CN113985197A - Event-triggered asynchronous detection method for equipment fault of water affair system - Google Patents

Event-triggered asynchronous detection method for equipment fault of water affair system Download PDF

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CN113985197A
CN113985197A CN202111208898.8A CN202111208898A CN113985197A CN 113985197 A CN113985197 A CN 113985197A CN 202111208898 A CN202111208898 A CN 202111208898A CN 113985197 A CN113985197 A CN 113985197A
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water
event
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filter
water supply
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CN113985197B (en
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张俊锋
李强
于飞
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Hangzhou Dianzi University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/34—Testing dynamo-electric machines

Abstract

The invention belongs to the field of automatic control, and discloses an event-triggered asynchronous detection method for equipment faults of a water service system, which comprises the following steps of 1, establishing a state space model of the water service system; step 2, establishing an event trigger condition of the water affair system; step 3, establishing a weighted fault model; step 4, establishing an event-triggered asynchronous filter model; step 5, constructing a fault detection model of the water service system; step 6, introducing a threshold alarm fault detection mechanism; and 7, designing an event trigger fault detection filter of the water service system. The invention provides a fault detection method of urban water affair system equipment, which is based on a positive half Markov jump system model, a self-adaptive event triggering strategy, an asynchronous detection strategy and a filtering fault detection method and is used for acquiring data of the flow velocity of water in a water supply pipe.

Description

Event-triggered asynchronous detection method for equipment fault of water affair system
Technical Field
The invention belongs to the field of automatic control, and particularly relates to an event-triggered asynchronous detection method for equipment faults of a water service system.
Background
With the recent development of smart cities, water supply management in each city is becoming more important, and the water service system is an indispensable part of the management of large cities. Water is a material source which people rely on to live in daily life, and nowadays when the quality of life is continuously improved, the demand of people for water is increased day by day, the water supply is unstable frequently in urban water supply, and even the water is cut off due to the problems of equipment failure and the like. Therefore, the fault of the urban water service system equipment needs to be detected in time, and the water supply accident that the water supply system cannot work normally due to the equipment problem is avoided. The water supply system of the urban water service mainly comprises a water source, a pump station, a water supply tank, a water supply network management, a water pipe valve, a water department and the like, wherein the pump station, the water pipe valve and the water supply network play an important role in the urban water supply system. In most cities, water service pipe networks and water pipe valves are buried underground, which makes it difficult to monitor and maintain. Therefore, many problems of the water pipe network and the water pipe valve in long-time work cannot be monitored and processed in time, so that the urban water supply system is unsafe, even the water in a local area is cut off, and the daily life of people is seriously influenced.
In an actual water service system network, engineers hope that the system model is as accurate as possible, so that the essential characteristics of the system can be truly reflected. Therefore, how to accurately model is the primary problem in dealing with the failure of the water system. The flow rate of water in the water pipe, the pressure of the water pipe wall, the water level of the water tank, etc., which are all non-negative values. If modeling with a general system is prone to cause modeling inaccuracies, the proposed fault resolution method cannot naturally function effectively in a real system in the case of inaccurate modeling. In consideration of the superiority of the positive system in modeling a non-negative variable system, it is more reasonable to model the water affair system by using the positive system. Because the flow rate of water in the water pipe is always fluctuated and random due to the influence of a plurality of factors, the flow rate is easy to generate sudden change when a system is in failure. Therefore, the half Markov jump process is adopted to describe the sudden change phenomenon of the variables such as the flow velocity and the like.
In general, due to technical and design costs, devices have problems of insufficient capacity and limited functions. These present some application barriers. For example, in a control system, it is desirable that the switching of the controller and the switching of the system are synchronous, and in fact, the switching of the controller and the system is asynchronous due to the fact that a sensor needs a certain time when the system is switched; in filter systems, the filters and corresponding system switching also cause asynchronous phenomena due to the low performance of the sensors. Another problem in applications is sampling, periodic sampling being often used to ensure system performance. However, periodic sampling is not easily implemented due to the availability of resources, e.g., network bandwidth, low efficiency of components, etc. When the network is in a congestion state, the method of still putting data packets into the network channel only makes the network congestion more serious; when the pipe network is already in a saturated state, the water pumping amount of the pump station is continuously increased, and pipe explosion is easier to occur. In addition, periodic sampling easily causes resource waste and high design cost. The system signals may not be updated, particularly if system performance has been expected.
Disclosure of Invention
The invention aims to provide an event trigger asynchronous detection method aiming at equipment faults of a water service system, so as to solve the technical problem that the existing water service system is unstable in water supply and easy to cut off water supply.
In order to solve the technical problem, the specific technical scheme of the event-triggered asynchronous detection method for the equipment fault of the water service system is as follows:
an event-triggered asynchronous detection method for equipment failure of a water service system comprises the following steps:
step 1, establishing a state space model of a water affair system;
step 2, establishing an event trigger condition of the water affair system;
step 3, establishing a weighted fault model;
step 4, establishing an event-triggered asynchronous filter model;
step 5, constructing a fault detection model of the water service system;
step 6, introducing a threshold alarm fault detection mechanism;
and 7, designing an event trigger fault detection filter of the water service system.
Further, the state space model of the water affairs system in step 1 is as follows:
Figure BDA0003308057310000021
Figure BDA0003308057310000022
wherein x (t) e RnRepresents the working state of the water supply network management system, u (t) epsilon RqExpressing the flow of water in the water supply network pipe in unit time, q expressing the quantity of the water supply network pipe, y (t) epsilon RpFor system output, p represents the dimension of y (t),
Figure BDA0003308057310000023
representing the disturbance of the external environment to the water flow in the water supply network pipes, m representing the number of water supply network pipes,
Figure BDA0003308057310000024
indicating a controller fault signal to be detected in a water supply network management, q indicating the number of controlled devices, ga(x(t))＝(ga1(x1(t)),ga2(x2(t)),…,gan(xn(t)))TRepresents the non-linearity of the system, gb(. is a number similar to g)aA non-linear function of (·); r istRepresenting a half-Markov jump in a finite set
Figure BDA0003308057310000025
Internal value taking; let r betI, i ∈ S, then Ai,Bi,Ci,Di,Ei,FiA coefficient matrix representing the system, wherein AiIs a Metzler matrix, others are known non-negative constant matrices of appropriate dimensions;
Figure BDA0003308057310000031
the mode representing the fault takes the value in Q ═ {1,2, …, L }, whichIn
Figure BDA0003308057310000032
Representing the total number of faults;
Figure BDA0003308057310000033
is defined as
Figure BDA0003308057310000034
Wherein
Figure BDA0003308057310000035
Is either 1 or 0 if
Figure BDA0003308057310000036
It is indicated that there is no failure,
Figure BDA0003308057310000037
further, the step 2 is constructed as follows:
tι+1d＝tιd+min{t-tιd||m(t)||1＞β(t)||y(t)||1}，
wherein the content of the first and second substances,
Figure BDA0003308057310000038
is a known constant, tιIndicating the iota event trigger time, m (t) indicating an error in measuring water flow in the water supply line,
Figure BDA0003308057310000039
wherein
Figure BDA00033080573100000310
Representing a natural number, which represents the time tlThe flow rate of water in the water supply pipe, beta (t), meets the following adaptive law:
Figure BDA00033080573100000311
wherein beta is0,
Figure BDA00033080573100000312
Are given constants.
Further, the structural form of step 3 is as follows:
Figure BDA00033080573100000313
fw(t)＝Cwga(xw(t))+Dwf(t),
wherein x isw(t)∈RnIs a vector of the weighted states of the state,
Figure BDA00033080573100000314
is a weighted fault signal, Aw,Bw,Cw,DwIs a matrix of known coefficients with suitable dimensions.
Further, the structural form of step 4 is as follows:
Figure BDA00033080573100000315
Figure BDA00033080573100000316
wherein x isf(t)∈RnRepresenting the state signal of the filter, rf(t)∈RqWhich represents the residual signal, is then used,
Figure BDA00033080573100000317
representing the filter input, deltatRepresenting a half-Markov jump in a finite set
Figure BDA00033080573100000318
Internal value taking; let deltat＝l,l∈S，Afl,Bfl,Cfl,Dfl,EflIs the filter matrix to be designed;
system mode rtAnd filter mode deltatThe relationship between them is represented by the following probability:
Pr{δt＝l|rt＝i}＝θil,
for any purpose
Figure BDA0003308057310000041
Further, the fault detection model of step 5 is as follows:
Figure BDA0003308057310000042
Figure BDA0003308057310000043
wherein
Figure BDA0003308057310000044
e(t)＝rf(t)-fw(t)
Figure BDA0003308057310000045
Figure BDA0003308057310000046
Figure BDA0003308057310000047
Further, step 6 introduces a threshold alarm failure detection mechanism as follows:
Figure BDA0003308057310000048
wherein T represents the evaluation time, Jr(T) residual evaluation functionNumber, according to the residual evaluation function, the threshold is defined as:
Figure BDA0003308057310000049
when J (T) is less than or equal to JthWhen the fault does not occur, the system operates normally, and when J (T) is more than JthWhen the alarm is in use, the alarm is generated.
Further, step 7 comprises the following specific steps:
step 7.1: the designed event triggered failure detection filter system matrix is as follows:
Figure BDA00033080573100000410
Figure BDA00033080573100000411
Figure BDA00033080573100000412
wherein R isn(Vector)
Figure BDA00033080573100000413
RqVector xiνl＞0,ρνl> 0, mu, v are intermediate variables for designing the filter, 1nRepresenting an n-dimensional vector with elements all being 1,
Figure BDA00033080573100000414
an n-dimensional vector representing the μ -th element as 1 and the remaining elements as 0, 1qRepresenting a q-dimensional vector with elements all being 1,
Figure BDA0003308057310000051
q-dimensional vector representing that the ν th element is 1 and the other elements are 0;
step 7.2: design constant
Figure BDA0003308057310000052
(Vector)
Figure BDA0003308057310000053
RpVector ηl＞0,ημl＞0,ξνl> 0 so that:
Figure BDA0003308057310000054
Figure BDA0003308057310000055
Figure BDA0003308057310000056
Figure BDA0003308057310000057
Figure BDA0003308057310000058
Figure BDA0003308057310000059
Figure BDA00033080573100000510
Figure BDA00033080573100000511
Figure BDA00033080573100000512
Figure BDA00033080573100000513
Figure BDA00033080573100000514
δμl＜δl,ημl＜ηl,α≥nσ,
for any v 1,2, <, n, v 1,2, <, q, under the event triggering condition of step 2, the filter designed in step 7.1 is used, so that the water affairs system fault detection system designed in step 4 is positive and L is L1Are randomly stabilized, wherein
Figure BDA00033080573100000515
Step 7.3: according to the conditions of step 2, step 7.1 and step 7.2, obtaining the condition for ensuring that the fault detection system is positive:
Figure BDA00033080573100000516
Figure BDA00033080573100000517
wherein the content of the first and second substances,
Figure BDA0003308057310000061
Cil＝(EflZ1Ci Cfl Dfl-Cw),D il＝(0 EflZ1Di),
step 7.4: considering the influence of various external uncertain factors on the water service system, considering the following constraint performance:
Figure BDA0003308057310000062
step 7.5: obtaining conditions for ensuring the random stability of the fault detection system according to the step 2 and the step 7.1:
Figure BDA0003308057310000063
Figure BDA0003308057310000064
wherein the content of the first and second substances,
Figure BDA0003308057310000065
Figure BDA0003308057310000066
step 7.6: designing a random Lyapunov function
Figure BDA0003308057310000067
Wherein
Figure BDA0003308057310000068
Its weak infinitesimal small operator is:
Figure BDA0003308057310000069
according to the conditions in step 7.2, one can obtain:
Figure BDA00033080573100000610
the fault detection system is L under the designed event triggered filter as illustrated by step 7.61And (4) random stabilization.
The event trigger asynchronous detection method for the equipment fault of the water service system has the following advantages that: the invention provides an event trigger strategy and an asynchronous detection method based on a positive half Markov jump system, which can effectively detect faults of conveying equipment by carrying out data acquisition on the flow of water in a water supply pipeline of a municipal water supply system, thereby effectively solving a series of problems of unstable water supply, water cut-off and the like in the municipal water supply system. The positive Markov jump system is utilized to model the system, a state space model of the system is established, and the problem of random interference caused by an external environment can be well solved. The event trigger filter is designed through the Lyapunov function of the design system to ensure that the fault detection system is L1And (4) the product is stable.
Drawings
FIG. 1 is a schematic diagram of a water supply network system framework of the present invention;
fig. 2 is a flow chart of a water supply network system fault detection method of the present invention.
Detailed Description
In order to better understand the purpose, structure and function of the present invention, the following describes an event-triggered asynchronous detection method for a water service system equipment failure in further detail with reference to the attached drawings.
The invention provides a fault detection method of urban water service system equipment, which is based on a positive half Markov jump system model, a self-adaptive event triggering strategy, an asynchronous detection strategy and a fault detection method based on a filter and used for acquiring data of the flow velocity of water in a water supply pipe.
As shown in fig. 1, a dynamic model of a water service water supply system is established by using the water supply system as a research object, using water flow in a water supply network pipe as a control input, and using a detection signal of a control device as an output. The method comprises the following specific steps:
step 1, establishing a state space model of a water affair system, wherein the specific method comprises the following steps:
1.1, collecting input and output data of a water affair system to describe an actual system:
considering the water supply network of a water service system, the water supply network is generally composed of water sources, pumping stations, water supply tanks, water supply network pipes, water pipe valves, water departments, and the like, and fig. 1 shows the relationship between these elements. The general flow of the water supply system is shown in figure 1, with black arrows indicating the water supply lines, the water supply being delivered via the pumping stations to the water tanks, and being delivered via the valves to the distribution devices, the distribution device starting to distribute the water on demand to the various places, the water tanks in each demand place supplying water on demand. In the water supply process, various uncertain factors cause unstable water supply and even water cut-off, and at the moment, the faults of the water supply equipment need to be found in time and maintained and processed in time. Fig. 2 shows a fault detection process of the water supply network system, which considers that water flow in a water supply network management is random and non-negative, so that a positive half-markov jump system is adopted to model the water service system and detect faults thereof, thereby preventing unstable water supply and water cut-off in the water supply process.
1.2, constructing a state space model of the water affair system:
Figure BDA0003308057310000071
Figure BDA0003308057310000072
wherein x (t) e RnRepresents the working state of the water supply network management system, u (t) epsilon RqExpressing the flow of water in the water supply network pipe in unit time, q expressing the quantity of the water supply network pipe, y (t) epsilon RpFor system output, p represents the dimension of y (t),
Figure BDA0003308057310000073
indicating disturbance of external environment to water flow in water supply network pipeAnd m represents the number of the water supply network pipes,
Figure BDA0003308057310000081
indicating a controller fault signal to be detected in a water supply network management, q indicating the number of controlled devices, ga(x(t))＝(ga1(x1(t)),ga2(x2(t)),…,gan(xn(t)))TRepresents the non-linearity of the system, gb(. is a number similar to g)aA non-linear function of (·). r istRepresenting a half-Markov jump in a finite set
Figure BDA0003308057310000082
An internal value. For convenience, let rtI, i ∈ S, then Ai,Bi,Ci,Di,Ei,FiA coefficient matrix representing the system, wherein AiIs a Metzler matrix, others are known non-negative constant matrices of appropriate dimensions.
Figure BDA0003308057310000083
A mode representing a fault, taken in Q ═ {1,2, L }, where
Figure BDA0003308057310000084
Indicating the total number of faults.
Figure BDA0003308057310000085
Is defined as
Figure BDA0003308057310000086
Wherein
Figure BDA0003308057310000087
Is either 1 or 0 if
Figure BDA0003308057310000088
It is indicated that there is no failure,
Figure BDA0003308057310000089
step 2, establishing an event trigger condition of the water affair system, wherein the structure form is as follows:
tι+1d＝tιd+min{t-tιd||m(t)||1＞β(t)||y(t)||1}，
wherein the content of the first and second substances,
Figure BDA00033080573100000810
is a known constant, tιIndicating the iota event trigger time, m (t) indicating an error in measuring water flow in the water supply line,
Figure BDA00033080573100000811
wherein
Figure BDA00033080573100000812
Representing a natural number, which represents the time tlThe flow rate of water in the water supply pipe, beta (t), meets the following adaptive law:
Figure BDA00033080573100000813
wherein beta is0,
Figure BDA00033080573100000814
Are given constants.
Step 3, establishing a weighted fault model, wherein the structural form is as follows:
Figure BDA00033080573100000815
fw(t)＝Cwga(xw(t))+Dwf(t),
wherein x isw(t)∈RnIs a vector of the weighted states of the state,
Figure BDA00033080573100000816
is a weighted fault signal, Aw,Bw,Cw,DwIs a matrix of known coefficients with suitable dimensions.
Step 4, establishing an event-triggered asynchronous filter model, wherein the structural form is as follows:
Figure BDA00033080573100000817
Figure BDA00033080573100000818
wherein x isf(t)∈RnRepresenting the state signal of the filter, rf(t)∈RqWhich represents the residual signal, is then used,
Figure BDA00033080573100000819
representing the filter input, deltatRepresenting a half-Markov jump in a finite set
Figure BDA00033080573100000820
An internal value. For convenience, let δt＝l,l∈S，Afl,Bfl,Cfl,Dfl,EflIs the filter matrix to be designed.
In addition, the system mode rtAnd filter mode deltatThe relationship between can be represented by the following probability:
Pr{δt＝l|rt＝i}＝θil,
for any i e S,
Figure BDA0003308057310000091
step 5, constructing a fault detection model of the water service system:
Figure BDA0003308057310000092
Figure BDA0003308057310000093
wherein
Figure BDA0003308057310000094
e(t)＝rf(t)-fw(t)
Figure BDA0003308057310000095
Figure BDA0003308057310000096
Figure BDA0003308057310000097
Step 6, introducing a threshold alarm fault detection mechanism:
Figure BDA0003308057310000098
wherein T represents the evaluation time, Jr(T) denotes a residual evaluation function, according to which the threshold is defined as:
Figure BDA0003308057310000099
when J (T) is less than or equal to JthWhen the fault does not occur, the system operates normally, and when J (T) is more than JthWhen the alarm is in use, the alarm is generated.
Step 7, designing an event trigger fault detection filter of the water service system:
the event-triggered failure detection filter system matrix of the 7.1 design is as follows:
Figure BDA00033080573100000910
Figure BDA00033080573100000911
Figure BDA00033080573100000912
wherein R isn(Vector)
Figure BDA0003308057310000101
RqVector xiνl＞0,ρνl> 0, mu, v are intermediate variables for designing the filter, 1nRepresenting an n-dimensional vector with elements all being 1,
Figure BDA0003308057310000102
an n-dimensional vector representing the μ -th element as 1 and the remaining elements as 0, 1qRepresenting a q-dimensional vector with elements all being 1,
Figure BDA0003308057310000103
and q-dimensional vectors representing that the ν -th element is 1 and the remaining elements are 0.
7.2 design constant
Figure BDA0003308057310000104
Rn(Vector)
Figure BDA0003308057310000105
RpVector ηl＞0,ημl＞0,ξνl> 0 so that:
Figure BDA0003308057310000106
Figure BDA0003308057310000107
Figure BDA0003308057310000108
Figure BDA0003308057310000109
Figure BDA00033080573100001010
Figure BDA00033080573100001011
Figure BDA00033080573100001012
Figure BDA00033080573100001013
Figure BDA00033080573100001014
Figure BDA00033080573100001015
Figure BDA00033080573100001016
δμl＜δl,ημl＜ηl,α≥nσ,
for any v 1,2, …, n, v 1,2, …, q, under the event triggering condition of step 2, the filter designed in step 7.1 is used, so that the water service system fault detection system designed in step 4 is positive and L is L1Are randomly stabilized, wherein
Figure BDA00033080573100001017
7.3 according to the conditions of step 2, step 7.1 and step 7.2, obtaining the condition for ensuring the fault detection system to be positive:
Figure BDA00033080573100001018
Figure BDA00033080573100001019
wherein the content of the first and second substances,
Figure BDA0003308057310000111
Cil＝(EflZ1Ci Cfl Dfl-Cw),D il＝(0 EflZ1Di),
7.4 considering the influence of various external uncertain factors on the water service system, and considering the following constraint performance:
Figure BDA0003308057310000112
7.5 obtaining the conditions for ensuring the random stability of the fault detection system according to the step 2 and the step 7.1:
Figure BDA0003308057310000113
Figure BDA0003308057310000114
wherein the content of the first and second substances,
Figure BDA0003308057310000115
Figure BDA0003308057310000116
7.6 design random Lyapunov function
Figure BDA0003308057310000117
Wherein
Figure BDA0003308057310000118
Its weak infinitesimal small operator is:
Figure BDA0003308057310000119
according to the conditions in step 7.2, one can obtain:
Figure BDA00033080573100001110
the fault detection system is L under the designed event triggered filter as illustrated by step 7.61And (4) random stabilization.
It is to be understood that the present invention has been described with reference to certain embodiments, and that various changes in the features and embodiments, or equivalent substitutions may be made therein by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (8)

1. An event-triggered asynchronous detection method for equipment failure of a water service system is characterized by comprising the following steps:
step 1, establishing a state space model of a water affair system;
step 2, establishing an event trigger condition of the water affair system;
step 3, establishing a weighted fault model;
step 4, establishing an event-triggered asynchronous filter model;
step 5, constructing a fault detection model of the water service system;
step 6, introducing a threshold alarm fault detection mechanism;
and 7, designing an event trigger fault detection filter of the water service system.
2. The method for asynchronous event-triggered detection of equipment failure in a water system according to claim 1, wherein the state space model of the water system of step 1 is as follows:
Figure FDA0003308057300000011
Figure FDA0003308057300000012
wherein x (t) e RnRepresents the working state of the water supply network management system, u (t) epsilon RqExpressing the flow of water in the water supply network pipe in unit time, q expressing the quantity of the water supply network pipe, y (t) epsilon RpFor system output, p represents the dimension of y (t),
Figure FDA0003308057300000013
representing the disturbance of the external environment to the water flow in the water supply network pipes, m representing the number of water supply network pipes,
Figure FDA0003308057300000014
indicating a controller fault signal to be detected in a water supply network management, q indicating the number of controlled devices, ga(x(t))＝(ga1(x1(t)),ga2(x2(t)),…,gan(xn(t)))TRepresents the non-linearity of the system, gb(. is a number similar to g)aA non-linear function of (·); r istRepresenting a half-markov jump process, in a finite set S ═ 1,2, N,
Figure FDA0003308057300000015
internal value taking; let r betI, i ∈ S, then Ai,Bi,Ci,Di,Ei,FiA coefficient matrix representing the system, wherein AiIs a Metzler matrix, others are known non-negative constant matrices of appropriate dimensions;
Figure FDA0003308057300000016
a mode representing a fault, taken in Q ═ {1,2, …, L }, where
Figure FDA0003308057300000017
Representing the total number of faults;
Figure FDA0003308057300000018
is defined as
Figure FDA0003308057300000019
Wherein
Figure FDA00033080573000000110
Is either 1 or 0 if
Figure FDA00033080573000000111
It is indicated that there is no failure,
Figure FDA00033080573000000112
3. the asynchronous event-triggered detection method of equipment failure in a water service system according to claim 2, wherein the step 2 is constructed in the form of:
tι+1d＝tιd+min{t-tιd|||m(t)||1＞β(t)||y(t)||1}，
wherein the content of the first and second substances,
Figure FDA0003308057300000021
Figure FDA0003308057300000022
is a known constant, tιIndicating the iota event trigger time, m (t) indicating an error in measuring water flow in the water supply line,
Figure FDA0003308057300000023
wherein
Figure FDA0003308057300000024
t∈[tι,tι+1),
Figure FDA0003308057300000025
Figure FDA0003308057300000026
Representing a natural number, which represents the time tlThe flow rate of water in the water supply pipe, beta (t), meets the following adaptive law:
Figure FDA0003308057300000027
wherein beta is0,
Figure FDA0003308057300000028
Are given constants.
4. The asynchronous event-triggered detection method of equipment failure in a water service system according to claim 3, wherein the step 3 is structured as follows:
Figure FDA0003308057300000029
fw(t)＝Cwga(xw(t))+Dwf(t),
wherein x isw(t)∈RnIs a vector of the weighted states of the state,
Figure FDA00033080573000000210
is a weighted fault signal, Aw,Bw,Cw,DwIs a matrix of known coefficients with suitable dimensions.
5. The asynchronous event-triggered detection method of equipment failure in a water service system according to claim 4, wherein the structure form of step 4 is as follows:
Figure FDA00033080573000000211
Figure FDA00033080573000000212
wherein x isf(t)∈RnRepresenting the state signal of the filter, rf(t)∈RqWhich represents the residual signal, is then used,
Figure FDA00033080573000000213
representing the filter input, deltatRepresenting a half-markov jump process, in a finite set S ═ 1,2, N,
Figure FDA00033080573000000214
internal value taking; let deltat＝l,l∈S，Afl,Bfl,Cfl,Dfl,EflIs the filter matrix to be designed;
system modertAnd filter mode deltatThe relationship between them is represented by the following probability:
Pr{δt＝l|rt＝i}＝θil,
for any i e S, S ═ {1,2, …, N },
Figure FDA00033080573000000215
0≤θil≤1,
Figure FDA00033080573000000216
6. the event-triggered asynchronous detection method of equipment failure in water service system according to claim 5, characterized in that the failure detection model of step 5 is as follows:
Figure FDA0003308057300000031
Figure FDA0003308057300000032
wherein
Figure FDA0003308057300000033
e(t)＝rf(t)-fw(t)
Figure FDA0003308057300000034
Figure FDA0003308057300000035
Figure FDA0003308057300000036
7. The method of claim 6, wherein step 6 introduces a threshold alarm failure detection mechanism as follows:
Figure FDA0003308057300000037
wherein T represents the evaluation time, Jr(T) denotes a residual evaluation function, according to which the threshold is defined as:
Figure FDA0003308057300000038
when J (T) is less than or equal to JthWhen the fault does not occur, the system operates normally, and when J (T) is more than JthWhen the alarm is in use, the alarm is generated.
8. The asynchronous event-triggered detection method for equipment failure in water system according to claim 7, wherein step 7 comprises the following specific steps:
step 7.1: the designed event triggered failure detection filter system matrix is as follows:
Figure FDA0003308057300000039
Figure FDA00033080573000000310
Figure FDA00033080573000000311
wherein R isn(Vector)
Figure FDA00033080573000000312
Rq(Vector)
Figure FDA00033080573000000313
μ, v are intermediate variables for designing the filter, 1nRepresenting an n-dimensional vector with elements all being 1,
Figure FDA0003308057300000041
an n-dimensional vector representing the μ -th element as 1 and the remaining elements as 0, 1qRepresenting a q-dimensional vector with elements all being 1,
Figure FDA0003308057300000042
q-dimensional vector representing that the ν th element is 1 and the other elements are 0;
step 7.2: the design constant alpha is more than 0,
Figure FDA0003308057300000043
γ＞0,σ＞0,ι1＞0,ι2＞0,κ1＞0,κ2＞0,Rn(Vector)
Figure FDA0003308057300000044
Rp(Vector)
Figure FDA0003308057300000045
Figure FDA0003308057300000046
such that:
Figure FDA0003308057300000047
Figure FDA0003308057300000048
Figure FDA0003308057300000049
Figure FDA00033080573000000410
Figure FDA00033080573000000411
Figure FDA00033080573000000412
Figure FDA00033080573000000413
Figure FDA00033080573000000414
Figure FDA00033080573000000415
Figure FDA00033080573000000416
Figure FDA00033080573000000417
Figure FDA00033080573000000418
α≥nσ,
for any v 1,2, …, n, v 1,2, …, q, under the event triggering condition of step 2, the filter designed in step 7.1 is used, so that the water service system fault detection system designed in step 4 is positive and L is L1Are randomly stabilized, wherein
Figure FDA00033080573000000419
Step 7.3: according to the conditions of step 2, step 7.1 and step 7.2, obtaining the condition for ensuring that the fault detection system is positive:
Figure FDA00033080573000000420
Figure FDA00033080573000000421
wherein the content of the first and second substances,
Figure FDA0003308057300000051
C il＝(EflZ1Ci Cfl Dfl-Cw),D il＝(0EflZ1Di),
step 7.4: considering the influence of various external uncertain factors on the water service system, considering the following constraint performance:
Figure FDA0003308057300000052
step 7.5: obtaining conditions for ensuring the random stability of the fault detection system according to the step 2 and the step 7.1:
Figure FDA0003308057300000053
Figure FDA0003308057300000054
wherein the content of the first and second substances,
Figure FDA0003308057300000055
Figure FDA0003308057300000056
step 7.6: designing a random Lyapunov function
Figure FDA0003308057300000057
Wherein
Figure FDA0003308057300000058
Its weak infinitesimal small operator is:
Figure FDA0003308057300000059
according to the conditions in step 7.2, one can obtain:
Figure FDA00033080573000000510
the fault detection system is L under the designed event triggered filter as illustrated by step 7.61And (4) random stabilization.
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