CN109469837B - Pressure pipeline multipoint leakage positioning method based on VMD-PSE - Google Patents
Pressure pipeline multipoint leakage positioning method based on VMD-PSE Download PDFInfo
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Abstract
The invention provides a VMD-PSE-based pressure pipeline multipoint leakage positioning method, which is characterized in that variational modal decomposition and power spectral entropy are combined, the power spectral entropy is introduced, a low-frequency area and a high-frequency area of a leakage signal are distinguished, the defect that the variational modal decomposition is not ideal in signal separation in the high-frequency area is overcome, the high-frequency area and the low-frequency area of the signal are effectively processed, and more effective leakage information is obtained; estimating source signals by extracting characteristic values through singular value decomposition, and separating each source leakage signal by combining a blind source separation method; and finally, extracting the time delay of each source leakage signal by using a mutual time-frequency analysis method, and realizing the accurate positioning of the multi-point leakage of the pipeline.
Description
Technical Field
The invention relates to the technical field of pipeline leakage detection and positioning, in particular to a VMD-PSE-based pressure pipeline multipoint leakage positioning method.
Background
Along with the continuous acceleration of urbanization construction speed, urban buried oil and gas pipelines are larger and larger in scale. When the pipeline is used for a long time, the pipeline wall is thinned or broken to cause leakage due to the influence of various factors such as internal and external corrosion and the like, particularly the early-stage tiny leakage is not easy to be noticed due to tiny leakage amount, is difficult to be captured by an online monitoring system, and has larger concealment.
The pipeline multi-point leakage source is not only interfered by non-leakage signals, but also the signals among the leakage sources are mutually influenced, so that the positioning error of the multi-point leakage source is larger, and the influence of factors such as environmental noise and the like brings difficulty to the accurate positioning of the multi-point leakage source. The method can effectively solve the problem that the leakage source signals of multiple points of the pipeline are difficult to extract due to the fact that the leakage source signals are mixed with interference signals such as noise and non-leakage signals, and corresponding delay information of the leakage source signals of the pipeline is difficult to extract and positioning is inaccurate.
In 2014, dragomirtski discloses a new adaptive signal processing method for Variable Modal Decomposition (VMD), which can eliminate the state of modal aliasing compared with empirical modal decomposition, local mean decomposition, and the like. Therefore, once the method is provided, the method is applied to different fields, and a plurality of documents indicate that the method can extract the characteristic information more accurately.
In the past, the division of high and low frequency regions of the components is ignored in the component extraction by utilizing the variation mode decomposition, and the variation mode decomposition method has poor separation in the high frequency regions of the signals, so that the high frequency noise signals in the high frequency signals are not easy to separate, and the high frequency noise signals are not ideal to remove. The pipeline leakage acoustic emission signal belongs to a low-frequency signal, although the high-frequency signal can be directly eliminated, effective information in the signal can be easily removed, so that the pipeline leakage acoustic emission signal can be divided into a low-frequency area and a high-frequency area, the signal in the high-frequency area is subjected to denoising treatment, and then signal reconstruction is carried out, so that the effective leakage signal can be obtained.
The power spectrum entropy can express the concentration degree of each frequency component distribution in the signal power spectrum. When the frequency component intensity distribution is more uniform, the power spectrum entropy value is maximum, which indicates that the signal mixing degree is large, whereas when the frequency distribution is concentrated in the power spectrum of a few frequency points, the power spectrum entropy is smaller, which indicates that the signal mixing degree is small. The power spectrum entropy is more outstanding in the expression of signal frequency, so that the power spectrum can be introduced into the extraction of the variation mode decomposition signal, and the low-frequency region and the high-frequency region of the leakage signal are divided by utilizing the power spectrum entropy. However, the conventional power spectrum entropy is applied only to the feature recognition of the signal, and is used as a feature amount to perform effective signal extraction, and is not applied to the discrimination in the high-frequency and low-frequency regions of the signal. The pipeline leakage signal is divided into high and low frequency area signals, the high and low frequency area signals can be processed in a targeted manner, and effective extraction of the pipeline leakage acoustic emission signal is achieved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in order to overcome the problem that effective signals of multi-point leakage of a pipeline are difficult to extract, the extraction of the effective leakage signals and the accurate positioning of the multi-point leakage are realized. The invention aims to provide a VMD-PSE based pressure pipeline multipoint leakage positioning method, which can accurately find the position of a single leakage source on a measured pipe section and can realize the positioning calculation of 3 leakage sources on the measured pipe section at the same time.
The technical scheme adopted for solving the technical problems is as follows: a pressure pipeline multipoint leakage positioning method based on VMD-PSE comprises the following steps:
step 1: two acoustic emission sensors are arranged at two ends of a pipeline to be detected, 1-3 leakage points exist on the pipeline between the two sensors, leakage signals are collected by the two acoustic emission sensors, and the obtained leakage signals are respectively upstream leakage signals X1(t), downstream leakage signal X2(t)。
Step 2: processing the leakage signal by using a Variational Modal Decomposition (VMD) to obtain a plurality of IMF components, dividing the leakage signal into a low-frequency region signal D (t) and a high-frequency region signal G (t) by combining a power spectrum entropy, and performing double-tree complex wavelet transform on the high-frequency region signal G (t) to perform denoising processing to obtain a denoised high-frequency region signal G' (t); the power spectrum entropy processes the variation modal components as follows:
step 2.1: for upstream leakage signal X1(t) decomposed into k natural mode function components using the VMD,
wherein u isk(t) is the kth natural mode function component.
Step 2.2: calculating power spectrum entropy values of the IMF components:
wherein H is power spectrum entropy, ukRepresenting IMF components, M being Fourier transformLength of (d).
Step 2.3: because the pipeline leakage acoustic emission signal belongs to a low-frequency signal, the variation modal decomposition has better noise separation capability in a low-frequency region, but has no better noise decomposition capability in a high-frequency region. When calculating the power spectrum entropy of each IMF component, a series of power spectrum entropy values are obtained, and the information entropy theory shows that if the low-frequency part and the high-frequency part of a leakage signal are mutually independent, the boundary u between a low-frequency region and a high-frequency region of the signal is obtained by searching the first local maximum power spectrum entropy valuei(ii) a If the IMF component in the high frequency region is directly discarded, the purpose of noise reduction can be achieved by reconstructing the low frequency region signal, but the useful information existing in the high frequency component is lost. Therefore, the high-frequency range component is subjected to dual-tree complex wavelet denoising processing, and the obtained denoised high-frequency range component and low-frequency range component are reconstructed to obtain an observation signal.
Wherein the boundary u between the low frequency region and the high frequency regioniCan be composed of ui＝first{max[H(uk，uk+1)]Get u and then1～uiA total of i low-frequency components as a low-frequency region signal D (t), wherein D (t) is [ u [ u ] ]1,u2,...,ui]The low frequency signal d (t) is directly retained, and the remaining components are the high frequency signal g (t), where g (t) is [ [ u ] ]i+1,ui+2,...,uk]And denoising the high-frequency signal G (t), because the dual-tree complex wavelet transform has the advantages of good direction selectivity, complete reconstruction and high calculation efficiency, the loss of useful information is reduced in signal denoising. Therefore, the dual-tree complex wavelet transform is applied to denoise the signal G (t) in the high frequency region, and the process is as follows:
the method for denoising the pipeline leakage signal high-frequency region signal G (t) by using dual-tree complex wavelet transform comprises the following steps:
①, performing dual-tree complex wavelet transform on the high-frequency region signal containing noise, and performing N-layer decomposition on the high-frequency region signal to obtain N sub-bands;
② estimating the noise variance of the high frequency region signal:
wherein,
is the noise variance, y (i) is the wavelet coefficient of the high frequency region signal G (t);
③ calculate the variance of each decomposition subband:
wherein,
the variance of each sub-band is obtained, and N is the number of decomposition layers;
④ calculate the respective subband threshold:
where ξ is the sub-band threshold.
⑤ performing threshold processing on wavelet coefficients of each layer;
and performing inverse transformation on the dual-tree complex wavelet to obtain a denoised high-frequency region signal G '(t), wherein G' (t) ═ ui+1′,ui+2′,...,uk′]，uk' is the denoised IMF component.
Step 2.4: processing the downstream leakage signal X according to the processing method of steps 2.1-2.32(t) processing to obtain corresponding low-frequency signal D (t) and high-frequency signal G' (t) after drying.
And step 3: reconstructing the low-frequency region signal D (t) and the denoised high-frequency region signal G' (t) to obtain an observation signal, and estimating the source number by using singular value decomposition and a characteristic value thereof to obtain the number of leakage sources, wherein the method specifically comprises the following steps of:
step 3.1: may be expressed as:
Nimf(t)＝[u1(t)，u2(t),...,ui(t),ui+1′(t)，ui+2′(t),...,uk′(t),]is composed ofThe multidimensional observation signal well solves the problem of blind source underdetermination, namely when the number of the sensors is less than that of the signal sources;
step 3.2: calculating a correlation matrix R of the observed signalsx＝E[Nimf(t)NimfH(t)](ii) a And to RxPerforming singular value decomposition Rx＝U∑VTObtaining s eigenvalues by using unitary matrixes with U and V being m × m and n × n respectively;
step 3.3: the number of signals is estimated based on the correlation matrix eigenvalues.
And 4, step 4: the method for separating the leakage source signals by using the blind source separation method comprises the following specific processes:
step 4.1: centralizing an observation signal Nimf (t), and whitening to obtain Z (t) ═ QNimf (t);
step 4.2: fourth order cumulant matrix C of joint approximation diagonalization Z (t)Z(Mp) Obtaining a unitary matrix U;
step 4.3: calculating the separation matrix W ═ UTQ；
Step 4.4: from Yα(t)＝WX1(t) obtaining a separate estimate Y of the source of the upstream leakage signalα(t)；
Step 4.5: according to the processing method of the steps 4.1-4.4, the leakage signals collected by the pipeline downstream sensor are processed by the method to obtain the separation estimation Y of the downstream acoustic emission leakage source signalsβ(t)。
Where Q is a whitening matrix derived from whitening the observed signal nimf (t)
D is a diagonal matrix formed by the autocorrelation matrix eigenvalues of nimf (t), and E is a feature matrix formed by the corresponding eigenvectors.
And 5: and performing positioning calculation on the pipeline leakage according to a mutual time-frequency analysis method.
Step 5.1: calculating the estimation correlation of the signals of the upstream and downstream signal sources by using a cross-correlation algorithm, extracting the corresponding signals of the upstream and downstream leakage sources, and if one pair of signals is Y11(t) and Y12(t), then signal Y11(t) and Y12(t) cross-correlation function:
where τ is the signal Y11(t) and Y12(t) delay time.
Step 5.2: analyzing the relation of time delay and frequency of the time-varying cross-correlation function by using Cohen time-frequency, namely:
wherein
Representing the time-frequency distribution of the cross-correlation function of two observed signals, omega being the frequency, theta being the frequency offset, j being the imaginary number,
is a fuzzy function;
step 5.3: cross correlation function time-frequency distribution of passing signals
The frequency corresponding to the peak is the strongest frequency of the delay, that is:
wherein, ω is1And Δ t is the frequency and signal Y corresponding to the highest peak of the time frequency distribution frequency11(t) and Y12(t) a delay time;
step 5.4: the position of the pipeline leakage point can be determined by a time difference positioning method, namely:
wherein l is the estimated leak location value, i.e. the leak point to upstream pressureDistance of the force sensor;Lis the distance between the two pressure sensors; v the propagation velocity of the leakage acoustic emission signal in the pipe.
The invention has the beneficial effects that: the pressure pipeline multipoint leakage positioning method based on the VMD-PSE, provided by the invention, combines variational modal decomposition with power spectral entropy, introduces the power spectral entropy, distinguishes a low-frequency region and a high-frequency region of a leakage signal, makes up the defect that the variational modal decomposition is not ideal in signal separation in the high-frequency region, effectively processes the high-frequency region and the low-frequency region of the signal, and obtains more effective leakage information; estimating source signals by extracting characteristic values through singular value decomposition, and separating each source leakage signal by combining a blind source separation method; and finally, extracting the time delay of each source leakage signal by using a mutual time-frequency analysis method, and realizing the accurate positioning of the multi-point leakage of the pipeline.
Drawings
The invention is further illustrated by the following figures and examples.
FIG. 1 is a schematic view of a pipe leak location;
FIG. 2 is a time domain plot of an upstream pipe leak acoustic emission raw signal;
FIG. 3 is a time domain plot of a downstream pipe leak acoustic emission raw signal;
FIG. 4 is a VMD decomposition of the upstream pipeline leakage emission raw signal into components;
FIG. 5 is a time domain plot of an upstream pipe leak acoustic emission reconstruction signal;
FIG. 6 is a time domain diagram of a separation signal obtained by blind source separation processing of an upstream pipeline leakage acoustic emission reconstruction signal;
FIG. 7 is a time domain diagram of a separation signal obtained by blind source separation processing of a downstream pipeline leakage acoustic emission reconstruction signal;
fig. 8 is a time-frequency analysis time-frequency diagram of leakage acoustic emission signals.
Detailed Description
The present invention will now be described in detail with reference to the accompanying drawings. This figure is a simplified schematic diagram, and merely illustrates the basic structure of the present invention in a schematic manner, and therefore it shows only the constitution related to the present invention.
As shown in fig. 1-8, the VMD-PSE based pressure conduit multi-point leakage locating method of the present invention includes the following steps:
step 1: two acoustic emission sensors are arranged at two ends of a pipeline to be detected, 1-3 leakage points exist on the pipeline between the two sensors, leakage signals are collected by the two acoustic emission sensors, and the obtained leakage signals are respectively upstream leakage signals X1(t), downstream leakage signal X2(t)。
Step 2: processing the leakage signal by using a Variational Modal Decomposition (VMD) to obtain a plurality of IMF components, dividing the leakage signal into a low-frequency region signal D (t) and a high-frequency region signal G (t) by combining a power spectrum entropy, and performing double-tree complex wavelet transform on the high-frequency region signal G (t) to perform denoising processing to obtain a denoised high-frequency region signal G' (t); the power spectrum entropy processes the variation modal components as follows:
step 2.1: for upstream leakage signal X1(t) decomposed into k natural mode function components using the VMD,
wherein u isk(t) is the kth natural mode function component.
Step 2.2: calculating power spectrum entropy values of the IMF components:
wherein H is power spectrum entropy, ukRepresenting the IMF component, M is the length under fourier transform.
Step 2.3: because the pipeline leakage acoustic emission signal belongs to a low-frequency signal, the variation modal decomposition has better noise separation capability in a low-frequency region, but has no better noise decomposition capability in a high-frequency region. When calculating the power spectrum entropy of each IMF component, a series of power spectrum entropy values are obtained, and the information entropy theory shows that if the low-frequency part and the high-frequency part of a leakage signal are mutually independent, searching the first local maximum power spectrum entropy value to obtain a signalBoundary u between low frequency region and high frequency regionx(ii) a If the IMF component in the high frequency region is directly discarded, the purpose of noise reduction can be achieved by reconstructing the low frequency region signal, but the useful information existing in the high frequency component is lost. Therefore, the high-frequency range component is subjected to dual-tree complex wavelet denoising processing, and the obtained denoised high-frequency range component and low-frequency range component are reconstructed to obtain an observation signal.
Wherein the boundary u between the low frequency region and the high frequency regioniCan be composed of ui＝first{max[H(uk，uk+1)]Get u and then1～ui-1A total of i-1 low-frequency components as a low-frequency region signal D (t), wherein D (t) is [ u ]1,u2,...,ui]The low frequency signal d (t) is directly retained, and the remaining components are the high frequency signal g (t), where g (t) is [ [ u ] ]i+1,ui+2,...,uk]And denoising the high-frequency signal G (t), because the dual-tree complex wavelet transform has the advantages of good direction selectivity, complete reconstruction and high calculation efficiency, the loss of useful information is reduced in signal denoising. Therefore, the dual-tree complex wavelet transform is applied to denoise the signal G (t) in the high frequency region, and the process is as follows:
the method for denoising the pipeline leakage signal high-frequency region signal G (t) by using dual-tree complex wavelet transform comprises the following steps:
①, performing dual-tree complex wavelet transform on the high-frequency region signal containing noise, and performing N-layer decomposition on the high-frequency region signal to obtain N sub-bands;
② estimating the noise variance of the high frequency region signal:
wherein,
is the noise variance, y (i) is the wavelet coefficient of the high frequency region signal G (t);
③ calculate the variance of each decomposition subband:
wherein,
the variance of each sub-band is obtained, and N is the number of decomposition layers;
④ calculate the respective subband threshold:
where ξ is the sub-band threshold.
⑤ performing threshold processing on wavelet coefficients of each layer;
and performing inverse transformation on the dual-tree complex wavelet to obtain a denoised high-frequency region signal G '(t), wherein G' (t) ═ ui+1′,ui+2′,...,uk′]，uk' is the denoised IMF component.
Step 2.4: processing the downstream leakage signal X according to the processing method of steps 2.1-2.32(t) processing to obtain the corresponding low-frequency region signal D (t) and the denoised high-frequency region signal G' (t).
And step 3: reconstructing the low-frequency region signal D (t) and the denoised high-frequency region signal G' (t) to obtain an observation signal, and estimating the source number by using singular value decomposition and a characteristic value thereof to obtain the number of leakage sources, wherein the method specifically comprises the following steps of:
step 3.1: the reconstructed observed signal can be expressed as:
Nimf(t)＝[u1(t)，u2(t),...,ui(t),ui+1′(t)，ui+2′(t),...,uk′(t),]the formed multidimensional observation signal well solves the problem of blind source underdetermination, namely when the number of the sensors is less than that of the signal sources;
step 3.2: calculating a correlation matrix R of the observed signalsx＝E[Nimf(t)NimfH(t)](ii) a And to RxPerforming singular value decomposition Rx＝U∑VTObtaining s eigenvalues by using unitary matrixes with U and V being m × m and n × n respectively;
step 3.3: the number of signals is estimated based on the correlation matrix eigenvalues.
And 4, step 4: the method for separating the leakage source signals by using the blind source separation method comprises the following specific processes:
step 4.1: centralizing an observation signal Nimf (t), and whitening to obtain Z (t) ═ QNimf (t);
step 4.2: fourth order cumulant matrix C of joint approximation diagonalization Z (t)Z(Mp) Obtaining a unitary matrix U;
step 4.3: calculating the separation matrix W ═ UTQ；
Step 4.4: from Yα(t)＝WX1(t) obtaining a separate estimate Y of the upstream leakage source signalα(t)。
Where Q is a whitening matrix derived from whitening the observed signal nimf (t)
D is a diagonal matrix formed by the autocorrelation matrix eigenvalues of nimf (t), and E is a feature matrix formed by the corresponding eigenvectors.
Step 4.5: according to the processing method of the steps 4.1-4.4, the leakage signals collected by the pipeline downstream sensor are processed by the method to obtain the separation estimation Y of the downstream acoustic emission leakage source signalsβ(t)。
And 5: and performing positioning calculation on the pipeline leakage according to a mutual time-frequency analysis method.
Step 5.1: calculating the estimation correlation of the signals of the upstream and downstream signal sources by using a cross-correlation algorithm, extracting the corresponding signals of the upstream and downstream leakage sources, and if one pair of signals is Y11(t) and Y12(t), then the signal Y11(t) and Y12(t) cross-correlation function:
where τ is the signal Y11(t) and Y12 (t).
Step 5.2: analyzing the relation of time delay and frequency of the time-varying cross-correlation function by using Cohen time-frequency, namely:
wherein
Representing the time-frequency distribution of the cross-correlation function of two observed signals, omega being the frequency, theta being the frequency offset, j being the imaginary number,
is a fuzzy function;
step 5.3: cross correlation function time-frequency distribution of passing signals
The frequency corresponding to the peak is the strongest frequency of the delay, that is:
wherein, ω is1And Δ t is the frequency and signal Y corresponding to the highest peak of the frequency in the time-frequency distribution11(t) and Y12(t) a delay time;
step 5.4: the position of the pipeline leakage point can be determined by a time difference positioning method, namely:
where l is the estimated leak location value, i.e. the distance from the leak point to the upstream pressure sensor, L is the distance between the two pressure sensors, v is the propagation velocity of the leak acoustic emission signal in the pipeline.
The advantageous effects of the present invention are illustrated by the following examples:
the experimental parameters were as follows: the pipeline length is 50m, the pipeline pressure is 0.25MPa, the distance between the two sensors is 42m, the two sensors are respectively arranged at the upstream and the downstream of the pipeline, and the leakage points are respectively positioned at the positions 6m, 16m and 30m away from the upstream sensorThe leakage pore diameter is 2 mm. As shown in fig. 1. In the pipeline leakage acquisition system formed by the acoustic emission instrument and the acoustic emission sensor, leakage holes at three positions are opened simultaneously to acquire leakage acoustic emission signals, as shown in fig. 2 and 3, which are leakage acoustic emission original signals X acquired by an upstream sensor and a downstream sensor in a pipeline leakage state respectively1(t)、X2(t) of (d). To collect the obtained upstream original signal X1(t) is an example. From signal X1And (t) the time domain diagram shows that the time domain signal of the signal has complex change, the amplitude of the signal is uncertain, the noise interference of the signal is large, and the pipeline leakage signal is difficult to confirm. The original signal X is then transformed using a metamorphic mode1(t) is divided into 7 IMF components as shown in FIG. 4, and power spectrum values of the respective IMF components are calculated as shown in Table 1:
TABLE 1 Power spectral entropy values for IMF components
| IMF component | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 |
| Entropy of power spectrum | 1.6464 | 1.5891 | 1.5428 | 1.7316 | 1.826 | 2.0243 | 2.2017 |
As can be seen from table 1, the power spectrum entropy is firstly decreased and then increased, and then decreased again, wherein the local minimum value of the first power spectrum entropy is 1.5428, the corresponding IMF component is IMF3, and it can be known from the information entropy theory that there is a large frequency jump at the IMF3, so the first 3 IMF components are used as low-frequency region signals d (t), and are directly retained, and the last 4 IMF components are used as high-frequency region signals G (t), and are subjected to dual-tree complex wavelet transform denoising processing to obtain denoised high-frequency signals G' (t), and then the signals are reconstructed with the low-frequency signals d (t) to obtain observed signals nimf (t), as shown in fig. 5, the signal-to-noise ratio between the signals and the signals before denoising is calculated with reference to the signals before denoising, and the signal-to-noise ratio is 9.84, so that the noise signals in the high-frequency region are better eliminated.
The obtained observation signal Nimf (t) calculates the correlation matrix R of the observation signalx(ii) a And singular value decomposition is carried out on Rx to obtain a correlation matrix to obtain 7 eigenvalues, and source number estimation is carried out on the observation signals to obtain the correlation matrix eigenvalue as shown in Table 2.
TABLE 2 correlation matrix eigenvalues
As can be seen from the table, the first 3 eigenvalues are larger, and the number of source signals is estimated to be 3 based on the eigenvalues of the correlation matrix.
Using blind source separation to obtain 3 estimated leakage signals at the upstream of the pipeline, as shown in fig. 6, calculating correlation coefficients 0.8741, 0.8982, 09103 of the separated original signals and the three separated signals; with the 3 estimated leakage signals downstream to the pipeline in this way, correlation coefficients 0.9431, 0.9482, 08803 of the separated original signal with the three separated signals are calculated as shown in fig. 7. Therefore, the blind source separation effect is better according to the correlation coefficient. In actual multi-source leakage positioning, because signals separated by the blind source separation method are all leakage signals, which estimation signal corresponds to which leakage source cannot be distinguished from a separated time domain diagram. Therefore, the cross-correlation principle is utilized to calculate the correlation between the upstream three separation signals and the downstream three separation signals, the signals with the correlation can obtain obvious peak values, and the uncorrelated signals do not have obvious peak values, so as to distinguish whether the signals come from the same leakage source or not and obtain corresponding upstream and downstream leakage signals.
Taking a pair of leakage signals therein as an example Y11(t) and Y12(t), performing cross-correlation analysis on the obtained cross-correlation function to obtain a cross-correlation function, and performing time-frequency conversion analysis on the cross-correlation function, as shown in fig. 8, wherein the frequency corresponding to a time-frequency spectrum peak of the obtained cross-correlation function is 27.1945kHz, the delay corresponding to the peak is 0.00202s, and according to an empirical value, the wave speed of an acoustic emission signal under the action of water load is 1500m/s, so that the delay and the sound speed are brought into a time difference positioning formula to determine the distance 5.895m from an upstream sensor to a leakage position, and the actual distance is 6m, so that the absolute positioning error is 0.105m, the relative error is 1.75%, and so on, the positions of the other two leakage points can be calculated to be 15.692m, 30.671m, and the relative errors are 1.91% and 2. It can be seen that the method can achieve three-point leak location of pipeline leakage, and the data results prove the effectiveness of the method.
In light of the foregoing description of preferred embodiments in accordance with the invention, it is to be understood that numerous changes and modifications may be made by those skilled in the art without departing from the scope of the invention. The technical scope of the present invention is not limited to the contents of the specification, and must be determined according to the scope of the claims.
Claims (3)
1. A pressure pipeline multipoint leakage positioning method based on VMD-PSE is characterized in that: the method comprises the following steps:
step 1: at two ends of the pipeline to be measuredRespectively arranging an acoustic emission sensor, collecting leakage signals by using the acoustic emission sensors at two ends, and respectively obtaining the leakage signals as upstream leakage signals X1(t), downstream leakage signal X2(t)；
Step 2: processing the leakage signal by utilizing Variation Modal Decomposition (VMD) to obtain a plurality of IMF components, dividing the leakage signal into a low-frequency region signal D (t) and a high-frequency region signal G (t) by combining power spectrum entropy, and performing double-tree complex wavelet transform on the high-frequency region signal G (t) to perform denoising processing to obtain a denoised high-frequency region signal G' (t);
and step 3: reconstructing the low-frequency region signal D (t) and the denoised high-frequency region signal G' (t) to obtain an observation signal, and estimating the source number by using singular value decomposition and a correlation matrix characteristic value to obtain the leakage source number;
and 4, step 4: separating each leakage source signal by using a blind source separation method;
and 5: performing positioning calculation on the pipeline leakage according to a mutual time-frequency analysis method;
the process of extracting effective signals of the IMF components subjected to the variation modal decomposition by using the power spectrum entropy in the step 2 comprises the following steps:
step 2.1: for upstream leakage signal X1(t) decomposed into k natural mode function components using VMD as shown in the following equation:
wherein: u. ofk(t) is the kth natural mode function component;
step 2.2: calculating the power spectrum entropy of each IMF component:
wherein H is power spectrum entropy, ukDenotes the IMF component, N is the length under fourier transform, m ═ 1, 2.. N;
step 2.3: obtaining a series of power spectrum entropy values, and searching the first partObtaining the boundary of a low-frequency area and a high-frequency area of the signal by the maximum power spectrum entropy; wherein the boundary u between the low frequency region and the high frequency regioniCan be composed of ui＝first{max[H(uk，uk+1)]Get u and then1～ui-1A total of i-1 low-frequency components as a low-frequency region signal D (t), wherein D (t) is [ u ]1,u2,...,ui]The low frequency signal d (t) is directly retained, and the remaining components are the high frequency signal g (t), where g (t) is [ [ u ] ]i+1,ui+2,...,uk]And carrying out dual-tree complex wavelet transform denoising processing on the high-frequency region signal G (t) to obtain a denoised high-frequency region signal G '(t), wherein G' (t) [ [ u ] ]i+1′,ui+2′,...,uk′]，uk' is the denoised IMF component;
step 2.4: processing the downstream leakage signal X according to the processing method of steps 2.1-2.32(t) processing to obtain a corresponding low-frequency region signal D (t) and a denoised high-frequency region signal G' (t);
the process of estimating the source number by using singular value decomposition and correlation matrix eigenvalues in the step 3 comprises the following steps:
step 3.1: for upstream leakage signal X respectively1(t) and downstream leakage signal X2(t) reconstructing the corresponding low-frequency region signal d (t) and the denoised high-frequency region signal G' (t) to obtain an observation signal, where the reconstructed observation signal may be represented as:
Nimf(t)＝[u1(t)，u2(t),...,ui(t),ui+1′(t)，ui+2′(t),...,uk′(t),]；
step 3.2: calculate its correlation matrix Rx＝E[Nimf(t)NimfH(t)]And to RxPerforming singular value decomposition;
step 3.3: the number of signals is estimated based on the correlation matrix eigenvalues.
2. The VMD-PSE based pressure conduit multipoint leak location method of claim 1, wherein: the process of separating each leakage source signal by using the blind source separation method in the step 4 comprises the following steps:
step 4.1: centralizing the reconstructed observation signal nimf (t), and whitening to obtain a new observation signal z (t) ═ qnimf (t);
step 4.2: fourth order cumulant matrix C of joint approximation diagonalization Z (t)Z(Mp) Obtaining a unitary matrix U;
step 4.3: calculating a separation matrix W ═ U from a unitary matrix U and a whitening matrix QTQ；
Step 4.4: from Yα(t)＝WX1(t) obtaining a separate estimate Y of the upstream leakage source signalα(t)；
Step 4.5: according to the processing method of the steps 4.1-4.4, the leakage signals collected by the pipeline downstream sensor are processed by the method to obtain the separation estimation Y of the downstream acoustic emission leakage source signalsβ(t)；
Where Q is a whitening matrix derived from whitening the observed signal nimf (t)
D is a diagonal matrix formed by the autocorrelation matrix eigenvalues of nimf (t), and E is a feature matrix formed by the corresponding eigenvectors.
3. The VMD-PSE based pressure conduit multipoint leak location method of claim 2, wherein: the step 5 of performing positioning calculation on the pipeline leakage according to the mutual time-frequency analysis method specifically comprises the following steps:
step 5.1: calculating the estimation correlation of the signals of the upstream and downstream signal sources by using a cross-correlation algorithm, extracting the corresponding signals of the upstream and downstream leakage sources, and if one pair of signals is Y11(t) and Y12(t), then the signal Y11(t) and Y12(t) cross-correlation function:
where τ is the signal Y11(t) and Y12(t) a delay time;
step 5.2: analyzing the relation of time delay and frequency of the time-varying cross-correlation function by using Cohen time-frequency, namely:
wherein
Representing the time-frequency distribution of the cross-correlation function of two observed signals, omega being the frequency, theta being the frequency offset, j being the imaginary number,
is a fuzzy function;
step 5.3: cross correlation function time-frequency distribution of passing signals
The frequency corresponding to the peak is the strongest frequency of the delay, that is:
wherein, ω is1And Δ t is the frequency and signal Y corresponding to the highest peak of the time frequency distribution frequency11(t) and Y12(t) a delay time;
step 5.4: the position of the pipeline leakage point can be determined by a time difference positioning method, namely:
where l is the estimated leak location value, i.e., the distance from the leak point to the upstream pressure sensor, L is the distance between the two pressure sensors, and v is the propagation velocity of the leaking acoustic emission signal in the pipe.
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