## 5 Conclusions  
In order to study the deformation characteristics of bolts and stress wave propagation characteristics in bolts under axial tensile stress, an experimental study was conducted and verified using the custom bolt tensile and stress wave detection test system. Based on the work completed, the following conclusions can be drawn:  
1. After processing and analyzing the displacement, load, and image data obtained in the bolt tensile test and when the low loading speed is applied, it is found that the bolt tensile process undergoes four stages, and, finally, ductile fracture occurs. The change rule of the diameter of the bolt in the necking position during the tensile process elucidates the axial and radial deformation characteristics of bolts in different positions during stretching. It lays a foundation for better research on the propagation characteristics of stress waves in the bolt during the tensile process in stages. 2. The time domain characteristic analysis of the stress wave signal during the bolt stretching process shows that the attenuation energy ratio of the bolt is generally increased. The deformation caused by the bolt tension makes the stress wave reflect and transmit in different degrees when it propagates in the bolt. It leads to the attenuation of stress wave energy, and the amplitude attenuation rule is different in the stress wave time domain diagram. The energy decay rate is faster in the elastic stage, yield stage, and necking fracture stage. The energy attenuation ratio is about 20% without stretching. When stretching to the elastic and yield stage, the attenuation ratio of stress wave energy increases linearly to 30-35%. After reaching the strengthening stage, the energy attenuation ratio of the stress wave remains at a relatively stable level, with slight oscillations between 33%. The attenuation of stress wave energy at the necking fracture stage reaches 35%. As necking continues to occur, the energy attenuation ratio increases exponentially. 3. The frequency domain characteristic analysis of the stress wave signal during the bolt stretching process shows that the frequency distribution of the stress wave signal in the frequency domain ranges from scattered to centralized. The dominant frequency of the stress wave signal becomes more and more prominent with the stretching, and the dominant frequency of the stress wave changes from low frequency to high frequency. High-frequency signals are more sensitive to the cracks and necking of the bolt, and the dominant frequency of necking is between 9500 and 10,000 Hz. Figure 15: Comparison of test results and error curve. Based on the fitting analysis of the test data, the fitting formula between the energy attenuation ratio of the stress wave signal and the diameter of the bolt necking position during the bolt stretching process is obtained. The verification test results showed that the error of the stress wave method is small and stable, which can effectively identify whether the bolt is in the necking state. The research in this paper demonstrates the successful application of the proposed method in the laboratory and provides a reference for research on nondestructive testing of bolt stress waves. Our future work will focus on field trials. Conceptualization, project administration, supervision: C.L. and R.F. ; methodology, data curation and writing--original draft: X.G. and X.X. ; investigation and software: X.C. ; validation and formal analysis: C.Q., Z.Z., J.B. and B.N. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (52174103), Anhui Provincial Natural Science Foundation (2008085 ME147) and open foundation from the Key Laboratory of Coal Mine Safety and Efficiently Caving of Ministry of Education (JYBSYS2018102). Not applicable. The data used to support the findings of the study are available from the corresponding author upon request.