## 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 intensification phase, although the curve segment shows a decreasing trend due to the oscillation of the energy attenuation ratio, the size of the diameter of the necking position does not correspond to the energy attenuation ratio. When the necking fracture stage is reached, there is a buffer zone in the curve, and the diameter reduction rate in the buffer zone is slow. At this time, the bolt necking has not yet shown obvious necking, cracks continue to develop, stress concentration appears, and after the stress concentration exceeds the limit of the bolt, a visible necking starts to appear, and the diameter reduction rate is rapid after the necking occurs. In order to verify the correct correspondence between the stress wave signal attenuation energy ratio and the diameter of the bolt necking position in the bolt stretching process obtained from the test, the data of the diameter of the necking position and the energy attenuation ratio were fitted, as shown in Figure 14. The curve fitting results show that the data conform to the exponential distribution, and the fitted curve expression is shown in the graph. R\({}^{2}\) is the coefficient of determination. The closer to 1 means the better the fitting effect [31]. R\({}^{2}\) = 0.93876 means that the fitting formula can show the correspondence between the diameter of the bolt necking fracture location and the attenuation energy ratio during bolt stretching. Figure 13: Diameter-stress wave energy attenuation ratio curve in bolt necking position during bolt tensioning. Experimental Verification of Bolt Necking Position Diameter Test Based on Stress Wave Energy Attenuation Ratio  
The bolt tension test is performed using the bolt tension and stress wave detection test system. By observing the axial load-displacement curve of bolt tension, the bolt tension can be well controlled after reaching the tensile strength (when the axial load starts to decrease) and before the bolt fracture. At this time, the bolt is in the necking fracture stage, and stress wave nondestructive testing is performed. The stress wave results are processed and analyzed to obtain the stress wave energy attenuation ratio at this moment, and the corresponding bolt necking position diameter size is calculated according to the fitting formula above, and then compared with the bolt diameter size obtained from the bolt state monitoring device to calculate the error rate size of the stress wave method detection results. A total of six sets of data were obtained from two bolts at three different random moments during the necking fracture stage using the stress wave method. The test results and errors of the validation experiments are shown in Figure 8:0 Comparing the measurement results of the bolt state monitoring device with the detection results of the stress wave method, the average error of the detection results of the stress wave method was 1.945%, and the maximum and minimum values of the detection error were 4.12% and 0.51%, respectively, with a maximum difference of 3.61% in the detection error. Figure 15 shows the comparison of the measurement results and the error curve. It can be seen that the overall error of the stress wave method is small and stable, which indicates that it is feasible to use the stress wave signal energy attenuation ratio as the standard for detecting the diameter of the bolt necking position, and it can identify whether the bolt is in the necking fracture stage. Figure 8:1 Diameter-energy attenuation ratio curve at bolt necking position. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Specimen Number**} & \multicolumn{2}{c}{**Measurement Results (mm)**} & \multirow{2}{*}{**Detection Error (\%)**} \\ \cline{2-3} \cline{5-5}  & **Bolt State Monitoring Device** & & **Stress Wave Method** \\ \hline yz 1-1 & 18.112 & 18.02 & 0.51 \\ yz 1-2 & 17.794 & 17.061 & 4.12 \\ yz 1-3 & 15.319 & 15.089 & 1.5 \\ yz 2-1 & 18.257 & 18.514 & 1.41 \\ yz 2-2 & 18.035 & 17.709 & 1.81 \\ yz 2-3 & 16.11 & 15.736 & 2.32 \\ \hline \hline \end{tabular}
\end{table}