Metaheuristic Algorithm-Based Multi-Boundary Cable Force Identification and Performance Analysis for Suspension Bridges

This study presents a new method for identifying the cable forces of short suspension rods in arch bridges, particularly under elastic boundary conditions. First, through mathematical derivation, a model based on the cable force–frequency matrix equation is established, which is then extended to hinged and fixed boundary conditions. To achieve accurate cable force identification under different boundary conditions, the study adjusts the rotational stiffness parameters, further optimizing the model. Next, by conducting experimental analysis on 27 virtual suspension rods and applying Friedman and Nemenyi statistical methods, the performance of five meta-heuristic algorithms is compared under different boundary conditions. The results show that the proposed method meets the error requirements for hinged and fixed boundary conditions, although significant performance differences exist between the algorithms. Under hinged boundary conditions, there is little variation in error between the algorithms, but the dung beetle optimization (DBO) algorithm performs best in terms of time efficiency. Under fixed boundary conditions, the DBO algorithm shows significant advantages in error reduction, while the particle swarm optimization (PSO) algorithm excels in time efficiency. Particularly, under elastic boundary conditions, the PSO algorithm achieves a relative error of less than 2% in the shortest time, demonstrating high precision and efficiency. To better reflect practical applications, the study also considers the impact of environmental disturbances on frequency measurement values, using the PSO algorithm as a case study. The results show that, under environmental disturbance, the error in cable force identification increases slightly but still meets the accuracy requirements for practical engineering applications. To address precision issues under uncertain boundary conditions, the study selects genetic algorithms and cuckoo search algorithms for analysis. Experimental results show that under simple boundary conditions, the precision improvement of genetic and cuckoo search algorithms is limited, with some cases exhibiting increased errors. However, under complex boundary conditions, both algorithms significantly reduce the cable force identification errors, showing greater adaptability and optimization capability, which presents a potential direction for future research. This study provides a new approach for the intelligent safety assessment and cable force prediction of arch bridge structures, laying the foundation for their application in practical engineering.