CN114417928A - Monitoring data noise reduction method based on urban pipeline leakage - Google Patents

Monitoring data noise reduction method based on urban pipeline leakage Download PDF

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CN114417928A
CN114417928A CN202210071470.1A CN202210071470A CN114417928A CN 114417928 A CN114417928 A CN 114417928A CN 202210071470 A CN202210071470 A CN 202210071470A CN 114417928 A CN114417928 A CN 114417928A
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李敏
郝永梅
蒋军成
刑志祥
许宁
杨健
吴凡
郑凯
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Changzhou University
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Abstract

The invention discloses a monitoring data noise reduction method based on urban pipeline leakage in the field of data noise reduction, which comprises the following steps: collecting leakage original data X of leakage pipeline infrasonic wavei(t); establishing a frequency domain signal XF,i(s) a magnitude spectrogram and an effective frequency window; will frequency domain signal XF,i(s) dividing into M sections of unit signal xmRemoving unit signals x affected by noise by using a differential energy modelmAnd recombined to form a stable signal xc,i(ii) a For the steady signal xc,iCarrying out Prony decomposition, and calculating an extreme value and a residue; screening the extreme values and the residual numbers according to the effective frequency window, and reconstructing a real signal to obtain a complete signal x (t) after noise elimination is finished; the invention can prevent the loss of the inherent information of the structure in the leakage signal, and simultaneously reduces the condition number of the matrix, thereby ensuring convenient and quick calculation and better stability.

Description

Monitoring data noise reduction method based on urban pipeline leakage
Technical Field
The invention belongs to the field of data noise reduction, and particularly relates to a monitoring data noise reduction method based on urban pipeline leakage.
Background
With the rapid advance of the urbanization process in China, the position of pipeline transportation in urban production and life is increasingly important. However, due to the influence of factors such as self aging, irregular construction process, external environment and the like, pipeline leakage accidents happen occasionally, which not only causes huge personal casualties and property losses, but also brings great threat to urban public safety and ecological environment. If the leakage can be found in time and the position of the leakage source can be accurately positioned, the method has important significance for guaranteeing the urban safety and the life of residents.
Infrasonic waves are used for urban pipeline leakage detection by people due to the advantages of long propagation distance, slow attenuation and the like, but due to the fact that a large number of high background noise signals are often carried in infrasonic wave leakage signals, signal interference is caused, and leakage positioning is inaccurate, various signal denoising methods are generated accordingly. However, when the noise energy changes greatly, the conventional method causes a small noise suppression rate and a large signal distortion rate, so that the signal denoising effect is poor.
Disclosure of Invention
The invention aims to provide a monitoring data noise reduction method and system based on urban pipeline leakage, which effectively solve the problem of poor noise reduction effect under the condition of large noise energy change.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention provides a monitoring data noise reduction method based on urban pipeline leakage, which comprises the following steps:
collecting leakage original data X of leakage pipeline infrasonic wavei(t)；
Will reveal the original data Xi(t) intercepting time domain signals x of equal lengthn,i(t) and calculating the frequency domain using Fourier transformSignal XF,i(s) establishing a frequency domain signal XF,i(s) a magnitude spectrogram; using the peak of the amplitude spectrogram to correspond to the frequency ftConstructing an effective frequency window for a reference;
will frequency domain signal XF,i(s) dividing into M sections of unit signal xmRemoving unit signals x affected by noise by using a differential energy modelmAnd recombined to form a stable signal xc,i；
For the steady signal xc,iCarrying out Prony decomposition, and calculating an extreme value and a residue; and after the extreme value and the residue are screened according to the effective frequency window, reconstructing a real signal to obtain a complete signal x (t) after the noise elimination is finished.
Preferably, the raw data X will be revealedi(t) intercepting time domain signals x of equal lengthn,i(t) and calculating the frequency domain signal X by Fourier transformF,i(s), the method comprising:
will reveal the original data Xi(t) intercepting time domain signals x of equal lengthn,i(t) applying each time domain signal x at regular time intervalsn,i(t) sampling to obtain a sampling signal xn,i(a) (ii) a For sampling signal xn,i(a) Fourier transform calculation is carried out to obtain frequency domain signal XF,i(s) the formula is:
Figure BDA0003482236370000021
in the formula, the first step is that,
Figure BDA0003482236370000022
is a twiddle factor, and j is an imaginary part; a is a sampling signal xn,i(a) The signal length of (2).
Preferably, a frequency domain signal X is establishedF,i(s) magnitude spectrogram, the method comprising:
calculating a frequency domain signal XF,i(s) corresponding frequency fsThe formula is as follows:
Figure BDA0003482236370000023
in the formula, s is a frequency domain signal XF,i(s) the corresponding sequence number; n is a time domain signal xn,i(t) time; f. ofcRepresented as a time domain signal xn,i(t) the corresponding frequency;
at a frequency fsAs abscissa, frequency domain signal XF,iAnd(s) establishing a magnitude spectrogram by taking the magnitude of the signal(s) as a vertical coordinate.
Preferably, the frequency f is associated with the peak of the amplitude spectrogramtConstructing an effective frequency window for a reference, the method comprising: the peak value of the amplitude frequency spectrum diagram is corresponding to the frequency ftAs a reference, an effective frequency width is set as b, and an effective frequency window is constructed as ft-b,ft+b]。
Preferably, the unit signal x affected by noise is removed by using a differential energy modelmAnd recombined to form a stable signal xc,i(ii) a The method comprises the following steps:
the calculation formula of the differential energy model is as follows:
Figure BDA0003482236370000031
Δxm＝xm+1-xm
Figure BDA0003482236370000032
in the formula,. DELTA.xmUnit signal x represented as adjacent segmentsmThe energy difference of (a); rho is a noise uncertainty parameter;
Figure BDA0003482236370000033
represented as a frequency domain signal XF,iUnit signal x in(s)mA statistical average of the energy difference;
when in use
Figure BDA0003482236370000034
Time, to unit signal xmRemoving; when in use
Figure BDA0003482236370000035
Time, to unit signal xmReserving; recombining the retained unit signals to form a stable signal xc,i。
Preferably, the method for calculating the noise uncertainty parameter ρ comprises the following steps;
setting frequency domain signal XF,i(s) is a noise-free signal Xw,i(s) and white Gaussian noise Xn,i(s) superposition;
for frequency domain signal XF,i(s) performing wavelet transform and removing noiseless signal Xw,i(s) obtaining a processed signal WX(α, β), the calculation formula is:
Figure BDA0003482236370000036
Figure BDA0003482236370000037
in the formula, the first step is that,
Figure BDA0003482236370000038
expressed as wavelet transform basis functions;
Figure BDA0003482236370000039
expressed as a wavelet function after expansion and translation; alpha is a scaling factor; beta is a translation factor;
according to the processing signal WX(alpha, beta) deducing the noise standard deviation
Figure BDA00034822363700000310
Sum noise variance
Figure BDA00034822363700000311
And calculating a noise uncertainty parameter rho, wherein the calculation formula is as follows:
Figure BDA00034822363700000312
Figure BDA00034822363700000313
Figure BDA0003482236370000041
in the formula, the first step is that,
Figure BDA0003482236370000042
expressed as the noise variance;
Figure BDA0003482236370000043
expressed as the noise standard deviation;
Figure BDA0003482236370000044
is represented as a processed signal WX(α, β) power; med [.]Is a median function.
Preferably, for the steady signal xc,iCarrying out Prony decomposition, and calculating an extreme value and a residue; the method comprises the following steps:
construction of a stabilizing Signal xc,iAnd alpha and beta are respectively used as the row number and the column number of the matrix H (c), and the expression formula is as follows:
Figure BDA0003482236370000045
deriving a system matrix Q according to the matrix H (c), and analyzing the system matrix Q to obtain an eigenvalue zr；
Will stabilize the signal xc,i(c 0, 1.., n-1) complex exponential decomposition into an extremum λrSum residue gammarThe expression formula is:
Figure BDA0003482236370000046
Figure BDA0003482236370000047
where P is the decomposition order and Δ t is the time interval between signal samples.
Preferably, after the extreme value and the residue are screened according to the effective frequency window, the real signal is reconstructed to obtain a complete signal x (t) after the noise cancellation is completed, and the method comprises the following steps:
will extreme value lambdarConversion to an extreme frequency frThe expression formula is:
Figure BDA0003482236370000048
screening of extreme frequencies frIn the effective frequency window ft-b,ft+b]Inner extreme lambdarAs an effective extremum λe,r(ii) a Will effectively extreme value lambdae,rCorresponding residue gammarAs effective residue gammae,r(ii) a According to the effective extreme value lambdae,rAnd effective residue gammae,rAnd reconstructing the real signal to obtain a complete signal x (t) after the noise elimination is finished.
Compared with the prior art, the invention has the beneficial effects that:
in the invention, a frequency domain signal X is converted into a frequency domain signalF,i(s) dividing into M sections of unit signal xmRemoving unit signals x affected by noise by using a differential energy modelmAnd recombined to form a stable signal xc,i(ii) a For the steady signal xc,iCarrying out Prony decomposition, and calculating an extreme value and a residue; screening the extreme values and the residual numbers according to the effective frequency window, and reconstructing a real signal to obtain a complete signal x (t) after noise elimination is finished; the denoising method can prevent the loss of the inherent information of the structure in the leakage signal, simultaneously reduces the condition number of the matrix, ensures that the calculation is convenient and fast, has better stability, and can obtain the noise suppression rate with smaller change and the larger signal distortion rate when the noise change is larger.
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FIG. 1 is a flow chart of a method for reducing noise of monitored data based on urban pipeline leakage according to the present invention;
FIG. 2 is a schematic diagram of an experimental setup for simulating urban pipelines;
FIG. 3 is a graph of an infrasonic signal of a leak in a pipe;
FIG. 4 is a graph of a leakage signal amplitude spectrum;
FIG. 5 is a leakage signal energy plot;
FIG. 6 is a Gaussian white noise power plot;
fig. 7 is a graph of the signal denoised amplitude spectrum.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in fig. 2, an experimental device for simulating urban pipelines is arranged, wherein the experimental device comprises a buried non-metal pipeline, a pressure sensor, a pressure gauge, a vortex flowmeter, a computer, an air compressor and an infrasonic wave acquisition instrument; the buried nonmetal pipeline comprises a U-shaped main pipeline and two branch pipelines; be equipped with the leakage opening on the ground non-metallic pipeline, the leakage opening aperture is 1mm, 2mm, 3mm, 8mm respectively.
As shown in fig. 1 to 7, a method for reducing noise of monitoring data based on urban pipeline leakage includes:
collecting leakage original data X of leakage pipeline infrasonic wavei(t)；
Will reveal the original data Xi(t) intercepting time domain signal x of 20 seconds lengthn,i(t) and calculating the frequency domain signal X by Fourier transformF,i(s), the method comprising:
will reveal the original data Xi(t) intercepting time domain signals x of equal lengthn,i(t) applying each time domain signal x at regular time intervalsn,i(t) sampling to obtain a sampling signal xn,i(a) (ii) a For sampling signal xn,i(a) Fourier transform calculation is carried out to obtain frequency domain signal XF,i(s) the formula is:
Figure BDA0003482236370000061
in the formula, the first step is that,
Figure BDA0003482236370000062
is a twiddle factor, and j is an imaginary part; a is a sampling signal xn,i(a) The signal length of (2). Calculating a frequency domain signal XF,i(s) corresponding frequency fsThe formula is as follows:
Figure BDA0003482236370000063
in the formula, s is a frequency domain signal XF,i(s) the corresponding sequence number; n is a time domain signal xn,i(t) time; f. ofcRepresented as a time domain signal xn,i(t) the corresponding frequency;
at a frequency fsAs abscissa, frequency domain signal XF,i(s) establishing a magnitude spectrogram with the magnitude as the ordinate; the peak value of the amplitude frequency spectrum diagram is corresponding to the frequency ftAs a reference, an effective frequency width b of 0.5 is set, and an effective frequency window f is constructedt-b,ft+b]The peak frequency f in the amplitude spectrum shown in FIG. 4tIs 0.805, and the frequency window for obtaining effective components is [0.305,1.305 ]]。
Will frequency domain signal XF,i(s) is divided into 60-segment unit signal xmRemoving unit signals x affected by noise by using a differential energy modelmAnd recombined to form a stable signal xc,i(ii) a The method comprises the following steps:
the Gaussian white noise can be expressed by a specific mathematical expression and can reflect the noise condition in an actual pipeline, so that the noise uncertainty parameter rho is estimated by means of the Gaussian white noise. Using MATLAB software programming, a set of white gaussian noises was generated for estimating the noise uncertainty parameter ρ, which is shown in fig. 6.
Setting frequency domain signal XF,i(s) is a noise-free signal Xw,i(s) And Gaussian white noise Xn,i(s) superposition;
for frequency domain signal XF,i(s) performing wavelet transform and removing noiseless signal Xw,i(s) obtaining a processed signal WX(α, β), the calculation formula is:
Figure BDA0003482236370000071
Figure BDA0003482236370000072
in the formula, the first step is that,
Figure BDA0003482236370000073
expressed as wavelet transform basis functions;
Figure BDA0003482236370000074
expressed as a wavelet function after expansion and translation; alpha is a scaling factor; beta is a translation factor;
using MATLAB software to make operation, calculating to obtain the wavelet median value of said signal 474.38, according to the processed signal WX(alpha, beta) deducing the noise standard deviation
Figure BDA0003482236370000075
Sum noise variance
Figure BDA0003482236370000076
Suppose signal XF,i(s) retaining only white Gaussian noise X after wavelet transformn,i(s), white Gaussian noise variance
Figure BDA0003482236370000077
Equal to its average power, and thus the noise uncertainty parameter p can be defined by the noise standard deviation and the noise variance, and is calculated as:
Figure BDA0003482236370000078
Figure BDA0003482236370000079
Figure BDA00034822363700000710
in the formula, the first step is that,
Figure BDA00034822363700000711
is represented as a processed signal WX(α, β) power; med [.]Is a median function.
The calculation formula of the differential energy model is as follows:
Figure BDA00034822363700000712
Δxm＝xm+1-xm
Figure BDA00034822363700000713
Figure BDA00034822363700000714
in the formula,. DELTA.xmUnit signal x represented as adjacent segmentsmThe energy difference of (a); rho is a noise uncertainty parameter;
Figure BDA0003482236370000081
represented as a frequency domain signal XF,iUnit signal x in(s)mA statistical average of the energy difference;
with x1、x2、x10、x11、x40、x41For example, the results are shown in table 1; when in use
Figure BDA0003482236370000082
Time, to unit signal xmRemoving; when in use
Figure BDA0003482236370000083
Time, to unit signal xmReserving; recombining the retained unit signals to form a stable signal xc,i；
TABLE 1 noise energy determination
Figure BDA0003482236370000084
For the steady signal xc,iCarrying out Prony decomposition, and calculating an extreme value and a residue; the method comprises the following steps:
construction of a stabilizing Signal xc,iAnd alpha and beta are respectively used as the row number and the column number of the matrix H (c), and the expression formula is as follows:
Figure BDA0003482236370000085
taking c to be 0, the Hankel matrix is expressed as:
Figure BDA0003482236370000086
and carrying out singular value decomposition on the matrix by using MATLAB software to obtain orthogonal matrixes U and V and a diagonal matrix S.
Taking c as 1, the Hankel matrix is expressed as
Figure BDA0003482236370000091
And the matrix Q at this time can be represented as:
Figure BDA0003482236370000092
eigenvalue of system matrix QAnalyzing to obtain a characteristic value zr(ii) a Will stabilize the signal xc,i(c 0, 1.., n-1) complex exponential decomposition into an extremum λrSum residue gammarThe expression formula is:
zr＝[-0.96+0.32i，-0.96-0.32i，...，0.76-0.11i]
Figure BDA0003482236370000093
Figure BDA0003482236370000094
where P is the decomposition order and Δ t is expressed as the time interval of signal sampling;
obtaining: lambda [ alpha ]r＝[λt,1 λt,2 … λt,r λf,1 λf,2 … λf,r]
γr＝[γt,1 γt,2 … γt,r γf,1 γf,2 … γf,r]
In the formula, λt,1…λt,r、γt,1…γt,rIs a true signal, λf,1…λf,r、γf,1…γf,rIs a false signal
Will extreme value lambdarConversion to an extreme frequency frThe expression formula is:
Figure BDA0003482236370000095
screening of extreme frequencies frIn the effective frequency window ft-b,ft+b]Inner extreme lambdarAs an effective extremum λe,r(ii) a Will effectively extreme value lambdae,rCorresponding residue gammarAs effective residue gammae,r(ii) a The final available extreme set λ and residue set γ are:
λ＝[λe,1 λe,2 … λe,r]
γ＝[γe,1 γe,2 … γe,r]
according to the effective extreme value lambdae,rAnd effective residue gammae,rReconstructing a real signal to obtain a complete signal x (t) after denoising is finished; and the complete signal X (t) and the original signal Xi(t) comparing; fig. 7 is a frequency domain diagram of the amplitude of the signal after noise cancellation, and comparing fig. 7 with fig. 4 shows that the noise cancellation method used herein can achieve the noise cancellation purpose.
Obtaining a signal X (t) after denoising by using the text method, obtaining a signal X' (t) after denoising by using the original prony denoising method, and obtaining a signal X (t) according to the signal X before denoisingi(t) the signal to noise ratio SNR was solved and compared as shown in Table 2.
TABLE 2 SNR COMPARATIVE TABLE
Figure BDA0003482236370000101
As can be seen from table 2, the signal to noise ratio of the signal x (t) denoised by the improved denoising method is greater than the signal to noise ratio of the signal x' (t) denoised by the original method. Therefore, the improved extreme value-residue noise reduction method adopted by the method has certain noise reduction effect, and the noise reduction effect is superior to that of the original method.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (8)

1. A monitoring data noise reduction method based on urban pipeline leakage is characterized by comprising the following steps:
collecting leakage original data X of leakage pipeline infrasonic wavei(t)；
Will reveal the original data Xi(t) intercepting time domain signals x of equal lengthn,i(t) and calculating the frequency domain signal X by Fourier transformF,i(s) establishing a frequency domainSignal XF,i(s) a magnitude spectrogram; using the peak of the amplitude spectrogram to correspond to the frequency ftConstructing an effective frequency window for a reference;
will frequency domain signal XF,i(s) dividing into M sections of unit signal xmRemoving unit signals x affected by noise by using a differential energy modelmAnd recombined to form a stable signal xc,i；
For the steady signal xc,iCarrying out Prony decomposition, and calculating an extreme value and a residue; and after the extreme value and the residue are screened according to the effective frequency window, reconstructing a real signal to obtain a complete signal x (t) after the noise elimination is finished.
2. The method for reducing noise of monitoring data based on urban pipeline leakage according to claim 1, wherein leakage raw data X is subjected to noise reductioni(t) intercepting time domain signals x of equal lengthn,i(t) and calculating the frequency domain signal X by Fourier transformF,i(s), the method comprising:
will reveal the original data Xi(t) intercepting time domain signals x of equal lengthn,i(t) applying each time domain signal x at regular time intervalsn,i(t) sampling to obtain a sampling signal xn,i(a) (ii) a For sampling signal xn,i(a) Fourier transform calculation is carried out to obtain frequency domain signal XF,i(s) the formula is:
Figure FDA0003482236360000011
in the formula, the first step is that,
Figure FDA0003482236360000012
is a twiddle factor, and j is an imaginary part; a is a sampling signal xn,i(a) The signal length of (2).
3. The method of claim 2, wherein a frequency domain signal X is establishedF,i(s) amplitude spectrogram ofThe method comprises the following steps:
calculating a frequency domain signal XF,i(s) corresponding frequency fsThe formula is as follows:
Figure FDA0003482236360000021
in the formula, s is a frequency domain signal XF,i(s) the corresponding sequence number; n is a time domain signal xn,i(t) time; f. ofcRepresented as a time domain signal xn,i(t) the corresponding frequency;
at a frequency fsAs abscissa, frequency domain signal XF,iAnd(s) establishing a magnitude spectrogram by taking the magnitude of the signal(s) as a vertical coordinate.
4. The method of claim 3, wherein the peak of the amplitude spectrogram corresponds to the frequency ftConstructing an effective frequency window for a reference, the method comprising: the peak value of the amplitude frequency spectrum diagram is corresponding to the frequency ftAs a reference, an effective frequency width is set as b, and an effective frequency window is constructed as ft-b,ft+b]。
5. The method for reducing the noise of the monitored data based on the urban pipeline leakage according to claim 4, wherein a differential energy model is used for removing a unit signal x affected by noisemAnd recombined to form a stable signal xc,i(ii) a The method comprises the following steps:
the calculation formula of the differential energy model is as follows:
Figure FDA0003482236360000022
Δxm＝xm+1-xm
Figure FDA0003482236360000023
in the formula,. DELTA.xmUnit signal x represented as adjacent segmentsmThe energy difference of (a); rho is a noise uncertainty parameter;
Figure FDA0003482236360000024
represented as a frequency domain signal XF,iUnit signal x in(s)mA statistical average of the energy difference;
when in use
Figure FDA0003482236360000025
Time, to unit signal xmRemoving; when in use
Figure FDA0003482236360000026
Time, to unit signal xmReserving; recombining the retained unit signals to form a stable signal xc,i。
6. The monitoring data noise reduction method based on urban pipeline leakage according to claim 5, wherein the calculation method of the noise uncertainty parameter p comprises;
setting frequency domain signal XF,i(s) is a noise-free signal Xw,i(s) and white Gaussian noise Xn,i(s) superposition;
for frequency domain signal XF,i(s) performing wavelet transform and removing noiseless signal Xw,i(s) obtaining a processed signal WX(α, β), the calculation formula is:
Figure FDA0003482236360000031
Figure FDA0003482236360000032
in the formula, the first step is that,
Figure FDA0003482236360000033
expressed as wavelet transform basis functions;
Figure FDA0003482236360000034
expressed as a wavelet function after expansion and translation; alpha is a scaling factor; beta is a translation factor;
according to the processing signal WX(alpha, beta) deducing the noise standard deviation
Figure FDA0003482236360000035
Sum noise variance
Figure FDA0003482236360000036
And calculating a noise uncertainty parameter rho, wherein the calculation formula is as follows:
Figure FDA0003482236360000037
Figure FDA0003482236360000038
Figure FDA0003482236360000039
in the formula, the first step is that,
Figure FDA00034822363600000310
is represented as a processed signal WX(α, β) power; med [.]Is a median function.
7. The method for reducing noise of monitoring data based on urban pipeline leakage according to claim 6, wherein the stable signal x is subjected to noise reductionc,iCarrying out Prony decomposition, and calculating an extreme value and a residue; the method comprises the following steps:
construction of a stabilizing Signal xc,iAnd a, b, and aThe number of rows and columns of the matrix h (c), respectively, is expressed as:
Figure FDA00034822363600000311
deriving a system matrix Q according to the matrix H (c), and analyzing the system matrix Q to obtain an eigenvalue zr；
Will stabilize the signal xc,i(c 0, 1.., n-1) complex exponential decomposition into an extremum λrSum residue gammarThe expression formula is:
Figure FDA0003482236360000041
Figure FDA0003482236360000042
where P is the decomposition order and Δ t is the time interval between signal samples.
8. The method for reducing the noise of the monitoring data based on the urban pipeline leakage according to claim 7, wherein after extreme values and residue numbers are screened according to an effective frequency window, a real signal is reconstructed to obtain a complete signal x (t) after noise elimination is completed, and the method comprises the following steps:
will extreme value lambdarConversion to an extreme frequency frThe expression formula is:
Figure FDA0003482236360000043
screening of extreme frequencies frIn the effective frequency window ft-b,ft+b]Inner extreme lambdarAs an effective extremum λe,r(ii) a Will effectively extreme value lambdae,rCorresponding residue gammarAs effective residue gammae,r(ii) a According to the effective extreme value lambdae,rAnd effective residue gammae,rAnd reconstructing the real signal to obtain a complete signal x (t) after the noise elimination is finished.
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CN116295539A (en) * 2023-05-18 2023-06-23 山东省地质矿产勘查开发局八〇一水文地质工程地质大队(山东省地矿工程勘察院) Underground space monitoring method based on urban underground space exploration data

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116295539A (en) * 2023-05-18 2023-06-23 山东省地质矿产勘查开发局八〇一水文地质工程地质大队(山东省地矿工程勘察院) Underground space monitoring method based on urban underground space exploration data
CN116295539B (en) * 2023-05-18 2023-08-11 山东省地质矿产勘查开发局八〇一水文地质工程地质大队(山东省地矿工程勘察院) Underground space monitoring method based on urban underground space exploration data

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