CN113486480A - Leakage fault filtering method for urban water supply pipe network system - Google Patents

Leakage fault filtering method for urban water supply pipe network system Download PDF

Info

Publication number
CN113486480A
CN113486480A CN202110663486.7A CN202110663486A CN113486480A CN 113486480 A CN113486480 A CN 113486480A CN 202110663486 A CN202110663486 A CN 202110663486A CN 113486480 A CN113486480 A CN 113486480A
Authority
CN
China
Prior art keywords
water supply
matrix
filter
supply network
leakage fault
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202110663486.7A
Other languages
Chinese (zh)
Inventor
张写
陈张平
陈云
郭闯
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hangzhou Dianzi University
Original Assignee
Hangzhou Dianzi University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hangzhou Dianzi University filed Critical Hangzhou Dianzi University
Priority to CN202110663486.7A priority Critical patent/CN113486480A/en
Publication of CN113486480A publication Critical patent/CN113486480A/en
Pending legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/14—Pipes

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Computer Hardware Design (AREA)
  • General Engineering & Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • Computational Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)

Abstract

The invention discloses a leakage fault filtering method of an urban water supply network system, which aims at the problem of limited communication channel bandwidth and takes the influence of Markov packet loss of transmission data on input signals of a filter into consideration to establish a state space model of the water supply network system. Then, a full-order water supply network fault detection filter is designed, and a filtering error amplification system is established. Then, by utilizing the Lyapunov stability theory, the random stability of the filtering and amplifying system is deduced and the given H is satisfied∞Sufficient condition of performance. And finally, solving the linear matrix inequality to obtain a leakage fault filter gain matrix of the urban water supply network. The method can accurately estimate the leakage fault of the urban water supply network pipe system, accurately obtain the leakage fault signal of the water supply network, and meet the leakage fault of the modern urban water supply network systemThe actual need for fault detection.

Description

Leakage fault filtering method for urban water supply pipe network system
Technical Field
The invention belongs to the technical field of automation, and relates to a leakage fault detection filtering method for an urban water supply pipe network system.
Background
The urban water supply system is an important infrastructure and plays a significant role in ensuring the stable development of urban economy and the improvement of the living standard of people. The water supply network leakage rate is one of important marks reflecting the management level of water supply enterprises, and the reduction of the urban water supply network leakage rate has important economic and social benefits. In long-term operation, due to the aging of a pipe network and the damage of external force, the pipeline is often damaged, and tap water leakage is caused. Because the pipe network is generally buried underground deeply, the leakage of the water supply pipe network is not easy to find in time, so that the leakage of the pipe network becomes a common problem in the domestic and foreign water supply industry, a large amount of water resources and energy consumed in each link of water supply are wasted, and secondary problems of ground collapse, environmental pollution and water quality risk can be caused. Therefore, the leakage fault of the urban water supply network system can be timely and accurately detected, and the problem caused by leakage of the water supply network can be effectively prevented.
Because urban water supply networks are very complicated, the current technology is difficult to accurately acquire real-time data of each node of the water supply network, so that a leakage fault filtering method for the water supply network is lacked, leakage of the water supply network cannot be timely acquired, and serious waste of water resources and secondary problems are caused. By arranging a large number of sensors at the nodes of the water supply network, the measured water affair data can be transmitted to the water affair 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, so that the random loss phenomenon of the water service data is caused, and the leakage fault signal of the water supply network is difficult to obtain in time. Therefore, an effective leakage fault filtering method is urgently needed to realize timely and accurate detection of the leakage fault of the water supply network system.
Disclosure of Invention
The invention provides a design method for realizing a pipe network leakage fault filter of an urban water supply pipe network system, aiming at the problem that the leakage fault detection cannot be timely and effectively carried out in the urban water supply pipe network system in China at present. Aiming at the problem of limited communication channel bandwidth, the invention considers Markov packet loss pair filter of transmission dataAnd (4) establishing a state space model of the water supply network system under the influence of the input signals. Then, a full-order water supply network fault detection filter is designed, and a filtering error amplification system is established. Then, by utilizing the Lyapunov stability theory, the random stability of the filtering and amplifying system is deduced and the given H is satisfied∞Sufficient condition of performance. And finally, solving the linear matrix inequality to obtain a leakage fault filter gain matrix of the urban water supply network.
The method comprises the following specific steps:
1. state space model for establishing urban water supply pipe network system
Firstly, based on the hydraulics Bernoulli equation and the measured data, the following water supply pipe 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
Wherein
Figure BDA0003116198980000021
Representing the water service state vector and symbol of the pipe network end node detected by the water supply pipe network system at the moment k
Figure BDA0003116198980000022
Figure BDA0003116198980000023
Respectively representing n-dimensional Euclidean space and n x m-dimensional real number matrix, and superscript T representing the transposition of the matrix; x is the number of1(k),x2(k),x3(k) Respectively representing the water pressure value, the water flow speed value and the water flow value measured by the sensor at the moment k;
Figure BDA0003116198980000024
representing a square-additive external perturbation;
Figure BDA0003116198980000025
indicating the fault of the water supply network system at the moment k;
Figure BDA0003116198980000026
the measured output value of the water supply pipe network system at the moment k is represented; θ (j) represents an initial value of the water state vector;
Figure BDA0003116198980000027
are all constant matrices obtained by modeling;
Figure BDA0003116198980000028
representing a non-linear uncertainty function generated by the sensor;
for arbitrary vectors
Figure BDA0003116198980000029
The nonlinear function g (·,. cndot.) satisfies the condition
Figure BDA00031161989800000210
Wherein the matrix
Figure BDA00031161989800000211
And S1-S2Is a symmetric positive definite matrix.
Considering random packet loss and external interference generated by transmission of sensor data in a communication network with limited bandwidth, signals received by the leakage fault detection filter are as follows:
yc(k)＝α0y(k)+α1y(k-1)+d(k)
wherein alpha is0Is a random variable, alpha, indicating whether packet is lost or not1A random variable indicating whether the last signal was sent,
Figure BDA00031161989800000212
Figure BDA00031161989800000213
is an integer set, and alpha0,α1∈[0,1]D (k) is the bounded interference signal from the sensor to the filter;
random packet loss obeys the Markov chain, including the following 4 possibilities,
α0＝0,α1when the ratio is 0: the filter does not receive any signal at all,
α0＝0,α11: packet loss at time k, the signal received at time k by the filter is still the signal at time k-1,
α0＝1,α1when the ratio is 0: no packet loss, normal network transmission,
α0＝1,α11: the filter receives the superposed signals at the k moment and the k-1 moment at the k moment without packet loss;
the four possible states form a finite set S ═ {1,2,3,4} in turn, i.e., S is a discrete Markov jump set, and transition probabilities between the states obey a Markov chain, i.e.:
Figure BDA0003116198980000031
wherein Prob {. cndot } represents a probability; transition probability pi from time k modality i to time k +1 modality jijIs shown as
Figure BDA0003116198980000032
Wherein, 0 is less than or equal to piij≤1,
Figure BDA0003116198980000033
Σ is the accumulated sign in mathematics. 2. Design of leakage fault detection filter
The following form of full-order leakage fault detection filter is designed
Figure BDA0003116198980000034
Figure BDA0003116198980000035
Wherein the content of the first and second substances,
Figure BDA0003116198980000036
is the state vector of the filter, representing the estimated value of the vector x (k);
Figure BDA0003116198980000037
Figure BDA0003116198980000038
is the filter gain matrix to be solved.
Defining an error vector
Figure BDA0003116198980000039
Order to
Figure BDA00031161989800000310
ω(k)＝[fT(k) wT(k) dT(k)]TThen, the following filtering and amplifying system can be obtained
Figure BDA00031161989800000311
Figure BDA00031161989800000312
Wherein
Figure BDA00031161989800000313
Figure BDA00031161989800000314
Wherein I represents a dimension-matched identity matrix; 0 represents a zero matrix of appropriate dimensions;
3. solution of fault detection filter
First, the Lyapunov function V (k) ═ η is constructedT(k)Piη(k)+ηT(k-1) Q eta (k-1), wherein PiAnd Q is suitably a dimensionA positive definite matrix of
Figure BDA0003116198980000041
Wherein ζ (k) ═ ηT(k) gT(k,x(k)) ηT(k-1)]TE {. cndot } represents a mathematical expectation,
Figure BDA0003116198980000042
in which symbol ≧ represents a quantity of symmetry in the symmetric matrix,
Figure BDA0003116198980000043
Pja positive definite matrix with appropriate dimensions.
According to the condition satisfied by the preceding non-linear function g (·, ·), for the positive scalar ε, there is
Figure BDA0003116198980000044
Wherein
Figure BDA0003116198980000045
E1＝[I 0]
Thus, it is required to
Figure BDA0003116198980000046
Only a positive scalar epsilon needs to be present so that
Figure BDA0003116198980000047
Is established or caused
Figure BDA0003116198980000048
Is formed in which
Figure BDA0003116198980000049
Obviously, when the perturbation vector w (k) is 0, it can be known from the dynamic system stability principle if
Figure BDA00031161989800000410
It can ensure E { Δ V (k) } < 0, so that the filtering and amplifying system is stable at random.
The following performance index functions J (N) are introduced and calculated
Figure BDA00031161989800000411
Wherein the content of the first and second substances,
Figure BDA00031161989800000412
gamma is a given positive number, indicating the interference suppression performance of the system,
Figure BDA0003116198980000051
obviously, make J (N)<0, as long as it is guaranteed
Figure BDA0003116198980000052
That is, using the foregoing similar method, only the presence of the positive scalar ε is required so that
Figure BDA0003116198980000053
Wherein
Figure BDA0003116198980000054
Can be obtained according to Schur supplement theory
Figure BDA0003116198980000055
And
Figure BDA0003116198980000056
equivalents in which
Figure BDA0003116198980000057
In the formula
Figure BDA0003116198980000058
Therefore, it is
Figure BDA0003116198980000059
Can guarantee J (N)<0, i.e.
Figure BDA00031161989800000510
Considering the initial conditions and the random stability of the system, it is possible to derive from the above inequality
Figure BDA00031161989800000511
Wherein, | | · | | represents the euclidean norm of the matrix or vector;
thus, for any bounded perturbation vector w (k), the filter augmentation system is randomly stable and satisfies a given H∞And (4) performance.
Second, the gain matrix of the fault detection filter is solved
To make it
Figure BDA00031161989800000512
Only matrices of appropriate dimensions need to be present
Figure BDA00031161989800000513
So that the following equation holds
Figure BDA0003116198980000061
Order to
Figure BDA0003116198980000062
Simultaneously substituting each matrix expression in the filtering and amplifying system
Figure BDA0003116198980000063
In (2), the following linear matrix inequality can be obtained
Figure BDA0003116198980000064
Wherein
Figure BDA0003116198980000065
Figure BDA0003116198980000066
Figure BDA0003116198980000067
Figure BDA0003116198980000068
Finally, solving omega less than 0 by using a linear matrix inequality tool box of MATLAB, wherein the gain matrix of the fault detection filter is provided by the invention
Figure BDA0003116198980000069
Can be directly obtained, and the other two gain matrixes can be obtained
Figure BDA00031161989800000610
And (6) obtaining.
For the problem of leakage fault detection of the water supply network pipe system, the method considers the influence of Markov packet loss in the data transmission process and establishes a state space model of the water supply network system. The filtering and amplifying system is obtained by designing a full-order leakage fault detection filter, and the filtering and amplifying system is established to be stable randomly and meet the given H∞The condition of sufficient performance is obtained by solving the linear matrix inequalityA gain matrix. By utilizing the method, the leakage fault of the urban water supply network pipe system can be accurately estimated, the leakage fault signal of the water supply network can be accurately obtained, and the actual requirement of leakage fault detection of the modern urban water supply network system can be met.
Detailed Description
The invention discloses a leakage fault filtering method of an urban water supply pipe network system, which specifically comprises the following steps:
the method comprises the following steps: state space model for establishing urban water supply pipe network system
Firstly, based on the hydraulics Bernoulli equation and the measured data, the following water supply pipe 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
Wherein
Figure BDA0003116198980000071
Representing the water service state vector and symbol of the pipe network end node detected by the water supply pipe network system at the moment k
Figure BDA0003116198980000072
Figure BDA0003116198980000073
Respectively representing n-dimensional Euclidean space and n x m-dimensional real number matrix, and superscript T representing the transposition of the matrix; x is the number of1(k),x2(k),x3(k) Respectively representing the water pressure value, the water flow speed value and the water flow value measured by the sensor at the moment k;
Figure BDA0003116198980000074
representing a square-additive external perturbation;
Figure BDA0003116198980000075
indicating the fault of the water supply network system at the moment k;
Figure BDA0003116198980000076
the measured output value of the water supply pipe network system at the moment k is represented; θ (j) represents an initial value of the water state vector;
Figure BDA0003116198980000077
are all constant matrices obtained by modeling;
Figure BDA0003116198980000078
representing a non-linear uncertainty function generated by the sensor;
for arbitrary vectors
Figure BDA0003116198980000079
The nonlinear function g (·,. cndot.) satisfies the condition
Figure BDA00031161989800000710
Wherein the matrix
Figure BDA00031161989800000711
And S1-S2Is a symmetric positive definite matrix;
considering random packet loss and external interference generated by transmission of sensor data in a communication network with limited bandwidth, signals received by the leakage fault detection filter are as follows:
yc(k)＝α0y(k)+α1y(k-1)+d(k)
wherein alpha is0Is a random variable, alpha, indicating whether packet is lost or not1A random variable indicating whether the last signal was sent,
Figure BDA00031161989800000712
Figure BDA00031161989800000713
is an integer set, and alpha0,α1∈[0,1]D (k) is the bounded interference signal from the sensor to the filter;
random packet loss obeys the Markov chain, including the following 4 possibilities,
α0＝0,α1when the ratio is 0: the filter does not receive any signal at all,
α0＝0,α11: packet loss at time k, the signal received at time k by the filter is still the signal at time k-1,
α0＝1,α1when the ratio is 0: no packet loss, normal network transmission,
α0＝1,α11: the filter receives the superposed signals at the k moment and the k-1 moment at the k moment without packet loss;
the four possible states form a finite set S ═ {1,2,3,4} in turn, i.e., S is a discrete Markov jump set, and transition probabilities between the states obey a Markov chain, i.e.:
Figure BDA0003116198980000081
wherein Prob {. cndot } represents a probability; transition probability pi from time k modality i to time k +1 modality jijIs shown as
Figure BDA0003116198980000082
Wherein, 0 is less than or equal to piij≤1,
Figure BDA0003116198980000083
Sigma is an accumulated symbol in mathematics;
step two: design of leakage fault detection filter
The following form of full-order leakage fault detection filter is designed
Figure BDA0003116198980000084
Figure BDA0003116198980000085
Wherein the content of the first and second substances,
Figure BDA0003116198980000086
is the state vector of the filter, representing the estimated value of the vector x (k);
Figure BDA0003116198980000087
a filter gain matrix to be solved;
defining an error vector
Figure BDA0003116198980000088
Order to
Figure BDA0003116198980000089
ω(k)＝[fT(k) wT(k) dT(k)]TThen, the following filtering and amplifying system can be obtained
Figure BDA00031161989800000810
Figure BDA00031161989800000811
Wherein
Figure BDA00031161989800000812
Figure BDA00031161989800000813
Wherein I represents a dimension-matched identity matrix; 0 represents a zero matrix of appropriate dimensions;
step three: solution of fault detection filter
First, the Lyapunov function V (k) ═ η is constructedT(k)Piη(k)+ηT(k-1) Q eta (k-1), wherein PiAnd Q is a positive definite matrix with appropriate dimension, then
Figure BDA0003116198980000091
Wherein ζ (k) ═ ηT(k) gT(k,x(k)) ηT(k-1)]TE {. cndot } represents a mathematical expectation,
Figure BDA0003116198980000092
in which symbol ≧ represents a quantity of symmetry in the symmetric matrix,
Figure BDA0003116198980000093
Pja positive definite matrix with appropriate dimension;
according to the condition satisfied by the preceding non-linear function g (·, ·), for the positive scalar ε, there is
Figure BDA0003116198980000094
Wherein
Figure BDA0003116198980000095
E1＝[I 0]
Thus, it is required to
Figure BDA0003116198980000096
Only a positive scalar epsilon needs to be present so that
Figure BDA0003116198980000097
Is established or caused
Figure BDA0003116198980000098
Is formed in which
Figure BDA0003116198980000099
Obviously, when the perturbation vector w (k) is 0, it can be known from the dynamic system stability principle if
Figure BDA00031161989800000910
E { delta V (k) } < 0 can be ensured, so that the filtering and amplifying system is random and stable;
the following performance index functions J (N) are introduced and calculated
Figure BDA00031161989800000911
Wherein the content of the first and second substances,
Figure BDA0003116198980000101
gamma is a given positive number, indicating the interference suppression performance of the system,
Figure BDA0003116198980000102
obviously, make J (N)<0, as long as it is guaranteed
Figure BDA0003116198980000103
That is, using the foregoing similar method, only the presence of the positive scalar ε is required so that
Figure BDA0003116198980000104
Wherein
Figure BDA0003116198980000105
Can be obtained according to Schur supplement theory
Figure BDA0003116198980000106
And
Figure BDA0003116198980000107
equivalents in which
Figure BDA0003116198980000108
In the formula
Figure BDA0003116198980000109
Therefore, it is
Figure BDA00031161989800001010
Can guarantee J (N)<0, i.e.
Figure BDA00031161989800001011
Considering the initial conditions and the random stability of the system, it is possible to derive from the above inequality
Figure BDA00031161989800001012
Wherein, | | · | | represents the euclidean norm of the matrix or vector;
thus, for any bounded perturbation vector w (k), the filter augmentation system is randomly stable and satisfies a given H∞Performance;
second, the gain matrix of the fault detection filter is solved
To make it
Figure BDA00031161989800001013
Only matrices of appropriate dimensions need to be present
Figure BDA00031161989800001014
So that the following equation holds
Figure BDA0003116198980000111
Order to
Figure BDA0003116198980000112
Simultaneously substituting each matrix expression in the filtering and amplifying system
Figure BDA0003116198980000113
In (b), the following wire can be obtainedNature matrix inequality
Figure BDA0003116198980000114
Wherein
Figure BDA0003116198980000115
Figure BDA0003116198980000116
Figure BDA0003116198980000117
Figure BDA0003116198980000118
Finally, solving the gain matrix of the fault detection filter with omega less than 0 by using a linear matrix inequality tool box of MATLAB
Figure BDA0003116198980000119
Can be directly obtained, and the other two gain matrixes can be obtained
Figure BDA00031161989800001110
And (6) obtaining.

Claims (1)

1. A leakage fault filtering method for an urban water supply pipe network system is characterized by comprising the following steps:
the method comprises the following steps: state space model for establishing urban water supply pipe network system
Firstly, based on the hydraulics Bernoulli equation and the measured data, the following water supply pipe 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
Wherein
Figure FDA0003116198970000011
Representing the water service state vector and symbol of the pipe network end node detected by the water supply pipe network system at the moment k
Figure FDA0003116198970000012
Respectively representing n-dimensional Euclidean space and n x m-dimensional real number matrix, and superscript T representing the transposition of the matrix; x is the number of1(k),x2(k),x3(k) Respectively representing the water pressure value, the water flow speed value and the water flow value measured by the sensor at the moment k;
Figure FDA0003116198970000013
representing a square-additive external perturbation;
Figure FDA0003116198970000014
indicating the fault of the water supply network system at the moment k;
Figure FDA0003116198970000015
the measured output value of the water supply pipe network system at the moment k is represented; θ (j) represents an initial value of the water state vector;
Figure FDA0003116198970000016
are all constant matrices obtained by modeling;
Figure FDA0003116198970000017
representing a non-linear uncertainty function generated by the sensor;
for arbitrary vectors
Figure FDA0003116198970000018
The nonlinear function g (·,. cndot.) satisfies the condition
Figure FDA0003116198970000019
Wherein the matrix S1,
Figure FDA00031161989700000110
And S1-S2Is a symmetric positive definite matrix;
considering random packet loss and external interference generated by transmission of sensor data in a communication network with limited bandwidth, signals received by the leakage fault detection filter are as follows:
yc(k)＝α0y(k)+α1y(k-1)+d(k)
wherein alpha is0Is a random variable, alpha, indicating whether packet is lost or not1A random variable, alpha, indicating whether the last signal was sent0,
Figure FDA00031161989700000111
Figure FDA00031161989700000112
Is an integer set, and alpha0,α1∈[0,1]D (k) is the bounded interference signal from the sensor to the filter;
random packet loss obeys the Markov chain, including the following 4 possibilities,
α0＝0,α1when the ratio is 0: the filter does not receive any signal at all,
α0＝0,α11: packet loss at time k, the signal received at time k by the filter is still the signal at time k-1,
α0＝1,α1when the ratio is 0: no packet loss, normal network transmission,
α0＝1,α11: the filter receives the superposed signals at the k moment and the k-1 moment at the k moment without packet loss;
a finite set S ═ {1,2,3,4} is formed by the four possible states, i.e., S is a discrete Markov jump set whose transition probabilities between the respective states obey a Markov chain, i.e.:
Figure FDA0003116198970000021
wherein Prob {. cndot } represents a probability; transition probability pi from time k modality i to time k +1 modality jijIs shown as
Figure FDA0003116198970000022
Wherein, 0 is less than or equal to piij≤1,
Figure FDA0003116198970000023
Sigma is an accumulated symbol in mathematics; step two: design of leakage fault detection filter
The following form of full-order leakage fault detection filter is designed
Figure FDA0003116198970000024
Figure FDA0003116198970000025
Wherein the content of the first and second substances,
Figure FDA0003116198970000026
is the state vector of the filter, representing the estimated value of the vector x (k);
Figure FDA0003116198970000027
a filter gain matrix to be solved;
defining an error vector
Figure FDA0003116198970000028
Order to
Figure FDA0003116198970000029
ω(k)＝[fT(k) wT(k) dT(k)]TThen, the following filtering and amplifying system can be obtained
Figure FDA00031161989700000210
Figure FDA00031161989700000211
Wherein
Figure FDA00031161989700000212
Figure FDA00031161989700000213
Wherein I represents a dimension-matched identity matrix; 0 represents a zero matrix of appropriate dimensions;
step three: solution of fault detection filter
First, the Lyapunov function V (k) ═ η is constructedT(k)Piη(k)+ηT(k-1) Q eta (k-1), wherein PiAnd Q is a positive definite matrix with appropriate dimension, then
Figure FDA0003116198970000031
Wherein ζ (k) ═ ηT(k) gT(k,x(k)) ηT(k-1)]TE {. cndot } represents a mathematical expectation,
Figure FDA0003116198970000032
in which symbol ≧ represents a quantity of symmetry in the symmetric matrix,
Figure FDA0003116198970000033
Pja positive definite matrix with appropriate dimension;
according to the condition satisfied by the preceding non-linear function g (·, ·), for the positive scalar ε, there is
Figure FDA0003116198970000034
Wherein
Figure FDA0003116198970000035
E1＝[I 0]
Thus, it is required to
Figure FDA00031161989700000310
Only a positive scalar epsilon needs to be present so that
Figure FDA0003116198970000036
Is established or caused
Figure FDA0003116198970000037
Is formed in which
Figure FDA0003116198970000038
Obviously, when the perturbation vector w (k) is 0, it can be known from the dynamic system stability principle if
Figure FDA0003116198970000039
E { delta V (k) } < 0 can be ensured, so that the filtering and amplifying system is random and stable;
the following performance index functions J (N) are introduced and calculated
Figure FDA0003116198970000041
Wherein the content of the first and second substances,
Figure FDA0003116198970000042
gamma is a given positive number, indicating the interference suppression performance of the system,
Figure FDA0003116198970000043
obviously, make J (N)<0, as long as it is guaranteed
Figure FDA0003116198970000044
That is, using the foregoing similar method, only the presence of the positive scalar ε is required so that
Figure FDA0003116198970000045
Wherein
Figure FDA0003116198970000046
Can be obtained according to Schur supplement theory
Figure FDA0003116198970000047
And
Figure FDA0003116198970000048
equivalents in which
Figure FDA0003116198970000049
In the formula
Figure FDA00031161989700000410
Therefore, it is
Figure FDA00031161989700000411
Can guarantee J (N)<0, i.e.
Figure FDA00031161989700000412
Considering the initial conditions and the random stability of the system, it is possible to derive from the above inequality
Figure FDA00031161989700000413
Wherein, | | · | | represents the euclidean norm of the matrix or vector;
thus, for any bounded perturbation vector w (k), the filter augmentation system is randomly stable and satisfies a given H∞Performance;
second, the gain matrix of the fault detection filter is solved
To make it
Figure FDA0003116198970000051
Only matrices of appropriate dimensions need to be present
Figure FDA0003116198970000052
So that the following equation holds
Figure FDA0003116198970000053
Order to
Figure FDA0003116198970000054
Simultaneously substituting each matrix expression in the filtering and amplifying system
Figure FDA0003116198970000055
In (2), the following linear matrix inequality can be obtained
Figure FDA0003116198970000056
Wherein
Φ11＝-Pi1+Qi1-0.5εR,
Figure FDA0003116198970000057
Φ12＝-Pi2+Q2,
Figure FDA0003116198970000058
Figure FDA0003116198970000059
Ψ1＝ATGi1+α0CTV,Ψ2＝ATGi2+α0CTV
Φ22＝-Pi3+Q3,
Figure FDA00031161989700000510
Ψ4＝Ψ5＝α1CTV
Figure FDA00031161989700000511
Finally, solving the gain matrix of the fault detection filter with omega less than 0 by using a linear matrix inequality tool box of MATLAB
Figure FDA0003116198970000061
Can be directly obtained, and the other two gain matrixes can be obtained
Figure FDA0003116198970000062
And (6) obtaining.
CN202110663486.7A 2021-06-16 2021-06-16 Leakage fault filtering method for urban water supply pipe network system Pending CN113486480A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110663486.7A CN113486480A (en) 2021-06-16 2021-06-16 Leakage fault filtering method for urban water supply pipe network system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110663486.7A CN113486480A (en) 2021-06-16 2021-06-16 Leakage fault filtering method for urban water supply pipe network system

Publications (1)

Publication Number Publication Date
CN113486480A true CN113486480A (en) 2021-10-08

Family

ID=77935155

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110663486.7A Pending CN113486480A (en) 2021-06-16 2021-06-16 Leakage fault filtering method for urban water supply pipe network system

Country Status (1)

Country Link
CN (1) CN113486480A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113985197A (en) * 2021-10-18 2022-01-28 杭州电子科技大学 Event-triggered asynchronous detection method for equipment fault of water affair system

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113985197A (en) * 2021-10-18 2022-01-28 杭州电子科技大学 Event-triggered asynchronous detection method for equipment fault of water affair system
CN113985197B (en) * 2021-10-18 2024-01-09 杭州电子科技大学 Event triggering asynchronous detection method for equipment faults of water service system

Similar Documents

Publication Publication Date Title
Li et al. Set-membership filtering for state-saturated systems with mixed time-delays under weighted try-once-discard protocol
CN110851774B (en) Leakage estimation method for urban water supply network
Zhang et al. H∞ filtering of networked discrete-time systems with random packet losses
CN109150639B (en) Finite time domain H-infinity control method of time-varying system under influence of high-rate communication network
CN109827629B (en) Distributed reliability estimation method for urban river water level
CN106529479B (en) A kind of uncatalyzed coking dissipation filtering method of nonlinear network networked control systems
CN110705892B (en) Water flow state detection method for urban drainage pipeline
CN109537671B (en) Method for controlling water supply and water balance of urban water supply system
CN113325821B (en) Network control system fault detection method based on saturation constraint and dynamic event trigger mechanism
CN104049533A (en) Network control system controller design method based on hidden semi-markov model
CN106227700A (en) A kind of uncatalyzed coking dissipation filtering method of network control system
CN108319147A (en) One kind has the H of the networking Linear Parameter-Varying Systems of short time-delay and data packetloss∞Fault tolerant control method
Li et al. H∞ fault detection filter design for discrete-time nonlinear Markovian jump systems with missing measurements
CN106383442B (en) A kind of H of networking Linear Parameter-Varying Systems∞Control method
CN113486480A (en) Leakage fault filtering method for urban water supply pipe network system
CN113325708B (en) Fault estimation method of multi-unmanned aerial vehicle system based on heterogeneous multi-agent
CN111062139A (en) Method for estimating water flow situation of urban underground drainage pipe network
CN111123696B (en) Redundant channel-based networked industrial control system state estimation method
Zhang et al. Decentralized Non-Fragile Event-Triggered ${{H} _ {\infty}} $ Filtering for Large-Scaled Power System Based on TS Fuzzy Model
CN113110321B (en) Distributed estimation method of networked industrial control system based on event trigger
CN107563103B (en) Consistency filter design method based on local conditions
CN115344975A (en) Sensor network-based urban drainage pipe network distributed leakage estimation method
CN113408085A (en) Gas pipeline leakage estimation method based on distributed sensing system
CN110955142B (en) Limited time control method for urban drainage pipeline
CN113411312B (en) State estimation method of nonlinear complex network system based on random communication protocol

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination