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This study introduces the Quick Group Search Optimizer with Passive Congregation (QGSOPC) coupled with the influence-matrix method to optimize cable forces in a completed 1 070 m, five-span, twin-tower cable-stayed bridge. Compared with the original design, QGSOPC reduces maximum tower-top displacement by 83.8% (84.1 → 13.6 mm), girder deflection by 41.9% (236.7 → 137.5 mm) and peak bending moment by 11% (118 078 → 105 120 kN·m), while lowering the composite objective function by 40.7%. A comparative analysis using GSO confirms the enhanced performance of the proposed algorithm. The results demonstrate that QGSOPC offers a practical, efficient tool for achieving the “straight-tower & level-beam” completion state of long-span cable-stayed bridges.

To enhance the reliability of cable force optimization in large-span cable-stayed bridges, this study presents a force optimization model that considers reliability indicators specific to these types of bridges. A structural surrogate model was established by employing a Radial Basis Function Neural Network (RBFNN) to accurately capture the mapping relationship between random variables and the structural response. Enhancements were introduced to address the limitations of the standard Seagull Optimization Algorithm (SOA) through refracted backpropagation learning and nonlinear convergence strategies. A combined force optimization method was devised by integrating the RBFNN and the improved SOA. An empirical analysis was performed on a large-span cable-stayed bridge to validate the feasibility of the proposed approach. The results demonstrated the RBFNN’s ability to effectively capture the nonlinear mapping between structural random variables and dynamic responses. The enhanced seagull algorithm exhibited substantial performance improvements compared to the original algorithm, providing better solutions for force optimization considering reliability indicators. Following optimization, although the overall trend of tension distribution remained similar to the original distribution, adjustments were made to specific tension points to varying degrees. Notably, the deflection of the main beam in the middle span was significantly improved, with a maximum reduction of approximately 36.21%. Furthermore, there was a slight improvement in the reliability indicators for tension, with a maximum increase of approximately 9%.

To compensate the incapability of traditional cable force adjustment methods to automatically optimize cable forces, this paper proposes Midas/Civil and MATLAB as a structure calculator and a cable force optimizer, and external memory as a data transfer. Initial solutions from conventional methods can be optimized by internalizing the influence matrix into the multiobjective particle swarm optimization algorithm with mutation operation and constructing the mathematical model of cable force optimization, and then, a series of Pareto frontier solution sets are obtained. For the first time, fuzzy set theory is introduced for selecting Pareto presolution set for the optimization of cable-stayed bridges, to solve the final reasonable dead load state of bridges. By using this method, the peak vertical displacement of a main girder of the optimized cable-stayed bridge decreased from −11 mm to −6 mm, with a reduction of 45%. Before and after optimization, the difference of peak negative bending moment at the top of the pier was 34.8%, indicating that the main beam was more evenly stressed and the alignment was more reasonable.

Optimizing cable forces in cable-stayed bridges is challenging due to structural nonlinearity and the limitations of traditional methods, which often focus on isolated performance indicators. This study proposes an integrated framework combining Gaussian process regression (GPR) with an enhanced whale optimization algorithm improved by the Salp Swarm Algorithm (EWOSSA). GPR is first used to model the nonlinear relationship between cable forces and structural responses. The EWOSSA then efficiently optimizes the GPR-based model to identify optimal cable forces. A case study on a cable-stayed bridge with a 2 × 145 m main spans demonstrates the effectiveness of the proposed approach. Compared with conventional methods such as the internal-force equilibrium and zero-displacement methods, the EWOSSA-GPR framework achieves superior performance across multiple structural metrics. It ensures a more uniform cable force distribution, reduces girder displacements, and improves bending moment profiles, offering a comprehensive solution for optimal structural performance in cable-stayed bridges.

To address the issue of cable force optimization during the cantilever casting stage of reinforced concrete arch bridge construction, this study proposes a cable force optimization method based on an Improved Whale Optimization Algorithm (IWOA) combined with a Support Vector Machine (SVM) model. First, the standard Whale Optimization Algorithm is enhanced through Tent chaotic mapping, a nonlinear iterative control parameter, adaptive weight factors, and adaptive threshold strategies. The improved algorithm is then used to optimize key parameters (C, g) in the SVM model, constructing a parameter-optimized cable force combination-structure response prediction model for the arch bridge. Next, with the average tensile stress of the arch ring’s top and bottom slabs during construction and the bending strain energy after bridge completion as target variables, a multi-objective optimization mathematical model for cable forces during the construction stage of reinforced concrete arch bridges based on IWOA-SVM was established. Finally, the feasibility of the method was validated using the Shatuo Bridge project as a case study. The results indicate that compared to the finite element optimization method, the IWOA-SVM cable force optimization method significantly improved computational efficiency while ensuring optimization effectiveness. After optimization, the peak tensile stress and vertical displacement of each arch segment were significantly reduced, leading to improved internal force distribution and alignment, thereby enhancing the overall structural safety and reliability of reinforced concrete arch bridges.

During the construction of large-span steel truss arch bridges, challenges such as complex control calculations, frequent adjustments of the cantilever structure, and deviations in the closure state often arise in the process of the assembly and closure of arch ribs. Based on the stress-free state control theory, this paper proposes a precise assembly control method for steel truss arch bridges, which takes the minimization of structural deformation energy and the maintenance of the stress-free dimensions of the closure wedge as the control objectives. By establishing a mathematical relationship between temporary buckle cables and the spatial position of the closure section, as well as adopting the influence matrix method and the quadprog function to determine the optimal parameters of temporary buckle cables (i.e., size, position, and orientation) conforming to actual construction constraints, the automatic approaching of bridge alignment to the target alignment can be achieved. Combined with the practical engineering case of Muping Xiangjiang River Bridge, a numerical calculation study of the precise assembly and closure of steel truss arch bridges was conducted. The calculated results demonstrate that, under the specified construction scheme, the proposed method can determine the optimal combination for temporary buckle cable tension. Considering the actual construction risk and the economic cost, the precise matching of closure joints can be achieved by selectively trimming the size of the closure wedge by a minimal amount. The calculated maximum stress of the structural rods in the construction process is 42% of the allowable value of steel, verifying the feasibility and practicality of the proposed method. The precise assembly method of steel truss arch bridges based on stress-free state control can significantly provide guidance and reference for the design and construction of bridges of this type.

In order to solve structural optimization problems in the past, it is necessary to integrate structure analysis software and optimization software. Since structural analysis has been the only function considered when developing most of structure analysis software, they suffer from closeness of system. Therefore, it is not easy to integrate them with optimization software. This study proposes an experimental design method to solve this problem including following steps: (1) generate experimental design, (2) implement experimental design, (3) construct a response variable model, (4) define optimization problem, (5) solve optimization problem. The purpose of step (1) through step (3) is to create a response variable model of alternative structure analysis software. This model is a set of regular and simple functions, it can easily define the optimization problem in step (4), in order to facilitate step (5) to solve the optimization problem. The reason to employ neural network instead of traditional regression analysis in step (3) is that the relationship between internal forces and displaced cross section dimension of the structure are often nonlinear. Neural network is a nonlinear system that gives itself the greatest advantage to accurately construct a nonlinear model. This case study is based on optimization design of cable force and tower height in an extradosed bridge, evaluating the feasibility of above method and comparing with published references to confirm the proposed method in this study is applicable to the optimization design of extradosed bridge.

The cable-stayed bridge is a type of the bridges that can utilize the material properties fully and rationally.They are most favored by designers both at home and abroad with its good economic performance and crossover capability. we use the method of the minimal stress with constraints to optimize the cable force of the completed bridge under dead loads. In this way, we can attain the goal of reducing the project cost.

In the premise of structural parameters of not changing, cable-stayed bridge state by taking the reasonable force will become the optimization of cable-stayed bridge under constant load by taking the reasonable under the bridge state superpositioning optimization problem. Basing on the engineering background of Dachongyong bridge with finite element analysis software of Midas/Civil, taking the unknown load coefficient method of Midas/Civil as study platform, arounding the theme of the reasonable state of cable-stayed bridge, This paper make full use of the characteristic of cable forces can be adjust, introduced the method of superpositioning optimization algorithm in detail under the reasonable cable-stayed bridge state.

The profile of the rail expansion joint (REJ) would affect the stable operation of high-speed trains, so it needs to be optimized. An optimization method was presented for the switch rail declining values (SRDV) of REJ at the beam end in a long-span cable-stayed bridge (CSB) through the co-simulation based on SIMPACK and MATLAB. First, based on the theory of rigid-flexible coupling, a high-speed vehicle-REJ-CSB multibody dynamics model was established. The model conducted a detailed simulation of the beam end track system and performed a parameterized design of the REJ profile. Then, 8 dynamic indicators of high-speed vehicles were selected as optimization objectives. The Simulated Annealing Particle Swarm Algorithm (SA-PSA) was employed to solve the objective function and obtain the optimal SRDV of REJ. Finally, the effect of the optimization was verified by the model test. The results indicated that the optimal SRDV had the most significant reduction in the wheel-rail forces, followed by the motion of the bogie frame. The wheel-rail vertical force was reduced by 9.59%, and the wheel-rail lateral force was reduced by 20.56%. The lateral acceleration of the bogie frame was reduced by 8.69%. Under the damping effect of the primary and secondary suspension system, the influence of the REJ profile on the acceleration of the vehicle was relatively small. Therefore, the optimization for SRDV had little effect on the acceleration of the vehicle. Through the model test, the superiority of the optimization results in this paper was verified.