to choose a suitable mother function of wavelet, but that based on EMD-CE don’t need. The results of PSO-SVM method based on WP-CE with the suitable mother function of wavelet are close to those of PSO-SVM method based on all the EMD-CE. Therefore, PSO-SVM method based on EMD-CE is more convenient. So, the leak location method of pipeline based on characteristic entropy is an effective method. It can improve the processing ability of pipeline leakage signal effectively. This method can also provide the fundamental input parameter for leak location of pipeline.
The j layer and the kth wavelet packet characteristic entropy of signal
(i )
The measure of the division of signal
Initial value of variables The residual of the sifting process ith fourier transform value of IMF(a)(i)
Ha
The empirical mode decomposition characteristic entropy of the a-th IMF The feature vectors of pressure signal The feature vectors of flow signal The normalized wavelet packet feature vector The position of the i-th particle The velocity of i-th particle The best particle in the search space The best particle in the group Acceleration constants Inertia weight Leave-one-out cross-validation on the training set Leave-one-out cross-validation on the prediction set
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HP HF T Xi Vi Pi Pg c1 and c2 Ψ Q2LOO Q2ext
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h0(t) rn(t) IMFF(a)(i)
Acknowledgements The authors are grateful for the support given by Jiangsu Graduate Scientific Innovation Projects (CXLX11_0380) and Jiangsu Natural Science Foundation of China (BK2007587).
References: 25
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►The characteristic entropy of pipeline leakage signal is extracted as the input vector. ►The characteristic entropy combines with PSO-SVM method. ►In high noise condition, the results of PSO-SVM based on characteristics entropy are better. ►PSO-SVM method based on EMD-CE is more convenient.