Uncertainty analysis of water supply networks using the fuzzy set theory and NSGA-II

This work introduces an approach for taking into account the uncertainty of pipe friction coefficients and nodal demands in the hydraulic analysis of water supply networks. For this purpose, uncertainties are represented by fuzzy numbers and incorporated into the network׳s governing equations. Input uncertainties are spread out on the network and influence its hydraulic responses, including pipe velocities and nodal pressures. To estimate the responses׳ uncertainty, input fuzzy numbers are discretized in some levels of membership function. Then, a multiobjective optimization problem is developed for each level to find the extreme values of the node pressures and pipe velocities. The raised problem is solved using the method of Non Dominated Sorting Genetic Algorithm (NSGA-II) coupled to the network hydraulic simulation model. The proposed approach is applied to an example and a real pipe network. It is found that small uncertainties in input variables can significantly influence the network׳s responses as well as its performance reliability. It is also concluded that NSGA-II has a great role in solving the problem systematically, and improves the computational efficiency of the whole process of network fuzzy analysis.