# Investigation on Eddy Current Sensor in Tension Measurement at a Resonant Frequency
## 1 Introduction  
Steel cables are widely used in many civil engineering structures, such as long-span bridges, large gymnasiums, industrial factory buildings and rail stations. An increasing number of new large infrastructures are equipped with recently emerged structural health monitoring (SHM) systems to minimize unpredicted structural failure, which may cause economic and environmental damage as well as human casualties [1; 2]. SHM is a fairly new concept to the field of civil engineering and SHM is intended to monitor structural behavior in real-time, evaluate structural performance under various loads and identify structural damage or deterioration [3]. Measuring cable tension in SHM is imperative during the service lives of steel structures. Damage in steel cables may induce collapse of whole bridges and result in the failure of entire infrastructures. The stress state of structures is used to determine when to replace them and how to prolong their useful lifetime or to retrofit them [4]. Traditional stress monitoring methods are the utilization of acceleration sensor, load cell and strain gauge. Based on the taut string theory, the vibration frequency measured by acceleration sensor is used to estimate cable tension [5]. However, due to the effects of sag and flexural rigidity of steel cables, the taut string theory will bring measurement inaccuracy. In addition, uncertainties of some parameters, such as mass, length and cross-sectional area, will produce significant errors in relation tothe actual tension value [6]. During construction, the cable tension is closely monitored using load cells or pressure meters at one end of the cable. This method of measurement is not applicable after construction [7]. The strain gauge method is unable to directly measure the actual tension because steel cables contain tens or hundreds of wires coated with the high-density polyethylene. Elasto-magnetic (EM) technology is a novel nondestructive method to monitor tension force of steel cables. EM sensor can overcome some of the problems associated with traditional methods and has many advantages of tension detection in long life-span, strong overloading capacity and measurement results not affected by the protective layer of steel cables with the high-density polyethylene. In addition, EM sensor can be moved to any location along steel cables, installed in structures during construction or after construction and is functional under many environmental conditions. Many researchers have explored the utilities of EM sensor in nondestructive examination. Based on [PERSON]'s law, [PERSON] et al. developed EM sensor composed of primary and secondary coils, which cooperatively work to formalize magneto-elastic characterization of ferromagnetic materials. EM tension sensors function by utilizing the direct dependence of the magnetic properties of steel structures on the state of stress. A primary coil provides variable flux to the measured steel specimen, and a secondary coil obtains induced signal [8; 9; 10; 11]. Changes in the magnetic flux of the primary coil allow magnetic properties of steel cables to be measured by the secondary coil. To easily fabricate EM sensor for tension measurement, [PERSON] et al. and [PERSON] et al. proposed the removable C-shaped and E-shaped sensors [12; 13; 14; 15]. Steel cables act as a part of the magnetic circuit and the tension variation is measured by the sensing coil. [PERSON] et al. designed a steel strand tension sensor with differential single bypass excitation structure for temperature compensation [16]. However, one difficulty associated with EM sensor is the need to wrap sensor around the cable, which can be laborious and costly. Hence, the utilization of a two-coil structure greatly restricts the application of EM sensor. [PERSON] et al. devised a smart elasto-magneto-electric (EME) sensor for the stress monitoring of steel structures, in which the secondary coil is replaced by magneto-electric (ME) laminated composites as the sensing unit [17; 18; 19].