CN117869808B - Pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering - Google Patents
Pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering Download PDFInfo
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Abstract
The invention discloses a pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering, which comprises the following steps: step 1, constructing a dynamic mathematical model of a gas pipeline based on theoretical modeling of the gas pipeline; step 2, designing an orthogonal projection optimal recursive filter aiming at a dynamic mathematical model of the gas pipeline; and 3, detecting and positioning the leakage point of the gas pipeline by taking the orthogonal projection optimal recursive filter as a state estimator. The invention not only has robustness to modeling errors and other uncertainties, but also can rapidly track the state of the system, thereby obtaining more accurate leakage positioning, and detecting leakage information more rapidly.
Description
Technical Field
The invention belongs to the technical field of pipeline leakage detection, and particularly relates to a pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering.
Background
Natural gas is an important component of energy systems in countries around the world, and at present, transportation of natural gas from production to consumption is mainly accomplished through large pipeline networks. However, the problem of pipe leakage has long plagued the industry. The leakage of the pipeline not only brings about great economic loss, but also causes serious environmental pollution. Therefore, from the viewpoints of economy and safety, it is important to accurately detect and locate the pipeline leakage point in time.
In recent years, the volumetric balance method is the simplest and most straightforward leak detection technique that requires only a flow meter and then detects leaks according to the principle of mass conservation. However, this method is only suitable for detection of large leakage points and cannot be used for positioning leakage points. The leak detection and localization method using the acoustic principle has the characteristics of simplicity and high accuracy, but cannot be used for small and slowly varying leak detection. In addition, remote field detection, magnetic line leakage detection, ultrasonic detection and the like have the defects of high manufacturing cost, expensive damage to the pipeline and the like, and larger error.
Disclosure of Invention
The invention aims to solve the technical problems of the prior art, and provides a pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering, which is used for detecting and positioning the pipeline leakage point, wherein the orthogonal projection optimal recursive filter is more effective than an extended Kalman filter when a system model has large modeling error and noise, can position the leakage point more accurately and more quickly, and is very beneficial to long pipeline maintenance.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
the pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering comprises the following steps:
step 1, constructing a dynamic mathematical model of a gas pipeline based on theoretical modeling of the gas pipeline;
Step 2, designing an orthogonal projection optimal recursive filter aiming at a dynamic mathematical model of the gas pipeline;
And 3, detecting and positioning the leakage point of the gas pipeline by taking the orthogonal projection optimal recursive filter as a state estimator.
In order to optimize the technical scheme, the specific measures adopted further comprise:
The dynamic mathematical model of the gas pipeline built in the step1 is as follows:
wherein p is pressure, q is mass flow, x is length, t is time, c is isothermal sound velocity in the gas, A is cross-sectional area of the pipe, D is diameter of the pipe, and λ is coefficient of friction;
the boundary conditions of the dynamic mathematical model of the gas pipeline are as follows:
Wherein L is the length of the pipeline, p (0, t) is the pressure at the beginning t of the pipeline, and is expressed by an expression f p (t); q (L, t) is the mass flow at the point of the pipe termination t, expressed by the expression f q (t).
The initial conditions of the dynamic mathematical model of the gas pipeline are as follows:
Where p (x, 0) is the pressure at which the pipe length is x at the initial time, expressed by expression p 0 (x); q (x, 0) is the mass flow at the initial time at which the pipe length is x, and is expressed by expression q 0 (x).
The design process of the orthogonal projection optimal recursive filter in the step 2 is as follows:
Consider the following discrete nonlinear system:
wherein, the state x ε R n, the input u ε R p, the output y ε R m, the nonlinear function f R n×Rp→Rn, and h R n→Rm has a continuous partial derivative of x, the pressure noise v (i) ε R q is Gaussian white noise with variance Q (i) and zero mean, the measurement noise e (i) ε R m is Gaussian white noise with variance R (i) and zero mean, Γ (i) is a known matrix with proper dimensions, v (i) and e (i) are statistically independent;
The initial state x (0) is a random vector of gaussian distribution, and satisfies statistical characteristics:
Ex(0)＝x0
E[x(0)-x0][x(0)-x0]T＝P0
and having x (0) and v (i), e (i) being statistically independent, T representing the transpose;
the design of the orthogonal projection optimal recursive filter is as follows:
wherein i, i+1 are time variables, State estimation value at time i+1,/>K (i+1) is a filter gain matrix to be designed, gamma (i+1) is innovation in a filtering algorithm,For the system state estimation equation, u (i) is the system control input,/>The state estimation value at the moment i;
In the case of the filter,
K(i+1)＝P(i+1|i)HT(i+1)[H(i+1)P(i+1|i)HT(i+1)+R(i)]-1
P(i+1|i)＝μ(i+1)F(i)P(i|i)FT(i)+Γ(i)Q(i)ΓT(i)
P(i+1|i+1)＝[I-K(i+1)H(i+1)]P(i+1|i)
μ(i+1)＝diag[λ1λ2…λn]
N(i+1)＝V0(i+1)-βR(i+1)-H(i+1)Γ(i)Q(i)ΓT(i)HT(i+1)
M(i+1)＝F(i)P(i|i)FT(i)HT(i+1)H(i+1)＝(Mjl)
Where f (u (i), x (i)) is a system state equation, h (x (i+1)) is a system measurement equation, x (i), x (i+1) is a state of the system i, i+1, Q (i) is a variance of system noise, R (i) is a variance of system measurement noise, Γ (i) is a system noise distribution matrix, P (i+ 1|i) is a state one-step prediction error covariance matrix, P (i+1|i+1) is a state estimation error covariance matrix, y (i+1) is a measured value of the i+1, μ (i+1) is an adaptive weighting factor, ρ is a forgetting factor, β is a predetermined weakening factor, α j is greater than or equal to 1, j=1, 2, … n, and is a predetermined coefficient.
And 3, detecting the pipeline leakage and positioning the leakage point by using a partial differential equation processing method and an on-line optimal recursion state estimation idea.
The step 3 for detecting and positioning the leakage point of the gas pipeline comprises the following steps:
The dynamic mathematical model of the gas pipeline in the form of partial differential equation is converted into a normal differential equation by a characteristic line method, and for x is not equal to x k, the following equation exists:
if r is selected to satisfy the condition: the feature line function defined in the (x, t) plane has the following result:
Thus, along the feature line function, the partial differential equation is converted into a normal differential equation, resulting in:
then, the ordinary differential equation is subjected to centralized processing, differential is replaced by differential, and the nonlinear friction term is approximated by second order, so that a finite differential form of the ordinary differential equation is obtained as follows:
wherein, p i,j＝p(xi,tj), X i＝(i-1)Δx,tj =jΔt, Δx and Δt represent the length and time of each lattice point, p 1,j＝fp(tj),qN,j＝fq(tj), respectively, N being the last lattice,/>Is a model leak;
Actual leakage point (q k(j),xk (j)) and model leakage point of gas pipeline The relationship between them is as follows:
The selection state variables are as follows:
discrete nonlinear system equation Can be rewritten into the following form:
g(x(j+1),x(j),u(j))＝0,
y(j)＝Hx(j),
Where u (j) = [ f p(j)fq(j)]T, H is a matrix with elements 0 or 1;
When estimating state variables with an orthogonal projection optimal recursive filter, the matrix F (i) is obtained by the hidden function theorem by the following equation:
The obtained estimated state value is substituted into the expression of (q k(j),xk (j)) to determine the position of the leak.
The invention has the following beneficial effects:
The invention uses the orthogonal projection optimal recursive filter as a fault model in a nonlinear distributed parameter system for representing the gas flow in a leakage pipeline, and introduces a manual leakage state. Thus, more accurate leak location can be obtained, and leak information can be obtained more quickly.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a discretized schematic diagram of a feature line method;
fig. 3 is a simulation result of the present invention:
(a) Model leakage; (b) Estimated leakage value (dashed line represents actual leakage value); (c) Estimated leak location (dashed line indicates actual leak location).
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Although the steps of the present invention are arranged by reference numerals, the order of the steps is not limited, and the relative order of the steps may be adjusted unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis. It is to be understood that the term "and/or" as used herein relates to and encompasses any and all possible combinations of one or more of the associated listed items.
For gas pipelines, the timeliness of leakage detection and the accuracy of positioning are of great importance, the former can avoid more economic losses, and the latter can save the time of positioning and repairing leakage points. Especially for long pipes, small relative errors in positioning may actually be thousands of meters, which makes it difficult for an inspector to find a true leak. In contrast, the invention develops the research of the gas pipeline leakage point detection and positioning method based on the orthogonal projection optimal recursive filtering, and provides the pipeline leakage point detection and positioning method based on the orthogonal projection optimal recursive filtering, and the specific implementation process of the method comprises the following steps:
step 1, constructing a dynamic mathematical model of a gas pipeline based on theoretical modeling of the gas pipeline;
The method comprises the steps of obtaining a dynamic mathematical model in the form of a hyperbolic partial differential equation with nonlinear distribution parameters of a pipeline through theoretical modeling of the gas pipeline, and realizing construction and analysis of the dynamic model of the gas pipeline;
step 2, designing an orthogonal projection optimal recursive filter for the gas pipeline model established in the step;
step 3, detecting and positioning the leakage point of the gas pipeline by using an orthogonal projection optimal recursive filter;
the method comprises the steps of completing detection of pipeline leakage and positioning of leakage points by using a partial differential equation processing method and an on-line optimal recurrence state estimation idea;
and 4, verifying a gas pipeline leakage point detection and positioning algorithm.
In an embodiment, a dynamic mathematical model of a gas pipeline can be obtained by theoretical modeling of the gas pipeline, and the steps of constructing the dynamic mathematical model of the gas pipeline based on the theoretical modeling of the gas pipeline are as follows:
simplified physical assumptions need to be made, such as: the fixed length diameter D, turbulence and isothermal conditions result in a uniform description of the gas dynamics. The one-dimensional isothermal model of the gas conduit is described by the following formula:
Where p Nm -2 is pressure, q kgs -1 is mass flow, xm is length, ts is time, c m s -1 is isothermal sound velocity in gas, A m 2 is cross-sectional area of the pipe, dm is diameter of the pipe, and lambda is friction coefficient.
The pipeline model is a set of hyperbolic partial differential equations with nonlinear distribution parameters, and the boundary conditions can be selected as follows:
Wherein Lm is the length of the pipeline, p (0, t) is the pressure at the beginning t of the pipeline, expressed by expression f p (t); q (L, t) is the mass flow at the point of the pipe termination t, expressed by the expression f q (t).
The initial conditions of the dynamic mathematical model of the gas pipeline are as follows:
Where p (x, 0) is the pressure at which the pipe length is x at the initial time, expressed by expression p 0 (x); q (x, 0) is the mass flow at the initial time at which the pipe length is x, and is expressed by expression q 0 (x).
If leakage q k[kgs-1 occurs at x=x k, the above equation is forStill, it is true. But when x=x k, due to mass conservation, there are:
q(xk-,t)-q(xk+,t)＝qk
Assuming that the momentum loss caused by the leak in the x-direction is negligible, the above equation is still unaffected at x=x k.
Further pressure measurements at discrete points along the pipeline are used to estimate leak size q k and position x k.
This requires the design of a state estimator or filter for the nonlinear distributed parameter system.
In an embodiment, the design steps of the orthogonal projection optimal recursive filter are as follows:
the method for designing the orthogonal projection optimal recursive filter is first given below.
Consider the following discrete-time nonlinear system:
wherein the state x ε R n, the input u ε R p, the output y ε R m, the nonlinear function f R n×Rp→Rn, and h R n→Rm have a continuous partial derivative of x, the pressure noise v (i) ε R q is Gaussian white noise with variance Q (i) and zero mean, the measurement noise e (i) ε R m is Gaussian white noise with variance R (i) and zero mean, Γ (i) is a known matrix with appropriate dimensions, and v (i) and e (i) are statistically independent.
The initial state x (0) is a random vector of gaussian distribution, and satisfies statistical characteristics:
E[x(0)-x0][x(0)-x0]T＝P0,
Ex(0)＝x0,
And having x (0) and v (i), e (i) being statistically independent, T represents the transpose.
In order to overcome the influence of modeling errors and other uncertainties and effectively track abrupt changes of system states, the invention provides an orthogonal projection optimal recursive filter, which is mainly obtained by adding orthogonal projections into original performance indexes of an extended Kalman filter. The time-varying gain matrix K (i+1) needs to satisfy the following two performance indexes:
E[γ(i+1+j)γT(i+1)]＝0,i＝0,1,2,…,j＝1,2,…,
the second index is the requirement of orthogonal projection processing, and the basic idea is to introduce an adaptive weighting factor to correct the covariance matrix of the original state prediction error in the extended kalman filter, so that the filter can still track the actual system under the condition of modeling error and other uncertainties by using the orthogonal projection method and the adaptive weighting factor. If the adaptive weighting factor is not less than 1, the impact of the historical data on the current filtering performance is reduced.
Based on the above work, the invention provides the following orthogonal projection optimal recursive filter:
wherein i, i+1 are time variables, State estimation value at time i+1,/>K (i+1) is a filter gain matrix to be designed, gamma (i+1) is innovation in a filtering algorithm,For the system state estimation equation, u (i) is the system control input,/>The state estimation value at the moment i;
In the case of the filter,
K(i+1)＝P(i+1|i)HT(i+1)[H(i+1)P(i+1|i)HT(i+1)+R(i)]-1
P(i+1|i)＝μ(i+1)F(i)P(i|i)FT(i)+Γ(i)Q(i)ΓT(i)
P(i+1|i+1)＝[I-K(i+1)H(i+1)]P(i+1|i)
μ(i+1)＝diag[λ1λ2…λn]
N(i+1)＝V0(i+1)-βR(i+1)-H(i+1)Γ(i)Q(i)ΓT(i)HT(i+1)
M jj (i+1) is a matrix, M (i+1) =F (i) P (i|i) F T(i)HT (i+1) H (i+1) elements on the diagonal,
M(i+1)＝F(i)P(i|i)FT(i)HT(i+1)H(i+1)＝(Mjl)
Wherein f (u (i), x (i)) is a system state equation, h (x (i+1)) is a system measurement equation, x (i), x (i+1) is a state of the system i, i+1, Q (i) is a variance of system noise, R (i) is a variance of system measurement noise, Γ (i) is a system noise distribution matrix, P (i+ 1|i) is a state one-step prediction error covariance matrix, P (i+1|i+1) is a state estimation error covariance matrix, y (i+1) is a measured value of the i+1, μ (i+1) is an adaptive weighting factor, which is determined according to an orthogonal projection method, in order to reduce the calculation amount, so that the algorithm can be realized online; wherein ρ=0.95 is a forgetting factor, β is not less than 1 is a pre-selected weakening factor, and the state estimation can be smoother by introducing the forgetting factor, and in addition, α j is not less than 1, j=1, 2, … n is a pre-determined coefficient, so that the filtering effects of different data channels can be adjusted in real time.
In an embodiment, the steps of detecting and positioning the leakage point of the gas pipeline by using the orthogonal projection optimal recursive filter are as follows:
In order to be able to estimate the leakage q k and its position x k with an orthogonal projection optimal recursive filter, a finite dimensional system is needed to approximate the distribution parameter system. First, the partial differential equation is converted into the ordinary differential equation by the characteristic line method. For x+.x k, there is the following equation:
if r is selected to satisfy the condition: this is the feature line function defined in the (x, t) plane, with the following consequences:
thus, along the feature line function, the partial differential equation can be converted into a normal differential equation, and then it is possible to obtain:
Then, the ordinary differential equation is centralized, the differential is replaced by a difference, and the nonlinear friction term is approximated by a second order, and as can be seen from fig. 2, the finite difference form of the equation is as follows:
wherein, p i,j＝p(xi,tj), X i＝(i-1)Δx,tj =jΔt (Δx, Δt represent the length and time of each lattice point, respectively, which satisfy the relation/>) P 1,j＝fp(tj),qN,j＝fq(tj) (N is the last lattice),/>Is model leakage (assuming the amount of leakage is constant).
Actual leakage point (q k(j),xk (j)) and model leakage point of gas pipelineThe relationship between them is as follows:
The more accurate the relationship is for smaller faults q k.
To apply a strong tracking filter, the state variables are selected as follows:
discrete nonlinear system equation Can be rewritten into the following form:
g(x(j+1),x(j),u(j))＝0,
y(j)＝Hx(j),
Where u (j) = [ f p(j)fq(j)]T, H is a matrix with elements 0 or 1. We note here that the dimension of the state variable is 3N-4, while g (-) consists of 3N-4 equations.
When estimating state variables with an orthogonal projection optimal recursive filter, the matrix F (i) is obtained by the hidden function theorem by the following equation:
Substitution of the resulting estimated state value into the expression of (q k(j),xk (j)) can determine the location of the leak.
In order that the practice of the invention may be better understood by those skilled in the art, the invention is simulated using Matlab software.
The specific information of the simulation software is as follows:
Software name: MATLAB;
Version information: 9.8.0.1380330 (R2020 a) Update 2;
License number: 919961
Operating system: microsoft Windows 10 Chinese Version 10.0 at home (Build 19042);
Java version: java 1.8.0_202-b08 with Oracle Corporation Java HotSpot (TM) 64-Bit Server VM mixed mode;
A special tool box: STATISTICS AND MACHINE LEARNING Toolbox-11.7 (R2020 a), aircraft Control Toolbox-1.0
The invention uses a pipeline simulator to simulate the noisy gas flow in the pipeline, and the pipeline parameters are as follows: the pipe length l=90 km, the diameter d=0.785 m, the speed of sound in the gas c=300 m/s, the coefficient of friction λ=0.02. Zero-mean white noise is added to the system equation and the measurement equation to simulate a random system. At time t=60 min, a burst leak of 2% (4 kg/s) occurred 50km from the upstream end of the pipe, and the simulation results are shown in fig. 3.
Boundary conditions of the simulation experiment are: Δx=10 km, p (0, t) =100 bar=10 7 Pa, q (L, t) =200 kg/s. The pressure values at 30, 60 and 90km are used as filter measurements.
The parameters for the filter are as follows: Δx=30km,Thus can obtainWhile assuming that the boundary conditions are accurately known. The initial conditions are thatThe process and observed noise covariance matrix is:
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (4)
1. The pipeline leakage point detection and positioning method based on orthogonal projection optimal recursive filtering is characterized by comprising the following steps of:
step 1, constructing a dynamic mathematical model of a gas pipeline based on theoretical modeling of the gas pipeline;
The dynamic mathematical model of the gas pipeline is built as follows:
wherein p is pressure, q is mass flow, x is length, t is time, c is isothermal sound velocity in the gas, A is cross-sectional area of the pipe, D is diameter of the pipe, and λ is coefficient of friction;
Step 2, designing an orthogonal projection optimal recursive filter aiming at a dynamic mathematical model of the gas pipeline;
the design process of the orthogonal projection optimal recursive filter is as follows:
Discrete nonlinear system:
wherein, the state x ε R n, the input u ε R p, the output y ε R m, the nonlinear function f R n×Rp→Rn, and h R n→Rm has a continuous partial derivative of x, the pressure noise v (i) ε R q is Gaussian white noise with variance Q (i) and zero mean, the measurement noise e (i) ε R m is Gaussian white noise with variance R (i) and zero mean, Γ (i) is a known matrix with proper dimensions, v (i) and e (i) are statistically independent;
The initial state x (0) is a random vector of gaussian distribution, and satisfies statistical characteristics:
Ex(0)＝x0；
E[x(0)-x0][x(0)-x0]T＝P0；
and having x (0) and v (i), e (i) being statistically independent, T representing the transpose;
the design of the orthogonal projection optimal recursive filter is as follows:
wherein i, i+1 are time variables, State estimation value at time i+1,/>K (i+1) is a filter gain matrix to be designed, gamma (i+1) is innovation in a filtering algorithm,For the system state estimation equation, u (i) is the system control input,/>The state estimation value at the moment i;
In the case of the filter,
K(i+1)＝P(i+1|i)HT(i+1)[H(i+1)P(i+1|i)HT(i+1)+R(i)]-1；
P(i+1|i)＝μ(i+1)F(i)P(i|i)FT(i)+Γ(i)Q(i)ΓT(i)；
P(i+1|i+1)＝[I-K(i+1)H(i+1)]P(i+1|i)；
μ(i+1)＝diag[λ1λ2…λn]；
N(i+1)＝V0(i+1)-βR(i+1)-H(i+1)Γ(i)Q(i)ΓT(i)HT(i+1)；
M(i+1)＝F(i)P(i|i)FT(i)HT(i+1)H(i+1)＝(Mjl)；
Wherein f (u (i), x (i)) is a system state equation, h (x (i+1)) is a system measurement equation, x (i), x (i+1) is a state of the system at the moment i, i+1, Q (i) is a variance of system noise, R (i) is a variance of system measurement noise, Γ (i) is a system noise distribution matrix, P (i+ 1|i) is a state one-step prediction error covariance matrix, P (i+1|i+1) is a state estimation error covariance matrix, y (i+1) is a measured value at the moment i+1, μ (i+1) is an adaptive weighting factor, ρ is a forgetting factor, β is a predetermined weakening factor, α j is equal to 1, j=1, 2, … n is a predetermined coefficient;
step 3, detecting and positioning a gas pipeline leakage point by taking an orthogonal projection optimal recursive filter as a state estimator;
The steps of detecting and positioning the leakage point of the gas pipeline are as follows:
The dynamic mathematical model of the gas pipeline in the form of partial differential equation is converted into a normal differential equation by a characteristic line method, and for x is not equal to x k, the following equation exists:
if r is selected to satisfy the condition: the feature line function defined in the (x, t) plane has the following result:
Thus, along the feature line function, the partial differential equation is converted into a normal differential equation, resulting in:
then, the ordinary differential equation is subjected to centralized processing, differential is replaced by differential, and the nonlinear friction term is approximated by second order, so that a finite differential form of the ordinary differential equation is obtained as follows:
wherein, p i,j＝p(xi,tj), X i＝(i-1)Δx,tj =jΔt, Δx and Δt represent the length and time of each lattice point, p 1,j＝fp(tj),qN,j＝fq(tj), respectively, N being the last lattice,/>Is a model leak;
Actual leakage point (q k(j),xk (j)) and model leakage point of gas pipeline The relationship between them is as follows:
The selection state variables are as follows:
discrete nonlinear system equation Is rewritten into the following form:
g(x(j+1),x(j),u(j))＝0；
y(j)＝Hx(j)；
Where u (j) = [ f p(j)fq(j)]T, H is a matrix with elements 0 or 1;
When estimating state variables with an orthogonal projection optimal recursive filter, the matrix F (i) is obtained by the hidden function theorem by the following equation:
The obtained estimated state value is substituted into the expression of (q k(j),xk (j)) to determine the position of the leak.
2. The method for detecting and locating a pipeline leakage point based on orthogonal projection optimal recursive filtering according to claim 1, wherein the boundary conditions of the dynamic mathematical model of the gas pipeline are as follows:
Wherein L is the length of the pipeline, p (0, t) is the pressure at the beginning t of the pipeline, and is expressed by an expression f p (t); q (L, t) is the mass flow at the point of the pipe termination t, expressed by the expression f q (t).
3. The method for detecting and locating a pipeline leakage point based on orthogonal projection optimal recursive filtering according to claim 2, wherein the initial condition of the dynamic mathematical model of the gas pipeline is:
Where p (x, 0) is the pressure at which the pipe length is x at the initial time, expressed by expression p 0 (x); q (x, 0) is the mass flow at the initial time at which the pipe length is x, and is expressed by expression q 0 (x).
4. The method for detecting and positioning the pipeline leakage point based on the orthogonal projection optimal recursive filtering according to claim 1, wherein the step 3 is characterized in that the method for detecting and positioning the pipeline leakage point is achieved by using a partial differential equation processing method and an online optimal recursive state estimation method.
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| Application Number | Priority Date | Filing Date | Title |
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