CN110469782B - Pipeline leakage positioning device based on self-adaptive filter - Google Patents
Pipeline leakage positioning device based on self-adaptive filter 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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- 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
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Abstract
The invention discloses a pipeline leakage positioning device based on an adaptive filter, which comprises two sensors arranged at two ends of a pipeline leakage source, a signal acquisition card, a signal characteristic analysis module, an L MS filter and a leakage positioning module, wherein the signal acquisition card is used for acquiring signals of the two sensors and then respectively sending the signals to the signal characteristic analysis module and the L MS adaptive filter, the signal characteristic analysis module is used for carrying out time-frequency domain analysis on the acquired signals and calculating relevant parameters of the signals, so that the number of the L MS filter is selected, the L MS filter is used for calculating the time delay of the signals of the two sensors, and the leakage positioning module is used for calculating the position of the leakage source through the obtained time delay.
Description
Technical Field
The invention relates to the technical field of geophysical prospecting, in particular to a pipeline leakage positioning device based on a self-adaptive filter.
Background
The pipeline is an important infrastructure for guaranteeing the life and the economic construction of people, but pipeline leakage accidents occur frequently due to corrosion, aging, natural disasters, construction damage and the like. The leakage of the pipeline not only causes huge waste of resources and energy, but also causes secondary accidents such as environmental pollution, foundation settlement, road collapse and the like. The pipeline system in China is mostly made of metal materials, and after two thirty years of service, the pipeline system enters the accident high-rise stage, and a large number of main pipelines have the problem of aging and leakage. Taking a water supply pipeline as an example, according to the statistical data of construction departments, the average leakage rate of the urban water supply network in China currently exceeds 15 percent, reaches more than 70 percent at most, exceeds the national CJJ 92-2002 standard (less than or equal to 12 percent), and is farther behind the level of developed countries (less than 10 percent). In addition, for historical reasons, many underground pipelines are not well-oriented, so that the pipelines are frequently accidentally cut off during construction of a building unit. The pipeline leakage is always a chronic disease which troubles the pipeline transportation industry, so that the research on the pipeline leakage detection and positioning method for maintaining the safe operation of a pipeline network has important theoretical significance and engineering application value.
Disclosure of Invention
The invention provides a pipeline leakage positioning device based on an adaptive filter, which is characterized in that two sensors (including an acceleration sensor or a hydrophone and other sound/vibration sensors) are arranged on a pipeline to acquire sound wave signals generated by a pipeline leakage source, then the signals acquired by the sensors are input into an L MS adaptive filter unit to obtain the time delay of the signals acquired by a sensor 1 and a sensor 2, and then the position information of the leakage source on the pipeline is calculated through a leakage positioning module.
In order to achieve the aim, the invention provides a pipeline leakage positioning device based on an adaptive filter, which comprises two sensors, a signal acquisition card, a signal characteristic analysis module, an L MS filter and a leakage positioning module, wherein the two sensors are arranged at two ends of a pipeline leakage source;
the signal acquisition card is used for acquiring signals of the two sensors and then respectively sending the signals to the signal characteristic analysis module and the L MS self-adaptive filter;
the signal characteristic analysis module is used for carrying out time-frequency domain analysis on the acquired signals, calculating relevant parameters of the signals and selecting L MS filter multiplicity;
the L MS filter is used for calculating the time delay of the two sensor signals;
and the leakage positioning module is used for calculating the position of a leakage source according to the obtained time delay.
As an improvement of the device, the sensor is a non-invasive acceleration sensor or a non-invasive vibration sensor and is arranged on the outer wall surface of the pipeline.
As an improvement of the above arrangement, the sensor is an invasive hydrophone or pressure transducer mounted inside the pipe.
As an improvement of the device, a preamplifier is arranged between each sensor and the signal acquisition card, and the preamplifier is a metal pipeline preamplifier with the amplification factor of 10-20 dB.
As an improvement of the device, a preamplifier is arranged between each sensor and the signal acquisition card, and the preamplifier is a plastic pipeline preamplifier with the amplification factor of 20-40 dB.
As an improvement of the above apparatus, the signal characteristic analysis module includes: a parameter calculation unit and a weight determination unit;
the parameter calculating unit is configured to perform time-frequency domain analysis on the acquired signal, and calculate a relevant parameter of the signal, where the relevant parameter includes: the energy, signal-to-noise ratio, self-power spectrum, cross-power spectrum and correlation coefficient of the signal; the calculation formula of the signal-to-noise ratio SNR is as follows:
the calculation formula of the correlation coefficient rho is as follows:
wherein, Psignal、PnoisePower s representing signal and noise respectively1(t) and s2(t) are the signals collected by the two sensors respectively;is s1(t) and s2(t), max represents taking the maximum value,andrespectively represents s1(t) and s2(t) an autocorrelation function value at a time when the time delay τ is 0;
the weight determining unit is used for determining L the weight of the MS filter according to the following criteria:
when the signal-to-noise ratio is greater than 10dB or the correlation coefficient is greater than 0.8, selecting a single L MS filter;
when-10 dB < signal-to-noise ratio <10dB or 0.5< correlation coefficient <0.8, select a double L MS filter;
when the signal-to-noise ratio is < -10dB or the correlation coefficient is less than 0.5, multiple L MS filters are selected, the multiple is three or more, and signal smoothing processing is required between each two filters.
As an improvement of the device, a low-pass digital filter is arranged between the signal acquisition card and the L MS filter and is used for filtering high-frequency electromagnetic and mechanical noise included in the signal.
As an improvement of the device, the single L MS filter comprises a first L MS adaptive filter and a second L MS adaptive filter;
by s1(t) as input signal, s2(t) as the desired response, input to a first L MS adaptive filter, output a filter coefficient vector h1(t); by s2(t) as input signal, s1(t) as the desired response, input to a second L MS adaptive filter, then output a filter coefficient vector h2(t);
Find h1(t) and h2(t) maximum value max [ h ]1(t)]And max [ h ]2(t)]Corresponding time delay, i.e.Andthe first L MS filter calculated time delay τ1The following were used:
the time delay τ is τ1。
As an improvement of the device, the double L MS filter comprises a first heavy L MS filter and a second heavy L MS filter, wherein the first heavy L MS filter comprises a first L MS adaptive filter and a second L MS adaptive filter, and the second heavy L MS filter comprises a third L MS adaptive filter and a fourth L MS adaptive filter;
in the first L MS filter, s1(t) as input signal, s2(t) as the desired response, input to a first L MS adaptive filter, output a filter coefficient vector h1(t); by s2(t) as input signal, s1(t) as the desired response, input to a second L MS adaptive filter, then output a filter coefficient vector h2(t);
In the second pass L MS Filter, the sum of h1(t) as input signal, h2(t) as the desired response, inputs to a third L MS adaptive filter, outputs a filter coefficient vector h3(t); by h2(t) as input signal, h1(t) as the desired response, the signal is input to a fourth L MS adaptive filter, and a filter coefficient vector h is output4(t); find h3(t) and h4(t) maximum value max [ h ]3(t)]And max [ h ]4(t)]Corresponding time delayAndthe second L MS filter calculated time delay τ2The following were used:
the time delay τ is τ2。
As an improvement of the device, the multiple L MS filter comprises n single L MS filters connected in series, wherein the output of the previous single L MS filter is used as the input of the next single L MS filter;
in the first single L MS filter, s1(t) as input signal, s2(t) as the desired response, input to a first L MS adaptive filter, output a filter coefficient vector h1(t); by s2(t) as input signal, s1(t) as the desired response, input to a second L MS adaptive filter, then output a filter coefficient vector h2(t);
In the second single L MS filter, the sum of h1(t) as input signal, h2(t) as the desired response, inputs to a third L MS adaptive filter, outputs a filter coefficient vector h3(t); by h2(t) as input signal, h1(t) as the desired response, input to a fourth L MS adaptive filter, then output the filter coefficient vector h4(t);
In the nth simplex L MS filter, the sum of h2n-3(t) as input signal, h2n-2(t) as a desired response, the signal is input to a (2n-1) th L MS adaptive filter, and a filter coefficient vector h is output2n-1(t); by h2n-2(t) as input signal, h2n-3(t) as the desired response, input to the 2n L MS adaptive filter, then the filter coefficient vector h is output2n(t);
h2n-1(t) and h2n(t) has time on the abscissa and amplitude on the ordinate, and the times corresponding to the maximum amplitudes are respectivelyAndthe time delay tau of the multiple L MS filtersnThe calculation is as follows:
the time delay τ is τn。
As an improvement of the above device, the specific implementation steps of the leakage positioning module are as follows:
leakage source location is calculated based on the time delay of the L MS filter output:
wherein c is the propagation speed of sound waves in the pipeline, d1The distance of the leakage source from one sensor; the calculation formula of the sound velocity c is as follows:
wherein, cfThe propagation speed of sound wave in free field, B is the bulk modulus of water, E is the Young's modulus of pipe wall, a is the pipe radius, and h is the pipe wall thickness.
The invention has the advantages that:
the device can realize accurate positioning of the leakage source under the condition of low signal-to-noise ratio.
Drawings
FIG. 1 is a schematic view of two sensor installations;
FIG. 2 is a schematic diagram of multiple L MS filter leakage localization;
FIG. 3 is a schematic diagram of dual L MS filter leakage localization;
FIG. 4 shows L MS filter results under high SNR conditions;
FIG. 5 is the result of a single L MS filter under low SNR conditions;
FIG. 6 shows the result of multiple L MS filters under low SNR conditions;
fig. 7 is a schematic diagram of the adaptive filter-based pipe leakage locator of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
The pipeline leakage positioning principle provided by the invention is as follows:
two sound/vibration sensors are arranged on an exposed part of a pipeline (such as an inspection well of the pipeline) and used for collecting sound wave signals generated by a leakage source of the pipeline, and the sensors are arranged as shown in figure 1, wherein the distance between the sensor 1 and the leakage source is d1The distance between the sensor 2 and the leakage source is d2And the distance D between 2 sensors is D1+d2。
In an actual leak detection process, the distance D between the two sensors has been determined at the time of sensor installation, but the location of the source of the leak is unknown, i.e. D1And d2Is unknown. Due to d2=D-d1I.e. known as d1Then d can be obtained2. In practical application, the position of the leakage source is accurately calculated through a formula (1) according to the propagation speed of sound waves in fluid inside a pipeline by calculating the time delay of signals acquired by two sensors.
The unknown variables in equation (1) are c and τ, where c is the speed of propagation of the sound wave in the pipe and τ is the time delay of sensor 1 and sensor 2. The calculation formula of the sound velocity c is as follows:
wherein c isfThe propagation speed of sound wave in free field, B is the bulk modulus of water, E is the Young's modulus of pipe wall, a is the pipe radius, and h is the pipe wall thickness.
Therefore, as can be seen from the formulas (1) and (2), the core of the positioning of the pipeline leakage is the calculation of the time delay τ, at present, in the field of pipeline leakage detection, the time delay τ is usually calculated by a cross-correlation (basic cross-correlation or generalized cross-correlation) algorithm, although the cross-correlation algorithm has high robustness, when the conditions of micro-leakage signals, large sound wave attenuation, low signal-to-noise ratio and the like are met, the positioning accuracy of the cross-correlation algorithm is seriously affected.
Fig. 2 is a schematic diagram of leakage localization of multiple L MS filters, which contains n single L MS filter banks, in practice, the number of filter multiples is selected according to the signal characteristics, i.e., if the signal-to-noise ratio is high, only a single filter can be used, and if the signal-to-noise ratio is low, multiple L MS can be used in a superposition mode, and the following is a detailed description of the case of a dual L MS filter, as shown in fig. 3.
FIG. 3 is a schematic diagram of leakage localization for dual L MS filters, the first L MS filter comprising L MS adaptive filter 1 and L MS adaptive filter 2, the second L MS filter comprising L MS adaptive filter 3 and L MS adaptive filter 4, the first L MS filter is s1(t) and s2And (t) are signals collected by the sensor 1 and the sensor 2 respectively. By s1(t) as input signal, s2(t) As the desired response, the input to L MS adaptive Filter 1, a filter coefficient vector h is obtained1(t) and time delayBy s2(t) as input signal, s1(t) As the desired response, the input to L MS adaptive Filter 2, a filter coefficient vector h is obtained2(t) and time delaySecond pass L MS Filter in h1(t) as input signal, h2(t) As the desired response, the filter coefficient vector h is obtained by inputting the signal into L MS adaptive filter 33(t) and time delayBy h2(t) as input signal, h1(t) As the desired response, the input to L MS adaptive Filter 4, a filter coefficient vector h is obtained4(t) and time delayWherein h is1(t) and h2(t) reaction of s1(t) and s2(t) time delay case, h3(t) and h4(t) reaction of h1(t) and h2(t) time delay cases. At high signal-to-noise ratio, h1(t) and h2An exemplary graph of (t) is shown in fig. 4.
H in FIG. 41The maximum value of the (t) curve corresponds to an abscissa of 0.02s, the physical meaning of which is s1(t) ratio s2(t) 0.02s advance; h is2(t) the maximum of the curve corresponds to an abscissa of-0.02 s, the physical meaning of this value being s2(t) ratio s1(t) leads by-0.02 s, i.e., lags by 0.02s, it can be seen that under the condition of high signal-to-noise ratio, the time delays of the sensor 1 and the sensor 2 can be obtained by only using the single L MS adaptive filter (filter 1 or filter 2), so as to realize accurate positioning of the leakage source, but for the conditions of micro-leakage signals, large sound wave attenuation, too low signal-to-noise ratio and the like, the accurate positioning cannot be effectively completed by only using the single L MS filter, as shown in fig. 5.
FIG. 5 shows the result of a single L MS filter under low SNR conditions, and it can be seen that h is the signal with low SNR1(t) and h2The peak of the (t) curve is not obvious, the selection of the maximum value can be interfered by the nearby peak value, so that the positioning result is wrong, in order to improve the positioning accuracy and reliability of the leak point, the invention provides a method for multiple L MS filters, namely, the peak value is further h1(t) as input signal, h2(t) as a desired response, the desired response is inputted to L MS adaptive filter 3, thereby obtaining filter coefficient vector h3(t); by h2(t) as input signal, h1(t) as a desired response, the desired response is inputted to L MS adaptive filter 4, thereby obtaining filter coefficient vector h4(t) FIG. 6 is an exemplary graph of the results of a double L MS filter under low signal-to-noise conditions, looking to see h3The abscissa corresponding to the maximum value of the (t) curve is 0.04s, h4(t) abscissa corresponding to maximum value of curve is-0.04 s when multiple L MS filters are used for leakage localization, h is calculated2n-1(t) and h2n(t) time value corresponding to peak valueAndthe time delay tau is calculated by first taking the absolute value and then dividing by 2nnAnd then the accurate positioning of the leakage source is realized by the formula (1).
As shown in fig. 7, the apparatus of the present invention specifically includes:
1. sensor unit
Two sensors are arranged on the exposed part of the pipeline, generally a non-invasive acceleration sensor or a non-invasive vibration sensor can be selected and arranged on the outer wall surface of the pipeline; or an intrusive hydrophone or pressure transmitter, is installed inside the pipe. Taking an acceleration sensor as an example, the frequency range is generally selected to be less than or equal to 6kHz, the distance between the sensors can be generally set to be about 300-500 meters due to small signal attenuation of a metal pipeline, and the distance between the sensors can be generally set to be about 50-100 meters due to large signal attenuation of a plastic pipeline.
2. Signal amplification and acquisition unit
For the selected sensor, the matched signal sampling frequency is generally 2-5 times of the sensor frequency. Taking an acceleration sensor with the frequency range less than or equal to 6kHz as an example, the signal sampling frequency can be set to be 12-30kHz, the amplification factor of the metal pipeline preamplifier can be set to be 10-20dB, and the amplification factor of the plastic pipeline preamplifier can be set to be 20-40 dB.
3. Signal characteristic analysis unit
The signal characteristic analysis unit analyzes the acquired signal in time and frequency domain, calculates the parameters of energy, signal-to-noise ratio, self-power spectrum, cross-power spectrum and correlation coefficient of the signal, and selects the specific weight of the multiple L MS adaptive filter according to the parameters, wherein the general signal-to-noise ratio is more than 10dB or the correlation coefficient is more than 0.8, the single L MS adaptive filter can meet the precision requirement of engineering positioning, when-10 dB < the signal-to-noise ratio <10dB or 0.5< the correlation coefficient <0.8, the double L MS adaptive filter can meet the precision requirement of the engineering positioning, when the signal-to-noise ratio <10dB or the correlation coefficient <0.5, the selection of the triple or more than triple L MS adaptive filters is suggested, and the signal smoothing processing is needed between each filter, the calculation formula of the signal-to-noise ratio and the correlation coefficient is as follows:
wherein, Psignal、PnoiseRespectively representing the power of the signal and the noise,is the cross-correlation function of signal 1 and signal 2, max represents the maximum value,andrespectively, the autocorrelation function values of signal 1 and signal 2 at the time τ -0.
4. Signal processing and positioning unit
The signal processing and locating unit comprises a filter, a multiple L MS filter and a leakage locator, wherein the filter adopts a low-pass digital filter and aims to filter high-frequency electromagnetic and mechanical noise included in the signal, the multiple L MS filter is used for calculating the time delay of two sensor signals, and the locator is used for calculating the position of a leakage source through the obtained time delay.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A pipeline leakage positioning device based on a self-adaptive filter is characterized by comprising two sensors, a signal acquisition card, a signal characteristic analysis module, an L MS filter and a leakage positioning module, wherein the two sensors are arranged at two ends of a pipeline leakage source;
the signal acquisition card is used for acquiring signals of the two sensors and then respectively sending the signals to the signal characteristic analysis module and the L MS self-adaptive filter;
the signal characteristic analysis module is used for carrying out time-frequency domain analysis on the acquired signals, calculating relevant parameters of the signals and selecting L MS filter multiplicity;
the L MS filter is used for calculating the time delay of the two sensor signals;
the leakage positioning module is used for calculating the position of a leakage source through the obtained time delay;
the signal feature analysis module includes: a parameter calculation unit and a weight determination unit;
the parameter calculating unit is configured to perform time-frequency domain analysis on the acquired signal, and calculate a relevant parameter of the signal, where the relevant parameter includes: the energy, signal-to-noise ratio, self-power spectrum, cross-power spectrum and correlation coefficient of the signal; the calculation formula of the signal-to-noise ratio SNR is as follows:
the calculation formula of the correlation coefficient rho is as follows:
wherein, Psignal、PnoisePower s representing signal and noise respectively1(t) and s2(t) are the signals collected by the two sensors respectively;is s1(t) and s2(t), max represents taking the maximum value,andrespectively represents s1(t) and s2(t) an autocorrelation function value at a time when the time delay τ is 0;
the weight determining unit is used for determining L the weight of the MS filter according to the following criteria:
when the signal-to-noise ratio is greater than 10dB or the correlation coefficient is greater than 0.8, selecting a single L MS filter;
when-10 dB < signal-to-noise ratio <10dB or 0.5< correlation coefficient <0.8, select a double L MS filter;
when the signal-to-noise ratio is < -10dB or the correlation coefficient is less than 0.5, multiple L MS filters are selected, the multiple is three or more, and signal smoothing processing is required between each two filters.
2. The adaptive-filter-based pipe leakage locator of claim 1, wherein the sensor is a non-invasive acceleration sensor or a vibration sensor mounted on the outer wall surface of the pipe.
3. The adaptive-filter-based pipe leak locator of claim 1, wherein the sensor is an invasive hydrophone or a pressure transducer mounted inside the pipe.
4. The adaptive-filter-based pipe leakage positioning device according to claim 2 or 3, wherein a preamplifier is arranged between each sensor and the signal acquisition card, and the preamplifier is a metal pipe preamplifier with amplification factor between 10-20 dB.
5. The adaptive-filter-based pipe leakage positioning device according to claim 2 or 3, wherein a preamplifier is arranged between each sensor and the signal acquisition card, and the preamplifier is a plastic pipe preamplifier with amplification factor of 20-40 dB.
6. The adaptive-filter-based pipeline leakage positioning device according to claim 1, wherein a low-pass digital filter is arranged between the signal acquisition card and the L MS filter for filtering high-frequency electromagnetic and mechanical noise included in the signal.
7. The adaptive-filter-based pipe leakage locator of claim 1, wherein the single L MS filters include a first L MS adaptive filter and a second L MS adaptive filter;
by s1(t) as input signal, s2(t) as the desired response, input to a first L MS adaptive filter, output a filter coefficient vector h1(t); by s2(t) as input signal, s1(t) as the desired response, input to a second L MS adaptive filter, then output a filter coefficient vector h2(t);
Find h1(t) and h2(t) maximum value max [ h ]1(t)]And max [ h ]2(t)]Corresponding time delay, i.e.Andthe first L MS filter calculated time delay τ1The following were used:
the time delay τ is τ1。
8. The adaptive-filter-based pipe leakage locator of claim 1, wherein the dual L MS filters include a first heavy L MS filter and a second heavy L MS filter, the first heavy L MS filter includes a first L MS adaptive filter and a second L MS adaptive filter, the second heavy L MS filter includes a third L MS adaptive filter and a fourth L MS adaptive filter;
in the first L MS filter, s1(t) as input signal, s2(t) as the desired response, input to a first L MS adaptive filter, output a filter coefficient vector h1(t); by s2(t) as input signal, s1(t) as the desired response, input to a second L MS adaptive filter, then output a filter coefficient vector h2(t);
In the second pass L MS Filter, the sum of h1(t) as input signal, h2(t) as the desired response, inputs to a third L MS adaptive filter, outputs a filter coefficient vector h3(t); by h2(t) as input signal, h1(t) as the desired response, the signal is input to a fourth L MS adaptive filter, and a filter coefficient vector h is output4(t); find h3(t) and h4(t) maximum value max [ h ]3(t)]And max [ h ]4(t)]Corresponding time delayAndthe second L MS filter calculated time delay τ2The following were used:
the time delay τ is τ2。
9. The adaptive-filter-based pipe leakage locator of claim 1, wherein the multiple L MS filters include n singleplex L MS filters in series with the output of the previous singleplex L MS filter as the input to the next singleplex L MS filter, the singleplex L MS filter includes 2L MS adaptive filters;
in the first single L MS filter, s1(t) as input signal, s2(t) as the desired response, input to a first L MS adaptive filter, output a filter coefficient vector h1(t); by s2(t) as input signal, s1(t) as the desired response, input to a second L MS adaptive filter, then output a filter coefficient vector h2(t);
In the second single L MS filter, the sum of h1(t) as input signal, h2(t) as the desired response, inputs to a third L MS adaptive filter, outputs a filter coefficient vector h3(t); by h2(t) as input signal, h1(t) as the desired response, input to a fourth L MS adaptive filter, then output the filter coefficient vector h4(t);
In the nth simplex L MS filter, the sum of h2n-3(t) as input signal, h2n-2(t) as a desired response, the signal is input to a (2n-1) th L MS adaptive filter, and a filter coefficient vector h is output2n-1(t); by h2n-2(t) as input signal, h2n-3(t) as the desired response, input to the 2n L MS adaptive filter, then the filter coefficient vector h is output2n(t);
h2n-1(t) and h2n(t) has time on the abscissa and amplitude on the ordinate, and the times corresponding to the maximum amplitudes are respectivelyAndthe time delay tau of the multiple L MS filtersnThe calculation is as follows:
the time delay τ is τn。
10. The adaptive-filter-based pipe leakage locator according to any one of claims 7-9, wherein the leakage locator module is implemented by:
leakage source location is calculated based on the time delay of the L MS filter output:
wherein c is the propagation speed of sound waves in the pipeline, d1The distance of the leakage source from one sensor; the calculation formula of the sound velocity c is as follows:
wherein, cfThe propagation speed of sound wave in free field, B is the bulk modulus of water, E is the Young's modulus of pipe wall, a is the pipe radius, and h is the pipe wall thickness.
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