Multi-objective Optimization Of U-beam In Rail Transit Based On Genetic Algorithm

As a relatively new type of viaduct,U-beam have become more and more important in the era of rapid development of rail transit.The overall alignment of U-beam is smooth,which makes it high environmental friendliness and landscape adaptability.The U-beam is a through type structure so that building height is significantly lower than other Bridges.However,the research and development of U beam in China is relatively late,the structure form of U is different with T-type Beam Bridge or box girder bridge,especially,in terms of statics,there are still many shortcomings in the research on strength,stiffness and ultimate bearing capacity.Therefore,designers will increase the use of materials to ensure the safety in the design process,resulting in large safety reserve redundancy.It is a developing trend to seek a reasonable optimal design scheme of U-beam among many or contradictory optimization objectives.The basic goal of bridge design is to ensure its safety,economy and applicability.Multi-objective optimization can not only achieve the basic goal of bridge design,but also make the reasonable use of materials to reduce the cost of the bridge,reduce economic waste and enhance the overall stiffness of the bridge.Multi-objective optimization is to balance and compromise among various objective functions so that each objective function can be optimized to a certain extent.The research and development of intelligent algorithms,especially genetic algorithms,lays a solid foundation for solving multi-objective optimization problems.The development of multi-objective optimization genetic algorithm(MOGA)has evolved many multi-objective optimization genetic algorithms such as non-dominated sorting genetic algorithm(NSGA)and fast classified non-dominated genetic algorithm(NSGA-II).And The emergence of NSGA-II algorithm has greatly improved the speed and efficiency of multi-objective optimization problems.The paper based on multi-objective optimization theory and genetic algorithm,takes Shanghai Rail Transit Line 11 as an engineering example.Write a U-beam optimization program by using MATLAB and establish finite element model by using Midas/Civil.The specific work content is as follows:(1)The stress characteristics of U-beam are analyzed,the objective functions to determine the optimal design of u-beam are the lowest cost of bridge and the maximum stiffness of bridge,the optimum design variable of U beam is determined to be the beam height h,Floor and web thickness x,Section area of prestressed steel strandsA,determine optimization constraints.Based on the above objective function,design variables and optimization constraints,write multi-objective optimization genetic algorithm program.(2)Based on multi-objective optimization genetic algorithm program,the Pareto optimal solution for U-beam optimization design with standard span of 30 m and 35 m is obtained,analyzed the trend of the optimal solution to obtain the lowest cost target and the full-section stiffness maximum target is negatively correlated.Therefore,when selecting the optimization scheme,we can only seek a balance point to achieve the purpose of reducing the cost and increase the stiffness of the full section.The range of the two objective functions is analyzed according to the actual situation.(3)Two optimization schemes of U-beams with standard spans of 30 m and 35 m are selected respectively,and the finite element model is established to analyze the changes of two objective functions.It is concluded that increasing the height of the U-beam is extremely obvious for improving the overall stiffness of the bridge.Reducing the amount of stressing tendons and the thickness of the floor and web can reduce the cost of the bridge.