1. A gas pipeline leakage estimation method based on a distributed sensing system is characterized by comprising the following steps: the method specifically comprises the following steps:

step 1, constructing a sensor network topological structure

Measuring the flow, the pressure and the temperature of the gas in the gas pipeline by using the N sensors; constructing a sensor network topological structure according to the signal transmission relation among the N sensors;

step 2, establishing a state space model of the system

Establishing the following state space model according to the sensor network topological structure established in the step 1 and the measured data of the gas pipeline transmission system:

x(k+1)＝Ax(k)+Bν(k)

y_i(k)＝β_i(k)C_ix(k)+D_iν(k)

z(k)＝Hx(k) (1)

wherein the content of the first and second substances,representing the state vector, x, of the pipeline gas at time k₁(k)、x₂(k)、x₃(k) Respectively representing the flow, the pressure and the temperature of the gas in the gas pipeline at the moment k;indicating the measurement output of the i-th sensor, y_i1(k)、y_i2(k) Respectively representing the gas flow and the pressure in the gas pipeline measured by the ith sensor;representing the output signal to be estimated at time k, z₁(k)、z₂(k) Respectively representing the gas flow and the pressure to be estimated at the moment k;is an external disturbance; beta is a_i(k)∈[0,1]A random sequence obeying a random distribution;are all known constant matrices; superscript T represents the transpose of the matrix;a real matrix representing n × m dimensions;

step 3, establishing a distributed estimator model

3.1, establishing the following distributed estimator model according to the system space state model established in the step 2:

wherein the content of the first and second substances,for the estimation vector of x (k) for the estimator node i at time k,respectively representing the estimated values of the gas flow, the pressure and the temperature of the node i at the moment k;representing the output signal to be estimated at node i at time k,respectively representing the gas flow and the pressure to be estimated of a node i at the moment k;representing the estimator gain matrix to be designed, is a collection of gas pipeline sensor nodes,is a set of neighboring nodes that includes node i itself;representing estimator gain variation,. DELTA.L_ij(k)＝δ(k)M_ijDelta (k) is an unknown time-varying scalar quantity which satisfies-1 is more than or equal to delta (k) is more than or equal to 1,is a known matrix; α (k) is a random sequence obeying a random distribution, α₁≤α(k)≤α₂The mathematical expectation of which isVariance ofα₁，α₂，And alpha^*Are all known constants;

step 3.2, define the augmentation vectorAnd outputting the estimated error vectorWhereinObtaining an estimation error augmentation system:

wherein the content of the first and second substances,

Γ(k)＝diag{β₁(k)I,β₂(k)I,…,β_N(k)I}；

wherein the content of the first and second substances,representation matrix I_NThe Kronecker product of A and A; i is_NAn identity matrix having a number of dimensions N × N; i represents an identity matrix; diag {. } represents a diagonal matrix;

step 4, solving distributed estimator gain

And (3) defining a Lyapunov function, analyzing the stability condition and the energy-peak value performance index of the estimation error augmentation system obtained in the step (3.2), and solving by using a linear matrix inequality tool box to obtain a gain matrix of the distributed estimator so as to realize the gas pipeline leakage estimation based on the distributed sensing system.

2. The gas pipeline leakage estimation method based on the distributed sensing system as claimed in claim 1, wherein: step 1, constructing a sensor network topology structure by directed graphsIt is shown that,representing a set of edges;representing the element as c_ijWeighted adjacency matrix of c_ijRepresenting the connection weight between the sensor nodes i and j,[·]_N×_Na matrix made up of N × N elements is represented.

3. The gas pipeline leakage estimation method based on the distributed sensing system as claimed in claim 1 or 2, wherein: when c is going to_ij>0, i.e., (i, j) e epsilon, indicates that a signal is transmitted from sensor node j to sensor node i; if i is j, c is noted_ii1, indicates that the sensor set is self-contained.

4. The gas pipeline leakage estimation method based on the distributed sensing system as claimed in claim 1, wherein: the external disturbance v (k) is additive squared and represents the noise external to the system and the noise disturbance experienced by the sensor during the measurement.

5. The gas pipeline leakage estimation method based on the distributed sensing system as claimed in claim 1, wherein: random sequence beta_i(k) Features of randomness, beta, for describing the measured attenuation of the measured data during transmission_i(k) Has a mean value ofVariance (variance)E {. means to find the mathematical expectation,is a known scalar.

6. The method of claim 1 wherein said step of distributing said data comprises distributing said data based on a predetermined distributionThe gas pipeline leakage estimation method of the formula sensing system is characterized in that: constant alpha₁、α₂、α^*And the sequence delta (k), the matrix M_ijThe value of (a) is obtained from a gas pipeline system modeling method and stochastic analysis.

7. The gas pipeline leakage estimation method based on the distributed sensing system as claimed in claim 1, wherein: the step 4 specifically comprises the following steps:

defining Lyapunov functionsWherein P₁,P₂,…,P_N+1Determining a diagonal matrix for positive determination;

step 4.1, assuming that the perturbation V (k) ═ 0, the mathematical expectation defining the difference E { Δv (k) } { (V (k +1) -V (k) }, calculated as:

matrix arrayWherein

Thus, it is possible to provideWherein:

thus, the following results were obtained:

wherein

And due to delta²(k) 1 or less, to obtain:

and is

Wherein the content of the first and second substances, e_irepresenting a matrix of column blocks corresponding to the ith sensor, e_iThe ith matrix block of the matrix is an identity matrix I, and the rest matrix blocks are all 0;

obtaining the following by the same method:

wherein the content of the first and second substances,

and calculating to obtain:

thus, it is possible to provideWherein the content of the first and second substances,

note the book

When it is satisfied withWhen there isThe number in the formula represents a symmetric item in the symmetric matrix;

and because ofSo E { V (k +1) } -E { V (k) }<0, i.e., there is a scalar ρ satisfying E { V (k +1) } ≦ ρ E { V (k) }, where ρ ∈ (0, 1); obtaining E { V (k) } ≦ rho through a recursion method^kV(0)；

According to the definition of the Lyapunov function, the following results are obtained:

wherein λ_min(. represents a minimum eigenvalue, λ)_max(. h) represents the maximum eigenvalue, | represents the euclidean norm of the vector or matrix; thus, for a given initial condition η (0), there is E { | η (k) |²}≤∈ρ^k‖η(0)‖²Wherein

Therefore, when Λ <0, the estimation error augmentation system is mean square exponential stable;

step 4.2, obtaining any non-zero disturbance v (k) according to the estimation error augmentation system:

and

let ζ (k) be [. eta. ]^T(k),ν^T(k)]^TObtaining:

wherein

For any positive integer k, [ delta ] V (k) [ | v (k) |²＝ζ^T(k) Λ ζ (k); let K equal to K +1, K>0, defining a performance index function

From the zero initial condition η (0) ═ 0, we obtainIs further composed of<0, obtaining J<0, therefore

For a given energy-peak performance index γ, and γ>0, whenIn time, there are:

when K tends to be infinite, it is,wherein sup {. denotes a supremum in mathematics; therefore, the estimation error augmentation system is stable in mean square index and meets the given energy-peak performance index gamma;

and 4.3, utilizing Schur complementary theory to equivalently develop the lambda <0 into:

wherein the content of the first and second substances,superscript-1 represents the inverse of the matrix;

inequality Ψ<0 two-side left-and right-multiplication matrix respectivelyAnd orderA linear matrix inequality is obtained:

wherein the content of the first and second substances,

for a given energy-peak performance index gamma, solving linear matrix inequalities simultaneously using a linear matrix inequality toolbox in MATLABAndobtaining a matrixAnda value of (d); then, the product is processedSolving a distributed estimator gain matrix

Background

The pipeline gas has the advantages of cleanness, high heat value, low price and easy storage and transportation, and is widely applied to industrial production in China and daily life of urban residents. Along with the wide application of pipeline gas, the types of gas safety accidents are diversified, and the safety accidents caused by gas leakage are increasing day by day. The coal gas has the characteristics of strong toxicity, flammability, explosiveness and easiness in leakage, once the coal gas is leaked, the danger of the coal gas is far greater than that of a common fire, and great influence is caused on the life and property safety of people. Therefore, the urban gas pipeline leakage condition is estimated in real time, a gas leakage event can be judged at the first time, effective measures can be taken in time, the safe operation and daily maintenance of the pipeline are guaranteed, and major safety accidents caused by gas leakage are avoided. However, with the rapid development of urbanization and the increasing population of cities, the scale of gas pipelines is larger and larger, the structure of pipe networks is more and more complex, and at present, the urban gas pipelines in China are underground concealed projects, and the current technology is difficult to accurately acquire accurate information leaked by the gas pipelines.

The sensor network is formed by arranging the sensors at each node of the underground gas pipeline, and the leakage state of the urban gas pipeline can be timely and accurately estimated by fully utilizing data measured by each node based on the distributed estimator. However, since data of a large number of sensor nodes are transmitted through a public network with limited bandwidth at the same time, a data collision phenomenon is easily caused, and a random measurement loss phenomenon in the data transmission process of the sensor network also needs to be considered. Moreover, random variation of the estimator gain is easily generated due to aging of estimator elements and environmental factor variation in application. Therefore, a new distributed estimation method based on a sensor network is urgently needed to effectively estimate the leakage state of the urban gas pipeline in real time.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a gas pipeline leakage estimation method based on a distributed sensing system, which measures the pipeline leakage state of each node by using a sensor network, introduces a distributed state estimator to estimate the state, and considers the random measurement attenuation phenomenon in the data transmission process and the influence of random gain change generated in the application of the state estimator. The method realizes timely and accurate estimation of the leakage of the urban gas pipeline and provides a method for safe operation and maintenance of the modern urban gas pipeline.

A gas pipeline leakage estimation method based on a distributed sensing system specifically comprises the following steps:

step 1, constructing a sensor network topological structure

Measuring the flow, the pressure and the temperature of the gas in the gas pipeline by using the N sensors; sensor network topology structure constructed according to signal transmission relation among N sensorsRepresenting a set of edges;representing the element as c_ijWeighted adjacency matrix of c_ijRepresenting the connection weight between the sensor nodes i and j,[·]_N×Na matrix made up of N × N elements is represented. When c is going to_ij>0 is thatIndicating that a signal is being transmitted from sensor node j to sensor node i; if i is j, c is noted_ii1, indicates that the sensor set is self-contained.Is a set of contiguous nodes that includes node i itself.

Step 2, establishing a state space model of the system

Establishing the following state space model according to the sensor network topological structure established in the step 1 and the measured data of the gas pipeline transmission system:

wherein the content of the first and second substances,representing the state vector, x, of the pipeline gas at time k₁(k)、x₂(k)、x₃(k) Respectively representing the flow, the pressure and the temperature of the gas in the gas pipeline at the moment k;indicating the measurement output of the i-th sensor, y_i1(k)、y_i2(k) Respectively representing the gas flow and the pressure in the gas pipeline measured by the ith sensor;representing the output signal to be estimated at time k, z₁(k)、z₂(k) Respectively representing the gas flow and the pressure to be estimated at time k.

The square additive external interference is used for representing the external noise of the system and the noise interference suffered by the sensor in the measuring process.

β_i(k)∈[0,1]Features of randomness, beta, for describing the measured attenuation of the measurement data during transmission, in order to obey random sequences that are randomly distributed_i(k) Has a mean value ofVariance (variance)E {. means to find the mathematical expectation,is a known scalar.

Are all known constant matrices; superscript T represents the transpose of the matrix;a real matrix representing n × m dimensions;

step 3, establishing a distributed estimator model

3.1, establishing the following distributed estimator model according to the system space state model established in the step 2:

wherein the content of the first and second substances,for the estimation vector of x (k) for the estimator node i at time k,respectively representing the estimated values of the gas flow, the pressure and the temperature of the node i at the moment k;representing the output signal to be estimated at node i at time k,respectively representing the gas flow and the pressure to be estimated of a node i at the moment k;representing the estimator gain matrix to be designed, is a gas pipelineA set of sensor nodes is provided, wherein,is a set of neighboring nodes that includes node i itself;representing estimator gain variation,. DELTA.L_ij(k)＝δ(k)M_ijDelta (k) is an unknown time-varying scalar quantity which satisfies-1 is more than or equal to delta (k) is more than or equal to 1,is a known matrix.

α (k) is a random sequence obeying a random distribution, α₁≤α(k)≤α₂The mathematical expectation of which isVariance ofα₁，α₂，And α are all known constants. Constant alpha₁、α₂、α^*And the sequence delta (k), the matrix M_ijThe value of (a) is obtained from a gas pipeline system modeling method and stochastic analysis.

Step 3.2, define the augmentation vectorAnd outputting the estimated error vectorWhereinSystem for obtaining estimation error augmentation：

Wherein the content of the first and second substances,

wherein the content of the first and second substances,representation matrix I_NThe Kronecker product of A and A; i is_NAn identity matrix having a number of dimensions N × N; i represents an identity matrix; diag {. } represents a diagonal matrix;

step 4, solving distributed estimator gain

A Lyapunov function is defined,wherein P₁,P₂,…,P_N+1Determining a diagonal matrix for positive determination; analyzing the stability condition and the energy-peak value performance index of the estimation error augmentation system obtained in the step 3.2, then solving by using a linear matrix inequality tool box to obtain a gain matrix of the distributed estimator, and realizing the gas pipeline leakage estimation based on the distributed sensing system, and specifically comprising the following steps:

step 4.1, assuming that the perturbation V (k) ═ 0, the mathematical expectation defining the difference E { Δv (k) } { (V (k +1) -V (k) }, calculated as:

matrix arrayWherein

Thus, it is possible to provideWherein:

thus, the following results were obtained:

wherein

And due to delta²(k) 1 or less, to obtain:

and is

Wherein the content of the first and second substances, e_irepresenting a matrix of column blocks corresponding to the ith sensor, e_iThe ith matrix block of the matrix is an identity matrix I, and the rest matrix blocks are all 0;

obtaining the following by the same method:

wherein the content of the first and second substances,

and calculating to obtain:

thus, it is possible to provideWherein the content of the first and second substances,

note the book

When it is satisfied withWhen there isThe number in the formula represents a symmetric item in the symmetric matrix;

and because ofSo E { V (k +1) } -E { V (k) }<0, i.e., there is a scalar ρ satisfying E { V (k +1) } ≦ ρ E { V (k) }, where ρ ∈ (0, 1); obtaining E { V (k) } ≦ rho through a recursion method^kV(0)；

According to the definition of the Lyapunov function, the following results are obtained:

wherein λ_min(. represents a minimum eigenvalue, λ)_max(. cndot.) represents the maximum eigenvalue, | | | - | | represents the euclidean norm of the vector or matrix; thus, for a given initial condition η (0), there is E { | | | η (k) | luminance²}≤∈ρ^k||η(0)||²Wherein

Therefore, when Λ <0, the estimation error augmentation system is mean square exponential stable;

step 4.2, obtaining any non-zero disturbance v (k) according to the estimation error augmentation system:

and

let ζ (k) be [. eta. ]^T(k),ν^T(k)]^TObtaining:

wherein

For any positive integer k, Δ V (k) | | ν (k) | non-calculation²＝ζ^T(k) Λ ζ (k); let K equal to K +1, K>0, defining a performance index function

From the zero initial condition η (0) ═ 0, we obtainIs further composed of<0, obtaining J<0, therefore

For a given energy-peak performance index γ, and γ>0, whenIn time, there are:

when K tends to be infinite, it is,wherein sup {. denotes a supremum in mathematics; therefore, the estimation error augmentation system is stable in mean square index and meets the given energy-peak performance index gamma;

and 4.3, utilizing Schur complementary theory to equivalently develop the lambda <0 into:

wherein the content of the first and second substances,superscript-1 represents the inverse of the matrix;

inequality Ψ<0 two-side left-and right-multiplication matrix respectivelyAnd orderA linear matrix inequality is obtained:

wherein the content of the first and second substances,

for a given energy-peak performance index gamma, solving linear matrix inequalities simultaneously using a linear matrix inequality toolbox in MATLABAndobtaining a matrixAnda value of (d); then, the product is processedSolving a distributed estimator gain matrix

The invention has the following beneficial effects:

1. the distributed estimation method for urban gas pipeline leakage based on the sensor network is provided, the measurement attenuation phenomenon when a large amount of sensor measurement data is transmitted is considered, the influence of random gain change of a state estimator on the estimation effect is considered, and the estimation accuracy is improved.

2. By analyzing the stability of the mean square index and the energy-peak value performance of the estimation error augmentation system and solving the distributed estimator by using a linear matrix inequality method, the leakage state of the urban gas pipeline is accurately estimated in time, and the safety and accuracy requirements of the leakage estimation of the urban gas pipeline are met.