CN111947045B - GVMD parameter optimization and singular value decomposition-based fluid pipeline leakage positioning method - Google Patents
GVMD parameter optimization and singular value decomposition-based fluid pipeline leakage positioning method Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F17—STORING OR DISTRIBUTING GASES OR LIQUIDS
- F17D—PIPE-LINE SYSTEMS; PIPE-LINES
- F17D5/00—Protection or supervision of installations
- F17D5/02—Preventing, monitoring, or locating loss
- F17D5/06—Preventing, monitoring, or locating loss using electric or acoustic means
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- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M3/00—Investigating fluid-tightness of structures
- G01M3/02—Investigating fluid-tightness of structures by using fluid or vacuum
- G01M3/04—Investigating fluid-tightness of structures by using fluid or vacuum by detecting the presence of fluid at the leakage point
- G01M3/24—Investigating fluid-tightness of structures by using fluid or vacuum by detecting the presence of fluid at the leakage point using infrasonic, sonic, or ultrasonic vibrations
- G01M3/243—Investigating fluid-tightness of structures by using fluid or vacuum by detecting the presence of fluid at the leakage point using infrasonic, sonic, or ultrasonic vibrations for pipes
Abstract
The invention relates to a fluid pipeline leakage positioning method based on GVMD parameter optimization and singular value decomposition, and belongs to the technical field of detection. Firstly, setting parameters such as iteration times of a GA (genetic algorithm), calculating fitness and optimal parameters of VMD (virtual matrix decomposition) decomposition by combining leakage vibration signals picked up by a sensor, and realizing VMD parameter selection self-adaptation; secondly, calculating the kurtosis of each IMF component after VMD decomposition, and reconstructing a signal; and finally, selecting corresponding singular values by SVD to reconstruct again. The invention can effectively inhibit a large amount of noise generated by the leakage vibration signal of the fluid pipeline due to frequency dispersion and multi-modal characteristics, and improve the signal-to-noise ratio of the leakage vibration signal, thereby reducing the time delay estimation error and finally effectively improving the leakage positioning precision.
Description
Technical Field
The invention belongs to the technical field of detection, and relates to a fluid pipeline leakage positioning method based on GVMD parameter optimization and singular value decomposition.
Background
Pipelines have been widely used in the transportation of fluids such as natural gas, oil, water supply, etc., as a way of efficiently and conveniently transporting fluids. Taking an urban water supply network as an example, leakage of pipelines sometimes occurs due to natural aging, corrosion, artificial damage and the like of the pipelines. According to statistics, the average leakage rate of the water supply network in China is 15.7%, and a large amount of water resources are wasted, so that the research on the fluid pipeline leakage positioning method has important social benefits and economic values. The fluid pipeline leakage positioning method based on time delay estimation has the advantages of being fast in detection response time and small in leakage positioning error. The patent application with publication number CN108332063A discloses a pipeline leakage positioning method based on cross-correlation time delay estimation, which directly performs fourier transform on a time domain signal detected by a sensor, and performs inverse fourier transform after weighting a cross-spectral density function in a frequency domain to obtain a cross-correlation result. According to the method, through weighting the cross-spectrum density function, the sound wave reflection and low-frequency background noise interference in the pipeline are weakened, the signal-to-noise ratio is improved, and the leakage positioning error is reduced. However, the leakage vibration signal of the fluid pipeline has multi-modal and dispersive characteristics, so that data acquired by the leakage detection system contains a large amount of relevant noise, and meanwhile, the signal-to-noise ratio of the leakage vibration signal is reduced due to the existence of working condition interference, so that the positioning error of the leakage vibration of the fluid pipeline estimated based on the cross-correlation time delay is large. Dragomirikiy et al thus propose a variational modal decomposition method that determines the frequency center and bandwidth of each modal component by iteratively searching the optimum solution of the variational model globally, thereby effectively separating the components in the frequency domain. However, the Variational Mode Decomposition (VMD) process needs to set the number of components and penalty parameters according to experience, and is poor in adaptability. Marginality proposes optimization of variational modal decomposition parameters using Genetic Algorithm (GA) to reduce signal noise and extract features (marginality. variational modal decomposition based on Genetic algorithm parameter optimization in combination with 1.5-dimensional spectral bearing fault diagnosis [ J ] propulsion technique, 2017,38(07): 1618-. The method adopts a genetic algorithm to optimize VMD parameters, and eliminates coupling harmonics through a third-order cumulant diagonal slicing method. However, this method is suitable for processing periodic data and is not suitable for random data such as a pipeline leakage vibration signal, and when the signal-to-noise ratio is low, the noise reduction effect is not good, and even a leakage information loss phenomenon occurs.
Disclosure of Invention
In view of this, the present invention provides a fluid pipeline leakage positioning method based on GVMD parameter optimization and singular value decomposition, which is suitable for time delay estimation and leakage point positioning of a leakage vibration signal of a fluid conveying pipeline under a low signal-to-noise ratio.
In order to achieve the purpose, the invention provides the following technical scheme:
a fluid pipeline leakage positioning method based on GVMD parameter optimization and singular value decomposition is characterized by specifically comprising the following steps:
s1: acquiring a leakage vibration signal of the fluid pipeline;
s2: searching VMD to obtain the optimal parameter by using Genetic algorithm optimization Variational modal Decomposition (GVMD) parameter;
s3: calculating the kurtosis of each IMF component after VMD decomposition, and reconstructing a signal;
s4: selecting a corresponding singular value for reconstruction again by using Singular Value Decomposition (SVD) of the reconstructed signal obtained in step S3;
s5: the time delay is estimated to locate the leak.
Further, the step S2 specifically includes the following steps:
s21: initializing genetic algorithm parameters including the number K of modal components and a secondary penalty factor alpha;
s22: calculating a fitness value;
s23: and selecting good individuals by adopting a roulette method according to the fitness value obtained in the step S22, and crossing, mutating and inverting the good individuals to form new individuals so as to form a new generation of population.
Further, the step S22 specifically includes: taking the local minimum amplitude spectrum entropy as a fitness value in the whole parameter optimization process, taking the minimum local minimum amplitude spectrum entropy as a final parameter optimization target, and searching a global optimal IMF component combination;
the fitness function magnitude spectral entropy is calculated as follows:
wherein X represents a component sequence, PiFor the probability distribution of the signal, N is the input signal length and Hs is the magnitude spectral entropy.
Further, in step S3, the VMD algorithm and the signal reconstruction are adopted, which specifically includes:
s31: initializing a secondary penalty factor alpha and the number K of modal components;
s32: calculating the central frequency and kurtosis value of K IMF components, performing cross-correlation operation on each component and a source signal to obtain a cross-correlation coefficient threshold, and selecting two components with higher correlation coefficients and not less than the threshold as sensitive component reconstruction signals.
Further, in step S4, the SVD algorithm and the signal reconstruction are adopted, which specifically includes:
s41: performing Hilbert transformation on the signal with noise, acquiring a Hankel matrix of the signal with noise, performing singular value decomposition, and respectively acquiring a left singular matrix U, a right singular matrix V and a singular value diagonal matrix S;
s42: finding the maximum singular value mutation point according to the differential spectrum of the singular value, determining the effective order of singular value decomposition by using the unilateral maximum value principle, and setting the rest smaller singular values to be 0;
s43: selecting a proper difference spectrum peak, and reconstructing a singular value matrix by using the corresponding singular value and order;
s44: and calculating a time domain sequence of the reconstructed signal according to the reconstructed singular value matrix to obtain the signal subjected to noise reduction.
Further, in step S42, determining the significant order of singular value decomposition specifically includes: the GVMD reconstructed signal sequence is set as a matrix A, and the matrix A can be decomposed into a matrix A according to the SVD theory
The matrix U, V is an orthogonal matrix of g × g and q × q, and D ═ diag (λ)1,λ2,…λr) R ═ min (g, q), singular value λiSatisfy lambda1≥λ2≥…≥λr>0，uiAnd viAre respectively g, q dimensional column vectors
Order to
bi＝λi-λi+1，i＝1,2,…,r-1
Selection of biThe component singular value difference spectrum B ═ (B)1,b2,…br-1) Maximum peak value bpRepresenting a boundary between the desired signal and noise, bpThe components corresponding to the previous p singular values are effective signals, bpThe component corresponding to the subsequent singular value is noise and is set to 0.
Further, the step S5 specifically includes: fluid pipeline leakage vibration signal x1(t)、x2(t) decomposing and reconstructing by GVMD and SVD to obtain a new sequence y1(t)、y2(t) the cross-correlation function of the two is:
wherein R isssRepresenting the autocorrelation function of the source signal, due to Rss(T + τ) ≦ R (0), and when T ═ τ, y1(t) and y2(t) source signal autocorrelation function RssReaches a maximum value at which the cross-correlation function is reached
Also reaches the maximum value, so find
T corresponding to maximum value0Then the time delay is-T0；
Based on a water supply pipeline leakage positioning principle of time delay estimation, and by combining the propagation speed c of sound in a pipeline and the distance d between two sensors, positioning a fluid pipeline leakage point according to the following formula;
wherein d is1The distance between the leak and the sensor I is shown, and d is the distance between two sensors of adjacent leaks.
The invention has the beneficial effects that: according to the method, the genetic algorithm has good global probability search capability, parameters such as the iteration times of GA are firstly set, and the leakage vibration signals picked up by the sensor are combined to calculate the fitness and the optimal parameters of VMD decomposition, so that the VMD parameter selection self-adaptation is realized; secondly, calculating the kurtosis of each IMF component after VMD decomposition, and reconstructing a signal; and finally, selecting corresponding singular values by SVD to reconstruct again. The invention can effectively inhibit a large amount of noise generated by the leakage vibration signal of the fluid pipeline due to frequency dispersion and multi-modal characteristics, and improve the signal-to-noise ratio of the leakage vibration signal, thereby reducing the time delay estimation error and finally effectively improving the leakage positioning precision.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a schematic diagram of the GVMD parameter optimization and singular value decomposition based joint noise reduction method of the present invention;
fig. 2 shows the principle of locating the leakage of a water supply pipeline based on time delay estimation in the present embodiment.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Referring to fig. 1 to 2, a method for positioning fluid pipeline leakage based on GVMD parameter optimization and singular value decomposition specifically includes the following steps:
the method comprises the following steps: acquiring a leakage vibration signal of the fluid pipeline;
the leakage of the fluid pipeline generates vibration signals, and the vibration signals are picked up by acceleration sensors at two ends of the pipeline to obtain two paths of signals x1(t)、x2(t), expressed as:
x1(t)＝s(t)+n1(t) (1)
x2(t)＝ms(t-D)+n2(t) (2)
where t is a discrete time variable, s (t) is a leakage source signal, n1(t) and n2(t) is noise, D is time delay, and m is attenuation factor.
Step two: genetic algorithm optimization of VMD parameters
(1) Initializing genetic algorithm parameters
After extensive testing, the GVMD parameters were set as follows: the number of the optimized parameters is 2, and the optimized parameters comprise a secondary penalty factor alpha and the number K of modal components; iteration number maxgen is 10; population size sizepop ═ 10; the crossover probability and the mutation probability are 0.8 and 0.1 respectively, and the range of alpha and K is set as bound ═ 5002000; 310].
(2) Fitness function
The information entropy can well evaluate the sparse characteristic of the signal, the size of the information entropy reflects the uncertainty of the signal, and the larger the entropy value is, the larger the uncertainty of the signal is. Therefore, the magnitude spectral entropy of each IMF component obtained by the VMD method with the input parameters (K, alpha) is used as the fitness function of the chromosome when the genetic algorithm parameters are optimized. In order to search the global optimal IMF component combination, the local minimum amplitude spectrum entropy value is used as a fitness value in the whole parameter optimization process, and the minimum local minimum amplitude spectrum entropy value is used as a final parameter optimization target.
The fitness function magnitude spectral entropy is calculated as follows:
wherein X represents a component sequence, PiFor the probability distribution of the signal, N is the input signal length and Hs is the magnitude spectral entropy.
(3) Cross and variance
And (3) selecting good individuals by adopting a roulette method according to the fitness value obtained in the step (2), and crossing, mutating and inverting to form new individuals so as to form a new generation of population.
The GVMD process is as follows:
step three: VMD signal decomposition and reconstruction
And searching VMD through GVMD to obtain optimal parameters: a secondary penalty factor alpha and the number K of modal components. The principle of the VMD algorithm is as follows:
1) firstly, performing Hilbert transform on a signal to be decomposed to calculate an analytic signal and obtain a single-side frequency spectrum:
[δ(t)+j/πt]*uk(t) (6)
2) the formula (6) and the estimated center frequency
And mixing, and modulating each modal function to the corresponding base frequency band.
3) By calculating the square L of the gradient of equation (7)2And estimating the bandwidth of each modal signal by using the norm, wherein a constraint variation expression is as follows:
4) and (3) solving the optimal solution of the formula (8) by introducing a secondary penalty factor alpha and a Lagrange multiplier lambda (t), and changing the constraint variable problem into an unconstrained variable problem, namely:
the VMD algorithm and signal reconstruction are implemented as follows:
1) the secondary penalty factor α is initialized to 1885 and the number of modal components K to 8.
2) And calculating the central frequency and kurtosis value of 8 IMF components, performing cross-correlation operation on each component and a source signal to obtain a cross-correlation coefficient threshold, and selecting two components with higher correlation coefficients and not less than the threshold as sensitive component reconstruction signals.
Step four: SVD signal decomposition and reconstruction
SVD can decompose a complex matrix into smaller, simpler multiplications of several sub-matrices. The GVMD reconstructed signal sequence is set as a matrix A, and the matrix A can be decomposed into a matrix A according to the SVD theory
The matrix U, V is an orthogonal matrix of g × g and q × q, and D ═ diag (λ)1,λ2,…λr) R ═ min (g, q), singular value λiSatisfy lambda1≥λ2≥…≥λr>0，uiAnd viRespectively g and q dimensional column vectors.
According to SVD theory, it can be known that: the first p larger singular values reflect the effective signal and the last r-p smaller singular values reflect the noise component. Therefore, r-p smaller singular values are set to be 0, only the previous p singularities are reserved, and the signal subjected to noise reduction can be obtained through SVD reconstruction.
The selection of the singular value effective rank order has a large influence on the denoising effect. The singular value difference spectrum can effectively describe the singular value difference of the effective signal and the noise component, and can realize the determination of the singular value effective rank order. Order to
bi＝λi-λi+1，i＝1,2,…,r-1 (11)
Selection of biThe component singular value difference spectrum B ═ (B)1,b2,…br-1) Maximum peak value bpRepresenting a boundary between the desired signal and noise, bpThe components corresponding to the previous p singular values are effective signals, bpThe component corresponding to the subsequent singular value is noise.
The SVD algorithm and signal reconstruction are implemented as follows:
1) and performing Hilbert transform on the signal with noise to obtain a Hankel matrix of the signal with noise, and performing singular value decomposition to obtain a left singular matrix U, a right singular matrix V and a singular value diagonal matrix S.
2) And finding the maximum singular value mutation point according to the differential spectrum of the singular value, determining the effective order of singular value decomposition by using the unilateral maximum value principle, and setting the smaller singular value to be 0.
3) And selecting a proper difference spectrum peak, and reconstructing a singular value S matrix by using the corresponding singular value and order.
4) And calculating a time domain sequence of the reconstructed signal according to the new singular value matrix to obtain the signal after noise reduction.
Step five: time delay estimation and positioning
Signal x1(t)、x2(t) decomposing and reconstructing by GVMD and SVD to obtain a new sequence y1(t)、y2(t) which are correlated as in formula (12):
wherein R isssRepresenting the autocorrelation function of the source signal, due to Rss(T + τ) ≦ R (0), and when T ═ τ, y1(t) and y2(t) the autocorrelation function of the source signal reaches a maximum value. The cross-correlation function at that time is obtained from equation (12)
Also reaches the maximum value, so find
T corresponding to maximum value0Then the time delay is-T0。
The principle of water supply pipe leakage localization based on time delay estimation is shown in fig. 2, and water supply pipe leakage localization can be performed according to equation (13) in combination with the propagation speed c of sound in the pipe and the distance d between the two sensors.
Wherein d is1Indicating the distance between the leak and the sensor i.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.
Claims (5)
1. A fluid pipeline leakage positioning method based on GVMD parameter optimization and singular value decomposition is characterized by specifically comprising the following steps:
s1: acquiring a leakage vibration signal of the fluid pipeline;
s2: searching VMD to obtain the optimal parameter by using Genetic algorithm optimization Variational modal Decomposition (GVMD) parameter;
s3: calculating the kurtosis of each IMF component after VMD decomposition, and reconstructing a signal;
s4: selecting a corresponding singular value for reconstruction again by using Singular Value Decomposition (SVD) of the reconstructed signal obtained in step S3;
s5: estimating time delay so as to locate leakage points;
the step S2 specifically includes the following steps:
s21: initializing genetic algorithm parameters including the number K of modal components and a secondary penalty factor alpha;
s22: calculating a fitness value;
s23: selecting excellent individuals by adopting a roulette method according to the fitness value obtained in the step S22, and crossing, mutating and inverting to form new individuals so as to form a new generation of population;
the step S22 specifically includes: taking the local minimum amplitude spectrum entropy as a fitness value in the whole parameter optimization process, taking the minimum local minimum amplitude spectrum entropy as a final parameter optimization target, and searching a global optimal IMF component combination;
the fitness function magnitude spectral entropy is calculated as follows:
wherein X represents a component sequence, PiFor the probability distribution of the signal, N is the input signal length and Hs is the magnitude spectral entropy.
2. The method for locating the leakage of the fluid pipeline according to claim 1, wherein in step S3, the VMD algorithm and the signal reconstruction are adopted, and specifically the method comprises:
s31: initializing a secondary penalty factor alpha and the number K of modal components;
s32: and calculating the central frequency and kurtosis value of K IMF components, performing cross-correlation operation on each component and a source signal to obtain a cross-correlation coefficient threshold, and selecting two components with high correlation coefficients not less than the threshold as sensitive component reconstruction signals.
3. The method according to claim 1, wherein the step S4 of using SVD algorithm and signal reconstruction comprises:
s41: performing Hilbert transformation on the signal with noise, acquiring a Hankel matrix of the signal with noise, performing singular value decomposition, and respectively acquiring a left singular matrix U, a right singular matrix V and a singular value diagonal matrix S;
s42: finding the maximum singular value mutation point according to the differential spectrum of the singular value, determining the effective order of singular value decomposition by using the unilateral maximum value principle, and setting the rest small singular values to be 0;
s43: selecting a proper difference spectrum peak, and reconstructing a singular value matrix by using the corresponding singular value and order;
s44: and calculating a time domain sequence of the reconstructed signal according to the reconstructed singular value matrix to obtain the signal subjected to noise reduction.
4. The method according to claim 3, wherein the step S42 of determining the singular value decomposition significance order comprises: the GVMD reconstructed signal sequence is set as a matrix A, and the matrix A can be decomposed into a matrix A according to the SVD theory
The matrix U, V is an orthogonal matrix of g × g and q × q, and D ═ diag (λ)1,λ2,…λr) R ═ min (g, q), singular value λiSatisfy lambda1≥λ2≥…≥λr>0，uiAnd viAre respectively g, q dimensional column vectors
Order to
bi＝λi-λi+1，i＝1,2,…,r-1
Selection of biThe component singular value difference spectrum B ═ (B)1,b2,…br-1)，Maximum peak bpRepresenting a boundary between the desired signal and noise, bpThe components corresponding to the previous p singular values are effective signals, bpThe component corresponding to the subsequent singular value is noise and is set to 0.
5. The method for locating the leakage of the fluid pipeline according to claim 1, wherein the step S5 specifically comprises: fluid pipeline leakage vibration signal x1(t)、x2(t) decomposing and reconstructing by GVMD and SVD to obtain a new sequence y1(t)、y2(t) the cross-correlation function of the two is:
wherein R isssRepresenting the autocorrelation function of the source signal, y when T ═ τ1(t) and y2(t) source signal autocorrelation function RssReaches a maximum value at which the cross-correlation function is reached
Also reaches the maximum value, so find
T corresponding to maximum value0Then the time delay is-T0；
Based on a water supply pipeline leakage positioning principle of time delay estimation, and by combining the propagation speed c of sound in a pipeline and the distance d between two sensors, positioning a fluid pipeline leakage point according to the following formula;
wherein d is set1The distance between the leak and the sensor I is shown, and d is the distance between two sensors of adjacent leaks.
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