## 1 Introduction  
Fatigue is a process of progressive local permanent structural change occurring in a material under cyclic loading. These permanent structural changes may culminate in cracks, which may further result in a failure of the entire structure after a certain number of additional loading cycles. Fatigue failures are often catastrophic since they usually occur without any warning, which may cause the loss of lives as well as significant property damage. Fatigue is one of the major factors for the failure of mechanical structures and members [1]. Statistics has shown that fatigue damages are responsible for 50% to 90% of the failures of mechanical structures [2,3]. Thus, the prediction of fatigue life of structures has been one of the dominant issues for structures exposed to repeated cyclic loading in various applications such as machines, civil infrastructures, transportation systems, aerospace structures and energy related structures. However, due to the complexity and uncertainty of service environments as well as multiple damage mechanisms, an accurate estimation of the remaining fatigue life is hard to achieve for aging infrastructures under cyclic loading. Structural Health Monitoring (SHM) is the basis of the life-cycle performance-based design approach, which helps improve the safety, durability, serviceability and sustainability of a structure for long-term operation [4]. A structure with a SHM system can be considered as a full-scale experimental model and system [5]. The rapid development of the SHM technique provides a potential solution for the fatigue life prediction. Fatigue damage, known as a stochastic phenomenon, makes online monitoring/sensing a significant need for a reliable estimate of the remaining fatigue life [6]. To meet this need, various sensing technologies have been developed in last century for fatigue damage monitoring and structural failure analysis, including acoustic emission [7,8], ultrasound [9,10] and eddy currents [11,12], fatigue life gauges [13], electrochemical fatigue sensors (EFSs) [14,15] and thermal imaging techniques [16]. The acoustic emission technique [7,8] takes advantage of the benefits of the correlation between the detected signals (e.g., the acoustic emission counts, the peak amplitudes and the energy) and the fatigue crack initiation. If high sensitivity for crack detection is achieved, this technique is able to capture the initiation of microstructural fatigue. However, the sensitivity of this method is limited by the signal-to-noise ratio. In noisy environments, the acoustic emission may not work well, taking account of the difficulty of separating the signal from noise. In an effort to detect fatigue crack in noisy environments, the ultrasonic sensing technique is recommended [9,10]. For this sensing technique, high-frequency ultrasonic pulses emitted by an ultrasonic sensor travel through the specimen carrying the structural behavior information, and are received by the transducers at the other end. The ultrasonic sensing technique could distinguish small changes of the specimen during the early stages of fatigue damage, which may even not be able to be detected by an optical microscope. The ultrasonic sensing technique has been utilized to monitor the small scale microstructural fatigue damage evolution. In addition, if the monitored structures are made up by conductive materials and only surface cracks are expected, the eddy current technique can also be employed [11,12]. The eddy current technique is based on the principles of electromagnetic induction, and it can detect the presence of faults through the affected eddy current flow patterns, which can be utilized to detect the evolution of small fatigue cracks. In the case that a high frequency fatigue response monitoring is required, the fatigue life gauge can be applied [13]. The fatigue life gauge is an electrical resistance-based fatigue strain sensor basedon a concept similar to that of a foil strain gauge for normal loading conditions.