Calculating Method For Friction Factors Of Pipeline In Water Network Based On The Anti-Analysis Method

Urban water distribution network is an important infrastructure for cities. They are often characterized by large scale, complex structure, and numerous variables, thus making the calculation of water distribution network simulation even more difficult. Water network simulation is an important content of the management of urban water systems. To correctly determine the friction coefficient is directly related to the accuracy of the simulation. At present, there are still some problems yet to be solved in calculating the friction coefficient resistance in pipeline such as slow calculation speed, poor accuracy of calculation results, monotonous algorithms, etc. Therefore, the optimization calculation of the friction coefficient is significance for optimizing dispatch and management of urban water distribution network.With the Hazen-Williams coefficient (value C) as its study subject, this paper, based on the water distribution network hydraulic calculation basic theory. Combining the hydraulic model of water network with the anti-analysis method, the solving theory of the variable metric method and dynamic range genetic algorithm were analysed which used in the anti-analysis theory for the friction coefficient of pipeline. The square sum of the difference between measured and calculated values of node pressure as a objective function, the hydraulic balance conditions and boundary conditions were used as a restriction, the anti-analysis model for the friction coefficient of pipeline was established, and the solving method of the variable metric method and dynamic range genetic algorithm and their calculation steps were given. Use measured date from both the indoor experimental platform of water distribution network and the actual urban water distribution network to compile the calculation program of variable metric method and dynamic range genetic algorithm on MATLAB. Based on the calculated friction coefficient, the EPANET software is used to simulate the water distribution network again. Original values, measured values, calculated values of node pressure and pipe flow are analyzed and compared. Meanwhile, the accuracy and universality of the anti-analysis model for the friction coefficient resistance of pipeline are verified.With the indoor experimental model of water distribution network as the study subject and the data measured in pipeline as the basis, the average absolute and relative error between measured and calculated values of node pressure and pipe flow under five working conditions are 0.19m,0.08L/s and 2.51%,3.89% when the variable metric method is used to calculated. The program operation takes 23 seconds in total. The average absolute and relative error between measured and calculated values of node pressure and pipe flow under five working conditions are 0.17m,0.06L/s and 2.43%,3.29% when the dynamic range genetic algorithm is used to calculated. The program operation takes 78 seconds in total.With the actual urban water distribution network as the study subject and the data measured in pipeline as the basis, the average absolute and relative error between measured and calculated values of node pressure and pipe flow under five working conditions are 0.17m,1.74L/s and 0.60%,0.92% when the variable metric method is used to calculated. The program operation takes 243 seconds in total. The average absolute and relative error between measured and calculated values of node pressure and pipe flow under five working conditions are 0.03m,0.32L/s and 0.12%,0.15% when the dynamic range genetic algorithm is used to calculated. The program operation takes 640 seconds in total.It indicates, through calculation and analysis, that variable metric method is preferable in calculating the friction coefficient in small-scale or pipeline group. Its advantages include smaller calculation amount, fast calculation speed and convenient programming. Whereas for medium-scale water distribution networks, the dynamic range genetic algorithm is a more suitable choice. Although its operation time and amount of calculation are both larger than those of the variable metric method, the dynamic range genetic algorithm is still superior in terms of computational accuracy, stability of calculation results, and global searching ability.