# Bol Looseness Detection Based on Piezoelectric Impedance Frequency Shift
## 1 Introduction  
There are many types of connection for engineering structures, and bolt connection is one of the most widely used. Currently, there are a few methods to monitor the condition of bolt joints by measuring the bolt axial load [1]. A common method is to employ a strain gauge to measure the bolt strain and determine the bolt preload. This method offers accurate bolt-strain monitoring, but integration of the strain gauge often requires significant hardware modification. Another technique uses a torque wrench to determine the torque applied on the bolt. Due to the effect of the friction between the bolt and the clamped parts and the screw thread, the torque wrench cannot accurately control the pre-tightening force. Acousto-elastic effect based ultrasonic methods are alternatives to estimate the bolt axial load by measuring the time-of-flight (TOF) [2, 3], the velocity ratio of longitudinal waves and transverse waves [4, 5], and the resonant frequency shift of the bolt [6]. The velocity change of waves in the bolt resulted from the bolt stress is very small, so specialized precision instruments are required to measure the variations of the TOF, velocity and frequency shift, which hinders the application of the method. To avoid the catastrophic consequences caused by bolt looseness, real-time monitoring of bolt connections is of great importance. Vibration-based damage assessment is a commonly used real time method for structural health monitoring and fault diagnosis. By comparing the transmittance function [7], power spectral density(PSD) of the recorded signal [8] and other modal parameters before and after structural damage [9], the structure's health state can be extracted. However, this method can only detect structural damage when the damage is developed to a certain degree. For the bolt-connected structures, the looseness of a bolt only affects the local dynamic characteristics of the structure, and the vibration based method is not so sensitive to the initial bolt looseness detection. Piezoceramics, with attractive features such as low cost, small size, wide bandwidth, and sensing and actuating functions, have been widely researched in real-time structural monitoring [10; 11; 12; 13]. Using the piezoelectric active sensing method and the ultrasonic attenuation-based method, [PERSON] and [PERSON] predicted the torque levels and identified the locations of loosened bolts [14; 15]. [PERSON] et al. [16; 17] analyzed the ultrasonic energy which is received through the interface of a bolted joint, and the status of bolt connection and bolt loosening are monitored using the response signal energy method and the time reversal method. [PERSON] [18] applied the active sensing technique incorporated with a wireless sensor network in health monitoring of wind turbine blades [19]. Another attractive feature of a piezoceramic transducer is the coupling between its electric impedance and the host structure's mechanical impedance, based on which [PERSON] et al. proposed the piezoelectric impedance-based structure health monitoring method [20]. Since then, research on structure health monitoring based on piezoelectric impedance technique has been widely carried out [21; 22] in many fields, such as in wind turbine blades [23] and composite material [24; 25], [PERSON] et al. [26; 27] performed the experiments on aircraft components and reinforced concrete bridges with the piezoelectric impedance technique, and demonstrated the effectiveness of the piezoelectric impedance technology for structure health monitoring. [PERSON] et al. [28] apply piezoelectric impedance technique in monitoring the gas pipeline damage and finds that it can detect the crack damage of underground pipeline. [PERSON] et al. [29] applied the piezoelectric impedance technique in monitoring weld cracks, and the results showed that the piezoelectric patches can be sensitive to detect small changes in cracks. [PERSON] et al.