CN206130547U - Gas transmission pipeline leak testing system under multiplex condition - Google Patents
Gas transmission pipeline leak testing system under multiplex condition Download PDFInfo
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- CN206130547U CN206130547U CN201620709981.1U CN201620709981U CN206130547U CN 206130547 U CN206130547 U CN 206130547U CN 201620709981 U CN201620709981 U CN 201620709981U CN 206130547 U CN206130547 U CN 206130547U
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Abstract
The utility model provides a gas transmission pipeline leak testing system under multiplex condition (being called for short this system), this system includes: the module is obtained to input module, gas transmission pipeline, gas transmission pipeline transmission mechanism model, neural network compensation model, pipe -line system signal acquisition module, correction output processing module and error, the working process of this system including the simplification mathematic model that establishs gas transmission pipeline, reach the gas transmission pipeline state space equation, the traffic signal in handling the gas transmission pipeline state space equation, establish the accuracy of detection model under RBF neural network and test and the verification different work condition. Change through the terminal load of research gas transmission pipeline, pipe diameter, pipeline bending and ambient temperature, gaseous wave speed, gas compressibility factor, pipeline flow resistance coefficient etc to train pipe model under the different work condition, the accurate model that adaptation pipeline normal condition changes is acquireed simultaneously to the adaptability that detects system under many states.
Description
Technical field
This utility model is related to the gas pipeline leak detection system under a kind of multi-state, belongs to and automatically controls and leak inspection
Survey technology and gas pipe leakage detection field.
Background technology
Through the development of decades, domestic and international research worker proposes pipelines Leak Detection and localization method and applies
In engineering reality.Hardware based method is let out using the sensor of the various different mechanism carried or on pipeline to detect
Leak and positioned, the method is the method for the early stage main leakage detection and localization for adopting.At present, it is soft, hard based on software
What part combined is widely paid close attention to based on monitoring control with the leakage detection and localization technology of data acquisition, and is increasingly becoming
The main flow of Discussion on Pipe Leakage Detection Technology.
It is by the measurement of flow and pressure, quality and volume conservation, pipeline stream in pipeline based on the detection method of software
The principles such as dynamic kinetic model realize Leak Detection by computer programming.Method based on software can be divided into based at signal
The method of reason, Knowledge based engineering method and the method based on pipeline mathematical model.Based on the method for signal processing have negative pressure wave method,
Mass/volume counterbalanced procedure, pressure spot analytic process, acoustic wave detection etc.；Knowledge based engineering method have based on the method for specialist system,
Based on the method for pattern recognition, the method based on neutral net；Pipeline leakage detection and location method based on mathematical model can
It is divided into transient model method, filter method, identification method etc..
Application No. 201210563120.3, entitled " a kind of pipeline gas leak detecting device "；Application No.
200920293127.1, entitled " a kind of pressure pipeline leakage testing device "；Application No. 200620127803.4, it is entitled
" a kind of underground pipeline leak detection means "；Application No. 200810104233.0, a kind of entitled " pipeline leakage testing system
System "；Application No. 201010002941.0, entitled " a kind of gas pipe leakage detection device "；Application number
201220078512.6, entitled " for leak source detection alignment system of gas pipeline " etc., above-mentioned these patents all stress
In design using various kinds of sensors and the device of instrument detection leakage, belong to hardware based Discussion on Pipe Leakage Detection Technology.Hardware
Detection technique has the advantages that to detect that accurate, sensitivity is high, and can determine the size of leak position and leakage rate, but firmly
Part detection technique has obvious shortcoming, this is because hardware detection needs to arrange that the hardware such as substantial amounts of sensor set on pipeline
Standby, cost of installation and maintenance is very huge, and will be bigger for the complexity of the detection hardware detection of buried pipeline, and current one
As not separately as pipe detection means, be generally mated software and use.
Application No. 201310169679.2, entitled " the gas pipeline leak detecting device based on sound wave signals and inspection
The patent of survey method ", proposes to adopt sound wave sensor acquisition fluids within pipes dynamic pressure signal, and to sound wave signals feature is carried out
The method for extracting and carrying out to leak judgement.But the dynamic pressure signal that sound wave sensor acquisition is arrived is fainter, easily by extraneous ring
Border is disturbed, unsuitable teletransmission.
Application No. 201310523173.7, the patent of entitled " a kind of pipe leakage experimental provision and experimental technique ",
Propose using instruments such as thermometer, volume flowmeter and pressure gauges, by comparing fluid steady state leakage rate calculations value and measurement
Fluid steady state leakage rate correction model is worth to, fluid leakage feature and rule under different operating modes is studied, is pipe-line maintenance
Foundation is provided with Leak Detection.
Application No. 200610172271.0, entitled " detection method based on the pipe leakage of artificial neural network "
Patent, it is proposed that carry out Leak Detection using neutral net, using the stronger adaptability of neural network and predictive ability, but lacks
Weary physical basis, to the data beyond training sample, prediction effect is not good, sometimes even with actual industrial process contradiction.
Application No. 201010004704.8, entitled " gas pipeline leakage detecting and positioning device and its detection positioning side
The patent of method ", proposes to set up the transient state mathematical model of the interior gas flowing of pipe and solved using the method for characteristic curves, using in model
Pressure, flow rate calculation value and pressure, flow transducer measured value error come judge leakage, because mechanism model is in solution procedure
In need to carry out some and simplify and approximate, therefore error will necessarily be brought.
In sum, above is referred to gas pipe leakage detection methods and techniques be mostly by pressure, flow, temperature,
The various kinds of sensors such as sound wave detection signal simultaneously carries out the apparatus and method that leakage information is extracted in signature analysis, various leakage inspections
Survey method respectively has pluses and minuses, and a kind of single leakage detection method is difficult to reach good effect in each performance indications, such as
Fruit is organically combined various methods, is learnt from other's strong points to offset one's weaknesses, and will can improve the performance of leakage detection and localization.The application is based on god
The method of Jing networks and combined based on the method for pipeline mathematical model, solve the problems, such as following two aspects：On the one hand, this Shen
Please pressure signal is gathered only with high-precision pressure sensor, reduce equipment initial investment, it is cost-effective；On the other hand, will have
There is the modelling of preferable physical basis in combination with stronger adaptability and predictive ability neutral net, improve gas pipeline
Leak Detection precision.
The application is devoted to " method based on gas pipeline flow mathematical model " together " Knowledge based engineering detection method "
Combine, have complementary advantages, research gas pipeline is in end load change, caliber changes, pipeline bends and environment
Detection model is suitable under the various states of Parameters variation such as temperature, gas velocity of wave, gas compressibility factor, the pipeline hydraulic coefficient of friction resistance
Ying Xing, the monitoring and Leak Detection for gas pipeline proposes a kind of gas pipeline modeling and leakage detection method.
The content of the invention
The application aim to overcome that hardware based gas pipeline leak detection technology high cost, operation maintenance it is difficult with
And based on traditional gas pipeline transporting mechanism Model suitability is poor, the present situation that precision is low, propose the gas transmission under a kind of multi-state
Pipeline leakage checking system.
The application proposes the gas pipeline leak detection system under a kind of multi-state, and (abbreviation the system) is specifically included：It is defeated
Enter module, gas pipeline, gas pipeline transporting mechanism model, neutral net compensation model, tubing signal acquisition module, repair
Positive output processing module and error acquisition module；
Wherein, described input module includes real system input, gas pipeline transporting mechanism mode input and nerve net
Network compensation model is input into；
Wherein, system input, gas pipeline transporting mechanism mode input and neutral net compensation model input three can be with
It is identical, it is also possible to different；Real system input is the initial condition of pipeline and the parameters of boundary condition and gas pipeline；
Wherein, described gas pipeline transporting mechanism model (follow-up referred to as " mechanism model "), it is set up process and is：To gas
The equation of continuity and the equation of motion that body is transmitted in gas pipeline is derived and simplified, and sets up gas pipeline stable state and dynamic
Mathematical model, and the mathematical model to gas pipeline non-linear partial differential form solves, and sets up gas pipeline state space
Equation, and flow signal in model is processed；
Wherein, described neutral net compensation model (follow-up referred to as " neutral net "), it is set up process and is：Due to RBF
(Radial Basis Function, RBF) existing biological context of neutral net can approach non-linear letter with arbitrary accuracy again
Number, as long as and center point selection is appropriate, it is only necessary to and little neuron is achieved with good Approximation effect, also with unique
The advantage of best approximate point, the application choose RBF neural, determine network topology structure, network inputs vector sum target to
Amount, sets up neural network model compensation；And network training and test are carried out under the different operating modes when load changes, is compensated defeated
Feed channel transporting mechanism model is because various states change brought error；
Wherein, described tubing signal acquisition module is referred to using the high accuracy on pipeline each node along the line
Pressure transducer, is acquired to each node pressure signal in gas pipeline transmission direction, that is, obtain pressure in the system
Signal measured value；
Wherein, described amendment output processing module is referred to the calculating output valve of gas pipeline transporting mechanism model and god
The output of Jing network building out models is sued for peace：Wherein, mechanism model is master cast, and neutral net is compensation model, for mending
The error of gas pipeline transporting mechanism model presence is repaid, master cast and compensation model are combined, and set up the mixed model of gas pipeline,
Gas pipeline running status can preferably be monitored and the generation for leaking is judged, so as to effectively improve accuracy of detection；
Wherein, described error acquisition module calculates each node pressure sensor measured value of gas pipeline and mechanism model meter
Calculate the error between output valve, output vector of the error as neural metwork training；Error acquisition module also calculates pressure letter
Error after number measured value and compensation between the mixed model output valve of gas pipeline, the error sum of squares is minimum as network instruction
Experienced desired value, the value is close to 0 or the smaller the better；
A kind of annexation of each module of gas pipeline leak detection system under multi-state is as follows：
Input module and gas pipeline transporting mechanism model, neutral net compensation model and tubing signal acquisition module
It is connected, corrects output processing module and gas pipeline transporting mechanism model, neutral net compensation model, pipe signal acquisition module
It is connected with error acquisition module, error acquisition module is connected with pipe signal acquisition module and amendment output processing module.
The course of work of the system carries out gas pipeline and lets out based on the gas pipeline leak detection system under a kind of multi-state
Missing inspection and compensation, comprise the following steps that：
Step one, former flow field can be destroyed and affect measuring accuracy in view of installing effusion meter, can also build-up of pressure loss,
When building the gas pipeline leak detection system under a kind of multi-state, conventional pipe is replaced using the higher pressure transducer of precision
Effusion meter in road leak detection system, the pressure signal on unified each node of collection gas pipeline；
Pressure value on step 2, each node of initial time gas pipeline for collecting step one as initial condition,
The pressure value that gas pipeline first and last side pressure force transducer was collected at each moment is used as boundary condition, initial condition and perimeter strip
The parameters of part and pipeline are used as input condition known to the system；
Step 3, gas pipeline transmission is set up based on gas pipeline transmission equation of continuity, the equation of motion and state equation
Mechanism model, comprises the following steps that：
Step 3.1 is derived and simplified and processes the equation of continuity and the equation of motion of gas pipeline transporting mechanism model, and is tied
The equation of gas state is closed, the simplified mathematical model of the dynamic partial differential equation form of gas pipeline is set up；
Wherein, described equation of continuity is：
Wherein, the described equation of motion is：
Wherein, p --- gas pressure in gas pipeline, Pa；
qm--- gas pipeline mass flow, kg/s；
T --- time variable, s；
X --- along the length variable of gas pipeline, m；
A --- gas pipeline cross-sectional area, m2；
A --- gas velocity of wave, m/s；
G --- acceleration of gravity, m/s2；
θ --- angle between gas pipeline axis direction and horizontal plane, rad；
λ --- gas pipeline hydraulic simulation experiment, dimensionless；
D --- gas pipeline internal diameter, m；
Step 3.2 is solved to the simplified mathematical model that step 3.1 is set up, specially：Based on center implicit difference method
Differencing is carried out to gas pipeline dynamical equation, gas pipeline state space equation is drawn；
Wherein, described gas pipeline state space equation is：
X (j)=[p in formula1, j... pN, j, qM1, j... qMn, j]T,For constant coefficient matrix；
With the function of the system state vector；It is the item relevant with boundary condition, it is assumed herein that it is known that head end side
Boundary's condition X0；
Flow signal is using gas flowing formula in the gas pipeline state space equation that step 3.3 is obtained to step 3.2
Calculating method, 2 pressure differential methods and approximate model method are processed；
Step 4, neutral net compensation model is set up, and is compensated because the error brought to mechanism model of approximate and simplification,
Comprise the following steps that：
Step 4.1 compares the pluses and minuses of various artificial neural networks and selects RBF neural to set up gas pipeline
Neutral net compensation model；
Step 4.2 sets up the neutral net compensation model of gas pipeline, its concrete structure on the basis of step 4.1：Specifically
Using three layers of RBF neural containing input layer, hidden layer and output layer, and determine the input vector of neutral net compensation model
For the calculation of pressure value of n node on j moment gas pipelines：P i.e. in step 3.21, j... pN, j, output vector is the j+1 moment
Pressure divergence on gas pipeline on each node between actual measured value and mechanism model value of calculation, hidden layer adopts gaussian kernel letter
Number is used as RBF；
Step 4.3 in order that the training and study of neutral net compensation model are more prone to, to the god determined in step 4.2
The input vector and output vector of Jing network building out models carries out data normalization process, is transformed to [- 1,1] or [0,1]
In the range of, difficulty when RBF neural is trained is mitigated with this, and avoid because inputoutput data order of magnitude difference
It is larger and cause neural network forecast error larger；
Step 4.4 is further designed on the basis of step 4.2 and 4.3 to RBF neural, is embodied in：
RBF neural is trained and is tested under the various different operating modes that the end gas consumption of gas pipeline changes；
Specifically .m file routines are write using MATLAB development environments, to the appendix under a kind of multi-state of the invention
Road leak detection system is implemented and experimental verification, verifies the accuracy of this detecting system under different operating modes, and right
The pressure data of abnormal conditions is tested, and analyzes basis for estimation when there is leakage in gas pipeline.
The course of work of the system is completed through aforementioned four step.
Beneficial effect
The utility model proposes a kind of multi-state under gas pipeline leak detection system, have the advantages that：
1. the gas pipeline leak detection system under a kind of multi-state of the present utility model, sets up suitable only with pressure signal
The gas pipeline leak detection system for answering multimode to change, therefore only need that high-precision pressure transducer collection pressure signal is installed i.e.
Can, further save initial investment and operation maintenance cost；
2. the gas pipeline leak detection system under multi-state of the present utility model, by gas pipeline equation of continuity
Theory analysis is carried out with the equation of motion, a pair of nonlinear partial differential equations are obtained, using center implicit difference method to the simplification mould
Type carries out numerical solution, establishes gas pipeline No leakage state space equation, can calculate pipeline based on this equation upper each along the line
The pressure at node all moment, for Leak Detection reference frame is provided, and can in time be found and is accurately positioned leak position, estimates
Meter leakage rate is simultaneously reported to the police, so as to more efficiently monitor gas pipeline operation conditions；
3. the gas pipeline leak detection system under a kind of multi-state of the present utility model, by determining pipeline in No leakage
When network topology structure, and network inputs vector sum object vector, using many in neutral net compensation pipeline mechanism model
The change of the state of kind, and network is trained and is tested under the various working that end load changes, establish gas
Pipeline RBF neural compensation model, can effective compensation mechanism model exist error；
4. the course of work of the system that this utility model is carried, adopts mechanism model and neutral net in gas pipeline
Combine, and mixed model is set up using MATLAB environment and implemented and theoretical simulation, demonstrate proposed by the invention
System be suitable for the change of pipeline various states and load, with higher precision, can accurate measurements gas pipeline operation
State, and can judge rapidly when pipeline is leaked, so as to realize efficient gas pipeline leakage positioning and detection.
Description of the drawings
Fig. 1 is the composition schematic diagram of the gas pipeline leak detection system under a kind of multi-state of this utility model；
Fig. 2 is the gas pipeline in the embodiment of the gas pipeline leak detection system under a kind of multi-state of this utility model
RBF neural network structure figure；
Fig. 3 is experimental channel pressure in the gas pipeline leak detection system embodiment under a kind of multi-state of this utility model
Sampled point and simulated leakage position schematic diagram；
Fig. 4 be operating mode 2 in the gas pipeline leak detection system embodiment under a kind of multi-state of this utility model each
The result figure contrasted between mixed model output valve, mechanism model value of calculation and measured value during node test RBF neural.
Specific embodiment
This utility model is described further and is described in detail with reference to the accompanying drawings and examples：
Fig. 1 is the composition schematic diagram of the gas pipeline leak detection system under a kind of multi-state of this utility model；Fig. 2 is this
RBF neural compensation model structure chart during the gas pipeline No leakage that invention is proposed, from Figure 2 it can be seen that the RBF neural is adopted
It is respectively input layer, hidden layer and output layer with Three Tiered Network Architecture, wherein network model's input vector is n on j moment pipelines
The calculation of pressure value of individual node, output vector is actual measured value on each node on j+1 moment pipelines and mechanism model value of calculation
Between pressure divergence, hidden layer using gaussian kernel function as RBF.
The utility model proposes a kind of multi-state under gas pipeline leak detection system in, mechanism model is by gas
What the equation of continuity and the equation of motion that body is transmitted in gas pipeline was set up, be master cast, plays main effect；RBF
Neutral net is used as model of error estimate, the angle, flow resistance system to temperature, caliber, pipe bending, pipeline and horizontal direction
The dynamic change of the various states parameter such as number, gas compressibility factor is compensated to the error that mechanism model brings, and is to improve mixed
Close model accuracy and play fine setting, and pipeline model under different operating modes is trained, acquisition is adapted to the normal work of pipeline
The accurate model of condition change.
Embodiment
The gas pipeline in gas pipeline leak detection system under a kind of multi-state of the present embodiment is internal diameter 10mm, length
The steel pipe of degree 75m, wherein source of the gas are air compressor, can produce the compressed gas that pressure limit is 0～0.7Mpa (gauge pressure),
High-precision pressure sensor collection pressure signal is installed in many places on gas pipeline, and it is big to simulate internal diameter along pipeline diverse location
Little different leak, gas pipeline end is followed by noise reduction by installing throttle valve adjustment flow simulation difference operating mode, choke valve
Device leads to air.Gas pipeline leak detection system under a kind of multi-state of the present embodiment simulates altogether five kinds of operating modes, end
Flow is 343.3,347.5,355.1,368.4,372.3, and unit is g/min (gram/minute), respectively operating mode 1, operating mode 2, work
Condition 3, operating mode 4 and operating mode 5.When setting up RBF neural, used as the data in training algorithm using the data of operating mode 1,3,5
In Training RBF Neural Network, using operating mode 2 and the test network state of operating mode 4.Specific pressure acquisition position and simulated leakage institute
It is as shown in Figure 3 in position.
Test RBF neural mixed model output valve of operating mode 2 (correction value), mechanism model output valve (value of calculation) and pressure
Comparing result between force transducer observed pressure data (measured value) on each force samples point is as shown in Figure 4.1st section
Point is head end boundary condition, shows the 2nd node to the 7th node pressure data in Fig. 4.
As can be seen from Figure 4 except on the 2nd point of gas pipeline indivedual sampled point mixed model error ratio mechanism models miss
Difference is slightly bigger outer, and mixed model error will be less than mechanism model error on all sampled points on other each aspects, and explanation is built
Vertical compensation model serves good adjustment effect.(except head end) mechanism model error on each force samples point on pipeline
(Error of Mechanism model, abbreviation EM) and mixed model error (Error of Hybrid model, abbreviation EH)
It is as shown in the table for the position (i) of maximum and minima and corresponding sampled point (moment), and unit is Pa.Can be with from table 1
Find out, mechanism model calculation of pressure value has between actual measured value certain error in node 3, on 4,5,6, and mixes
Error very little between modal pressure predictive value and measured value, even less than pressure transducer measurement error (are pressed in experimental system
Force transducer maximum error of measuring is in 1220Pa or so), precision of prediction is very high.
The mechanism model of 1 operating mode of table 2 and mixed model error are contrasted
Embodiment described above is the preferable of the gas pipeline leak detection system under a kind of multi-state of this utility model
Embodiment, this utility model should not be limited to the embodiment and accompanying drawing disclosure of that.It is every without departing from this practicality
The equivalent or modification completed under new disclosed spirit, both falls within the scope of this utility model protection.
Claims (1)
1. the gas pipeline leak detection system under a kind of multi-state, it is characterised in that：Including：It is input module, gas pipeline, defeated
Feed channel transporting mechanism model, neutral net compensation model, tubing signal acquisition module, amendment output processing module and mistake
Difference acquisition module；
Wherein, input module includes real system input, gas pipeline transporting mechanism mode input and neutral net compensation model
Input；Real system input is the initial condition of pipeline and the parameters of boundary condition and gas pipeline；
Described tubing signal acquisition module is referred to using the high-precision pressure sensing on pipeline each node along the line
Device, is acquired to each node pressure signal in gas pipeline transmission direction；
Described amendment output processing module is referred to mends the calculating output valve of gas pipeline transporting mechanism model and neutral net
The output for repaying model is sued for peace：
Wherein, gas pipeline transporting mechanism model is master cast, and neutral net compensation model is compensation model, master cast and compensation
Models coupling, sets up the mixed model of gas pipeline；
Wherein, described error acquisition module calculates each node pressure sensor measured value of gas pipeline and gas pipeline conveyer
Reason model calculates the error between output valve, output vector of the error as neutral net compensation model；
The annexation of each module is as follows：
Input module and gas pipeline transporting mechanism model, neutral net compensation model and tubing signal acquisition module phase
Even, amendment output processing module and gas pipeline transporting mechanism model, neutral net compensation model, pipe signal acquisition module and
Error acquisition module is connected, and error acquisition module is connected with pipe signal acquisition module and amendment output processing module.
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108051035A (en) * | 2017-10-24 | 2018-05-18 | 清华大学 | The pipe network model recognition methods of neural network model based on gating cycle unit |
| CN108591836A (en) * | 2018-04-13 | 2018-09-28 | 中国石油大学(北京) | The detection method and device of pipe leakage |
| CN108930915A (en) * | 2018-08-01 | 2018-12-04 | 北京中彤节能技术有限公司 | A kind of pipe leakage recognition methods based on Qualitative Mapping, apparatus and system |
| CN109538944A (en) * | 2018-12-03 | 2019-03-29 | 北京无线电计量测试研究所 | A kind of pipeline leakage detection method |
| CN113722973A (en) * | 2020-05-25 | 2021-11-30 | 中国石油化工股份有限公司 | Correction system and correction method of computer simulation model |
| CN113806999A (en) * | 2020-06-17 | 2021-12-17 | 中国石油天然气股份有限公司 | Method and device for determining water dew point index value of gas pipeline |
| CN117869808A (en) * | 2024-03-13 | 2024-04-12 | 南京工业大学 | Pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering |
| CN117869808B (en) * | 2024-03-13 | 2024-05-24 | 南京工业大学 | Pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering |
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- 2016-07-07 CN CN201620709981.1U patent/CN206130547U/en not_active Expired - Fee Related
Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108051035A (en) * | 2017-10-24 | 2018-05-18 | 清华大学 | The pipe network model recognition methods of neural network model based on gating cycle unit |
| CN108591836A (en) * | 2018-04-13 | 2018-09-28 | 中国石油大学(北京) | The detection method and device of pipe leakage |
| CN108591836B (en) * | 2018-04-13 | 2020-06-26 | 中国石油大学(北京) | Method and device for detecting pipeline leakage |
| CN108930915A (en) * | 2018-08-01 | 2018-12-04 | 北京中彤节能技术有限公司 | A kind of pipe leakage recognition methods based on Qualitative Mapping, apparatus and system |
| CN109538944A (en) * | 2018-12-03 | 2019-03-29 | 北京无线电计量测试研究所 | A kind of pipeline leakage detection method |
| CN109538944B (en) * | 2018-12-03 | 2020-07-07 | 北京无线电计量测试研究所 | Pipeline leakage detection method |
| CN113722973A (en) * | 2020-05-25 | 2021-11-30 | 中国石油化工股份有限公司 | Correction system and correction method of computer simulation model |
| CN113806999A (en) * | 2020-06-17 | 2021-12-17 | 中国石油天然气股份有限公司 | Method and device for determining water dew point index value of gas pipeline |
| CN113806999B (en) * | 2020-06-17 | 2022-11-01 | 中国石油天然气股份有限公司 | Method and device for determining water dew point index value of gas pipeline |
| CN117869808A (en) * | 2024-03-13 | 2024-04-12 | 南京工业大学 | Pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering |
| CN117869808B (en) * | 2024-03-13 | 2024-05-24 | 南京工业大学 | Pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering |
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