A leakage fault filtering method for urban water supply network system

Abstract

The present invention discloses a leakage fault filtering method for a city water supply network system. The invention aims at the problem of limited communication channel bandwidth, considers the influence of Markov packet loss of transmission data on the filter input signal, and establishes a state space model of the water supply network system. Then, a full-order water supply network fault detection filter is designed, and a filter error augmentation system is established. Then, the Lyapunov stability theory is used to derive that the filter augmentation system is randomly stable and satisfies a given H ∞ Sufficient conditions for performance. Finally, the gain matrix of the urban water supply network leakage fault filter is obtained by solving the linear matrix inequality. The present invention can accurately estimate the leakage fault of the urban water supply network management system, accurately obtain the leakage fault signal of the water supply network, and meet the actual needs of leakage fault detection of modern urban water supply network systems.

Description

Technical Field

[0001] The present invention belongs to the field of automation technology and relates to a leakage fault detection filtering method for a city water supply pipe network system. By designing a leakage fault detection filter based on an observer, accurate and timely leakage fault detection of the city water supply pipe network system can be achieved, which can significantly reduce the problems caused by leakage of urban underground water supply pipes and can be used in the modern urban water supply industry. Background Art

[0002] The urban water supply system is an important infrastructure, which plays a vital role in ensuring the stable development of the urban economy and improving people's living standards. The leakage rate of the water supply network is one of the important indicators reflecting the management level of water supply enterprises. Reducing the leakage rate of the urban water supply network has important economic and social benefits. In long-term operation, due to the aging of the network and external damage, pipes often break, causing water leakage. Since the network is generally buried deep underground, it is difficult to detect leakage in the water supply network in time, making network leakage a common problem faced by the water supply industry at home and abroad, which not only wastes a lot of water resources and energy consumed in various links of water supply, but also may cause secondary problems such as ground collapse, environmental pollution, and water quality risks. Therefore, timely and accurate detection of leakage failures in the urban water supply network system can effectively prevent the problems caused by leakage of the water supply network.

[0003] Due to the complexity of urban water supply networks, current technology makes it difficult to accurately obtain real-time data from each node of the water supply network. Therefore, there is a lack of leakage fault filtering methods for the water supply network, and it is impossible to obtain leakage in the water supply network in a timely manner, resulting in serious waste of water resources and the emergence of secondary problems. By arranging a large number of sensors at the nodes of the water supply network, the measured water service data can be transmitted to the water service monitoring center in real time through the communication network. However, the limited bandwidth of the transmission channel seriously affects the real-time transmission effect of a large amount of water service data, resulting in random loss of water service data, making it difficult to obtain leakage fault signals of the water supply network in a timely manner. Therefore, there is an urgent need for an effective leakage fault filtering method to achieve timely and accurate detection of leakage faults in the water supply network system. Summary of the invention

[0004] The present invention aims to solve the problem that the current urban water supply network system in my country cannot detect leakage faults in a timely and effective manner, and provides a design method for realizing a network leakage fault filter in an urban water supply network system. The present invention aims to solve the problem of limited communication channel bandwidth, considers the impact of Markov packet loss of transmitted data on the filter input signal, and establishes a state space model of the water supply network system. Then, a full-order water supply network fault detection filter is designed, and a filter error augmentation system is established. Then, using the Lyapunov stability theory, it is derived that the filter augmentation system is randomly stable and satisfies a given H ∞Finally, the gain matrix of the urban water supply network leakage fault filter is obtained by solving the linear matrix inequality.

[0005] The specific steps of this method are:

[0006] 1. Establish a state space model of the urban water supply network system

[0007] First, based on the hydraulic Bernoulli equation and measured data, the following water supply network system model is established:

[0008] x(k+1)=Ax(k)+g(k,x(k))+Dw(k)+Ff(k)

[0009] y(k)=Cx(k)

[0010] x(j)=θ(j),j=-1,0

[0011] in It represents the water service state vector of the pipe network end node detected by the water supply network system at time k, symbol They represent n-dimensional Euclidean space and n×m-dimensional real matrix respectively, and the superscript T represents the transpose of the matrix; x1(k), x2(k), x3(k) represent the water pressure value, water flow velocity value, and water flow value measured by the sensor at time k respectively; represents a square-additive external disturbance; represents the fault in the water supply network system at time k; represents the measured output value of the water supply network system at time k; θ(j) represents the initial value of the water service state vector; They are all constant matrices obtained through modeling; Represents the nonlinear uncertainty function generated by the sensor;

[0012] For any vector The nonlinear function g(·,·) satisfies the condition

[0013]

[0014] The matrix And S1-S2 is a symmetric positive definite matrix.

[0015] Considering the random packet loss and external interference caused by the transmission of sensor data in a communication network with limited bandwidth, the signal received by the leakage fault detection filter is:

[0016] y c (k) = α0y(k) + α1y(k-1) + d(k)

[0017] Among them, α0 is a random variable indicating whether the packet is lost or not, and α1 is a random variable indicating whether the previous signal was sent. is an integer set, and α0, α1∈[0,1], d(k) is the bounded interference signal from the sensor to the filter;

[0018] Random packet loss follows the Markov chain, including the following 4 possibilities:

[0019] α0=0,α1=0: The filter does not receive any signal.

[0020] α0=0,α1=1: Packet is lost at time k, and the signal received by the filter at time k is still the signal at time k-1.

[0021] α0=1,α1=0: No packet loss, network transmission is normal,

[0022] α0=1,α1=1: No packet loss, filter at time k receives the superposition signal of time k and time k-1;

[0023] The above four possible states sequentially constitute a finite set S = {1, 2, 3, 4}, that is, S is a discrete Markov jump set, and the transition probability between its states obeys the Markov chain, that is:

[0024]

[0025] Where Prob{·} represents the probability; the transition probability π from mode i at time k to mode j at time k+1 ij Expressed as Where 0≤π ij ≤1, Σ is the symbol for accumulation in mathematics. 2. Design of leakage fault detection filter

[0026] Design a full-order leakage fault detection filter of the form

[0027]

[0028]

[0029] in, is the state vector of the filter, representing the estimated value of the vector x(k); is the filter gain matrix to be determined.

[0030] Defining the error vector make ω(k)=[f T (k) w T (k) dT (k)] T , then we can get the following filter augmentation system

[0031]

[0032]

[0033] in

[0034]

[0035]

[0036] Where I represents the identity matrix of matching dimensions; 0 represents the zero matrix of appropriate dimensions;

[0037] 3. Solution of Fault Detection Filter

[0038] The first step is to construct the Lyapunov function V(k)=η T (k)P i η(k)+η T (k-1)Qη(k-1), where P i and Q are positive definite matrices of appropriate dimension, then

[0039]

[0040] Where ζ(k)=[η T (k) g T (k,x(k)) η T (k-1)] T , E{·} represents the mathematical expectation,

[0041]

[0042] The symbol ★ in the formula represents the symmetric quantity in the symmetric matrix. P j is a positive definite matrix of appropriate dimension.

[0043] According to the conditions satisfied by the nonlinear function g(·,·) above, for the positive scalar ε, we have in

[0044]

[0045] E1=[I 0]

[0046] Therefore, to make There only needs to be a positive scalar ε such that to establish or make Established, of which

[0047]

[0048] Obviously, when the disturbance vector w(k) = 0, according to the principle of dynamic system stability, if It can be guaranteed that E{ΔV(k)}<0, so the filter augmentation system is randomly stable.

[0049] Introducing the following performance index function J(N) and calculating it, we can get

[0050]

[0051] in, γ is a given positive number, indicating the interference suppression performance of the system.

[0052]

[0053] Obviously, to make J(N) < 0, we only need to ensure Then, using a similar method as above, we only need to have a positive scalar ε such that in

[0054]

[0055] According to Schur's complement lemma, we can get and Equivalent, where

[0056]

[0057] In the formula

[0058] Therefore It can ensure that J(N)<0, that is

[0059] Considering the initial conditions and the random stability of the system, the above inequality gives Among them, ||·|| represents the Euclidean norm of the matrix or vector;

[0060] Therefore, for any bounded perturbation vector w(k), the filter-augmented system is stochastically stable and satisfies the given H ∞ performance.

[0061] The second step is to solve the fault detection filter gain matrix

[0062] To make There only needs to be a matrix of appropriate dimension So that the following formula holds

[0063]

[0064] make

[0065]

[0066] At the same time, substitute the matrix expressions of the filter augmentation system into In the equation, we can get the following linear matrix inequality:

[0067]

[0068] in

[0069]

[0070]

[0071]

[0072]

[0073] Finally, the linear matrix inequality toolbox of MATLAB is used to solve Ω<0. The gain matrix of the fault detection filter in the present invention is It can be directly calculated, and the other two gain matrices can be obtained by To obtain.

[0074] For the leakage fault detection problem of the water supply network system, the present invention considers the influence of Markov packet loss in the data transmission process and establishes a state space model of the water supply network system. By designing a full-order leakage fault detection filter, a filter augmentation system is obtained, and a filter augmentation system is established that is randomly stable and satisfies a given H ∞ The sufficient condition for performance is obtained by solving the linear matrix inequality to obtain the gain matrix of the fault detection filter. The method of the present invention can accurately estimate the leakage fault of the urban water supply network system, accurately obtain the leakage fault signal of the water supply network, and meet the actual needs of leakage fault detection of the modern urban water supply network system. DETAILED DESCRIPTION

[0075] The present invention provides a leakage fault filtering method for a city water supply pipe network system, the method specifically comprising the following steps:

[0076] Step 1: Establish a state space model of the urban water supply network system

[0077] First, based on the hydraulic Bernoulli equation and measured data, the following water supply network system model is established:

[0078] x(k+1)=Ax(k)+g(k,x(k))+Dw(k)+Ff(k)

[0079] y(k)=Cx(k)

[0080] x(j)=θ(j),j=-1,0

[0081] in It represents the water service state vector of the pipe network end node detected by the water supply network system at time k, symbol They represent n-dimensional Euclidean space and n×m-dimensional real matrix respectively, and the superscript T represents the transpose of the matrix; x1(k), x2(k), x3(k) represent the water pressure value, water flow velocity value, and water flow value measured by the sensor at time k respectively; represents a square-additive external disturbance; represents the fault in the water supply network system at time k; represents the measured output value of the water supply network system at time k; θ(j) represents the initial value of the water service state vector; They are all constant matrices obtained through modeling; Represents the nonlinear uncertainty function generated by the sensor;

[0082] For any vector The nonlinear function g(·,·) satisfies the condition

[0083]

[0084] The matrix And S1-S2 is a symmetric positive definite matrix;

[0085] Considering the random packet loss and external interference caused by the transmission of sensor data in a communication network with limited bandwidth, the signal received by the leakage fault detection filter is:

[0086] y c (k) = α0y(k) + α1y(k-1) + d(k)

[0087] Among them, α0 is a random variable indicating whether the packet is lost or not, and α1 is a random variable indicating whether the previous signal was sent. is an integer set, and α0, α1∈[0,1], d(k) is the bounded interference signal from the sensor to the filter;

[0088] Random packet loss follows the Markov chain, including the following 4 possibilities:

[0089] α0=0,α1=0: The filter does not receive any signal.

[0090] α0=0,α1=1: Packet is lost at time k, and the signal received by the filter at time k is still the signal at time k-1.

[0091] α0=1,α1=0: No packet loss, network transmission is normal,

[0092] α0=1,α1=1: No packet loss, filter at time k receives the superposition signal of time k and time k-1;

[0093] The above four possible states sequentially constitute a finite set S = {1, 2, 3, 4}, that is, S is a discrete Markov jump set, and the transition probability between its states obeys the Markov chain, that is:

[0094]

[0095] Where Prob{·} represents the probability; the transition probability π from mode i at time k to mode j at time k+1 ij Expressed as Where 0≤π ij ≤1, Σ is the symbol for accumulation in mathematics;

[0096] Step 2: Design of leakage fault detection filter

[0097] Design a full-order leakage fault detection filter of the form

[0098]

[0099]

[0100] in, is the state vector of the filter, representing the estimated value of the vector x(k); is the filter gain matrix to be determined;

[0101] Defining the error vector make ω(k)=[f T (k) w T (k) d T (k)] T , then we can get the following filter augmentation system

[0102]

[0103]

[0104] in

[0105]

[0106]

[0107] Where I represents the identity matrix of matching dimensions; 0 represents the zero matrix of appropriate dimensions;

[0108] Step 3: Solution of Fault Detection Filter

[0109] The first step is to construct the Lyapunov function V(k)=η T (k)P i η(k)+η T (k-1)Qη(k-1), where P i and Q are positive definite matrices of appropriate dimension, then

[0110]

[0111] Where ζ(k)=[η T (k) g T (k,x(k)) η T (k-1)] T , E{·} represents the mathematical expectation,

[0112]

[0113] The symbol ★ in the formula represents the symmetric quantity in the symmetric matrix. P j is a positive definite matrix of appropriate dimension;

[0114] According to the conditions satisfied by the nonlinear function g(·,·) above, for the positive scalar ε, we have in

[0115]

[0116] E1=[I 0]

[0117] Therefore, to make There only needs to be a positive scalar ε such that to establish or make Established, of which

[0118]

[0119] Obviously, when the disturbance vector w(k) = 0, according to the principle of dynamic system stability, if It can ensure that E{ΔV(k)}<0, so the filter augmentation system is stochastically stable;

[0120] Introducing the following performance index function J(N) and calculating it, we can get

[0121]

[0122] in, γ is a given positive number, indicating the interference suppression performance of the system.

[0123]

[0124] Obviously, to make J(N) < 0, we only need to ensure Then, using a similar method as above, we only need to have a positive scalar ε such that in

[0125]

[0126] According to Schur's complement lemma, we can get and Equivalent, where

[0127]

[0128] In the formula

[0129] Therefore It can ensure that J(N)<0, that is

[0130] Considering the initial conditions and the random stability of the system, the above inequality gives Among them, ||·|| represents the Euclidean norm of the matrix or vector;

[0131] Therefore, for any bounded perturbation vector w(k), the filter-augmented system is stochastically stable and satisfies the given H ∞ performance;

[0132] The second step is to solve the fault detection filter gain matrix

[0133] To make There only needs to be a matrix of appropriate dimension So that the following formula holds

[0134]

[0135] make

[0136]

[0137] At the same time, substitute the matrix expressions of the filter augmentation system into In the equation, we can get the following linear matrix inequality:

[0138]

[0139] in

[0140]

[0141]

[0142]

[0143]

[0144] Finally, the linear matrix inequality toolbox of MATLAB is used to solve Ω<0, and the gain matrix of the fault detection filter is can be directly obtained, and the other two gain matrices can be obtained by To obtain.

Claims

1. A leakage fault filtering method for a city water supply pipe network system, characterized in that: The method specifically comprises the following steps: Step 1: Establish a state space model of the urban water supply network system First, based on the hydraulic Bernoulli equation and measured data, the following water supply network system model is established: x(k+1)=Ax(k)+g(k,x(k))+Dw(k)+Ff(k) y(k)=Cx(k) x(j)=θ(j),j=-1,0 in It represents the water service state vector of the pipe network end node detected by the water supply network system at time k, symbol They represent n-dimensional Euclidean space and n×m-dimensional real matrix respectively, and the superscript T represents the transpose of the matrix; x1(k), x2(k), x3(k) represent the water pressure value, water flow velocity value, and water flow value measured by the sensor at time k respectively; represents a square-additive external disturbance; represents the fault in the water supply network system at time k; represents the measured output value of the water supply network system at time k; θ(j) represents the initial value of the water service state vector; They are all constant matrices obtained through modeling; Represents the nonlinear uncertainty function generated by the sensor; For any vector The nonlinear function g(·,·) satisfies the condition The matrix And S1-S2 is a symmetric positive definite matrix; Considering the random packet loss and external interference caused by the transmission of sensor data in a communication network with limited bandwidth, the signal received by the leakage fault detection filter is: y c (k)=α0y(k)+α1y(k-1)+d(k) Among them, α0 is a random variable indicating whether the packet is lost or not, and α1 is a random variable indicating whether the previous signal was sent. is an integer set, and α0, α1∈[0,1], d(k) is the bounded interference signal from the sensor to the filter; Random packet loss follows a Markov chain, which includes the following four possible states: α0=0,α1=0: The filter does not receive any signal. α0=0,α1=1: Packet is lost at time k, and the signal received by the filter at time k is still the signal at time k-1. α0=1,α1=0: No packet loss, network transmission is normal, α0=1,α1=1: No packet loss, filter at time k receives the superposition signal of time k and time k-1; The above four possible states constitute a finite set S = {1, 2, 3, 4}, that is, S is a discrete Markov jump set, and the transition probability between its states obeys the Markov chain, that is: Where Prob{·} represents the probability; the transition probability π from mode i at time k to mode j at time k+1 ij Expressed as in, Σ is the symbol for accumulation in mathematics; Step 2: Design of leakage fault detection filter Design a full-order leakage fault detection filter of the form in, is the state vector of the filter, representing the estimated value of the vector x(k); is the filter gain matrix to be determined; Defining the error vector make ω(k)=[f T (k)w T (k)d T (k)] T , then we can get the following filter augmentation system in Where I represents the identity matrix of matching dimensions; 0 represents the zero matrix of appropriate dimensions; Step 3: Solution of Fault Detection Filter The first step is to construct the Lyapunov function V(k)=η T (k)P i η(k)+η T (k-1)Qη(k-1), where P i and Q are positive definite matrices of appropriate dimension, then Where ζ(k)=[η T (k)g T (k,x(k))η T (k-1)] T , E{·} represents the mathematical expectation, The symbol ★ in the formula represents the symmetric quantity in the symmetric matrix. P j is a positive definite matrix of appropriate dimension; According to the conditions satisfied by the nonlinear function g(·,·) above, for the positive scalar ε, we have in E1=[I 0] Therefore, to make There only needs to be a positive scalar ε such that to establish or make Established, of which Obviously, when the disturbance vector w(k) = 0, according to the principle of dynamic system stability, if It can ensure that E{△V(k)}<0, so the filter augmentation system is stochastically stable; Introducing the following performance index function J(N) and calculating it, we can get in, γ is a given positive number, indicating the interference suppression performance of the system. Obviously, to make J(N) < 0, we only need to ensure Then, using a similar method as above, we only need to have a positive scalar ε such that in According to Schur's complement lemma, we can get and Equivalent, where In the formula Therefore It can ensure that J(N)<0, that is Considering the initial conditions and the random stability of the system, the above inequality gives Among them, ||·|| represents the Euclidean norm of a matrix or vector; Therefore, for any bounded perturbation vector w(k), the filter-augmented system is stochastically stable and satisfies the given H ∞ performance; The second step is to solve the fault detection filter gain matrix To make There only needs to be a matrix of appropriate dimension So that the following formula holds make At the same time, substitute the matrix expressions of the filter augmentation system into In the equation, we can get the following linear matrix inequality: in Finally, the linear matrix inequality toolbox of MATLAB is used to solve Ω<0, and the gain matrix of the fault detection filter is can be directly obtained, and the other two gain matrices can be obtained by To obtain.

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