Optimal Design of Pressure Sampling in Water Distribution Networks for Calibration of Hydraulic Models

Simulating and understanding of abnormal conditions is one of the most important applications of hydraulic models of water distribution networks. Hence, existence of calibrated models is essential to network behavior realization. This process requires field data collection to improve model's performance by comparing predicted and actual data. Sampling from network has different constraints. Therefore the sampling design process is performed in order to optimize it, which includes different aspects of sampling, such as location, number and frequency. This paper focuses on pressure sampling nodes for hydraulic model calibration. To implement sampling design, first by sensitivity analysis, uncertainty of each nodal pressure is divided between model inputs.

In this paper, a global sensitivity analysis method, Sobol, is used which divides the variance of model into model inputs and their interactions. Then, two criteria for selecting sampling points are defined. The first criterion maximizes the entropy and magnitude of sensitivity values of each parameter for the set of sampling design points. The second criterion, by replacing number of points with sampling costs, follows minimization of sampling costs. To solve the integer multi-objective optimization problem, the multi-objective integer genetic algorithm called MI-NSGA-II is employed.

Investigating different scenarios demonstrates effect of parameter type on the position of selected points. In the meantime, similarity between the results of combinatorial and individual scenarios decreases from cases including roughness to cases involving demand. This indicates effective role of roughness in selecting points in combinatorial scenarios. Also, analysis of combinatorial scenarios suggests that parameter interactions are effective in selecting points.

The results showed that the developed approach offers good performance in selecting sampling points with different scenarios. The MI-NSGA-II algorithm has a good ability to find the solutions of the integer multi-objective optimization problem. The use of pressure driven simulation method is effective on the results of sensitivity analysis and sampling design.