Frequency-Based Cable Force Identification Correction Considering an Attached Concentrated Mass under Permanent Active Excitation

For long-term cable force monitoring in situations with insufficient ambient excitation, a permanently installed active-excitation system combined with the frequency-based method provides a feasible technical solution. However, the attached mass of the excitation unit may introduce non-negligible bias into conventional frequency-based cable force identification. To address this issue, an analytical vibration model of a tensioned cable with a single attached concentrated mass is established in this study. The exact characteristic equation, incorporating both the mass ratio and the attachment location, is derived, and the corresponding exact frequency-cable force relationship is obtained. In addition, an explicit approximate correction formula is developed for the small-mass-ratio case. To validate the proposed formulations, a pretensioned cable numerical model is established in LMGC90. The fundamental frequency is identified from impact-induced free-decay responses, and parametric studies are carried out to compare the conventional method, the exact correction, and the approximate correction. The results show that the attached concentrated mass causes a significant systematic underestimation when the conventional frequency-based method is directly applied. The error increases with the mass ratio and shows a clear dependence on the attachment location. The exact correction based on the rigorous characteristic equation can effectively eliminate the bias. The approximate correction is explicit and computationally efficient, and it provides satisfactory accuracy for small to moderate mass ratios. When the mass ratio becomes relatively large or the attachment is located in a sensitive region, the exact correction should be adopted. The proposed correction framework provide a practical basis for parameter selection, sensor/exciter installation design, and online cable force identification in permanently installed active-excitation monitoring systems.