Multi-objective optimization algorithm for upper stiffened double-deck steel truss girder bridge based on response surface

To optimize the design parameters of the upper stiffened double-deck steel truss girder bridge to ensure structural safety and reduce the engineering workload of the superstructure, an improved AdaDelta algorithm based on the response surface method suitable for multi-objective optimization was proposed. Based on a bridge serving both highways and railways, a multi-scale hybrid element model was established for the initial design parameters, and its calculation accuracy was validated. Based on the structural and mechanical characteristics of the bridge, the height of the upper and lower chords, the height of the truss, the maximum length of the stiffened vertical rods, and the thickness of the bridge deck were selected as the structural parameters to be optimized. In addition, the mid-span live load deflection, the maximum tensile stress of stiffened chords, the maximum bending stress of the bridge deck, the maximum compressive stress of lower chords at the top section of piers, the maximum stabilizing compressive stress of web rods, and the engineering workload of the superstructure were selected as the objective functions. A set of response surface fitting equations reflecting the nonlinear relationships between the parameters to be optimized and the objective functions was established. The improved AdaDelta algorithm was applied to optimize the design parameters of the upper stiffened double-deck steel truss girder bridge and compared with the optimization results of PSO and NSGA-Ⅲ. Analysis results show that the response surface method can accurately fit the numerical relationship between the parameters to be optimized and the target response function. The lightweight equation can achieve a fitting accuracy exceeding 97% and a variation coefficient below 1%. This approach significantly enhances computational efficiency while maintaining accuracy. The improved AdaDelta algorithm retains the fast convergence speed and low fluctuation characteristic of the traditional AdaDelta algorithm. By introducing a dual-weight control criterion based on satisfaction and importance, the optimization results become more targeted and applicable for engineering projects. The multi-objective optimization satisfaction results can be improved by an average of 6%. After the optimization of design parameters, the structural internal forces are redistributed. The mid-span live load deflection, the maximum tensile stress of stiffened chords, and the maximum bending stress of the bridge deck increase by 10.37%, 4.65%, and 4.99%, respectively. The maximum compressive stress of the lower chord at the top section of piers and the maximum stabilizing compressive stress of web rods decrease by 0.86% and 4.34%, respectively, and the engineering workload of the superstructure decreases by 4.11%. The project cost is greatly reduced under the premise of ensuring structural safety. The proposed algorithm is efficient and user-friendly. The weights can be flexibly adjusted according to specific optimization requirements to achieve design decisions oriented toward different goals. It is suitable for application in the optimization design practice of bridges in other systems.