## 1 Introduction  
Bolt connections are widely used in many industrial fields. Bolt connections are influenced by cyclic loading and various working conditions, and the bolt connections tend to loosen. In practice, accidents have been caused by bolt looseness, and monitoring of the bolt preload force has become important in the engineering field to ensure the safety of the structures. With the development of structural health monitoring (SHM), more theories and technologies are being developed regarding bolt health monitoring and bolt looseness detection [1]. Coin-tap is commonly used in engineering practices, including in the detection of bolt looseness. According to the change of the sound during an impact, engineers estimate whether the bolt is loosened or not. Based on this, [PERSON] and [PERSON] [2; 3] proposed a theory that structural imperfection causes the changes of the response signals, thus the structural damage can be identified according to the width of the time domain curves or the area ratio of the frequency domain. After a series of research, [PERSON] et al. [4; 5] proposed a controlled tap detection method for bolt tightness based on a controlledtap detection principle, and the bolt loosening status can be determined quantitatively by using the support vector machine method. However, the tap method cannot provide real time monitoring of bolt looseness. Piezoceramics with such attractive features as low cost, small size, wide bandwidth, and sensing and actuating functions have been widely researched in real-time active vibration control [6; 7; 8], stress-wave based communication [9; 10; 11], and structural health monitoring [12; 13; 14; 15; 16]. Another attractive feature of a piezoceramic transducer is the coupling between its electric impedance and the host structure's mechanical impedance. The piezoelectric impedance method was proposed to monitor structure health status in 1994 by [PERSON] et al. [17]. The analytical relationship between the piezoelectric impedance and the mechanical impedance of the host structure was established for the first time. [PERSON] et al. [18] used a piezoelectric transducer (PZT) as an actuator-sensor collectively in conjunction with the numerical model-based spectral element method (SEM) in structural health monitoring to quantitatively detect damage of bolted joints. By analyzing the characteristics of the piezoelectric element under the bolt looseness condition, [PERSON] et al. [19] concluded that the conductance of the piezoelectric patches changes significantly under the high-frequency (more than 50 kHz) voltage excitation. [PERSON] et al. [20] enhanced the PZT to form a washer for monitoring individual bolt looseness by examining the electro-mechanical impedance (EMI) at resonance. [PERSON] et al. [21] used multi-channel wireless impedance sensor nodes and multiple PZT-interfaces to monitor bolt loosening in bolted connection. The ultrasonic method is employed in some SHM fields. As a valuable way to monitor bolt looseness, the ultrasonic method is continually improved by many researchers [22]. An ultrasonic instrument for the accurate measurement of bolt stress was described by [PERSON] in 1984 [23]. [PERSON] et al. [24] used the ultrasonic method to quantitatively detect the preload between the bolt and the connect surface. [PERSON] et al. [25] proposed an ultrasonic velocity ratio method for measuring bolt axial load. [PERSON] et al. [26] used the phase detection technique to measure the TOF (time of flight) of a tone-burst ultrasonic wave; the method improved the precision of the ultrasonic velocity method for measuring bolt stress. The propagation velocity of the ultrasonic method is affected by bolt material, stress and some other factors, and it is not easy to accurately determine the axial force of the bolt. Additionally, it requires a special precision instrument for the measurement, and it is difficult to apply to real time application. The active sensing method utilizes the sensing and actuation capability of the piezoelectric transducers.