Frequency-based tension assessment of an inclined cable with complex
  boundary conditions using the PSO algorithm
  The frequency-based method is the most commonly used method for measuring
cable tension. However, the calculation formulas for the conventional
frequency-based method are generally based on the ideally hinged or fixed
boundary conditions without a comprehensive consideration of the inclination
angle, sag-extensibility, and flexural stiffness of cables, leading to a
significant error in cable tension identification. This study aimed to propose
a frequency-based method of cable tension identification considering the
complex boundary conditions at the two ends of cables using the particle swarm
optimization (PSO) algorithm. First, the refined stay cable model was
established considering the inclination angle, flexural stiffness, and
sag-extensibility, as well as the rotational constraint stiffness and lateral
support stiffness for the unknown boundaries of cables. The vibration mode
equation of the stay cable model was discretized and solved using the finite
difference method. Then, a multiparameter identification method based on the
PSO 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 multiorder
frequencies in a synchronous manner. The feasibility and accuracy of this
method were validated through numerical cases. Finally, the proposed approach
was applied to the tension identification of the anchor span strands of a
suspension bridge (Jindong Bridge) in China. The results of cable tension
identification using the proposed method and the existing methods discussed in
previous studies were compared with the on-site pressure ring measurement
results. The comparison showed that the proposed approach had a high accuracy
in cable tension identification.
