A VMD adaptive decomposition and reconstruction method for long pipeline leakage detection and positioning based on center frequency method
Through the VMD adaptive decomposition and reconstruction method based on the center frequency method, the problem of long-distance pipeline leakage detection and positioning is solved, and high-precision leakage point positioning is achieved with an error of no more than 5%. It is suitable for leakage signal detection in long-distance buried pipelines.
Patent Information
- Application Number
- CN202411478635.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-22
- Publication Date
- 2025-10-14
- Estimated Expiration
- 2044-10-22
AI Technical Summary
Existing pipeline leakage detection methods are mainly targeted at short-term and short-distance pipelines, and are difficult to apply to leak detection and positioning of long-distance pipelines, especially leakage signal detection of underground buried pipelines.
The VMD adaptive decomposition and reconstruction method based on the center frequency method is adopted. The leakage signals are collected at both ends of the long-distance pipeline, the energy spectral density and mutual interference function of the signals are calculated, Butterworth broadband filtering is performed, the segmented signals are processed by VMD, the modal components with larger kurtosis values are selected for reconstruction, and the cross-correlation function is calculated to determine the leakage location.
It significantly improves the positioning accuracy of long-distance pipeline leakage detection, with an error of no more than 5%. It has good application prospects and can accurately locate the leakage points of buried long-distance pipelines.
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Figure CN119469589B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the field of industrial electronic information engineering, industrial fault detection, and relates to a VMD adaptive decomposition reconstruction long pipeline leakage detection and positioning method based on a center frequency method, in particular to a VMD decomposition reconstruction cross-correlation analysis method combined with adaptive filtering and a center frequency method to detect and position the leakage point of a water supply pipeline, which is suitable for long-distance buried pipeline leakage signal detection scenarios based on passive hydrophones. BACKGROUND
[0002] 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 methods such as negative pressure wave method, mass balance method and pressure gradient method.
[0003] The existing pipeline monitoring methods can be classified into several forms, usually divided into three categories: external-based detection methods, internal calculation-based monitoring methods, and visual inspection-based methods. Among these methods, hydrophones are widely used in pipeline external detection due to their low cost, high practicality, simple operation, and ability to work with computer software, and have more advantages than the other two methods. The method of acoustic detection is mainly divided into leakage feature extraction for pipeline leakage detection problem, there are pipeline leakage positioning methods based on wavelet packet decomposition and high-order cumulant method, and particle swarm optimization least squares support vector machine method is used to identify the leakage aperture of the pipeline. Cao Wanying. Pipeline acoustic detection and leakage positioning technology research[D]. North China Electric Power University (Beijing), 2023.10.27140 / d.cnki.ghbbu.2023.001067. EMD signal analysis method, Sun Liying, Li Yibo, Qu Zhigang, et al. Acoustic emission pipeline leakage detection research 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-time and short-distance pipeline leakage problems, and obviously are not suitable for long-distance pipeline transportation problems in actual engineering. Therefore, it is necessary to detect long-distance pipeline leakage. SUMMARY
[0005] Technical problems to be solved
[0006] In order to avoid the shortcomings of the prior art, the application provides a VMD adaptive decomposition reconstruction long pipeline leakage detection and positioning method based on a center frequency method.
[0007] Technical scheme
[0008] A VMD adaptive decomposition and reconstruction method for long pipeline leakage detection and positioning based on center frequency method, characterized in that the steps are as follows:
[0009] Collecting leakage signals x(t) and y(t) at both ends of the long pipeline, calculating the energy spectrum density and mutual coherence function of the two signals, and analyzing the strong correlation frequency band between the two signals;
[0010] Performing Butterworth wideband filter filtering on the strong correlation frequency band to improve the signal-to-noise ratio of the useful signal;
[0011] Segmenting the filtered leakage signal into sub-signals x i (t) and y i (t), each segment of sub-signal has a length of Inter=M / Num, and there are Num segments of sub-signals, wherein M is the signal length of x(t) and y(t);
[0012] Performing VMD signal processing on the segmented sub-signals x i (t) and y i (t) respectively, and using the center frequency method to optimize the decomposition layer number K x and K y of VMD, to obtain each decomposition modal component IMF x and IMF y ;
[0013] Calculating the kurtosis values Kurtosis xim and Kurtosis yim of each modal component of x i (t) and y i (t);
[0014] Selecting the modal components of x i (t) and y i (t) after decomposition whose kurtosis values are greater than the set threshold (average kurtosis value+0.5 times kurtosis standard deviation) to reconstruct, to obtain the reconstructed signal:
[0015]
[0016] Wherein and are the selected modal components;
[0017] Calculating the cross-correlation function of the reconstructed signals and to determine the time delay between the front-end and rear-end signals, i.e. the time offset of the rear-end signal relative to the front-end signal;
[0018] Substituting the time delay into the theoretical leakage distance D' as the distance from the front-end 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 signals x(t) and y(t) are collected using a hydrophone, and the sampling rate of the leakage signal is fs.
[0023] The analysis of the frequency bands with strong correlation between the two signals adopts cross-correlation and power spectrum analysis to find the frequency bands with 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 the 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 of (t)x im (t), and use this transformation to get K 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 use this transformation to get K 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 long-distance pipeline leakage detection and positioning method based on the center frequency method of VMD adaptive decomposition and reconstruction 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 method for long-distance pipeline leakage detection and positioning 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] This paper proposes a long-distance pipeline leak detection and location method based on the center frequency method using VMD adaptive decomposition and reconstruction. For multipath pulse estimation, a VMD decomposition and reconstruction cross-correlation analysis (CF-VMD) leak detection and location method combining adaptive filtering and the center frequency method is proposed. This method first preprocesses the leakage signal, calculates the coherence function and cross-spectral density, finds the similar frequency bands (i.e., the leakage bands) between the two signal segments, and performs broadband filtering. To facilitate computer processing, the preprocessed 60-second long signal is then segmented. The Hilbert transform is then used to obtain the analysis signals of the segmented signals. The number of VMD decomposition layers, K, is determined using the center frequency method. Modal components with large kurtosis values after decomposition are then selected to reconstruct a signal with a high signal-to-noise ratio and good robustness. The cross-correlation function is then calculated to obtain the time delay, which is then used to determine the leak location and relative error. Compared to traditional methods, this method significantly improves location accuracy, with an error of less than 5%, demonstrating promising application prospects.
[0050] Compared with existing pipeline leakage locating technologies, the present invention has the following beneficial effects:
[0051] 1) Preprocess 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, thus reducing the redundant environmental noise and improving 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 segments 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 back-end leakage signals
[0057] Figure 3 This is the time-frequency comparison of the front-end and back-end 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 back 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 processed by VMD 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 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 where the front-end hydrophone collects 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 acquisition scenario of the embodiment is described as follows: the distance between the front and rear hydrophones is 209m, the leakage point is 99m away from the front hydrophone, and the speed of sound is 1500m / s. The time delay of the leakage point estimated by the present invention is Figure 7 The position estimated by Formula 7 is 101m, and the error between this and the actual result is 0.96%, indicating that the present invention can more accurately locate the leakage point of a long-distance buried water pipe. DETAILED DESCRIPTION
[0074] The present invention will now be further described with reference to the embodiments and accompanying drawings:
[0075] A long-distance pipeline leak detection and location method based on the center frequency method VMD (CF-VMD) adaptive decomposition and reconstruction method is proposed. The method is characterized by: first, preprocessing the front-end and rear-end leakage signals to find similar frequency segments, namely the leakage signal frequency segments; then performing broadband filtering to remove environmental noise; to facilitate computer processing, the long-term leakage signal is segmented and VMD processing is performed on the segmented signals. After decomposition to a certain number of layers, the center frequencies of each component are close. The kurtosis value of each component is calculated, and the signal with the 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 leak location.
[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 60 seconds and a distance greater than or equal to 219 meters.
[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 leakage signal 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, with values closer to 1 indicating a stronger linear correlation between the two signals at that frequency.
[0080] Step 2: Perform Butterworth broadband filtering on the strongly correlated frequency band to improve the signal-to-noise ratio of the useful signal; for the strongly correlated frequency band, a Butterworth broadband filtering method with n=5 is adopted to filter out the ambient 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] Segment the filtered leakage signal 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 180 sub-signals with a length of 2500.
[0090] Step 4: Pair the segmented sub-signal x i (t), y i (t) Perform VMD signal processing separately 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 the IMF y ;
[0091] The decomposed modal components IMF x and the 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 of (t)x im (t), and use this transformation to get K 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 use this transformation to get K 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 levels K is too large, it will lead to over-decomposition, increasing the execution time of the algorithm. Conversely, when K is too small, it will lead to insufficient decomposition. Therefore, the optimal number of decomposition levels K is achieved when the center frequencies of the modal components are close.
[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, kurtosis is an effective indicator for detecting equipment faults, 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] Where x in is the modal component 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. 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 value is greater than the set threshold (mean kurtosis + 0.5 times the standard deviation of kurtosis) 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 cross-correlation, 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, 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 between the front detection end and 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 after different decomposition layers.
[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 VMD decomposition center frequency of back-end leakage signal
[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 by Here are the steps: Collect leakage signals x(t) and y(t) at both ends of a long-distance pipeline, calculate the energy spectral density and mutual interference function of the two signals, and analyze the frequency band with strong correlation between the two signals; Perform Butterworth broadband filter on the frequency band with strong correlation to improve the signal-to-noise ratio of useful signals; Segment the filtered leakage signal 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); Paired sub-signal x i (t), y i (t) Perform VMD signal processing separately 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 the 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 value is greater than the set threshold 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 between the front detection end and the leakage point: Where L is the total length of the pipe and c is the speed of sound.
2. The method for long-distance pipeline leak detection and location based on the center frequency method of VMD adaptive decomposition and reconstruction according to claim 1 is characterized by: The collected leakage signals are all leakage signals with a duration of 60 seconds and a long distance greater than or equal to 219 meters.
3. The method for long-distance pipeline leak detection and location based on the center frequency method of VMD adaptive decomposition and reconstruction according to claim 1 is characterized by: The leakage signals x(t) and y(t) are collected using a hydrophone, and the sampling rate of the leakage signals is fs.
4. The method for long-distance pipeline leak detection and location based on the center frequency method of VMD adaptive decomposition and reconstruction according to claim 1 is characterized by: The analysis of the frequency bands with strong correlation between the two signals adopts cross-correlation and power spectrum analysis to find the frequency bands with strong correlation between the two signals.
5. The method for long-distance pipeline leak detection and location based on the center frequency method of VMD adaptive decomposition and reconstruction according to claim 1 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 method for long-distance pipeline leak detection and location based on the center frequency method of VMD adaptive decomposition and reconstruction according to claim 1 is characterized by: The decomposed modal components IMF x and the 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 use this transformation to get K 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 use this transformation to get K 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 method for long-distance pipeline leak detection and location based on the center frequency method of VMD adaptive decomposition and reconstruction 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 configured to implement the steps of the method for detecting and locating long-distance pipeline leakage by using VMD adaptive decomposition and reconstruction based on the center frequency method as claimed in any one of claims 1 to 7 when executing a computer program stored in the memory.
9. A readable storage medium, characterized in that: The readable storage medium stores a computer program, which, when executed by a processor, implements 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 described in any one of claims 1 to 7.
10. A computer program product, characterized in that The invention comprises 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 any one of claims 1 to 7 when being executed.