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The frequency-based method is the most commonly used method for measuringcable tension. However, the calculation formulas for the conventionalfrequency-based method are generally based on the ideally hinged or fixedboundary conditions without a comprehensive consideration of the inclinationangle, sag-extensibility, and flexural stiffness of cables, leading to asignificant error in cable tension identification. This study aimed to proposea frequency-based method of cable tension identification considering thecomplex boundary conditions at the two ends of cables using the particle swarmoptimization (PSO) algorithm. First, the refined stay cable model wasestablished considering the inclination angle, flexural stiffness, andsag-extensibility, as well as the rotational constraint stiffness and lateralsupport stiffness for the unknown boundaries of cables. The vibration modeequation of the stay cable model was discretized and solved using the finitedifference method. Then, a multiparameter identification method based on thePSO algorithm was proposed. This method was able to identify the tension,flexural stiffness, axial stiffness, boundary rotational constraint stiffness,and boundary lateral support stiffness according to the measured multiorderfrequencies in a synchronous manner. The feasibility and accuracy of thismethod were validated through numerical cases. Finally, the proposed approachwas applied to the tension identification of the anchor span strands of asuspension bridge (Jindong Bridge) in China. The results of cable tensionidentification using the proposed method and the existing methods discussed inprevious studies were compared with the on-site pressure ring measurementresults. The comparison showed that the proposed approach had a high accuracyin cable tension identification.

Frequency-based tension assessment of an inclined cable with complex boundary conditions using the PSO algorithm