applied sciences Article
Pipeline Leak Localization Based on FBG Hoop Strain Sensors Combined with BP Neural Network Ziguang Jia 1 , Liang Ren 2, * 1 2 3
*
ID
, Hongnan Li 2,3 and Wei Sun 1
School of Ocean Science and Technology, Dalian University of Technology, Panjin 124221, Liaoning, China;
[email protected] (Z.J.);
[email protected] (W.S.) Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China;
[email protected] School of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, Liaoning, China Correspondence:
[email protected]; Tel.: +86-411-8470-6384
Received: 14 December 2017; Accepted: 19 January 2018; Published: 24 January 2018
Featured Application: A pipeline leakage localization method using self-developed FBG hoop strain sensors combined with BP neural network is proposed and validated. Abstract: Pipelines function as blood vessels serving to bring life-necessities, so their safe usage is one of the foremost concerns. In our previous work, a fiber Bragg grating (FBG) hoop strain sensor with enhanced sensitivity was developed to measure the pressure drop induced by pipeline leakage. Some hoop strain information during the leakage transient process can be extracted from the amount of FBG hoop strain sensors set along the pipeline. In this paper, an integrated approach of a back-propagation (BP) neural network and hoop strain measurement is first proposed to locate the leak points of the pipeline. Five hoop strain variations are employed as input neurons to achieve pattern recognition so as to predict the leakage point. The RMS error can be as low as 1.01% when choosing appropriate hidden layer neurons. Furthermore, the influence of noise on the network’s performance is investigated through superimposing Gaussian noise with a different level. The results demonstrate the feasibility and robustness of the neural network for pipeline leakage localization. Keywords: FBG hoop strain sensor; pipeline leakage localization; transient model; BP neural network
1. Introduction Pipelines are widely used for transportation or conveying fluids from one place to another, for which automotive transportation is often dangerous or impractical. Pipeline leaks are among the most difficult problems causing both loss of product, as well as serious environmental pollution. Therefore, it is important to locate the leak point accurately to mitigate problems and avoid potentially crippling costs. Currently, some methods and systems for detecting pipeline leakage have been developed. Recent innovations on pipeline leak detection techniques can be classified into two categories: new sensors and new algorithms. From the aspect of the sensor, some novel sensing techniques are used to detect the pipeline fault due to higher sensitivity and reliability, like fiber optic sensing [1,2], wireless sensor networks [3,4] and the acoustic method [5,6]. Among these techniques, fiber optic sensors emerged as the most appropriate for long distance pipelines with no potential safety hazard compared with traditional electrical gauges. From the aspect of algorithms, the fluid transient state due to leakage occurrence is always analyzed, then the leak accidents can be identified, thus locating the leak point, in combination with signal processing techniques and mathematic analysis, including artificial neural network [7,8], support vector machine (SVM) [9,10], harmonic wavelet analysis [11],
Appl. Sci. 2018, 8, 146; doi:10.3390/app8020146
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etc. Until now, no integrated solution for leakage detection combining both advantages of the fiber sensor and advanced algorithm has been proposed in the literature. Fiber optic sensors, with the advantages of immunity to electromagnetic interference, high accuracy and multiplexibility, are now widely used to detect pipeline fault since there are many probable dangers related to gas or liquid pipelines [12,13]. A novel FBG hoop strain sensor has been developed and encapsulated in our lab to measure the pipeline hoop strain variation induced by leaks or other pressure drop cases [14,15]. This sensor provides a nondestructive testing (NDT) method for pipeline leakage detection and localization by installing multiple sensors along the pipeline. In addition, more information during the leakage transient flow process can be extracted so as to describe the leakage characteristics at different leak points or with different leak rates, which provides a potential approach to locate the leak point. The pipeline leakage detection and localization can be treated as a classification problem in which a leak fault condition is considered to be a sample. Different leakage scenarios can be identified by some machine learning algorithms, like k nearest neighbor (kNN) [16], support vector machine [10], multi-layer perceptron neural network (MLPNN) [9], etc. The fundamental idea of these methods is to extract features from flow, pressure and temperature measurements at the inlet and outlet of the pipeline and then to train the classifier. Until now, signals from the pipeline mid-section have not been utilized as feature extractions to enhance the reliability and accuracy of the classification algorithms because no additional sensors can be mounted along the pipeline. This paper provides a new pipeline leakage localization method integrating advanced FBG hoop strain sensors and an effective BP neural network-based classification algorithm. The research work can be split into two branches. On the one hand, the FBG hoop strain sensor developed in our previous work will be briefly demonstrated to show its performance in pipe pressure drop. On the other hand, the neural network system is trained by using multi-hoop strain characteristic values, then used to locate different leak points. The remainder of this paper is organized as follows: in the next part, the developed FBG hoop strain sensor with enhanced sensitivity is introduced. Then, the theory of the neural network for pipeline leak localization is provided in detail. In the next section, a case study of a long-distance pipeline is presented, including cases considering different levels of signal noise. Finally, conclusions are drawn. 2. FBG Hoop Strain Sensor A novel FBG-based hoop strain sensor was developed in our previous work to monitor the hoop strain drop induced by pressure reduction [15]. This sensor has the advantages of optical sensing technology, such as high accuracy, long-term stability, multiplexibility and immunity to electromagnetic interference. This part briefly reviews the design and encapsulation of the FBG hoop strain sensor, as well as its performance in a preliminary leakage experiment on a model pipeline. 2.1. FBG Hoop Strain Sensor Development Figure 1 shows the schematic diagram and the encapsulated FBG hoop strain sensor. Generally, the sensor is composed of a fiber Bragg grating, two gripper tubes, two gripper blocks, a protective tube, a movable end and a fixed end. The mechanical structure of the FBG hoop strain sensor has the function of strain sensitivity amplification, which is demonstrated in the previous research [15]. The encapsulated sensor shown in Figure 1b has a specially-designed pre-tension function to ensure tight connection to the curved surface of the pipe. The anchorage member is fixed onto the surface of the measured pipeline before installing the optic fiber component. Then, the fiber can be tensioned and tightly installed. The method of fixing the anchorage member on the pipeline may be adhesion or welding, depending on the pipeline material. For example, in the following model pipeline experiment, the anchorage member is adhered using epoxy resin.
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L1
L2
L1
bare fiber and FBG
L2
protective tube（d = 1.0 mm） bare fiber and FBG gripper tube（d = 0.8 mm） protective tube（d = 1.0 mm） epoxy gripperresin tube（d = 0.8 mm） gripper block epoxy resin fixed end gripper block movable end fixed end movable end
Lf (a)
Lf
anchorage member
(a) anchorage member
fixed block pre-tension block fixed block pre-tension block protective tube
(b) protective tube Figure 1. Developed FBG hoop strain sensor. (a) Schematic diagram of an FBG hoop strain sensor; Figure 1. Developed FBG hoop strain sensor. (a)(b) Schematic diagram of an FBG hoop strain sensor; (b) picture of the encapsulated FBG hoop strain sensor with a pre-tension system. (b) picture of the encapsulated FBG hoop strain sensor with a pre-tension system. Figure 1. Developed FBG hoop strain sensor. (a) Schematic diagram of an FBG hoop strain sensor; (b) picture of the encapsulated hoop strain sensor with a pre-tension system. 2.2. Leakage Detection by FBG HoopFBG Strain Sensor
2.2. Leakage Detection by FBG Hoop Strain Sensor
The preliminary experiment conducted 2.2. Leakage Detection by FBG Hoop is Strain Sensor on a PVC model pipeline (shown in Figure 2) to test
The preliminary conducted on adetection. PVC model (shown inbe Figure 2) to test the developed FBGexperiment hoop strain is sensor for leakage The pipeline leakage process can simulated The preliminary experiment is the conducted onpressure a PVC model (shown inacan Figure 2) to leak test by by opening a valve pre-installed on A sensor isleakage also installed as traditional the developed FBG hoop strain sensor formodel. leakage detection. Thepipeline process be simulated the developed FBG hoop strain sensor for leakage detection. The leakage process can be simulated detection method to compare the FBGAhoop strainsensor sensor. is It also can be seen that FBG hoop leak opening a valve pre-installed on with the model. pressure installed as the a traditional by opening a is valve pre-installed on the model. Athe pressure sensor isusing also installed as a traditional leak strain sensor tightly fixed onto the surface of model pipe by the pre-tension mechanism. detection method to compare with the FBG hoop strain sensor. It can be seen that the FBG hoop strain detection method to compare with the FBG hoop strain sensor. It can be seen that the FBG hoop sensor is tightly ontofixed the onto surface the model pipe by using the pre-tension mechanism. strain sensorfixed is tightly the of surface of the model pipe by using the pre-tension mechanism.
Figure 2. Picture of model pipeline and FBG sensors. Figure 2. Picture of model pipeline and FBG sensors.
Figure 2. Picture of model pipeline and FBG sensors.
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The leakage occurrence leadsleads to the dropdrop at the pointpoint and and thenthen forms a negative pressure The leakage occurrence topressure the pressure at leak the leak forms a negative wavepressure (NPW), which propagates along the pipeline. NPW arrives a sensor, the at pressure drop wave (NPW), which propagates alongWhen the pipeline. WhenatNPW arrives a sensor, theor the pressure drop or the strain drop can be detected to determine the arrival time of NPW and even strain drop can be detected to determine the arrival time of NPW and even to calculate the locationtoof the calculate the location the leak point by two sensors. Figure 3 shows theFBG timehoop domain signals of the leak point by two sensors.ofFigure 3 shows the time domain signals of the strain sensor and the FBGsensor hoop strain theispressure when adrop leak can valve opened. The drop pressure whensensor a leak and valve opened. sensor The sudden beisconsidered as sudden the arrival ofcan NPW at be considered as the arrival of NPW at the sensors. It can be found that the FBG hoop strain sensor the sensors. It can be found that the FBG hoop strain sensor has a similar function in leak detection and is has a similar function in leak detection and is used as a substitute for the traditional pressure sensor. used as a substitute for the traditional pressure sensor. The main advantage of this FBG hoop strain sensor The main advantage of this FBG hoop strain sensor over the traditional pressure gauge is that it can be over the traditional pressure gauge is that italong can be installed nondestructively and flexibly along the pipeline. installed nondestructively and flexibly the pipeline. Therefore, one potential application of the Therefore, one potential application of the FBG hoop strain sensor is to install a series of sensors along FBG hoop strain sensor is to install a series of sensors along the pipeline to acquire the characteristic the pipeline to acquire characteristic information of different leakage conditions. information of the different leakage conditions. 140
50
Pressure (kPa)
120 0
100 -50 80
Wavelength variation (pm)
NPW arrival time
-100
Pressure sensor FBG hoop strain sensor
-150
60 0
5
10
15
Time (s)
20
25
Figure 3. Time history curve of the FBG hoop strain sensor for leak detection. NPW, negative pressure wave.
Figure 3. Time history curve of the FBG hoop strain sensor for leak detection. NPW, negative pressure wave.
3. Calculation of Hoop Strain Time-History 3. Calculation of Hoop Strain Time-HistoryCurve Curve Theoretically, thethe pipeline leakage bothsimulated simulatedbyby experiment numerical Theoretically, pipeline leakagecase case can can be be both experiment and and numerical simulation, during which thesignals signalscan can be be collected. it isitimpractical to open a hole aonhole a on simulation, during which the collected.However, However, is impractical to open pipeline simulate aa leakage. leakage. Thus, obtain thethe keykey characteristics of hoop by a realreal pipeline totosimulate Thus,toto obtain characteristics of strain hoopinduced strain induced leakage,the the time-history time-history curve to be firstfirst calculated by numerical simulation. In this work, thework, by leakage, curveneeds needs to be calculated by numerical simulation. In this method of characteristics is applied to solve the hydraulic transient process of a leakage occurrence. the method of characteristics is applied to solve the hydraulic transient process of a leakage occurrence. 3.1. The Method of Characteristics
3.1. The Method of Characteristics
The method of characteristics (MOC) is a common method to solve the hydraulic transient. The
The method of characteristics (MOC) is a common method to solve the hydraulic transient. derivative of the model can be integrated into the total differential, and the characteristics of the The derivative of the modelBased can beonintegrated into equation the total and differential, andequation the characteristics fixed grid are changed. the continuity momentum for unsteadyof the fixedpipe gridliquid are changed. Based on the continuity equation and momentum equation for unsteady pipe flow, the characteristics are converted into the following form: liquid flow, the characteristics are converted into the following form:
f dV g dH + + V V =0 g f dH dV 2 dt a dt D + + + V (1) a dt 2D |V | = 0 dt CC+ :: dx (1) dx =aa dt = dt ( g dH f dV dt − a dt + 2D V |V | = 0 (2) C − : dV dx g dH f = −a V V 0 + = dt − dt a dt 2 D C − : of the pipeline, t is time, V is average velocity, (2) where x is the distance of the centerline H is the dx a = − piezometric head, a is NPW velocity, D is the inner diameter and g is gravity acceleration. dt + − (
C and C are the two characteristic equations of the transient flow problem. Since the friction is nonlinear, the equations can be solved by the finite difference method to get the numerical solution, as shown in Figure 4. In this method, the length of the pipeline is discretized, and the length of each section ∆x = L/N. The time step ∆t is the travelling time of NPW along (∆t = ∆x/a). In Figure 4, the horizontal axis is the discretized pipeline and the vertical axis is the transient time, respectively.
where x is the distance of the centerline of the pipeline, t is time, V is average velocity, H is the piezometric head, a is NPW velocity, D is the inner diameter and g is gravity acceleration. C+ and C− are the two characteristic equations of the transient flow problem. Since the friction is nonlinear, the equations can be solved by the finite difference method to get the numerical solution, as shown in Figure 4. In this method, the length of the pipeline is discretized, and the length of each Appl. Sci. 2018,Δx 8, 146 section = L/N. The time step Δt is the travelling time of NPW along (Δt = Δx/a). In Figure 4, the 5 of 13 horizontal axis is the discretized pipeline and the vertical axis is the transient time, respectively. t
3Δt
C+
C−
P
2Δt
C
C−
+
N
M
Δt t=0
i-1
Δx
i
i+1
x
Figure Differencegrid grid for for the the method (MOC). Figure 4. 4. Difference methodofofcharacteristics characteristics (MOC).
Equations (1) and (2) are integrated along the characteristic lines. The pressure head and mass Equations and (2) are along characteristic The pressure and flow rate at(1) any point canintegrated be solved by the the intersection of twolines. characteristic lines head C+ and C−mass . For flow + − rate at any point can be solved the intersection of two characteristic lines C and C . For instance, instance, the pressure head Hby P at node P can be expressed as:
the pressure head HP at node P can be expressed as:
C : H P = H M − B(QP − QM ) − R QM QP ( C+C: −H: PH= =HH Q M) )+−R RQ| Q M |QP M −+BB((Q −Q QPP − − P N N N QP C : HP = H N + B ( Q P − Q N ) + R | Q N | Q P +
(3)
(3)
where B is the characteristic impedance and R is the friction loss. Then, the mass flow rate QP at node cancharacteristic be solved by the above simultaneous equations, where B isPthe impedance and R is the frictionas: loss. Then, the mass flow rate QP at node P can be solved by the above simultaneous equations, as: H − H + BQ + BQ
QP =
M
N
M
N
(4)
( QBQ+MQ+N BQ ) N B +HR H 2− N +M QP = M R(|be QM | + | Q Nfrom |) the previous time step by using Therefore, the fluid state of any time 2B step+can obtained
(4)
two linear equations. Therefore, the fluid state of any time step can be obtained from the previous time step by using For the leak point, the mass flow rate on the left side is equal to the sum of the leak flow rate two linear and theequations. mass flow rate on the right side. Based on this assumption, the pressure head and the mass For the point, the mass flow rate on thefollowing left side is equal to flow rateleak at the leak point can be derived as the equation set:the sum of the leak flow rate and
the mass flow rate on the right side. Based on this assumption, the pressure head and the mass flow CP = H M + BQM − R QM QM rate at the leak point can be derived as the following equation set: C = H − BQ + R Q Q
N N N N M C =C H+ C+ BQ − R| Q | Q M M M CVP = P M M BN − BQ N + R| Q N | Q N C = H M C CV==2 CP +BCM B B2 CB = B √ 2C2C (CCddAAl )l )22−−C 4CVV CCBB All ((CCddAAl l))22 + CB++( Cdd A +4C VC VB H = H = PP 22 2C 2 C B B Q P = HP − C M H −C B
QP =
P
(5)
(5)
M
B
where Cd is the orifice discharge coefficient and Al is the leakage area, respectively. The product term Cd Al is used to describe leakage magnitude. When using the above equations, the leak occurrence time is considered to be the initial time step. In other words, at the first time step, the fluid state changes only at the leak point while the other points remain unchanged. If the terminal time is set, the pressure or even the hoop strain time-history curve can be solved. The hoop strain reaches a new steady state after certain steps’ calculation. 3.2. Simulation Study The above-mentioned MOC is employed in the following pipeline leakage simulation. The parameters of the pipeline are as follow: length of pipeline L = 55 km, steady mass flow rate Q = 0.0319 m3/s, acceleration of gravity g = 9.81 m/s2, NPW velocity a = 1100 m/s, hydraulic friction coefficient f = 0.015, inlet pressure
steps’ calculation. 3.2. Simulation Study The above-mentioned MOC is employed in the following pipeline leakage simulation. The 6 of 13 parameters of the pipeline are as follow: length of pipeline L = 55 km, steady mass flow rate Q = 0.0319 m3/s, acceleration of gravity g = 9.81 m/s2, NPW velocity a = 1100 m/s, hydraulic friction f = 0.015, pressure in = 1717 kPa, diameter outlet pressure out = 1570 kPa, pipet diameter Pcoefficient outlet inlet pressure Pout = P1570 kPa, pipe D = 341Pmm, pipe thickness = 8 mm, in = 1717 kPa, D = 341modulus mm, pipe t = 8pipeline mm, Young’s modulus E into = 210 Thethus, pipeline is manually Young’s E =thickness 210 GPa. The is manually divided 50 GPa. sections; the length of each divided∆xinto 50km sections; thus, the section = 1.1 and time step ∆tlength = 1 s. of each section Δx = 1.1 km and time step Δt = 1 s. All of ofthe thegrid grid nodes (except inlet outlet nodes) are the potential leak points. each All nodes (except inlet andand outlet nodes) are the potential leak points. For eachFor leakage leakage condition, hoopvariation strain variation of any nodethe along the pipeline be calculated the condition, the hoopthe strain of any node along pipeline can be can calculated by the by MOC MOC method. Several FBG strain hoop strain sensors are assumed to be installed the pipeline; thus, method. Several FBG hoop sensors are assumed to be installed along along the pipeline; thus, hoop hoop strain variation anycan node can be extracted. As an example, three leakages strain variation of any of node be extracted. As an example, three leakages (5.5 km, (5.5 27.5km, km, 27.5 49.5 km, km 49.5 km away from the inlet, respectively) are simulated to get the hoop strain variations at the away from the inlet, respectively) are simulated to get the hoop strain variations at the outlet node outlet node after leak occurrence. 5, the oscillation hoopdue strain during 1000during s after1000 leak soccurrence. As shownAs in shown Figurein 5, Figure the oscillation of hoopof strain to due the to the impact of speed high speed flowing the boundary condition observed.AAsudden sudden drop drop impact of high flowing fluidfluid withwith the boundary condition cancan bebe observed. occurs in the the first first few few seconds seconds and and finally finally reaches reaches aa smaller smaller value value than than the the initial initial hoop hoop strain. strain. It is is occurs noticed that thatdue duetotothe thedamping damping transient events, hoop strain variation is greater the noticed ofof transient events, thethe hoop strain variation is greater whenwhen the leak leak point is closer the downstream the pipeline. point is closer to thetodownstream of theofpipeline. Appl. Sci. 2018, 8, 146
160
5.5 km 27.5 km 49.5 km
Hoop strain (με)
158 156 154 152 150
0
200
400
600
800
1000
Time (s)
Figure 5. 5. Hoop Hoop strain strain time time history history at at the the end end node node in in different different leak leak locations. locations. Figure
Generally, a different leak location induces a different hoop strain variation. Therefore, potential Generally, a different leak location induces a different hoop strain variation. Therefore, potential relationships can be established between hoop strain variations and leak locations. In other words, relationships can be established between hoop strain variations and leak locations. In other words, the leak point can be located from some crucial hoop strain characteristics. In the following part, the the leak point can be located from some crucial hoop strain characteristics. In the following part, machine learning method is employed to predict leak location based on hoop strain information. the machine learning method is employed to predict leak location based on hoop strain information. 4. Leakage Leakage Localization Localization Based Based on on BP BP Neural Neural Network Network 4. As discussed discussedabove, above,thethe FBG hoop strain sensors can be installed along the pipeline as the As FBG hoop strain sensors can be installed along the pipeline as the sensing sensing element to measure the hoop strain variations. A series of hoop strain values composes element to measure the hoop strain variations. A series of hoop strain values composes eigenvectors eigenvectors to predict leakage locations. Compared with the traditional leakmethod monitoring to predict leakage locations. Compared with the traditional leak monitoring basedmethod on the based on the pressure sensor, this hoop strain-based method can provide more characteristic pressure sensor, this hoop strain-based method can provide more characteristic information since information since the FBG sensors can be nondestructively installed on the pipeline and arranged the FBG sensors can be nondestructively installed on the pipeline and arranged flexibly. In this part, a leakage localization based on the BP neural network is proposed by using multiple hoop strain characteristics. 4.1. Back-Propagation Neural Network The back-propagation neural network is a type of multilayer network that trains the weights of the nonlinear differential function. This kind of algorithm of the neural network was first put forward in 1986 by the parallel distributed processing group Rumelhart et al. Currently, the BP-based multilayer perception is one of the most widely-used neural networks. It is suitable to process the massive amount of data in long-distance pipeline monitoring with good properties of fault-tolerance, self-organized learning and self-adaptivity. The typical back-propagation network consists of an input
The back-propagation neural network is a type of multilayer network that trains the weights of the nonlinear differential function. This kind of algorithm of the neural network was first put forward in 1986 by the parallel distributed processing group Rumelhart et al. Currently, the BP-based multilayer perception is one of the most widely-used neural networks. It is suitable to Appl. Sci. 2018, 8, 146 7 of 13 process the massive amount of data in long-distance pipeline monitoring with good properties of fault-tolerance, self-organized learning and self-adaptivity. The typical back-propagation network consists an input anleast output and at least one hidden layer, as shown in Figure 6. The layer, an of output layerlayer, and at one layer hidden layer, as shown in Figure 6. The BP neural network has BP network has greatapproximation capabilities for nonlinear approximation pattern recognition, greatneural capabilities for nonlinear and pattern recognition, whichand have been used in many which have been used in many fields acrossfinance mathematics, medical science, finance and engineering. fields across mathematics, medical science, and engineering. X1
wij
Y1
w jk
……
……
……
……
X2
Y2
X3
input layer
hidden layer
output layer
Figure graph of of the the BP BP neural neural network. network. Figure 6. 6. Topological Topological graph
4.2. BPNN for Leakage Localization 4.2. BPNN for Leakage Localization The basic idea of this method is to use the BP neural network to recognize the leakage point of The basic idea of this method is to use the BP neural network to recognize the leakage point of the the pipelines through the hoop strain distribution acquired by some FBG hoop strain sensors. pipelines through the hoop strain distribution acquired by some FBG hoop strain sensors. Different Different leakage accidents bring distinct hoop strain distributions, which can be seen as a pattern leakage accidents bring distinct hoop strain distributions, which can be seen as a pattern for leakage of for leakage of a specific point. a specific point. Thus, the BP neural network for leakage localization can be established as follows. Several Thus, the BP neural network for leakage localization can be established as follows. Several hoop hoop strain sensing points are chosen as the neurons of the input layer. The variable parameter in the strain sensing points are chosen as the neurons of the input layer. The variable parameter in the output output layer is the different leakage point. It is noted that the neurons both in the input and the output layer is the different leakage point. It is noted that the neurons both in the input and the output layer layer are from the nodes in MOC as mentioned in Section 3.1. The number of neurons in the hidden are from the nodes in MOC as mentioned in Section 3.1. The number of neurons in the hidden layer layer can be determined by the input and the output layer and optimized through trial calculation. can be determined by the input and the output layer and optimized through trial calculation. In the training or learning mode, the hoop strain variations are fed to the input layer. A neuron In the training or learning mode, the hoop strain variations are fed to the input layer. A neuron of the network calculates the weighted sum of its inputs and passes it through a transfer function to of the network calculates the weighted sum of its inputs and passes it through a transfer function generate an output. The most popular transfer function is the sigmoid logistic function, which is to generate an output. The most popular transfer function is the sigmoid logistic function, which is defined as: defined as: 1 1 f (x) = (6) f ( x) =1 + e−− xx (6)
1+ e
A neuron of the output (leak point) goes to the inputs of all hoop strain neurons of the succeeding A neuron of the output (leak point) to layer. the inputs of all hoop strainOneurons the layer. The leakage point is collected at the goes output The calculated outputs k and theoferror succeeding layer. The leakage collected at the output layer. compared with desired outputspoint ek canisbe expressed respectively as: The calculated outputs Ok and the error compared with desired outputs ek can be expressed respectively as: l
Ok =
∑ Hj w jk − bk l
Ok = j=1 H j w jk − bk
(7) (7)
ek = Yk − Ok
(8)
j =1
ek = output Yk − Ok of the hidden layer. The network learns(8)by where wjk is the connection weight and H is the adjusting its weights; thus, the error is smaller in the next iteration. The weight can be shown in the following formula by considering the learning rate constant η: m
wij = wij + ηHj (1 − Hj ) x (i ) ∑ w jk ek
(9)
w jk = w jk + ηHj ek
(10)
k =1
The parameters used in the leakage prediction network need to be set for a specific pipeline. There is no integrated theory to determine the number of neurons in the hidden layers. Thus, the number is often set
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with a given performance by trial in simulation. Appropriate parameters of the network should be obtained by repeating tests. 4.3. Method Validation The BP neural network-based leakage detection system is established on the 55-km long-distance pipeline. The parameters of the pipeline are presented in Section 3.2. The pipeline is averagely divided into 50 sections, so there are 51 nodes along the pipeline (inlet and outlet included). The 49 intermediate nodes are considered as the possible leak points. Generally, the input neurons are the sensing points where the FBG hoop strain sensors are installed. However, it is not necessary to employ all of the sensing points, which may bring the problem of over fitting in the BP neural network. In this case study, five averagely divided hoop strain sensors along the pipeline are chosen as the input neurons. It is still worth mentioning for other leakage localization applications, the number of input neurons should be determined by trial to obtain the best localization results. Through leakage analysis using MOC, hoop strain variations of the five sensing points are obtained and shown in Table 1. The first column is the number of leak points, corresponding to the mid-side nodes of the present pipeline. It is noted that the values of hoop strain variations are very close; hence, it is difficult for traditional strain sensors to distinguish the differences. However, as presented in Section 2, the developed FBG hoop strain sensor is characterized by enhanced sensitivity; thus, the measured hoop strain can by amplified. Table 1. Distribution of hoop strain variations.
Leak Point 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Hoop Strain Sensing Point 1
2
3
4
5
23.04 23.03 23.02 23.02 23.01 23.00 22.99 22.98 22.98 22.97 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51
22.63 22.62 22.61 22.61 22.60 22.59 22.58 22.57 22.57 22.56 22.55 22.54 22.53 22.53 22.52 22.51 22.50 22.49 22.49 22.48 23.01 23.01 23.01 23.01 23.01
22.22 22.21 22.20 22.20 22.19 22.18 22.17 22.16 22.16 22.15 22.14 22.13 22.12 22.11 22.11 22.10 22.09 22.08 22.07 22.07 22.06 22.05 22.04 22.04 22.03
21.81 21.80 21.79 21.79 21.78 21.77 21.76 21.75 21.74 21.74 21.73 21.72 21.71 21.70 21.70 21.69 21.68 21.67 21.66 21.66 21.65 21.64 21.63 21.63 21.62
21.40 21.39 21.38 21.38 21.37 21.36 21.35 21.34 21.33 21.33 21.32 21.31 21.30 21.29 21.29 21.28 21.27 21.26 21.25 21.25 21.24 21.23 21.22 21.21 21.21
Leak Point 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Hoop Strain Sensing Point 1
2
3
4
5
23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51 23.51
23.01 23.01 23.01 23.01 23.01 23.01 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02 23.02
22.02 22.01 22.00 22.00 21.99 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52 22.52
21.61 21.60 21.59 21.59 21.58 21.57 21.56 21.56 21.55 21.54 21.53 21.53 21.52 21.51 21.50 22.03 22.03 22.03 22.03 22.03 22.03 22.03 22.03 22.03
21.20 21.19 21.18 21.18 21.17 21.16 21.15 21.15 21.14 21.13 21.12 21.11 21.11 21.10 21.09 21.08 21.08 21.07 21.06 21.06 21.05 21.04 21.03 21.03
To make the network with good convergence and mapping capability, the following equation is used to normalize the data to [0, 1] before developing the model: xi0 =
xi − xmin xmax − xmin
(11)
26
23.51
23.01
22.03
21.62
21.21
To make the network with good convergence and mapping capability, the following equation is used to normalize the data to [0, 1] before developing the model: Appl. Sci. 2018, 8, 146
xi' =
xi − xmin xmax − xmin
9 of 13
(11)
where x andxxmin arethe themaximum maximumand andminimum minimumof ofthe thehoop hoopstrain strain values values in in Table Table 1. 1. xxii is is the the max and minare where xmax 0 is the normalized value. Then, the structure of the network for original hoop strain value, and x original hoop strain value, and xii′ is the normalized value. Then, the structure of the network for leakage localization localization on on this this pipeline pipeline is is established established as as shown shown in in Figure Figure 7. 7. In In the the input input layer, layer, the the five five leakage parameters are the five hoop strain sensing points evenly spaced along the pipeline. The variable parameters are the five hoop strain sensing points evenly spaced along the pipeline. The variable parameter in in the the output output layer layer is parameter is the the leakage leakage point, point, corresponding corresponding to to 49 49 leakage leakage patterns. patterns.
5
1 1
15
Hoop strain sensing points
Leakage point
Figure 7. The BP neural network structure for leakage localization. Figure 7. The BP neural network structure for leakage localization.
The number of neurons in the hidden layer can be estimated according to the following empirical The and number of neurons the hidden layer by cantrial be estimated according to the following empirical formula, 15 neurons is aninoptimal selection calculation. In the equations, m and n are the formula, and 15 neurons is an optimal selection by trial calculation. In the equations, m and number of inputs and outputs, respectively, and a is a random integer ranging from 0–10. n are the number of inputs and outputs, respectively, and a is a random integer ranging from 0–10. l < n − 1 −1 l < n m+ + nn + + aa ll
