Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 70 (2014) 924 – 933 12th International Conference on Computing and Control for the Water Industry, CCWI2013 Holistic diagnosis of pipeline system with impedance method S Kima* a Department of Environmental Engineering, College of Engineering, Pusan National University Busandaekak-ro 63beon-gil, Geumjeong-gu, Busan, 609-735 Republic of Korea Abstract In this study, a diagnosis potential of impedance method implementing several unsteady friction models for a pipeline system with or without leakage The development based on impedance approach provides a feasible and flexible modelling environment that can address not only for various fundamental system properties, but also for dynamic variables in transient generation Calibration parameters cover conventional diagnostic parameters such as friction parameters and leakage, steady and transient condition parameters such as the initial flow rate and valve closure duration, and system characteristics such as pipeline length and wave propagation speed Based on the perspective of the impedance for system definition, corresponding response functions in the frequency domain approach were derived Time domain responses of pipeline systems were integrated into the genetic algorithm for inverse transient analysis Unsteady models addressed both frequency-dependent friction and acceleration-based frictions Parameter calibrations with experimental data have shown that the impedance-based approach provides a versatile and feasible optimization structure via the objective fitting function of the pressure head variation The performance of the integrated optimization examples demonstrates the robustness of the impedance-based approach for a representation of a real-life system, a diagnosis of system abnormality and a configuration of system characteristics © © 2013 2013The TheAuthors Authors.Published PublishedbybyElsevier ElsevierLtd Ltd Selection thethe CCWI2013 Committee Selectionand andpeer-review peer-reviewunder underresponsibility responsibilityofof CCWI2013 Committee Keywords: Pipeline system; impedance method; inverse transient analysis; unsteady friction * Corresponding author E-mail address: kimsangh@pusan.ac.kr 1877-7058 © 2013 The Authors Published by Elsevier Ltd Selection and peer-review under responsibility of the CCWI2013 Committee doi:10.1016/j.proeng.2014.02.103 S Kim / Procedia Engineering 70 (2014) 924 – 933 Introduction Traditionally, transient analysis in water distribution system have been explored in the context of discretization methods such as the method of characteristics (MOC), even with its substantial limitations in the representation of system characteristics such as pipeline length, and location of abnormalities such as leakage and unauthorized use (Liggett and Chen 1994; Wylie and Streeter 1993) Inverse transient analysis (ITA) of a pipeline system was developed after the introduction of the leakage detection approach (Liggett and Chen 1994) based on the Levenberg-Marquardt (LM) method However, uncertainty in pipeline systems and boundary conditions may substantially diminish the leakage calibration potential of ITA (Jung and Karney 2008; Puust et al 2010; Vitkovsky et al 2007) An alternative approach for the detection of any irregularity in a pipeline is applying algorithms in the frequency domain There are two different approaches to frequency domain modeling: one is the frequency response method, which explores the amplitude of pressure oscillation in the frequency domain (Ferrante and Brunone 2003; Lee et al 2006; Mpesha et al 2001; Sattar et al 2008), and the other is the impedance-based approach, which formulates transient responses in the frequency domain but converts them into the time domain and uses the results for the calibration (Kim 2005, 2008; Zecchine et al 2009, 2010) As there are various uncertainties in real-life systems, further generic calibration of the system characteristics such as material properties and various anomalies can contribute to the robustness of the detection algorithm (Covas and Ramos 2010; Kim 2008; Meniconi et al 2011) Recent research on impedance-based frequency domain modeling has demonstrated several strengths over other approaches, e.g., computational efficiency and representation of system properties, in the transient simulation (Kim 2008, 2011) On the basis of the development of unsteady friction considerations (Kim 2005; 2011), the impedance-based method is extended to highlight the robustness of the proposed method for generic calibration of a reservoir pipeline valve (RPV) system with leakage Comprehensive inverse transient analysis is performed to calibrate various parameters, including leakage, system characteristics, and flow and valve modulation conditions The proposed method is tested for an experimental RPV system to demonstrate the potential of the impedance-based approach for the generic configuration of pipeline system characteristics Nomenclature a D f g H k t x V wave propagation speed diameter Darcy-Weisbach friction factor gravitational acceleration piezometric head unsteady friction coefficient time distance mean velocity Material and Method 2.1 Transient Models for the Pipeline System The one-dimensional governing equations for transient flow in a pipeline consist of the motion and continuity equations, which can be expressed as follows (Wylie and Streeter 1993) 925 926 S Kim / Procedia Engineering 70 (2014) 924 – 933 ∂V ∂H + + J =0 g ∂t ∂x (1) a ∂V ∂H (2) =0 + g ∂x ∂t where, J = head loss per unit length due to friction The friction head loss component J can be divided into two components, namely, the steady friction based on the Darcy-Weisbach friction relationship (Wylie and Streeter 1993) and the unsteady friction based on instantaneous acceleration (Brunone et al 1991, 1995; Vitkovsky et al 2006), as follows fV V k ∂V ∂V (3) ) J= −a + ( gD g ∂t ∂x 2.2 Impedance expression for a pipeline system with leakage Fig A reservoir pipeline valve(RPV) system with a leakage A leakage is introduced into an RPV system, as shown in Fig In order to define the impedance, the ratio of head to discharge must be determined along the system in Fig The expressions of complex head and discharge can be derived by applying the constant head condition of the upstream reservoir Assuming the relationship between head and discharge (based on the unsteady friction, originated from the instantaneous acceleration) the impact of a leakage can be implemented using the point matrix for the leakage (Mpesha et al 2001), and the head and discharge downstream of the leakage can be expressed as follows H dsl = Qdsl = ( γ 1γ ( e −γ ( l − xl ) − eγ ( l − xl ) ) QU Cs( γ + γ ) (4) γ 1e −γ ( l − xl ) + γ eγ 1( l − xl ) Qolk γ 1γ ( e −γ ( l − xl ) − eγ 1( l − xl ) ) )QU − 2H0 Cs( γ + γ ) γ1 + γ2 (5) γ 1,2 = ( ∓ mCs + ( mCs )2 + 4( s 2CL' + RCs ) ) / (6) where, m = (ak′)/(2gA), and L”= (1+ k′)/(gA); k′ is the unsteady friction coefficient determined via frequency domain analysis, xl is the distance between the leakage and the downstream valve, Qolk is the mean leakage discharge, and H0 is the mean pressure head Applying the transfer relationships between downstream and upstream points (Kim 2005), the complex head and discharge at the downstream valve, H valve and Qvalve , can be obtained, and the head response at the downstream valve due to the discharge impulse can be expressed as follows: 927 S Kim / Procedia Engineering 70 (2014) 924 – 933 rh ,v = π ∞ Re[ ∫0 Z valve ⋅ eiωt dω ] (7) where, Z valve = H valve / Qvalve If frequency-dependent friction (Suo and Wylie 1989) is used for unsteady friction, the head response at the downstream valve of Fig due to the discharge impulse is as follows: ∞ rh ,v ' = Re[ ∫0 Z valve ' ⋅eiωt dω ] (8) − Z S cosh Γ x sinh Γl − x + Qolk Z S sinh Γ x sinh Γl − x /( H ) + sinh Γ x cosh Γl − x sinh Γ x sinh Γl − x + Qolk Z S cosh Γ x sinh Γl − x + cosh Γ x cosh Γl − x (9 π Z valve' = Γ x = sx /( a − J ( iD / s / ν ) ( iD / s / ν J ( iD / s / ν )) (10) Z S = a /( gA − J ( iD / s / ν ) ( iD / s / ν J ( iD / s / ν )) where, J0 and J1 are the first-type Bessel functions of the zeroth and first orders, respectively (11) 2.3 Parameter calibration with Genetic Algorithm In order to calibrate parameters for pipeline system, the impedance expressions with leakage were integrated into the GA (Goldberg 1989) Once the transient analysis with the impulse response function was completed, the time histories of the pressure head for the designated locations were generated Using the pressure head measured from the water hammer phenomenon, the fitness of each candidate solution was estimated To find the global optimum via calibration, the difference between the measured and estimated pressure heads should be minimized The objective function (OF) for minimizing the measured and calibrated pressure head variation can be expressed in terms of the pressure head time series, as follows: n OF = Minimize ∑ ( hio − him )2 (12) i =1 where hio is the optimized pressure head and him is the measured pressure head The evolutionary computation starts from randomly generated individuals, and the fitness of all candidate solutions is evaluated using response functions such as Eqs (7) and (8) Multiple surviving solutions are selected from the contemporary generation and are mixed and modified to form the population of the next generation Propagation constants and impedance characteristics are renewed with different combinations of the surviving solutions The final solution can be obtained via the identification of the best fitness in Eq (11) from all iterations 928 S Kim / Procedia Engineering 70 (2014) 924 – 933 2.4 A pilot scale pipeline system Energy Line B A 23.20 m C Data Acquisition System Pressure Transducer Control Valve 22.8 m Leakage Pressurized Tank 65.42 m 87.22 m Fig A pilot scale pipeline system for transient experiment A pilot-scale pipeline system equipped with multiple water tanks, valves, and a pressurized water tank along a pipeline was constructed, as shown in Fig The internal diameter of the stainless steel pipeline is 0.02 m The pipe wall has a thickness of mm and an elastic modulus of 193 Gpa The theoretical wave speed is estimated as 1429.9 m/s but it is measured in the time domain to be as low as 1395 m/s In order to accurately secure the designated steady flow, water was supplied to water tank A and free surface elevations were maintained in the water tanks, allowing overflow through multiple valves in the water tanks (16 for each water tank) A steady flow was controlled by the difference in the opening valve elevations between the two water tanks Experiments were performed for both steady flows with leakage and those with no leakage The flow rates for the initial steady state were estimated using multiple volumetric measurements No difference was found in steady flow rates for the three tests with identical head differences for six different Reynolds numbers (RNs) A water hammer was introduced by rapid closure of the ball valve, as shown in Fig The pressure transducers(LapTP14, AEP) monitored head variations at the point of the ball valve Pressure data were recorded 1000 times per second using a data acquisition card (DAQCard-6024E from National Instruments) Result and Discussion The sampling frequency of pressure measurements and the modeling time interval should be matched and the maximum frequency range for the impedance-based analysis was specified to 3141.59 rad/s The number of samples for the Fast Fourier Transform was 8192 The valve action was specified as a linear closure from τ = to τ S Kim / Procedia Engineering 70 (2014) 924 – 933 929 = 0, where τ = CD Α /( CD Α )0 ; C D = valve coefficient, A = valve opening area, and subscript indicates the initial reference state Table The parameter calibrations using a frequency domain model (Kim 2005) employing Brunone’s approach (Brunone et al 1991) and the pressure series at the end of the RPV system with a leakage Q0 RN Xleak Qleak wave speed pipe VCD k (m/s) length 10-6 10-5 (m) (m) (s) (m3/s) (m3/s) 1414.8 0.0957 4.10 84.70 0.0173 2252 21.72 14.99 (12.60) (3.54) (87.22) (21.80) 2732 21.80 5.52 1415.6 0.0814 4.41 85.38 0.0158 (21.80) (5.14) (4.29) (87.22) 3151 18.74 15.00 1418.6 0.0273 4.51 88.90 0.0494 (21.80) (17.50) (4.95) (87.22) 3915 17.25 4.05 1418.8 0.0897 5.37 85.51 0.0297 (21.80) (5.36) (6.16) (87.22) where, RN: Reynolds number; Xleak: the distance to leakage from the end valve; Qleak: the leakage discharge; k: the unsteady friction coefficient for the model by Kim (2005); Q0: the steady flowrate; VCD: valve closure duration The numbers in brackets are field measurements Using the pressure time series obtained from the end of the pipeline system with a leakage, GA optimizations were performed for four different RNs in order to calibrate parameters using Eq (12) In order to estimate the pressure response, Eq (7) was implemented and used for the optimized head in Eq (12) Considering the broad characteristics in the search parameters, the population size was 100 and the maximum generation was 101 Other parameters such as mutation probabilities and crossover probability were determined according to the recommendation of Carroll (2002) The search ranges of parameters were specified either by considering physically meaningful limits of both the maximum and minimum of the parameters such as lengths and discharges or by referring to the upper and lower bounds from previous studies (Adamkowski and Lewandowski 2006; Bergant et al 2001; Kim 2011; Pezzinga 2009) for parameters such as friction coefficient and wave speed Table presents simultaneous calibrations using the model by Kim (2005) for various parameters, such as the distance to the leakage (m), leakage discharge (m3/s), wave speed (m/s), unsteady friction coefficient, initial steady flow rate (m3/s), length of the pipeline (m), and the valve closure duration (VCD) (s) The predictions for leakage location and discharge, pipeline length, and initial discharge agreed well with the measurements of the system for four different RNs The calibrations of wave speeds were also similar, but those for the unsteady friction coefficients provided one calibration, 0.0273, that was significantly different from the other three results, which were 0.0957, 0.0814, and 0.0897, which may be associated with the difference in VCDs for corresponding RNs Slower valve closure may introduce a less abrupt pressure surge, which results in a lower unsteady friction impact than that of a more rapid surge Table The parameter calibrations using frequency dependent friction model (Suo and Wylie 1989) and the pressure series at the end of the RPV system with a leakage Qleak wave speed Q0 pipe VCD RN Xleak (m/s) length 10-6 10-5 (m) (m) (s) (m3/s) (m3/s) 1416.2 4.09 88.14 0.0173 2252 19.05 14.62 (12.60) (3.54) (87.22) (21.80) 2732 24.87 7.34 1387.4 4.37 86.42 0.0156 (21.80) (5.14) (4.29) (87.22) 3151 20.45 15.00 1382.1 4.68 86.42 0.0494 930 S Kim / Procedia Engineering 70 (2014) 924 – 933 (21.80) (17.50) (4.95) (87.22) 20.78 7.56 1403.8 5.49 87.41 0.0325 (21.80) (5.36) (6.16) (87.22) where, RN: Reynolds number; Xleak: the distance to leakage from the end valve; Qleak: the leakage discharge; Q0: the steady flowrate; VCD: valve closure duration The numbers in brackets are field measurements 3915 Employing the frequency-dependent model of Suo and Wylie (1989), the comprehensive calibration procedure was performed with pressure measurement at the end of the pipeline system (see Table 2) Predictions for leakage location and quantity agreed well with the field measurements, and other system parameters, such as the length of the pipeline and the steady flow rate, also agreed well with the measurements The consistency between the VCDs and wave speeds in Table appears to be greater than that between the VCDs and wave speeds in for Table Figure (a) and (b) shows the time series of pressure measurements and predictions at the end of the pipeline system when the system has a leakage with an initial RN = 2733, using the head measurements at the end with the models of Kim (2005) and Suo and Wylie (1989) The impact of a leakage can be observed as the sinking portion of the high-pressure response and the rising part for the low-pressure response The impact of leakage appeared as sinks of pressure before and after the positive peak, and vice versa for the negative peak The generic parameter calibration illustrated in Table and Table indicates that the requirements of inverse transient analysis, known as well-defined system characteristics and boundary conditions (Covas and Ramos, 2010; Puust et al 2010; Vítkovský et al 2007), can be feasibly addressed in the proposed calibration structure The strength of this approach is associated mainly with the structure of the impedance method The impedance method allows a simultaneous consideration of a range of parameters, such as the leak location, quantity, wave speed, pipeline, and friction parameter, into a single response function (see equations (7) and (8)) depending on the friction consideration A direct implementation of the response function into GA introduces substantial feasibility in the parameter searching capability The parameters for the initial flow rate and valve action can also be considered in a transient computation This calibration structure provides the parameter searching environment for continuous and real number ranges, whereas the time domain approach only allows limited searching space or a designated spatial scale in the pipeline length and leak location, which should also be corrected with the wave speed in every iteration in calibration The complexity in the calibration scheme implementation in the impedance based method is more straightforward than that of the time domain approach 931 S Kim / Procedia Engineering 70 (2014) 924 – 933 50 Head(m) 40 30 20 10 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.0 1.2 Time (seconds) (a) 50 Head(m) 40 30 20 10 0.0 0.2 0.4 0.6 0.8 Time (seconds) (b) Fig Time series of pressure measurements(solid black line) and the unsteady friction models of Kim (2005) (dotted line) (a); and Suo and Wylie (1989) (grey line) at the end of the pipeline system with calibrated parameters using pressure measurements at the end 932 S Kim / Procedia Engineering 70 (2014) 924 – 933 Conclusion In the practical application of inverse transient analysis, the uncertainty of real-life systems (especially underground systems), e.g., dimensions of systems, and additional costs in the collection of supplementary data for the modeling can present challenging issues The uncertainty in a real-life system cannot be adequately considered in the structure of grid based modeling approaches In this study, the capability of the proposed method of system configuration not only covers conventional parameters such as the leakage and friction factor but also expands to initial flow rate, wave speed, pipeline length, and valve closure duration As an alternative modeling approach, the platform of the impedance-based method provides substantial feasibility in the description of various properties of a pipeline system in the context of generic calibration Combining the evolutionary searching algorithm with the analytical expression provides a modeling structure for calibrating parameters in the continuous domain Furthermore, the frequency-based expression eliminates time-dependent characteristics for transient modeling, and this facilitates the expression of information transfer in conjunction with wave speed and geometric features Acknowledgements This subject is supported by Basic Science Program through the National Research Foundation of Korea (NRF) (2010-0021511) References Adamkowski, A., and Lewandowski, M., 2006 Experimental examination of unsteady friction models for 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in pipe networks with compound nodes using a Laplace-domain admittance matrix Journal of Hydraulic Engineering 136(10), 739-755 933