Optimal Size and Placement of Water Hammer Protective Devices in Water Conveyance Pipelines

Positive and negative pressure waves caused by water hammer possibly may lead to high damages to the water conveyance pipelines. To decrease the negative effects of pressure waves, costly equipment are implemented in pipelines. An economic design of these devices that also provides the safety of the pipeline against water hammer pressure waves and cavitation can be achieved by simulation and optimization tools. In this paper, the simulation task was carried out by meta modeling. The accuracy of three meta models: artificial neural network (ANN), support vector regression (SVR) and adaptive neuro-fussy inference system (ANFIS) was evaluated. According to the results, SVR was identified as the inferior method due to low capability of generalization, ANFIS as the median, and ANN as the superior method for function approximation. Then, ANN was coupled with an evolutionary algorithm (EA), Differential Evolution (DE) to find the optimal size and location of water hammer control devices in a water pipeline. Optimization was carried out on two single- and multi-objective approaches. The results showed that multi-objective optimization approach presents better designs than the single objective approach and optimal designs obtained by both approaches outperform the current setup of the water hammer facilities in terms of both costs and functionality. The single objective-based design could decrease the costs up to 12.5% whereas multi-objective approach was able to reach nearly 30% cost saving with higher level of the safety against cavitation. Results also showed that air chamber is the most effective device and air-valves have little effect for pipeline protection against water hammer.