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http://dx.doi.org/10.3741/JKWRA.2013.46.4.389

Application of Levenberg Marquardt Method for Calibration of Unsteady Friction Model for a Pipeline System  

Park, Jo Eun (Dept. of Environ. Engrg., Pusan National Univ.)
Kim, Sang Hyun (Dept. of Environ. Engrg., Pusan National Univ.)
Publication Information
Journal of Korea Water Resources Association / v.46, no.4, 2013 , pp. 389-400 More about this Journal
Abstract
In this study, a conventional pipeline unsteady friction model has been integrated into Levenberg Marquardt method to calibrate friction coefficient in a pipeline system. The method of characteristics has been employed as the modeling platform for the frequency dependant model of unsteady friction. In order to obtain Hessian and Jacobian matrix for optimization, the direct differentiation of pressure to friction factor was calculated and sensitivities to friction for heads and discharges were formulated for implementation to the integration constant in the characteristic method. Using a hypothetical simple pipeline system, time series of pressure, introduced by a sudden valve closure, were obtained for various Reynolds numbers. Convergency in fiction factors were evaluated both in steady and unsteady friction models. The comparison of calibration performance between the proposed method and genetic algorithm indicates that faster and stabler behaviour of Levenberg Marquardt method than those of evolutionary calibration.
Keywords
calibration of unsteady friction model; levenberg marquart method; waterhammer; method of characteristics;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Adamkowski, A., and Lewandowski, M.L. (2006). "Experimental examination of unsteady friction models for transient pipe flow simulation." Journal of Fluid En1eering, ASME, Vol. 128, No. 6, pp. 1351-1361   DOI   ScienceOn
2 Bergant, A., Simpson, A.R., and Vitkovsky, J. (2001). "Developments in unsteady pipe flow friction modelling." Journal of Hydraulic Research, Vol. 39, No. 3, pp. 249- 258.   DOI   ScienceOn
3 Boulos, P.F., and Wood, D.J. (1990). "Explicit calculation of pipe network parameters." Journal of Hydraulic Engineering, ASCE, Vol. 116, No. 11, pp. 1329-1344.   DOI
4 Chaudhry, M.H. (1987). Applied Hydraulic Transients, Van nostrand reinhold company, NY.
5 Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Co., Inc.
6 Jang, I., Kim, S.H., and Kim, J.H. (2008). "Transient analysis of pipeline system considering unsteady friction models." Journal of the Korean Society of Water and Wastewater, Vol. 22, No. 6, pp. 657-664.
7 Jung, B.S., and Karney, B.W. (2006). "Optimization of transient protection devices using GA and PSO approaches." Journal of Water Resources Planning and Management, Vol. 132, No. 1, pp. 44-52.   DOI   ScienceOn
8 Jung, B.S., Karney, B.W. (2004). "Particle swarm optimization compared to a genetic algorithm for calibration of water distribution system." Proceeding of 9th International Conference on Pressure Surges, Chester, UK, March.
9 Kapelan, Z.S., Savic, D.A., Walters, G.A. (2003). "A hybrid inverse transient model for leakage detection and roughness calibration in pipe networks." Journal of Hydraulic Research, Vol. 41, No. 5, pp 481-492.   DOI
10 Karney, B.W., and McInnis, D. (1992). "Efficient calculation of transient flow in simple pipe networks." Journal of Hydraulic Engineering, ASCE, Vol. 118, No. 7, pp. 1014-1030.   DOI
11 Kim, M.G., Noh, J.S., Park, N.S., and Kim, S.H. (1998). "Unsteady pipeflow friction characteristics." Proceedings of Korea Society of Civil Engineers Conference, Vol. 1998, No. 3, pp. 93-96.
12 Lansey, K.E., and Basnet, C. (1991). "Parameter estimation for water distribution networks." Journal of Water Resources Planning and Management, Vol. 117, No. 1, pp. 126-144.   DOI
13 Liggett, J.A., and Chen, L.C. (1994). "Inverse transient analysis in pipe networks." Journal of Hydraulic Engineering, ASCE, Vol. 120, No. 8, pp. 934-955.   DOI   ScienceOn
14 Ministry of Environment, Republic of Korea (2010). Statistics of Waterworks.
15 Nash, G.A., and Karney, B.W. (1999) "Efficient inverse transient analysis in series pipeline systems." Journal of Hydraulic Engineering, ASCE, Vol. 125, No. 7, pp. 761-764.   DOI
16 Ormsbee, L.E., and Wood, D.J. (1986). "Explicit pipe network calibration." Journal of Water Resources Planning and Management, Vol. 112, No. 2, pp. 166- 182.   DOI   ScienceOn
17 Pudar, R.S., and Liggett, J.A. (1992). "Leaks in pipe networks." Journal of Hydraulic Engineering, ASCE, Vol. 118, No. 7, pp. 1031-1046.   DOI
18 Roberson, J.A., and Crowe, C.T. (1985). Hydraulic Engineering Fluid Mechanics, 3rd Ed. Houghton Mifflin, Boston.
19 Son, K.I. (1997) "Predicting flow resistance coefficients in water supply mains" Journal of Korea Water Resources Association, Vol. 29, No. 4, pp. 223- 231.
20 Vitkovsky, J., Stephens, M., Bergant, A., Simpson, A., and Lambert, M. (2006). "Numerical error in weighting function-based unsteady friction models for pipe transients." Journal of Hydraulic Engineering, ASCE, Vol. 132, No. 7, pp. 709-721.   DOI   ScienceOn
21 Vitkovsky, J.P., Simpson, A.R., and Lambert, M.F. (2000). "Leak detection and calibration using transients and genetic algorithms." Journal of Water Resource Planning and Management, Vol. 126, No. 4, pp. 262- 265.   DOI   ScienceOn
22 Zielke, W. (1968). "Frequency-dependent friction in transient pipe flow." Journal of Basic Engineering, Vol. 90, No. 1, pp. 109-115.   DOI
23 Walski, T.M. (1983). "Techniques for calibrating network models." Journal of Water Resources Planning and Management, Vol. 109, No. 4, pp. 360-372.   DOI
24 Walski, T.M. (1987).Water supply system rehabilitation, Task Committee on Water Supply Rehabilitation Systems, ASCE, New York.
25 Wylie, E.B., and Streeter, V.L. (1993). Fluid transients in system, Prentice-Hall, Englewood cliffs, N.J.