spsa algorithm

This paper presents an optimal cross-section of a composite parabolic channel by considering four models based on freeboard changes. In this research, four models were presented separately to present the optimal shape of the parabolic cross-section. In the first model, the freeboard was considered zero. In the second model, a freeboard of 0.5 m was considered. In the third model, the freeboard was considered as a function of the discharge according to the standard regulations of India; in the fourth model, the freeboard was considered as a function of the flow depth in the optimization process. The objective function is to minimize the cost of lining and excavation costs. Design variables include flow depth and side slopes. Constraints include the Manning equation constraint to maintain a uniform flow, the Froud number constraint to ensure subcritical flow in the channel, total top width, and the velocity constraint to control sedimentation and erosion. The above optimization problem is solved using the optimization algorithm and the method of simultaneous perturbation stochastic approximation (SPSA). The results show that increasing the discharge increases the flow depth, left and right side slopes, total top width and water surface width, channel cross-sectional area and flow area, the total channel perimeter and wetted perimeters, flow velocity, Froud number, and the cost. By examining the relationship between cost with design variables, constraints and geometric parameters of parabolic channel cross-section at different iterations, the characteristic of the model that won the most number of iterations is based on the increase in left and right side slopes, total top width and water surface width, the cross-sectional area of the canal and the flow area, the total channel perimeter and the wetted perimeters, the Froud number, the cost increase. In contrast, increasing the depth and flow velocity reduces the cost. Comparison of the results of the four models with each other shows that the cost values in the first model are lower than those in other models. In the third model, they are higher than all models.

Arch bridges are generally considered widely as esthetically pleasing bridges and its different variations can be found from both historical and modern times all over the word. Arch bridges can be divided into several different types by different definition. One possibility to divide them is through the spandrel. Spandrel can be open or closed. When it is open، there are usually columns to transmit the loads from the deck to the arch. The purpose of this study is to determine the optimum design of arch longitudinal no prismatic single-cell section. In this study، Cetina Bridge، which is a long span open reinforced concrete arch bridge spanning Cetina river canyon near the town of Trilj. The arch is of span 140m with a rise of 21. 5 m، giving rise-to-span ratio of 1/6. 5. The FE model of the Cetina open spandrel arch bridge was constructed using the Ansys. The main span and columns was simulated with Beam4، and element solid45 was used for reinforced concrete non prismatic single cell arch. For definition of arch geometry in longitudinal sections، parabolic conic functions are employed. In this present work the optimum design is carried out by taking total material volume of substructure of bridge as objective function. Substructure includes of column and reinforced concrete arch. Height of skewback abutment، Height of crown of arch، back and soffit radii of arch and position of crown respect to global axes are considered as design variables. The distance between the columns is assumed constant and equal to 21. 6 m in optimization process. Also the cross sections of column are not taken as design variables. Instead of this، cross section of piers is selected proportionally with these of application project. During problem formulation most of practical design variables and constraints are considered. Three type of design constraints were taken into account: stress constraints of arch، transversal displacement constraints of arch crown and geometric constraint. Initially، a program is developed in MATLAB in order to generate coordinate of nodes، then is taken finite element software ANSYS for modelling the geometry of an arch dam. Finally، the optimization technique is performed by Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. Shape optimization for each of the arch web thickness to be examined (i. e. t_w=0. 3-0. 5m). The following، some of important conclusions are drawn from the present work: It is concluded that SPSA can be effectively used in the shape optimization of the bridges. The total reinforced concrete volume obtained in this study is 23% less than the application project. For each t_w، the optimum arch geometry is obtained، when the volume of the arches and columns is minimized. Minimum volume of substructure achieved for t_w=0. 35m with 1131 m3.