## 3 Test Results and Analysis
### Stress Wave Propagation Characteristics of Bolt Tension Process
#### 3.2.2 Time and Frequency Domain Analysis of Stress Wave Signals at Different Stages of Bolt Tension
During the yielding stage, the reflected and transmitted energy of stress wave propagation in the bolt increases, showing that the attenuation energy continues to increase and the attenuation gradually becomes slower. At the beginning of the strengthening stage, the stress wave propagation in the bolt is similar to the yielding stage, and the attenuation energy of the stress wave also increases slowly. At the later stage of the strengthening stage, the attenuation of the stress wave energy starts to increase and the energy attenuation rate is accelerated. After reaching the necking fracture stage, cracks begin to appear in the bolt and necking occurs. When the stress wave propagation meets the crack and necking, the reflection and transmission are stronger, and the energy decay is more and faster than that in the later stage of strengthening. After analyzing the incident energy, reflected energy, and attenuation energy at the moment of applying different axial displacements to the bolt, a stress wave energy attenuation ratio, i.e., the ratio of attenuation energy to incident energy, is proposed to determine the tensile state at the time of bolt detection. The stress wave energy attenuation ratio curve of the tensile process of the bolt is shown in Figure 11.  
Figure 10: The stress wave energy change curve during bolt tension. (**a**) Incident energy change curve; (**b**) Reflected energy change curve; (**c**) Attenuated energy change curve; (**d**) mg1 energy change curve; (**e**) mg2 energy change curve; (**f**) mg3 energy change curve. As can be observed in Figure 11, after converting the energy attenuation process occurring during the stress wave detection of the bolt tension process into the attenuation ratio, it is obvious that the trend of the stress wave attenuation ratio varies at different tension stages. The stress wave energy attenuation ratio increases linearly during the elastic and yielding phases, with an initial attenuation ratio of about 20%. After reaching the strengthening phase, the stress wave energy attenuation ratio remains at a relatively stable level, with a slight oscillation in the attenuation ratio of 33%. In the necking fracture stage, the stress wave energy attenuation ratio reaches 35% (marked with a purple dotted line in the figure) and increases exponentially until the bolt fractures. The analysis found that the energy attenuation ratio of the stress wave signal can be employed as an indicator for early warning when the bolt is necked, and the bolt is necked when the stress wave energy attenuation ratio reaches 35%. In addition, the energy attenuation ratio increases exponentially as necking continues to take place. Frequency domain feature analysis  
The Fourier transform of the time domain waveform of the stress waveform of the bolt stretching process was performed to obtain the frequency domain diagram at different axial displacements of the stretching. Figure 12 shows the frequency domain diagram of the stress wave signal at different stages of bolt tension. Figure 12a,b shows the frequency domain diagram of stress wave detection in the elastic stage of bolt stretching. From Figure 12a, it can be seen that the dominant frequency of the stress wave signal is around 8 kHz when it is not stretched. The frequency domain diagram contains multiple wave peaks. With the application of axial displacement, the stress wave frequency concentrates toward 6 k-12 kHz and the dominant frequency is more prominent. Reaching the yielding stage, as shown in Figure 12c, the dominant frequency starts to increase slowly and the frequency interval becomes more concentrated, with frequencies mainly distributed in the 6 k-10 kHz frequency interval. Figure 12d-f shows the frequency domain diagram of the stress wave signal when the bolt is in the strengthening stage. There is a clear wave in the frequency domain plot in addition to the dominant frequency. The dominant frequency in the pre-strengthening phase is 8500 Hz and the second wave peaks at 9500 Hz.