Non-Contact Spatial Vibration Measurement of Cable with a Small Sag: OMA Application for Tension Force Estimation

This paper presents a method for estimating the tensile force in a cable with a small sag (0 ≤ d/L ≤ 1/8) based on analytical calculations and Operational Modal Analysis (OMA) using non-contact displacement sensors. The in-plane and out-of-plane natural frequencies, as well as the mode shapes, were identified and subsequently compared with Irvine’s theory. The laboratory test stand, methodology, and modal results are presented. The findings demonstrate that the method is also applicable to cables with significant sag (characterized by a high Irvine parameter), where a distinct first symmetric mode featuring three local extrema occurs—a phenomenon inherently absent in idealized tensioned strings. Furthermore, the investigation reveals that a one-dimensional signal analysis (along either the y- or z-axis) yields an underestimation of the tensile force when compared with a comprehensive two-dimensional (yz) approach. Ultimately, the study demonstrates that the identification of the first symmetric and first antisymmetric modes, supported by their corresponding two-dimensional mode shapes, enables reliable modal interpretation and cable tension estimation within the investigated parameter range.