dx.doi.org/ /wwj ( ).(Haghighi & Keramat 2012)

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1 - - a.haghighi@scu.ac.ir ( ) - (// // ) :..(Haghighi & Keramat 1)

2 SQP..(Shamloo & Haghighi 9)..(Haghighi 1) Sequential Quadratic Programming (SQP) 6 Gradient-based Method.(Ligget & Chen 1994; Vitkovsky et al. ; Kapelan et al., 3, 4; Jung & Karney 8; Shamloo & Haghighi 9, 1; Haghighi & Ramos 1). (Ligget & Chen 1994) LM. GA.(Vitkovsky et al. ).(Kapelan et al. 3; 4) GA LM. LM GA. GA GA LM (Kapelan et al. 3; 4).. 1 Levenberg-Marquardt (LM) Genetic Algorithms (GA) 3 Hybrid optimization 4 Inverse Backward Transient Analysis (IBTA)

3 *..(Wylie & Streeter 1993) Q=(qQ ) H=(hH ) q h "". h a t ga h x = 1 ga q x q f Q t gd A 16ν q gd A a ˆ iωĥ ga dĥ dx iω ga dqˆ dx q ( * W )(t) = t () () = f Q gda iωŵ16ν qˆ = DA () () ". " ω i = 1. (Chaudhry ω l 1 qˆ D = (cosh µ l)qˆ U (sinh µ l) ĥ U z ĥ = Z(sinh µ l)qˆ (cosh µ l) ĥ D U 14) () () D U µ U..(Covas & Ramos 1; Kim 1) ) ( (Vitkovsky et al. 11) H a t ga H x = 1 ga Q x Q fq Q t gd A 16ν gd A Q ( * W)(t) = t A D g () () a H W ν ρ. t x 36

4 R u R s Z iω µ = a (1 R S R U () (a) a Z = (1 RS R U ga 3ν iωd RS = f Q iωda for laminar flow for turbolentflow () () (b) Fig. 1. Hypothetical stimulation a) in the time domain and b) in the frequency domain (b (a -. (b- ). FRD... R U ν16ŵ = D ()... (a-).. (b-) (b-) -. * 3 Freqency Respons Diagram (FRD) 1 Propagation constant Characteristic impedance 37

5 : :. :. : (γ β α). : C = ( h h ) N M = = i 1 j 1 m ji nij () i h mij h nij ( ) j ) j i N M (. C h. ) (γ β : α). ( 1 Fast Fourier Transform (FFT) - (Vitkovsky et al. 11; Wylie & Streeter 11; Chaudhry 14; Kim 7, 8; Zecchin et al. 9). ( : ( ( ( ). (. -. γ β α.. β α ) (γ. 38

6 . α. ε ε α * ε 1.51 = log D f 3.7 Re f () α (Haghighi 9) ) ( (Vitkovsky et 1 iω i D 1 R ω U = ga 4 * C ν al. 3) () C * 1 Vardy Brown 3 Shear decay coefficient... (γ β α) (γ β α) R S f Q = jω ε 1.51 = log D f 3.7 Re f -- f DA () ε. ε 39

7 (IST).() (Covas & Ramos 1) * 7.41 C = k Re, k = log Re.5 () β.. ' R U = β * R U () α β. -- (Chaudhry 14) Fig.. Model adapted from Ref. (Covas & Ramos 1) Covas & Ramos 1 - m. (PN1) 1 kg/m PVC. α = K / ρ 1 (k / E) Ψ () α E K ρ ψ. γ a = γa () Instituto Superior Técnico (IST), Technical University of Lisbon 1 Bulk Modulus 4

8 H(m) T Time (s) H(m) T Time (s) 4 T3 4 T4 H(m) 3 5 H(m) Time (s) Time (s) 4 T5 4 T6 H(m) 3 5 H(m) Time (s) Time (s) Fig. 3. Pressure variations versus time related to reference points T1 to T6 T6 T1 -.. :.. / T6 T1.. /. D =mm e = / mm -. ε = * m. a = m/s. ( ) T6 T1.. 1 Gate valve Ball valve 3 Electromagnetic flow meter 41

9 : ( ). ( ).. : FFT ( ). :. ( ) T6 T1.. h (m) T1 h (m) T.5.5 h (m) T h (m) T h (m) T5.3 T Fig. 4. and experimental frequencies of reference points T1 to T6 T6 T1 - h (m) 4

10 .... Fig. 5. Optimization trend - - Table 1. Accuracy of the numerical model of transient flow analysis versus frequency for the points calculated Reference node No. T1 T T3 T4 T5 T6 Max. Error percent ( : (. / / (γ β α ) / / / - - * m /* m / /. / /. γ β α.... / / Uniform Cross Over Method 43

11 h (m) h (m) T T3 h (m) h (m) T T4 h (m) T5 h (m) Fig. 6. Calibrated numerical and experimental frequencies of reference points T1 to T6 T6 T T

12 .. Didia Covas - Helena Ramos (IST) ( ( References Chaudhry, M.H., 14, Applied hydraulic transients, 3 rd Ed., Springer New York Heidelberg Dordrecht London. ISBN (ebook) Covas, D. & Ramos, H., 1, "Hydraulic transients used for leakage detection in water distribution systems", In:Proceedings of the 4th Conference on Water Pipeline Systems: Managing Pipeline Assets in an Evolving Market, York, UK Haghighi, A. & Keramat, A., 1, "A fuzzy approach for considering uncertainty in transient analysis of pipe networks", Journal of Hydroinformatics, 14 (4), Haghighi, A. & Ramos, H.M., 1, "Transient detection of leakage freshwater and friction factor calibration in drinking networks using central force optimization", Water Resource Management, 6, Haghighi, A., 1, "Multi criteria calibration of pipelines under unsteady flows", Journal of Hydraulic, 5(1), Haghighi, A., 9, "Development of leak detection and calibration methods in pipelines based on inverse transient modeling", PhD Thesis, K.N. Toosi Univversity of Technology, Tehran, Iran. (In Persian) Jung, B.S. & Karney, B.W., 8, "Systematic exploration of pipeline network calibration using transients", Journal of Hydraulic Research, 46(1),

13 Kapelan, Z.S., Savic, D.A. & Walters, G.A.,, "Hybrid GA for calibration of water distribution models", In: Proc. EWRI, Roanoke, VA. Kapelan, Z.S., Savic, D.A. & Walters, G.A., 3, "A hybrid inverse transient model for leakage detection and roughness calibration in pipe networks", Journal of Hydraulic Research, 41 (5), Kapelan, Z.S., Savic, D.A. & Walters, G.A., 4, "Incorporation of prior information on parameters in inverse transient analysis for leak detection and roughness calibration", Urban Water Journal, 1 (), Kim, S., 7, "Impedance matrix method for transient analysis of complicated pipe networks", Journal of Hydraulic Research, 45(6), Kim, S. H., 8, "Address-oriented impedance matrix method for generic calibration of heterogeneous pipe network systems", Journal of Hydraulic Engineering, 134(1), Kim, S.H., 1, "Dynamic memory computation of impedance matrix method", Journal of Hydraulic Engineering, 137 (1), Liggett, J.A. & Chen, L. C., 1994, "Inverse transient analysis in pipe networks", Journal of Hydraulic Engineering, 1 (8), Shamloo, H. & Haghighi, A., 9, "Leak detection in pipelines by inverse backward transient analysis", Journal of Hydraulic Research, 47(3), Shamloo, H. & Haghighi, A., 1, "Optimum leak detection and calibration of pipe networks by inverse transient analysis", Journal of Hydraulic Research, 48(3), Vítkovský, J. P., Lee, P.J., Zecchin, A.C., Simpson, A.R. & Lambert, M.F., 11, "Head-and flow-based formulations for frequency domain analysis of fluid transients in arbitrary pipe networks", Journal of Hydraulic Engineering, 137(5), Vitkovsky, J.P., Lambert, M.F., Simpson, A.R. & Bergant, A., 3, "Steady-oscillatory flow solution including unsteady friction in : Pumps", Cebrera E., and Cebrera, E. Jr.,A.A. (Eds.): Electromechanical devices and systems applied to urban water management, Balkema Publishers, Lisse. Vitkovsky, J.P., Simpson, A.R. & Lambert, M.,, "Leak detection and calibration using transients and genetic algorithms", Journal of Water Resources Planning and Management, 16 (4), Wylie, E.B. & Streeter, V.L., 1993, Fluid transientsin systems, Prentice Hall, Englewood Cliffs, New Jersey, USA. Zecchin, A. C., Simpson, A. R., Lambert, M. F., White, L. B. & Vítkovský, J. P., 9, "Transient modeling of arbitrary pipe networks by a Laplace-domain admittance matrix", Journal of Engineering Mechanics, 1(6),