VMD adaptive decomposition reconstruction long-distance pipeline leakage detection and positioning method based on center frequency method

Abstract

The invention relates to a VMD self-adaptive decomposition reconstruction long-distance pipeline leakage detecting and positioning method based on a center frequency method, which comprises the following steps: firstly, preprocessing leakage signals, calculating a coherence function and cross spectrum density, finding out similar frequency bands (namely leakage frequency bands) of two sections of signals, and carrying out broadband filtering; in order to facilitate computer processing, a preprocessed 60s long signal is segmented, an analysis signal of the segmented signal is obtained through Hilbert change, the number K of VMD decomposition layers is determined according to a center frequency method, a modal component with a large kurtosis value after decomposition is selected to reconstruct a signal with a high signal-to-noise ratio and good robustness, a cross-correlation function of the signal is calculated, and the signal with the high signal-to-noise ratio and good robustness is obtained. Obtaining the time delay, and determining the leakage position and the relative error. Compared with a traditional method, the positioning precision is remarkably improved, the error does not exceed 5%, and the method has good application prospects.

Description

Technical Field

[0001] The present invention belongs to the fields of industrial electronic information engineering, industrial fault detection, etc., and relates to a VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on a center frequency method, and specifically relates to a VMD decomposition and reconstruction cross-correlation analysis combining adaptive filtering and the center frequency method to detect and locate the leakage point of a water supply pipeline, which is suitable for long buried pipeline leakage signal detection scenarios based on passive hydrophones. Background Art

[0002] In order to improve the utilization efficiency of land resources, the laying of underground pipeline transportation plays a vital role in national and urban development. At present, domestic pipeline maintenance mainly relies on manual inspection, and the commonly used monitoring methods are mostly post-monitoring, such as negative pressure wave method, mass balance method and pressure gradient method.

[0003] Existing pipeline monitoring methods can be classified in several forms, usually divided into three categories: external detection methods, internal calculation-based monitoring methods, and visual inspection-based methods. Among these methods, hydrophones are widely used in pipeline external detection because of their low price, high practicality, simple operation, and ability to work with computer software, which is more advantageous than the other two methods. Acoustic detection methods are mainly divided into leakage feature extraction. For pipeline leakage detection problems, there are pipeline leakage location methods based on wavelet packet decomposition and high-order cumulant methods, and the least squares support vector machine method based on particle swarm optimization is used to identify the leakage aperture of the pipeline. Cao Wanying. Research on pipeline acoustic detection and leakage location technology[D]. North China Electric Power University (Beijing), 2023.10.27140 / d.cnki.ghbbu.2023.001067. For EMD signal analysis method, see Sun Liying, Li Yibo, Qu Zhigang, et al. Research on acoustic emission pipeline leakage detection based on EMD signal analysis method[J]. Vibration and Shock, 2007, 26(10):161-164. DOI:10.3969 / j.issn.1000-3835.2007.10.035.

[0004] However, the above methods are all aimed at short-term and short-distance pipeline leakage problems, and are obviously not applicable to long-distance pipeline transportation problems in actual projects. Therefore, it is very necessary to detect long-distance pipeline leakage. Summary of the invention

[0005] Technical issues to be solved

[0006] In order to avoid the shortcomings of the prior art, the present invention proposes a VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on the center frequency method.

[0007] Technical Solution

[0008] A VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and location method based on center frequency method, characterized by the following steps:

[0009] Collect leakage signals x(t) and y(t) at both ends of the long-distance pipeline, calculate the energy spectrum density and mutual interference function of the two signals, and analyze the frequency band with strong correlation between the two signals;

[0010] The Butterworth broadband filter is used to filter the strongly correlated frequency band to improve the signal-to-noise ratio of the useful signal;

[0011] The filtered leakage signal is segmented into sub-signals x i (t) and y i (t), the length of each sub-signal is Inter=M / Num, and there are Num sub-signals in total, where M is the signal length of x(t) and y(t);

[0012] For the segmented sub-signal x i (t), y i (t) Perform VMD signal processing respectively and use the center frequency method to optimize the number of VMD decomposition layers K x and K y , and obtain the IMF of each decomposed modal component x and IMF y ;

[0013] Calculate x i (t) and y i (t) Kurtosis of each modal component xim and Kurtosis yim ;

[0014] Select x i (t) and y i (t) After decomposition, the modal components whose kurtosis values ​​are greater than the set threshold (mean kurtosis value + 0.5 times the kurtosis standard deviation) are reconstructed to obtain the reconstructed signal:

[0015]

[0016] in and is the selected modal component;

[0017] Calculate the reconstructed signal and The cross-correlation function determines the delay of the front-end and back-end signals That is, the time offset of the back-end signal relative to the front-end signal;

[0018] Delay Substitute the theoretical leakage distance D' as the distance from the front detection end to the leakage point:

[0019]

[0020] Where L is the total length of the pipe and c is the speed of sound.

[0021] The collected signals are all leakage signals with a duration of 60 seconds and a long distance greater than or equal to 219 meters.

[0022] The acquisition signals x(t) and y(t) are acquired by using a hydrophone, and the sampling rate of the leakage signal is fs.

[0023] The analysis of the frequency band with strong correlation between the two signals adopts cross-correlation and power spectrum analysis to find out the frequency band showing strong correlation between the two signals.

[0024] The decomposition expression of x(t) is:

[0025]

[0026] where x i (t) is the segmented signal, T is the sampling time, Num is the number of segments, and Inter is the number of sampling points in each segment;

[0027] The decomposition expression of y(t) is:

[0028]

[0029] Where: y i (t) is the segmented signal, T is the sampling time, Num is the number of segments, and Inter is the number of sampling points in each segment.

[0030] The decomposed modal components IMF x and IMF y The calculation is:

[0031] Each modal component IMF x The center frequency is w xim The decomposition constraints are that the center frequencies of the modes are close and the modal sum is equal to the sub-signal x i (t), the method is as follows:

[0032]

[0033] in: Represents the original signal x i The Hilbert transform x of (t) im (t), and K is obtained by using this transformation x The analytical signal of the modal component is obtained to obtain a one-sided spectrum; by multiplying the exponential factor The signal is modulated to baseband;

[0034] After introducing the quadratic penalty factor α and the Lagrangian multiplier τ(t), the problem is transformed into an unconstrained variational problem, and the extended Lagrangian expression is obtained, and the center frequency of each mode is solved as:

[0035]

[0036] When the center frequencies of the modal components are highly adjacent or the spectrum overlaps, it indicates that the signal decomposition has reached the optimal number of layers, and an appropriate number of modal components are obtained. For the x(t) signal, the optimal decomposition layer number K is x , then we get m x modal component IMF x ;

[0037] Each modal component IMF y The center frequency is w yim The decomposition constraints are that the center frequencies of the modes are highly adjacent and the modal sum is equal to the sub-signal y i (t), the method is as follows:

[0038]

[0039] in: Represents the original signal y i The Hilbert transform y of (t) im (t), and K is obtained by using this transformation y The analytical signal of the modal component is obtained to obtain a one-sided spectrum; by multiplying the exponential factor The signal is modulated to baseband;

[0040] After introducing the quadratic penalty factor α and the Lagrangian multiplier τ(t), the problem is transformed into an unconstrained variational problem, and the extended Lagrangian expression is obtained, and the center frequency of each mode is solved as:

[0041]

[0042] When the center frequencies of the modal components are highly adjacent or the spectrum overlaps, it indicates that the signal decomposition has reached the optimal number of layers, and an appropriate number of modal components are obtained. For the y(t) signal, the optimal decomposition layer number K is y , then we get m y modal component IMF y .

[0043] The delay of the front-end and back-end signals The expression is:

[0044]

[0045] An electronic device, characterized in that it includes a processor and a memory, wherein the processor is used to implement the steps of the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on the center frequency method when executing the computer program stored in the memory.

[0046] A readable storage medium, characterized in that a computer program is stored on the readable storage medium, and when the computer program is executed by a processor, the steps of the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on the center frequency method are implemented.

[0047] A computer program product, characterized by comprising computer executable instructions, which, when executed, are used to implement the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on the center frequency method.

[0048] Beneficial Effects

[0049] The present invention proposes a VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on the center frequency method. For the estimation of multi-path pulses, a VMD decomposition and reconstruction cross-correlation analysis leakage detection and positioning method (CF-VMD) combining adaptive filtering and the center frequency method is proposed. The invention first pre-processes the leakage signal, calculates the coherence function and the cross-spectral density, finds the similar frequency band (i.e., the leakage band) of the two segments of the signal, and performs broadband filtering; in order to facilitate computer processing, the pre-processed 60s long signal is then segmented, and then the analysis signal of the segmented signal is obtained through the Hilbert change, and the VMD decomposition layer number K is determined according to the center frequency method, and then the modal component with a larger kurtosis value after decomposition is selected to reconstruct a high signal-to-noise ratio and a good robustness signal, and then the cross-correlation function is calculated to obtain the time delay, and the leakage position and relative error are determined. Compared with the traditional method, the positioning accuracy is significantly improved, and the error does not exceed 5%, which has a good application prospect.

[0050] Compared with the existing pipeline leakage location technology, the present invention has the following beneficial effects:

[0051] 1) Pre-process the real leakage data collected by the hydrophone, perform coherence analysis, find the similar frequency band, i.e. the leakage frequency band, and perform broadband filtering on it, which reduces the redundant environmental noise and improves the positioning accuracy.

[0052] 2) For buried long-distance pipelines (distance > 200 meters), the leakage signal has multi-path arrival. Therefore, it is processed in sections and decomposed and reconstructed based on the different center frequencies of its components after VMD decomposition, which is robust.

[0053] 3) The kurtosis value of the IMF component of the decomposed signal is selected to reconstruct a high signal-to-noise ratio signal. After cross-correlation analysis, the error does not exceed 5%, and the positioning accuracy is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is the leak detection and positioning flow chart based on CF-VMD

[0055] Figure 2 The actual leakage data collected by the hydrophone and related functions

[0056] a: Original leakage signal timing diagram b: Frequency correlation function of front-end and rear-end leakage signals

[0057] Figure 3 This is the time-frequency comparison of the front and rear leakage signals after CF-VMD processing.

[0058] a: Time-frequency diagram of the front-end leakage signal b: Time-frequency diagram of the front-end leakage signal after cf-vmd decomposition and reconstruction

[0059] c: Time-frequency diagram of the leakage signal in the rear section d: Time-frequency diagram of the leakage signal in the front section after CF-VMD decomposition and reconstruction

[0060] Figure 4 This is the IMF component diagram of VMD processing based on the center frequency

[0061] a. Front-end IMF component

[0062] b. Back-end IMF component

[0063] Figure 5 is the peak value of the front-end and back-end leakage signals

[0064] a. Peak value of front-end leakage signal

[0065] b. Peak value of back-end leakage signal

[0066] Figure 6 This is a comparison chart of the original signal and the decomposed and reconstructed signal.

[0067] a. Original signal

[0068] b. Processed signal

[0069] Figure 7 It is a real acquisition scenario and cross-correlation analysis of decomposed and reconstructed signals.

[0070] a: Scenario of front-end hydrophone collecting signals

[0071] b: Scenario of front-end hydrophone collecting signals

[0072] c: Time correlation function of front-end and back-end signals

[0073] The data collection scenario of the embodiment is described as follows: the distance between the front and rear hydrophones is 209 m, the distance between the leakage point and the front hydrophone is 99 m, and the speed of sound is 1500 m / s. The estimated time delay of the leakage point according to the present invention is Figure 7 The position estimated by Formula 7 is 101m, and the error between it and the actual result is 0.96%, which shows that the present invention can more accurately locate the leakage point of the long-distance buried water pipe. DETAILED DESCRIPTION

[0074] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0075] A VMD (CF-VMD) adaptive decomposition and reconstruction method for long-distance pipeline leakage detection and positioning based on the center frequency method is characterized by: firstly, the front and rear leakage signals are preprocessed to find the similar frequency band, i.e., the leakage signal band, and then broadband filtering is performed to filter out the environmental noise; in order to facilitate computer processing, the long-term leakage signal is segmented, and the segmented signal is processed by VMD. After decomposition to a certain number of layers, the center frequency of each component is close, the kurtosis value of each component is calculated, and the signal with a larger kurtosis value is selected to reconstruct a high signal-to-noise ratio signal; finally, the cross-correlation delay of the two reconstructed signals is calculated to locate the leakage position.

[0076] In the present invention, the pipeline length D is 209m, and the specific steps are as follows:

[0077] Step 1: Use hydrophones at both ends of the long-distance pipeline with a sampling rate of fs to collect leakage signals x(t) and y(t). The collected signals are leakage signals with a duration of 60s and a long distance greater than or equal to 219m.

[0078] Calculate the energy spectral density and mutual interference function of the two signals, and use cross-correlation and power spectrum analysis to find the frequency bands that show strong correlation between the two signals;

[0079] When calculating the energy spectral density and mutual coherence function of two signals, the energy spectral density describes the energy distribution of each of the two leakage signals in the frequency domain; the coherence function reflects the degree of coherence between the leakage signals. The coherence function value ranges from 0 to 1. The closer the value is to 1, the stronger the linear correlation between the two signals at this frequency.

[0080] Step 2: Perform Butterworth broadband filter filtering on the strongly correlated frequency band to improve the signal-to-noise ratio of the useful signal; for the strongly correlated frequency band, adopt the Butterworth broadband filter filtering method with n=5 to filter out the environmental noise and improve the signal-to-noise ratio of the useful signal.

[0081] Step 3: Set the sampling frequency to 7500Hz, the sampling time to 60s, and the number of sampled data points is 450,000 points. In order to facilitate computer processing of this long data, it is segmented and the front-end and rear-end leakage signals x(t) and y(t) are divided into N segments of sub-signals x i (t) and y i (t), the length of each sub-signal is 450000 / N.

[0082] The filtered leakage signal is segmented into sub-signals x i (t) and y i (t), the length of each sub-signal is Inter=M / Num, and there are Num sub-signals in total, where M is the signal length of x(t) and y(t);

[0083] The decomposition expression of x(t) is:

[0084]

[0085] where x i (t) is the segmented signal, T is the sampling time, Num is the number of segments, and Inter is the number of sampling points in each segment;

[0086] The decomposition expression of y(t) is:

[0087]

[0088] Where: y i (t) is the segmented signal, T is the sampling time, Num is the number of segments, and Inter is the number of sampling points in each segment.

[0089] In this paper, according to the actual situation, it is divided into sub-signals with a length of 2500 and a total of 180 segments.

[0090] Step 4: Segment sub-signal x i (t), y i (t) Perform VMD signal processing respectively and use the center frequency method to optimize the number of VMD decomposition layers K x and K y , and obtain the IMF of each decomposed modal component x and IMF y ;

[0091] The decomposed modal components IMF x and IMF y The calculation is:

[0092]

[0093] Each modal component IMF x The center frequency is w xim The decomposition constraints are that the center frequencies of the modes are close and the modal sum is equal to the sub-signal x i (t), the method is as follows:

[0094]

[0095] in: Represents the original signal xi The Hilbert transform x of (t) im (t), and K is obtained by using this transformation x The analytical signal of the modal component is obtained to obtain a one-sided spectrum; by multiplying the exponential factor The signal is modulated to baseband;

[0096] After introducing the quadratic penalty factor α and the Lagrangian multiplier τ(t), the problem is transformed into an unconstrained variational problem, and the extended Lagrangian expression is obtained, and the center frequency of each mode is solved as:

[0097]

[0098] When the center frequencies of the modal components are highly adjacent or the spectrum overlaps, it indicates that the signal decomposition has reached the optimal number of layers, and an appropriate number of modal components are obtained. For the x(t) signal, the optimal decomposition layer number K is x , then we get m x modal component IMF x ;

[0099] Each modal component IMF y The center frequency is w yim The decomposition constraints are that the center frequencies of the modes are highly adjacent and the modal sum is equal to the sub-signal y i (t), the method is as follows:

[0100]

[0101] in: Represents the original signal y i The Hilbert transform y of (t) im (t), and K is obtained by using this transformation y The analytical signal of the modal component is obtained to obtain a one-sided spectrum; by multiplying the exponential factor The signal is modulated to baseband;

[0102] After introducing the quadratic penalty factor α and the Lagrangian multiplier τ(t), the problem is transformed into an unconstrained variational problem, and the extended Lagrangian expression is obtained, and the center frequency of each mode is solved as:

[0103]

[0104] When the center frequencies of the modal components are highly adjacent or the spectrum overlaps, it indicates that the signal decomposition has reached the optimal number of layers, and an appropriate number of modal components are obtained. For the y(t) signal, the optimal decomposition layer number K is y , then we get m y modal component IMF y .

[0105] When the number of decomposition layers K is too large, it will lead to over-decomposition and increase the execution time of the algorithm. On the contrary, when K is too small, it will lead to insufficient decomposition. Therefore, when the center frequencies of the modal components are close, the optimal number of decomposition layers K is reached.

[0106] Step 5: After determining the optimal number of decomposition layers, calculate the kurtosis of each modal component after VMD decomposition. The kurtosis describes the thickness of the signal tail and the sharpness of the peak. A high kurtosis value indicates that there may be sharp pulse components in the signal, while a low kurtosis value indicates that the signal is relatively smooth. In vibration analysis and mechanical fault diagnosis, the kurtosis value is an effective indicator for detecting equipment failures, such as defects in bearings and gears. When a device fails, the kurtosis value of the vibration signal usually increases significantly. The kurtosis expression is as follows:

[0107]

[0108] In the formula, x in are the modal components of each IMF, u is the modal mean of each IMF, and m is the total number of modal components.

[0109] The modal component with the larger kurtosis value in the decomposed mode is selected for reconstruction, and the reconstructed signal has the characteristics of high signal-to-noise ratio and robustness. The first three IMF components with the larger kurtosis value in the decomposed signal are selected for reconstruction to obtain the reconstructed signal.

[0110] Calculate x i (t) and y i (t) Kurtosis of each modal component xim and Kurtosis yim ;

[0111] Select x i (t) and y i (t) After decomposition, the modal components whose kurtosis values ​​are greater than the set threshold (mean kurtosis value + 0.5 times the kurtosis standard deviation) are reconstructed to obtain the reconstructed signal:

[0112]

[0113] in and is the selected modal component;

[0114] Step 6: Calculate the cross-correlation function of the reconstructed signal. Through the cross-correlation, the delay of the front-end and rear-end signals, that is, the time offset of the rear-end signal relative to the front-end signal, can be determined.

[0115] Calculate the reconstructed signal and The cross-correlation function determines the delay of the front-end and back-end signals That is, the time offset of the back-end signal relative to the front-end signal;

[0116] Step 7: Delay Substitute the theoretical leakage distance D' as the distance from the front detection end to the leakage point:

[0117]

[0118] The delay of the front-end and back-end signals The expression is:

[0119]

[0120] Where L is the total length of the pipe and c is the speed of sound.

[0121] In the present invention, the pipeline length D is 209m, the distance between the front hydrophone and the leakage point is 99m, the speed of sound c is 1500m / s, and the time delay obtained in step 7 is Substituting into the following formula, the theoretical leakage distance is x'

[0122]

[0123] Table 1 and Table 2 are the center frequencies of the front and rear leakage signals at different decomposition levels.

[0124] Table 1 Front-end leakage signal VMD decomposition center frequency

[0125] K 5 6 7 8 9 10 11 12 13 14 frequency 1946 2027 2085 2128 2162 2189 2211 2229 2245 2258

[0126] Table 2 Back-end leakage signal VMD decomposition center frequency

[0127] K 5 6 7 8 9 10 11 12 13 14 frequency 3891 4053 4169 4256 4324 4378 4422 4459 4490 4516

Claims

1. A VMD adaptive decomposition and reconstruction method for long-distance pipeline leakage detection and location based on the center frequency method, characterized in that Here are the steps: Collect leakage signals x(t) and y(t) at both ends of the long-distance pipeline, calculate the energy spectrum density and mutual interference function of the two signals, and analyze the frequency band with strong correlation between the two signals; The Butterworth broadband filter is used to filter the strongly correlated frequency band to improve the signal-to-noise ratio of the useful signal; The filtered leakage signal is segmented into sub-signals x i (t) and y i (t), the length of each sub-signal is Inter=M / Num, and there are Num sub-signals in total, where M is the signal length of x(t) and y(t); For the segmented sub-signal x i (t), y i (t) Perform VMD signal processing respectively and use the center frequency method to optimize the number of VMD decomposition layers K x and K y , and obtain the IMF of each decomposed modal component x and IMF y ; Calculate x i (t) and y i (t) Kurtosis of each modal component xim and Kurtosis yim ; Select x i (t) and y i (t) After decomposition, the modal components whose kurtosis values ​​are greater than the set threshold (mean kurtosis value + 0.5 times the kurtosis standard deviation) are reconstructed to obtain the reconstructed signal: in and is the selected modal component; Calculate the reconstructed signal and The cross-correlation function determines the delay of the front-end and back-end signals That is, the time offset of the back-end signal relative to the front-end signal; Delay Substitute the theoretical leakage distance D' as the distance from the front detection end to the leakage point: Where L is the total length of the pipe and c is the speed of sound.

2. According to claim 1, the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and location method based on the center frequency method is characterized by: The collected signals are all leakage signals with a duration of 60 seconds and a long distance greater than or equal to 219 meters.

3. According to claim 1, the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and location method based on the center frequency method is characterized by: The acquisition signals x(t) and y(t) are acquired by using a hydrophone, and the sampling rate of the leakage signal is fs.

4. According to claim 1, the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and location method based on the center frequency method is characterized by: The analysis of the frequency band with strong correlation between the two signals adopts cross-correlation and power spectrum analysis to find out the frequency band showing strong correlation between the two signals.

5. According to claim 1, the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and location method based on the center frequency method is characterized by: The decomposition expression of x(t) is: where x i (t) is the segmented signal, T is the sampling time, Num is the number of segments, and Inter is the number of sampling points in each segment; The decomposition expression of y(t) is: Where: y i (t) is the segmented signal, T is the sampling time, Num is the number of segments, and Inter is the number of sampling points in each segment.

6. The VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and location method based on the center frequency method according to claim 1 is characterized by: The decomposed modal components IMF x and IMF y The calculation is: Each modal component IMF x The center frequency is w xim The decomposition constraints are that the center frequencies of the modes are close and the modal sum is equal to the sub-signal x i (t), the method is as follows: in: Represents the original signal x i The Hilbert transform of (t)x im (t), and K is obtained by using this transformation x The analytical signal of the modal component is obtained to obtain a one-sided spectrum; by multiplying the exponential factor The signal is modulated to baseband; After introducing the quadratic penalty factor α and the Lagrangian multiplier τ(t), the problem is transformed into an unconstrained variational problem, and the extended Lagrangian expression is obtained, and the center frequency of each mode is solved as: When the center frequencies of the modal components are highly adjacent or the spectrum overlaps, it indicates that the signal decomposition has reached the optimal number of layers, and an appropriate number of modal components are obtained. For the x(t) signal, the optimal decomposition layer number K is x , then we get m x modal component IMF x ; Each modal component IMF y The center frequency is w yim The decomposition constraints are that the center frequencies of the modes are highly adjacent and the modal sum is equal to the sub-signal y i (t), the method is as follows: in: Represents the original signal y i The Hilbert transform y of (t) im (t), and K is obtained by using this transformation y The analytical signal of the modal component is obtained to obtain a one-sided spectrum; by multiplying the exponential factor The signal is modulated to baseband; After introducing the quadratic penalty factor α and the Lagrangian multiplier τ(t), the problem is transformed into an unconstrained variational problem, and the extended Lagrangian expression is obtained, and the center frequency of each mode is solved as: When the center frequencies of the modal components are highly adjacent or the spectrum overlaps, it indicates that the signal decomposition has reached the optimal number of layers, and an appropriate number of modal components are obtained. For the y(t) signal, the optimal decomposition layer number K is y , then we get m y modal component IMF y .

7. The VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and location method based on the center frequency method according to claim 1 is characterized by: The delay of the front-end and back-end signals The expression is:

8. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the processor is used to implement the steps of the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on the center frequency method as claimed in any one of claims 1 to 7 when executing the computer program stored in the memory.

9. A readable storage medium, characterized in that: The readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the VMD adaptive decomposition and reconstruction method for long-distance pipeline leakage detection and positioning based on the center frequency method as claimed in any one of claims 1 to 7 are implemented.

10. A computer program product, characterized in that It includes computer executable instructions, which are used to implement the VMD adaptive decomposition and reconstruction long-distance pipeline leakage detection and positioning method based on the center frequency method as described in claims 1 to 7 when being executed.

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