CN113985197B - Event triggering asynchronous detection method for equipment faults of water service system - Google Patents
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Abstract
The invention belongs to the field of automatic control, and discloses an event triggering 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 event triggering conditions of the water service system; step 3, building a weighted fault model; step 4, establishing an event triggering 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-triggered fault detection filter of the water service system. The invention provides a fault detection method of urban water service system equipment based on a positive semi-Markov jump system model, a self-adaptive event triggering strategy, an asynchronous detection strategy and a filtering fault detection method, which is used for collecting data of the flow rate of water in a water supply pipe.
Description
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, supply management of water resources by each city is becoming more important, and water service systems are an indispensable part of management of large cities. Water is a living material in daily life, and the demand of people for water is increasing day by day, and water supply is unstable frequently in urban water supply and even water is cut off due to equipment faults and other problems. 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 equipment problems is avoided. The water supply system for urban water service mainly comprises a water source, a pump station, a water supply tank, a water supply network pipe, 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, the water service pipe network and the water pipe valve are buried underground, which makes it difficult to monitor and maintain. Therefore, various problems of the water service pipe network and the water pipe valve in long-time work cannot be monitored and treated in time, so that the urban water supply system is unsafe, and even the problem of water interruption in a local area occurs, which seriously affects the daily life of people.
In an actual water service system network, engineering personnel hope that the more accurate and the better the system model is, the more the engineering personnel can truly reflect the essential characteristics of the system. Thus, how to accurately model is a primary problem in dealing with water service system failures. The flow rate of the water in the water pipe, the pressure of the water pipe wall, the water level of the water tank, etc., are all in a non-negative state. If modeling is easy to cause inaccuracy in modeling by using a general system, the fault solution method proposed in the case of inaccurate modeling cannot naturally play an effective role in a practical system. In view of the superiority of positive systems in modeling non-negative variable systems, it is more reasonable to model water service systems with positive systems. Since the flow rate of water in a water pipe is always fluctuated due to many factors, the flow rate is random, and the flow rate is easy to be suddenly changed when the system is in fault. Therefore, a half Markov jump process is used to describe abrupt changes in variables such as flow rate.
In general, components have problems of insufficient capacity and limited functions due to technical and design costs and the like. These can 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 practice, the switching of the controller and the system is asynchronous due to the fact that the sensor requires a certain time when measuring the switching of the system; in a filter system, the filters and corresponding system switching also cause asynchronization due to the inefficiency of the sensors. Another problem in applications is sampling, which is often used to ensure system performance. However, periodic sampling is not easily implemented due to resource availability, e.g., bandwidth of the network, inefficiency of components, etc. When the network is in a congestion state, the method of still putting the data packets into the network channel only causes the network congestion to be more serious; when the pipe network is in a saturated state, the pumping water quantity of the pump station is continuously increased, and pipe explosion is more likely to occur. Furthermore, periodic sampling is prone to resource waste and high design costs. The system signal may not be updated, especially in case the system performance has reached expectations.
Disclosure of Invention
The invention aims to provide an event triggering asynchronous detection method aiming at equipment faults of a water service system, so as to solve the technical problem that water supply of the existing water service system is unstable and water is easy to break.
In order to solve the technical problems, the specific technical scheme of the event-triggered asynchronous detection method for the equipment faults of the water service system is as follows:
an event-triggered asynchronous detection method for equipment faults of a water service system comprises the following steps:
step 1, establishing a state space model of a water service system;
step 2, establishing event triggering conditions of the water service system;
step 3, building a weighted fault model;
step 4, establishing an event triggering 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-triggered fault detection filter of the water service system.
Further, the state space model of the water service system in step 1 is as follows:
wherein x (t) ∈R n Indicating the working state of the water supply network pipe, u (t) epsilon R q The flow of water in the water supply network pipe in unit time is represented, q represents the number of the water supply network pipes, y (t) epsilon R p For the system output, p represents the dimension of y (t),represents disturbance of external environment to water flow in water supply network management, m represents number of water supply network management, and +.>A controller fault signal to be detected in a water supply network management is represented, q represents the number of controlled devices, g a (x(t))＝(g a1 (x 1 (t)),g a2 (x 2 (t)),…,g an (x n (t))) T Representing the nonlinearity of the system g b (. Cndot.) is a similar g a A nonlinear function of (-); r is (r) t Representing a semi-Markov jump process in a finite set +.>Taking an internal value; let r t =i, i e S, then a i ,B i ,C i ,D i ,E i ,F i Representing a coefficient matrix of the system, wherein A i Is a Metzler matrix, the others are all known to be non-negative constant matrices of appropriate dimensions; />Representing the mode of failure, take a value in q= {1,2, …, L }, where +.>Representing the total fault number;defined as->Wherein->Either 1 or 0, if +.>It is an indication that there is no fault,
further, the construction form of the step 2 is as follows:
t ι+1 d＝t ι d+min{t-t ι d||m(t)|| 1 ＞β(t)||y(t)|| 1 }，
wherein,is a known constant, t ι Indicating the trigger time of the iota event, m (t) indicating the error in measuring the water flow of the water supply line,/->Wherein->Represents a natural number, which represents the time t l The flow rate of water in the water supply pipe, beta (t), satisfies the following adaptive law:
wherein beta is 0 ,Are given constants.
Further, the structural form of step 3 is as follows:
f w (t)＝C w g a (x w (t))+D w f(t),
wherein x is w (t)∈R n Is a weighted state vector of the states,is a weighted fault signal, A w ,B w ,C w ,D w Is a matrix of known coefficients with suitable dimensions。
Further, the structural form of step 4 is as follows:
wherein x is f (t)∈R n Representing the state signal of the filter, r f (t)∈R q The residual signal is represented by a signal representing,representing the filter input, delta t Representing a semi-Markov jump process in a finite set +.>Taking an internal value; let delta t ＝l,l∈S，A fl ,B fl ,C fl ,D fl ,E fl Is a filter matrix to be designed;
system mode r t And filter mode delta t The relationship between these is expressed by the following probabilities:
Pr{δ t ＝l|r t ＝i}＝θ il ,
for any one
Further, the fault detection model of step 5 is as follows:
wherein the method comprises the steps ofe(t)＝r f (t)-f w (t)
Further, the threshold alarm fault detection mechanism introduced in step 6 is as follows:
wherein T represents the evaluation time, J r (T) represents a residual evaluation function, from which the threshold is defined as:
when J (T) is less than or equal to J th When J (T) > J, the system is normal th When a fault is indicated, an alarm is generated.
Further, the step 7 comprises the following specific steps:
step 7.1: the designed event-triggered fault detection filter system matrix is as follows:
wherein R is n (Vector)R q Vector xi νl ＞0,ρ νl > 0, μ, v is an intermediate variable in the design of the filter, 1 n N-dimensional vector representing all elements 1, < ->N-dimensional vector representing the mu-th element as 1 and the remaining elements as 0, 1 q Q-dimensional vector representing all elements 1, < ->A q-dimensional vector representing that the v-th element is 1 and the remaining elements are 0;
step 7.2: design constant(Vector)R p Vector eta l ＞0,η μl ＞0,ξ νl > 0 such that:
δ μl ＜δ l ,η μl ＜η l ,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 1 Randomly stable, wherein
Step 7.3: according to the conditions of the step 2, the step 7.1 and the step 7.2, the condition that the fault detection system is positive is obtained:
wherein,
C il ＝(E fl Z 1 C i C fl D fl -C w ),D il ＝(0 E fl Z 1 D i ),
step 7.4: considering the influence of various external uncertain factors on the water service system, consider the following constraint performance:
step 7.5: obtaining the condition for ensuring the random stability of the fault detection system according to the step 2 and the step 7.1:
wherein,
step 7.6: design of random Liapunov functionWherein the method comprises the steps ofThe weak infinite small operator is:
from the conditions in step 7.2, it is possible to obtain:
description of the Fault detection System being L under the designed event triggered Filter according to step 7.6 1 Randomly stable.
The event triggering asynchronous detection method for the equipment faults of the water service system has the following advantages: the invention provides an event triggering asynchronous detection method for equipment faults of a water service system, which is based on an event triggering strategy of a positive semi-Markov jump system and an asynchronous detection method and aims at data acquisition of water flow in a water supply pipeline of the water service system. The system is modeled by using the positive Markov jump system, a state space model of the system is established, and the problem of random interference caused by external environment can be well solved. Event triggered filter design by lyapunov function of design system to ensure fault detection system is L 1 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 method for detecting faults of a water supply network system according to the present invention.
Detailed Description
For better understanding of the purpose, structure and function of the present invention, the following describes in further detail an event-triggered asynchronous detection method for equipment failure of a water service system with reference to the accompanying drawings.
The invention provides a fault detection method of urban water service system equipment, which is based on a positive semi-Markov jump system model, a self-adaptive event triggering strategy, an asynchronous detection strategy and a fault detection method based on a filter, and can be used for effectively detecting faults of the urban water service control water supply equipment in real time, so that the problems of unstable water supply and water interruption are effectively solved.
As shown in fig. 1, the water supply system is taken as a study object, the water flow in the water supply network management is taken as a control input, and the detection signal of the control equipment is taken as an output, so as to establish a dynamic model of the water supply system. The method comprises the following specific steps:
step 1, a state space model of a water service system is established, and the specific method is as follows:
1.1, collecting input and output data of a water service system to describe an actual system:
considering the water supply network of a water service system, the water supply network is generally composed of a water source, a pump station, a water supply tank, a water supply network pipe, a water pipe valve, a water department and the like, and fig. 1 shows the connection between these elements. In fig. 1, the general flow of the water supply system is shown, with black arrows indicating the water supply lines, the water supply being fed through the pump stations to the water tanks, and the distribution equipment starting to distribute the water on demand to the different places, where the water tanks in each demand place supply the water on demand, when fed through the valves to the distribution means. Various uncertain factors exist in the water supply process to cause unstable water supply and even water interruption, and then the fault of the water supply equipment needs to be found in time and the water supply equipment needs to be maintained in time. In fig. 2, a fault detection flow of a water supply network system is shown, and the situation that water supply is unstable and water is cut off in the water supply process is prevented by taking into consideration that the water flow in the water supply network system has randomness and is non-negative, so that a positive half markov jump system is adopted to model a water service system and perform fault detection on the water service system.
1.2 constructing a state space model of the water service system:
wherein x (t) ∈R n Indicating the working state of the water supply network pipe, u (t) epsilon R q The flow of water in the water supply network pipe in unit time is represented, q represents the number of the water supply network pipes, y (t) epsilon R p For the system output, p represents the dimension of y (t),represents disturbance of external environment to water flow in water supply network management, m represents number of water supply network management, and +.>A controller fault signal to be detected in a water supply network management is represented, q represents the number of controlled devices, g a (x(t))＝(g a1 (x 1 (t)),g a2 (x 2 (t)),…,g an (x n (t))) T Representing the nonlinearity of the system g b (. Cndot.) is a similar g a (-) nonlinear function. r is (r) t Representing a semi-Markov jump process in a finite set +.>And (5) taking an internal value. For convenience let r t =i, i e S, then a i ,B i ,C i ,D i ,E i ,F i Representing a systemCoefficient matrix, wherein A i Is a Metzler matrix, the others are all known to be non-negative constant matrices of appropriate dimensions. />Representing the mode of failure, take the value in Q= {1,2, L }, where +.>Indicating the total number of faults. />Defined as->Wherein->Either 1 or 0, if +.>Then it indicates no fault ++>
Step 2, establishing event triggering conditions of the water service system, wherein the construction form is as follows:
t ι+1 d＝t ι d+min{t-t ι d||m(t)|| 1 ＞β(t)||y(t)|| 1 }，
wherein,is a known constant, t ι Indicating the trigger time of the iota event, m (t) indicating the error in measuring the water flow of the water supply line,/->Wherein->Represents a natural number, which represents the time t l The flow rate of water in the water supply pipe, beta (t), satisfies the following adaptive law:
wherein beta is 0 ,Are given constants.
Step 3, building a weighted fault model, wherein the structural form is as follows:
f w (t)＝C w g a (x w (t))+D w f(t),
wherein x is w (t)∈R n Is a weighted state vector of the states,is a weighted fault signal, A w ,B w ,C w ,D w Is a matrix of known coefficients having suitable dimensions.
Step 4, establishing an event triggering asynchronous filter model, wherein the structure form is as follows:
wherein x is f (t)∈R n Representing the state signal of the filter, r f (t)∈R q The residual signal is represented by a signal representing,representing the filter input, delta t Representing a semi-Markov jump process in a finite set +.>And (5) taking an internal value. For convenience let delta t ＝l,l∈S，A fl ,B fl ,C fl ,D fl ,E fl Is a filter matrix to be designed.
Further, system mode r t And filter mode delta t The relationship between them can be expressed with the following probabilities:
Pr{δ t ＝l|r t ＝i}＝θ il ,
for any i e S,
step 5, constructing a fault detection model of the water service system:
wherein the method comprises the steps ofe(t)＝r f (t)-f w (t)
Step 6, introducing a threshold alarm fault detection mechanism:
wherein T represents the evaluation time, J r (T) represents a residual evaluation function, from which the threshold is defined as:
when J (T) is less than or equal to J th When J (T) > J, the system is normal th When a fault is indicated, an alarm is generated.
Step 7, designing an event-triggered fault detection filter of the water service system:
7.1 the event triggered failure detection filter system matrix designed is as follows:
wherein R is n (Vector)R q Vector xi νl ＞0,ρ νl > 0, μ, v is an intermediate variable in the design of the filter, 1 n N-dimensional vector representing all elements 1, < ->N-dimensional vector representing the mu-th element as 1 and the remaining elements as 0, 1 q Q-dimensional vector representing all elements 1, < ->A q-dimensional vector representing the v-th element as 1 and the remaining elements as 0.
7.2 design constantR n (Vector)R p Vector eta l ＞0,η μl ＞0,ξ νl > 0 such that:
δ μl ＜δ l ,η μl ＜η l ,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 1 Randomly stable, wherein
7.3 according to the conditions of step 2, step 7.1 and step 7.2, the condition of ensuring that the fault detection system is positive is obtained:
wherein,
C il ＝(E fl Z 1 C i C fl D fl -C w ),D il ＝(0 E fl Z 1 D i ),
7.4 consider the influence of external various uncertain factors on the water service system, consider the following constraint performance:
7.5, obtaining the condition for ensuring the random stability of the fault detection system according to the step 2 and the step 7.1:
wherein,
7.6 design of random Liapunov functionWherein->The weak infinite small operator is:
from the conditions in step 7.2, it is possible to obtain:
description of the Fault detection System being L under the designed event triggered Filter according to step 7.6 1 Randomly stable.
It will be understood that the invention has been described in terms of several embodiments, and that various changes and equivalents may be made to these features and embodiments 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 (7)
1. An event-triggered asynchronous detection method for equipment faults of a water service system is characterized by comprising the following steps:
step 1, establishing a state space model of a water service system;
the state space model of the water service system is as follows:
wherein x (t) ∈R n Indicating the working state of the water supply network pipe, u (t) epsilon R q The flow of water in the water supply network pipe in unit time is represented, q represents the number of the water supply network pipes, y (t) epsilon R p For system output, p tableThe dimension of y (t) is shown,represents disturbance of external environment to water flow in water supply network management, m represents number of water supply network management, and +.>A controller fault signal to be detected in a water supply network management is represented, q represents the number of controlled devices, g a (x(t))＝(g a1 (x 1 (t)),g a2 (x 2 (t)),…,g an (x n (t))) T Representing the nonlinearity of the system g b () Is similar to g a () Is a nonlinear function of (2); r is (r) t Representing a semi-Markov jump process in a finite set +.>Taking an internal value; let r t =i, i e S, then a i ,B i ,C i ,D i ,E i ,F i Representing a coefficient matrix of the system, wherein A i Is a Metzler matrix, the others are all known to be non-negative constant matrices of appropriate dimensions; />Representing the mode of failure, take a value in q= {1,2, …, L }, where +.>Representing the total fault number; />Defined as->Wherein->Either 1 or 0, if +.>It is an indication that there is no fault,
step 2, establishing event triggering conditions of the water service system;
step 3, building a weighted fault model;
step 4, establishing an event triggering 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-triggered fault detection filter of the water service system.
2. The method for event-triggered asynchronous detection of equipment failure of a water service system according to claim 1, wherein the configuration of step 2 is as follows:
t ι+1 d＝t ι d+min{t-t ι d|||m(t)|| 1 ＞β(t)||y(t)|| 1 }，
wherein, is a known constant, t ι Indicating the trigger time of the iota event, m (t) indicating the error in measuring the water flow of the water supply line,/->Wherein-> Represents a natural number, which represents the time t l The flow rate of water in the water supply pipe, beta (t), satisfies the following adaptive law:
wherein the method comprises the steps ofAre given constants.
3. The event-triggered asynchronous detection method for equipment failure of water service system according to claim 2, wherein the structural form of step 3 is as follows:
f w (t)＝C w g a (x w (t))+D w f(t),
wherein x is w (t)∈R n Is a weighted state vector of the states,is a weighted fault signal, A w ,B w ,C w ,D w Is a matrix of known coefficients having suitable dimensions.
4. The method for event-triggered asynchronous detection of equipment failure in a water service system according to claim 3, wherein the structural form of step 4 is as follows:
wherein x is f (t)∈R n Representing the state signal of the filter, r f (t)∈R q The residual signal is represented by a signal representing,representing the filter input, delta t Representing a semi-Markov jump process in a finite set +.>Taking an internal value; let delta t ＝l,l∈S，A fl ,B fl ,C fl ,D fl ,E fl Is a filter matrix to be designed;
system mode r t And filter mode delta t The relationship between these is expressed by the following probabilities:
Pr{δ t ＝l|r t ＝i}＝θ il ,
for any one
5. The method for event-triggered asynchronous detection of equipment failure in a water service system of claim 4, wherein the failure detection model of step 5 is as follows:
wherein the method comprises the steps ofe(t)＝r f (t)-f w (t)
6. The method for event-triggered asynchronous detection of equipment failure in a water service system according to claim 5, wherein the threshold alarm failure detection mechanism introduced in step 6 is as follows:
wherein T represents the evaluation time, J r (T) represents a residual evaluation function, from which the threshold is defined as:
when J (T) is less than or equal to J th When J (T) > J, the system is normal th When a fault is indicated, an alarm is generated.
7. The method for event-triggered asynchronous detection of equipment failure in a water service system of claim 6, wherein step 7 comprises the specific steps of:
step 7.1: the designed event-triggered fault detection filter system matrix is as follows:
wherein R is n (Vector)R q Vector->Mu, v is an intermediate variable of the design filter, 1 n N-dimensional vector representing all elements 1, < ->N-dimensional vector representing the mu-th element as 1 and the remaining elements as 0, 1 q Q-dimensional vector representing all elements 1, < ->A q-dimensional vector representing that the v-th element is 1 and the remaining elements are 0;
step 7.2: design constant(Vector)R p Vector-> Such that:
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 1 Randomly stable, wherein
Step 7.3: according to the conditions of the step 2, the step 7.1 and the step 7.2, the condition that the fault detection system is positive is obtained:
wherein,
C il ＝(E fl Z 1 C i C fl D fl -C w ),D il ＝(0 E fl Z 1 D i ),
step 7.4: considering the influence of various external uncertain factors on the water service system, consider the following constraint performance:
step 7.5: obtaining the condition for ensuring the random stability of the fault detection system according to the step 2 and the step 7.1:
wherein,
step 7.6: design of random Liapunov functionWherein->The weak infinite small operator is:
according to the conditions in step 7.2, we get:
description of the Fault detection System being L under the designed event triggered Filter according to step 7.6 1 Randomly stable.
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| CN113486480A (en) * | 2021-06-16 | 2021-10-08 | 杭州电子科技大学 | Leakage fault filtering method for urban water supply pipe network system |
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| CN113110383A (en) * | 2021-04-13 | 2021-07-13 | 杭州电子科技大学 | Water supply fault detection method for urban water service system |
| CN113393691A (en) * | 2021-05-31 | 2021-09-14 | 杭州电子科技大学 | Urban road system traffic signal lamp fault detection method |
| CN113486480A (en) * | 2021-06-16 | 2021-10-08 | 杭州电子科技大学 | Leakage fault filtering method for urban water supply pipe network system |
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