Study on Vibration Characteristics of Natural Gas Pipeline Explosion Based on Improved MP-WVD Algorithm

In order to meet the requirement of precise analysis of nature gas pipeline explosion, authors combined MP algorithm andWVD distribution to improve the time-frequency resolution and to solve the problem of cross-terms interference. *e HHTalgorithm was applied to the data preprocessing of MP algorithm to reduce the computational complexity of the MP algorithm. It improved the computing efficiency and laid the foundation for big data analysis. In this paper, authors carried out a full-size pipeline explosion experiment at the CNPC pipeline fracture control State Key Laboratory. Advantages of the improved MP-WVD algorithm were taken to obtain the time-frequency distribution characteristics of the pipeline explosion vibration. *e research provided a new algorithm for the time-frequency distribution of nonstationary random vibration, and the result provided a reference for the safe operation and construction of natural gas pipeline.


Introduction
With the popularization of natural gas, the construction mileage of pipeline is increasing year by year.e explosion accidents of natural gas pipeline that occurred occasionally brought a variety of damage effects [1,2].Shock wave and thermal radiation were the main damage effects to people, and a lot of research has been done at present [3][4][5].e vibration wave, which mainly destroyed the buildings, has not been studied deeply yet.Taking the vibration signal generated by natural gas pipeline explosion as the research object, the authors improved the traditional time-frequency analysis algorithms and obtained more accurate timefrequency characteristics of the vibration.
At present, all the algorithms used in the field of timefrequency analysis had their own advantages and disadvantages.
e STFT algorithm initially provided the possibility for Fourier transform to be applied to time-frequency analysis [6,7].However, the bases of the algorithm were still trigonometric function, which could not match with the unsteady process of blasting vibration accurately.Da-chao et al. [8] analyzed an experimental recording signal of ground motion by means of Fourier transform, short-time Fourier transform (STFT), continuous wavelet (CWT), and discrete wavelet transform (DWT).
e results showed that wavelet transform introduced the wavelet bases which were more suitable for vibration wave, but its time-frequency resolution was still limited by the uncertainty principle [9,10].Renshu et al. [11] did the comparison between HHT and short-time Fourier transformation (STFT) of blast wave signals, the HHT transform method proposed adaptive bases, but the interference of the EMD algorithm's boundary effect to the original signal was still a difficult problem.In the field of time-frequency analysis, the WVD distribution has an accurate time-frequency resolution, but its cross-term problem has plagued researchers for a long time [12,13].With the indepth study, authors, combining HHT, MP, and WVD algorithms, solved the cross-term interference and reduced the complexity of the MP algorithm greatly, which laid the foundation for large amount of data analysis.Compared with the traditional algorithms (STFT, Wavelet, and HHT), this algorithm had higher time-frequency resolution and better algorithm efficiency.

WVD Distribution.
e WVD algorithm was first applied by Ville to the domain of time-frequency analysis.At the same time, Ville further demonstrated the Wegener Distribution.According to the eigenfunction method, he derived the WVD expression of the signal [14].
As can be seen from formula (1), there was no window function in the WVD expression of the signal.It also meant that there was no inverse relation between the frequency resolution and time resolution of WVD, which was not constrained by the Heisenberg uncertainty principle.
e distribution of WVD was nonlinear time-frequency distribution.erefore, it did not have the additivity of linear distribution.at is, the WVD of the sum of two signals were not equal to the sum of the WVD of each signal.

MP Algorithm.
e principle of the MP algorithm was to decompose the signal based on the dictionary atoms.e process is shown in Figure 1. e atom Q n with the highest matching degree to the signal T n was selected, and the projection value T n and the residual signal T n+1 were found.After the residual signal T n+1 was obtained, the process of atomic matching was repeated.T n+1 was projected to the closest atom Q n+1 , and the residual signal T n+2 was obtained.
is cycle was repeated until the residual signal energy was less than the preset threshold [15], according to the actual needs of different accuracy of analysis.

Defect and Improvement of the Algorithm
As mentioned above, the existence of the cross terms had greatly disturbed the time-frequency distribution of the signal.erefore, in this paper, the MP algorithm was used to subdivide the original signal into the basic atoms, and then calculated the WVD of each atom [16,17].e calculation results were summed up and a clearer time-frequency distribution was obtained.Figure 2 was a synthetic sample signal.
e first method was to calculate its WVD directly.e second method was to calculate its WVD after subwave decomposition.e results obtained by the two methods were compared as shown in Figure 3.
As could be seen from the WVD time-frequency distribution, cross terms appeared at the middle points of the central connection of valid signals.
is meant that the WVD transform would produce a cross term between any two valid signals.In Figure 3(a), the sample signal had 3 components, and a total of 3 cross terms were produced.
at is to say, N * (N − 1)/2 crosses would be produced for N components.However, in Figure 3(b), the subwave decomposition method was adopted to eliminate the interference of the cross terms successfully.
On the other hand, for the current research status, the biggest defect of the MP algorithm was the complexity.It took a long time to complete signal decomposition.e amount of data in the usual time-frequency analysis was very large, so the researchers hoped to get a more efficient algorithm by improving it.
e control parameters of the Gabor atom used in the MP algorithm were amplitude, frequency, central time, and phase.e process of scanning was the optimization of the four parameters by the exhaustive method.To simplify the calculation process, in this paper, the HHT method was introduced.
e HHT method consists of two steps, the EMD algorithm and Hilbert transform.
Firstly, the signal Z(t) was decomposed into multiple intrinsic modal functions c(t) by EMD algorithm.en a Hilbert transformation was performed on c(t): where PV represents the Cauchy principal value.An analytic signal z(t) was established: where a(t) is the amplitude function, and ( Further, the instantaneous frequency of the signal could be obtained by differentiating the phase function.Bringing the results into the MP algorithm, the 4 parameters (amplitude, It could be seen from the comparative analysis of Table 1 that the e ciency of the algorithm had been signi cantly improved.e time used to deal with the same signal has been reduced by about 40 times.

Introduction of the Experiment.
e experiment selected the Chinese third-generation natural gas pipeline [18].e diameter of the pipe was 1422 mm, and the material was X80 pipeline steel.is speci cation pipeline has been widely used in the West-East Gas Pipeline Project.e parameters are shown in Table 2. e pipeline was lled with natural gas; inner pressure was 13.3 MPa, and the gas composition is shown in Table 3.
e total length of the experimental pipeline was 430 m.It consisted of two sections.e length of the gas storage part at both ends was 150 m, and the length of the experimental part in the middle of the pipeline was 130 m. e experimental site is shown in Figure 5. e gas storage parts were buried rst.After the preparation was nished, the experimental part was also buried [19].
In this experiment, taking the initiation point as the coordinate origin, the measurement lines were set in two directions.On the vertical line, there were measurement points 1#∼10#.On the parallel line, there were measurement points 11#∼20#.At each measurement point, a vibration

Shock and Vibration 3
velocity sensor and a vibration acceleration sensor were placed.e distribution of the measurement points is shown in Figure 6. e vibration recorders used in the experiment were type TC-4850 and type Blast-UM.ey were all equipped with three-vector sensors, which could record three mutually perpendicular vibrations (X-axis, Y-axis, and Zaxis).When the sensor was installed, the X-axis pointed to the initiation point.Technical parameters are shown in Table 4.In this experiment, the trigger threshold was set to 0.1 cm/s (velocity recorders) and 0.1 g (acceleration recorders), the sampling frequency was set to 10000 Sps, and the acquisition time was set to 10 s. e explosion process is shown in the Figure 7. e maximum diameter of the fireball was about 150 m, and the height of the mushroom cloud was about 300 m. e

Data Processing.
Taking the vertical component (Z-axis) data of measuring point 1# as an example, the improved MP-WVD algorithm was used to analyze.e first step was MP decomposition [20].
As could be seen from Figure 9, the decomposed subwave had good compactness and could show the details of the signal accurately.At the same time, it was found that the MP algorithm had an excellent high-frequency dryness effect for blasting vibration signal [21].Compared with other filtering algorithms, the results are shown in Table 5.
As could be seen from the table, the reconstruction signal obtained by the MP algorithm preserved almost all the details of the original signal [22].At the same time, noise was eliminated.However, the result of traditional low-pass filtering had a serious phase difference compared with the original signal.erefore, the time information of the signal was changed.Due to the adaptive basement algorithm, the

Shock and Vibration
EMD algorithm was very fast, but the filtering effect was not stable.So it was easy to remove the useful information together [23][24][25].On the other hand, the boundary effect also introduced interference signals.As shown in the table, the difference between the reconstructed signal and the original signal was large.e obtained atomic matrix was brought into the WVD algorithm and calculated the time-frequency distribution of each atom, respectively, and added them up.
e overall time-frequency distribution of the signal was obtained, and the results of the wavelet transform and HHT were compared, as shown in the Figure 10.
It could be seen from the figure that both the time resolution and frequency resolution of the wavelet transform were not as good as the MP-WVD algorithm.At the same time, there was some boundary overflow.e time spectrum obtained by the HHT algorithm had a very obvious boundary effect.ere was a fairly strong energy distribution in the VLF part, which was not consistent with the fact.e MP-WVD algorithm not only had a high-frequency resolution, but also described the frequency distribution of the wave with time.
e characteristics of the vibration signal could be identified clearly from the figure.In the time range of 0.1∼0.15s, there was the first group of waves in the time-frequency domain.Its main energy was distributed around 20 Hz. e frequency range was relatively concentrated.In the time range of 0.18 s∼0.22 s, there was the second group of waves.eir energy was mainly concentrated in the range of 10∼50 Hz, and the amplitude was larger than that of the first group.In the time range of 0.23∼0.27s, the third peak appeared.e  Shock and Vibration frequency of this group mainly concentrated in the range of 5∼50 Hz.Its amplitude was smaller than the rst two.Further, taking the horizontal radial signal (X-axis) and the horizontal tangential signal (Y-axis) into the algorithm, the time-frequency distribution was obtained, as shown in Figure 11.
e time-frequency distribution characteristics of the vibration in three directions were compared.
eir similarities and di erences were obtained: e vibration energy of the X-axis was mainly around 8 Hz, and the duration of the vibration was about 0.15 s.Its energy distribution was more concentrated.In comparison, the energy of the horizontal tangential distribution was more dispersed in the time-frequency domain.Its duration of the vibration was about 0.25 s. e main energy was distributed in the frequency range of 0∼40 Hz.
Further, the time integral and frequency integral of the WVD distribution were carried out, and the marginal spectrum and the instantaneous energy spectrum were obtained.
As shown in the Figure 12, the marginal spectrum described the accumulation of the frequency spectrum in the time domain, and its result was in general agreement with the WVD distribution.e di erence was that it was more accurate to see the Z-axis signal accumulated more at the 17.5 Hz and 22 Hz in the marginal spectrum.e Shock and Vibration data of several measurement points were processed, and the results are shown in Figure 13.e following conclusions could be obtained by comparing the results of several groups.(1) e energy of the pipeline explosion vibration wave was mainly distributed between 0 and 40 Hz.(2) On the vertical measurement line, the frequency center of the Z-axis and Y-axis was about 20 Hz, and that of the X-axis was about 10 Hz. (3) On the parallel measurement line, the frequency center of the Z-axis was about 20 Hz, and that of the Y-axis was about 10 Hz. e frequency center of the X-axis was uncertain.
In Figure 14, it could be clearly seen that the vibration energy has three stages of loading.Compared with Figure 15, the same conclusion could still be obtained.e di erence was that the vibration intensity of the Y-axis on the parallel measurement line was obviously higher than that on the vertical measurement line.It could be seen from the gures that the vibration mode of natural gas pipeline explosion di ered in di erent directions.
rough the analysis above, some conclusions could be obtained.Since the X-axes of all the sensors pointed to the initiation point, the X-axis of the sensors on the vertical line and the Y-axis of the sensors on the horizontal line were all perpendicular to the direction of the pipeline axis.
at is to say, the horizontal vibration caused by pipeline explosion was mainly perpendicular to  Shock and Vibration the pipeline direction.erefore, the buildings around the pipeline need to strengthen the aseismic strength perpendicular to the pipe direction.From the point of view of vibration frequency, when engineers conduct pipeline safety design, special attention must be paid to the range of 0∼40 Hz. e natural frequencies of buildings around pipelines, such as pressurized stations or parallel pipelines, should avoid this range of frequencies, especially around 10 Hz and 20 Hz.

Discussion
(1) e combination of HHT, MP, and WVD algorithm has achieved good results in signal analysis.It not only solved the problem of cross terms, but also showed high computing e ciency.At the same time, it was found that the improved MP algorithm had a good denoising e ect.Compared with low-pass ltering and EMD ltering, it behaved more eciently and accurately. is research provided a new algorithm for the time-frequency distribution of nonstationary random vibration.
(2) e vibration energy of the natural gas pipeline explosion was mainly distributed in the frequency range of 0∼40 Hz, and the duration was 0.1∼0.25 s. e natural frequencies of buildings around pipelines should avoid this range of frequencies, especially around 10 Hz and 20 Hz. e pipeline explosion vibration had three stages of loading, and the vibration mode di ered in di erent directions.e horizontal vibration caused by pipeline explosion was mainly perpendicular to the pipeline direction.So it was suggest that the buildings around the pipeline strengthen the aseismic strength perpendicular to the pipe direction.
(3) Since the characteristics of the vibration generated by the explosion are related to the source of explosion and the soil medium, the results obtained in this experiment were applicable to the X80-OD 1422 mm pipeline and buried in the Gobi soil similar to the test site.At present, in the West-East Gas Pipeline Project, a considerable length of pipeline meets this applicable condition.For other speci cations of pipelines or other soil media, there is still a lot of work needed to be supplemented by scholars.
is research was supported by the National Natural Science Foundation of China (nos.11672331 and 51608530).e authors would like to gratefully acknowledge this support.12 Shock and Vibration

2
Shock and Vibration frequency, central time, and phase) scanning operation could be reduced to 2 parameters (amplitude and central time) scanning, which greatly reduced the number of steps of the program.e program ow is shown in the Figure 4. e e ciency of the conventional MP algorithm and the improved MP algorithm were compared.

Figure 5 :
Figure 5: Aerial photograph of experimental site.

Table 1 :
CPU time comparison of the two methods.

Table 2 :
Parameters of the experimental pipeline.

Table 3 :
Composition of the experimental gas.