Investigating the Effect of Uncertainty in the Optimal Design of a Trapezoidal Channel

In this article, the optimal shape of the compound trapezoidal cross-section is presented by considering the deterministic constraints and the probabilistic constraint of channel flooding as uncertainty with the SPSA algorithm and with three discharge of 10, 50, and 120 (m^3/s). The objective function is to minimize the cost of excavation and lining, the design variables of depth and width of the canal bottom, side slopes and constraints include uniform flow, maximum and minimum velocity, water surface width and the overtopping probability. The values of the freeboard and the slope of the channel bed are fixed and equal to 0.5 meters and 0.0028, respectively. The results show that with the increase in overtopping Probability, the flow depth increases, but the side slopes, velocity and Froud number decrease. The cost of construction and the width of the bed, initially decreases with the increase of the overtopping probability, and at a certain value, the probability reaches its minimum value, and then with the increase of the overtopping probability, the cost of construction and bed width increases.