Stress detection method of pipeline based on vibration characteristics

Stress concentration during the operation of long-distance transmission pipelines is an inevitable problem. In this paper, a pipeline stress detection method based on vibration characteristics is proposed. We establish a finite element model for knock detection and determine the law of vibration frequency and pipeline stress. The reliability of the model is verified by the knock detection experiments. It is found that the natural frequency stress of the vibration of the sample shows a close correlation under the knocking effect. The study results provide an innovative process for pipeline stress detection.


Introduction
During the operation of long-distance transmission pipelines, the stress concentration in the local area of the pipeline is caused by geological disasters and improper installation processes.At present, there have been many fracture accidents caused by changes in pipeline structure [1] .The non-destructive testing method is a significant technique for assessing and ensuring the safety of pipelines [2] .
At present, the non-destructive testing methods for pipeline stress are mainly classified as X-ray diffraction method, Barkhausen noise method, IMU inertial navigation method, etc.The free vibration characteristics of the structure can reflect the stress state of the structure to some extent.Zhang et al. measured the boom load through the change of natural frequency, and the error was about 5% [3] .Tang and Gao studied the rectangular plate with residual stress by using the method of pulse excitation and found that the greater the residual stress is, the greater the change in natural frequency is [4] .Liao et al. studied the structural modal of the parts with residual stress and found that the existence of residual stress will increase the natural frequency [5] .
There have been a lot of studies at home and abroad based on the non-destructive testing methods of vibration characteristics [6][7][8] .However, no scholars have studied pipeline steel at present, so it is difficult to apply the knock detection method to pipeline stress measurement.The material of the sample selected in this study is X80 pipeline steel, and the rattle vibration model of plate specimens under different stresses is established.The relationship between stress and vibration frequency of plate specimens is studied, and the reliability of the simulation model is proved by experiments, to provide support for the engineering application of the rattle detection method.

Natural frequency solution
The differential equation of motion of an undamped free vibration system is expressed as [9] : where M represents the mass matrix of the system; a (t) represents the second derivative of node displacement concerning time; K represents the stiffness matrix of the system; a(t) is the displacement array of nodes.Its solution can be expressed in the following form: where I is a vector; Z represents the vibration frequency; t represents the variables of time; t0 represents the constant of time.
If Equation ( 1) is substituted into Equation ( 2), it will become a problem of solving eigenvalues.

Tap detection principle
When a structural system is excited, it vibrates at a specific frequency, which is called the natural frequency of the structure.For undamped single-degree-of-freedom systems, the tapping natural frequency is calculated, as shown in Equation ( 4).
where k is the stiffness; m represents the mass (unit: kg); fn represents the n-th natural frequency of the structure (unit: Hz).
The natural frequency of the structure is affected by the stiffness and mass.In the knock test of the structural system, the multi-order natural frequency can usually be obtained [10] .The stiffness is different, the natural frequency is different, and the vibration signal generated by the knock is different.This is the principle of judging whether there is stress concentration in the specimen by the vibration generated by the knock.In this study, the sample was subjected to free vibration by tapping excitation, and the natural frequency was obtained by collecting the vibration signal.

Model establishment
The knock vibration model of the X80 plate sample was established by COMSOL, and the vibration of the sample under different stress states was analyzed.The modeling process is as follows: (1) Modeling and meshing: The model was constructed based on an actual pipeline sample, and the grid was divided by sweeping (seen in Figure 1); (2) Material properties: According to the actual situation, the selected material is X80 pipeline steel, E is 210 GPa, v is 0.3, and ȡ is 7, 860 kg/m 3 ; (3) Boundary conditions: The left side of the sample is subject to fixed constraints as boundary conditions.The specimens are loaded to different stress states (0-160 MPa, every 20 MPa) by applying different X-direction displacements to the right side of the model.On this basis, the transient force is applied to the middle position of the XY plane of the model to realize the simulation of knocking vibration; (4) Solution and post-processing: The model was solved transiently, and a probe was set in the middle of the model to record and store the vibration signal of the model.

Simulation results and analysis
The vibration of the sample under different tensile stress states is studied.Firstly, different stress states are obtained by changing the boundary conditions.On this basis, the transient knocking vibration simulation is carried out in the middle of the model, and the vibration signal is obtained (seen in Figure 2).With the increase of time, the amplitude of vibration will decrease, and there is a certain attenuation phenomenon.There is an obvious peak in the spectrum, and the frequency corresponding to the peak represents the natural frequency of the structure.The vibration amplitude will decrease with time in Figure 6.This is because during the vibration of the specimen, the amplitude of the vibration will be reduced due to the influence of air and other damping.There is also a dominant frequency in the spectrogram.The experimental results are similar to the simulation results.To further analyze the regularity of the experimental results, the main frequency of vibration under different tensile stress is obtained.The experimental results are very similar to the finite element simulation results in Figure 7.The main frequency of the sample vibration is positively correlated with the tensile stress, but there are some differences in the value, as seen in Table 1.Under various stress states, the difference between the simulation results and the experimental result is small, and the dominant frequencies of both are in the range of 1, 775-1, 840 Hz.After comparison, the error is less than 1%.The reasons for the differences may be as follows: First, the model is relatively simplified compared with the experiment; Second, environmental factors have some influence; Third, equipment accuracy also has an influence.From the comparison of the results, both the change trend and the absolute value error are relatively small, which can prove the feasibility of the tapping vibration method to obtain pipeline stress states.It is a reliable method for non-destructive testing and evaluation of small sample stress.

Conclusion
This study came up with a pipeline tap detection means based on vibration characteristics.The reliability of the finite element method is verified by the experimental method.The feasibility of the knock detection stress method is illustrated.According to the results of the tapping vibration detection method, there is a quantitative relationship between the natural frequency of the vibration and the tensile stress.It can evaluate the situation of pipe stress and can be used as an effective means to estimate the safety status of pipelines in active service.

Figure 3 .
Figure 3. Relationship between tensile stress and dominant frequency of vibration (simulation).

Figure 7 .
Figure 7. Relationship between tensile stress and dominant frequency of vibration (experiment).

Table 1 .
Vibration results under various stress states.