CN113393691B - Urban road system traffic signal lamp fault detection method - Google Patents

Urban road system traffic signal lamp fault detection method Download PDF

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CN113393691B
CN113393691B CN202110599844.2A CN202110599844A CN113393691B CN 113393691 B CN113393691 B CN 113393691B CN 202110599844 A CN202110599844 A CN 202110599844A CN 113393691 B CN113393691 B CN 113393691B
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CN113393691A (en
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张俊锋
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Hangzhou Dianzi University
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Abstract

The invention discloses a method for detecting faults of traffic signal lamps of an urban road system. The invention provides a method for detecting faults of traffic lights of an urban road system based on a positive half Markov jump system modeling method, an event triggering strategy and a fault detection filter technology, aiming at carrying out data acquisition on traffic flow which randomly occurs on a road, and the method can effectively carry out fault detection on the traffic lights, thereby effectively solving a series of problems of traffic paralysis, traffic accidents and the like caused by vehicle blockage, pedestrian flow congestion and other various uncertain factors on the urban road. The fault detection filter is triggered by the design event, so that the fault of the traffic signal lamp can be detected timely, and smooth operation of a road is guaranteed.

Description

Urban road system traffic signal lamp fault detection method
Technical Field
The invention belongs to the technical field of traffic engineering, and relates to a fault detection method for an urban road system traffic signal lamp, which utilizes a random switching technology, an event triggering strategy and a filter design method to realize the fault detection of the urban traffic signal lamp.
Background
Road traffic systems play an important role in urban infrastructure. The road traffic system mainly comprises a road network system, a traffic flow and a traffic monitoring and control system, wherein the road network system mainly comprises roads and intersections and is a carrier for the traffic flow to run, and the traffic monitoring and control system is responsible for guiding the traffic flow to sequentially pass through conflict points in the road network. The road network system and the traffic monitoring and control system are like valves between the water storage tanks and the water storage tanks, and the valves control traffic flow passing through road network nodes on roads, so that traffic flow can pass through the valves safely and orderly.
With the continuous progress of the construction of smart cities in China, more and more people choose to live in cities, the construction of urban roads is continuously increased in order to meet the development requirements of the cities, the occupied area of the roads of all the people in the cities is continuously enlarged, but the urban traffic volume is continuously increased at the speed of 20 percent of the year. A strange phenomenon appears, the construction of the Mingming urban roads is increased all the time, but the urban road system does not run smoothly and is even more and more crowded. The main reason is that different areas of the city have different plans for road construction, and a large number of people are flooded in areas such as new development areas, business parks and suburbs of the city. Because the development rhythm in city is fast, people's work rhythm is fast, in order to let the travel of urban people more convenient, these regional road construction constantly increase, but this also leads to more population to gush into the city to the urban road is built and has been equipped with bigger demand. Therefore, the traffic congestion in the city cannot be solved by increasing road construction, not only traffic flow congestion factors, but also many factors can cause traffic congestion and even traffic paralysis, such as traffic signal lamp failure, randomly appearing crowds on the road, sudden traffic accidents and the like. In addition, urban traffic control and safety management in China are not perfect enough, and the method is also an important reason for urban road system congestion. In order to effectively alleviate congestion in an urban road system, a method for detecting faults of traffic lights of the urban road system is provided, and a positive half Markov jump system is adopted to model the urban road system in consideration of randomness and nonnegativity of the number of vehicles on the road. Various uncertain factors which may cause traffic congestion, such as sudden inflow of traffic, occurrence of traffic accidents, etc., are also considered. In order to effectively prevent traffic jam caused by overlarge traffic flow, an event trigger mechanism is provided, and a traffic signal lamp is adjusted to guide the traffic flow when an event trigger condition is met. Fault detection is also carried out on the traffic signal lamp, wherein a fault detection method based on a filter is most commonly used, so that an event-triggered fault detection filter is designed, and an alarm is given in time when the traffic signal lamp fails, so that traffic jam is relieved to a certain extent.
Disclosure of Invention
The invention provides a method for detecting faults of traffic signal lamps of an urban road system. The invention provides a fault detection method of an urban road system traffic signal lamp based on a positive half Markov jump system model, an event triggering strategy and a fault detection method based on a filter, aiming at data acquisition of traffic flow which randomly occurs on a road, and the method can effectively detect the fault of the traffic signal lamp, thereby effectively solving a series of problems of traffic accidents, traffic paralysis and the like caused by the influence of vehicle blockage, congestion of people and other uncertain factors on the urban road.
The technical scheme adopted by the invention for solving the problems comprises the following steps:
step 1, establishing a state space model of an urban road system, wherein the specific method comprises the following steps:
1.1, the actual traffic network is described by collecting input and output data of an urban road system:
considering the annular crossing of the urban road system, the annular crossing of the urban road system consists of four main roads, four branch roads and traffic lights for guiding vehicles, and the annular crossing is shown in a schematic diagram (see the attached drawing of the specification) in figure 1. Fig. 1 shows the relationship between the main roads, branch roads and traffic lights in the circular intersection, and the driving direction of the vehicles on each road is marked in the figure. Traffic signal lamps at each intersection in fig. 1 can play a role in regulating traffic flow of each road segment in an annular traffic network, and play a vital role in preventing vehicle congestion or traffic accidents. It is known that the time for switching traffic lights is generally fixed, however, the road conditions in the urban road system are quite complex, and congestion is easily caused when the traffic flow at the intersection is very large, for example, in fig. 1, when the main road R1 and R3 are green lights, at this time, c1 goes straight from the main road R1 to the main road R3, d1 from the branch R1 turns right, c2 from the main road R2 and d2 from the branch R2 turn right and merge into the straight traffic flow, so that traffic congestion is easily caused when vehicles from different intersections converge together, at this time, the event generator detects that the traffic flow is too large, the system switches to the working mode of prolonging the green light time of congestion and prolonging the red light time of non-congestion intersections, and when the traffic flow is normal, the system switches to the normal working mode. When the traffic signal lamp has a fault, an alarm can be sent out in time to inform related staff to process the fault. Considering that the traffic flow at the road junction is not fixed, random and non-negative, the modeling is carried out by using a positive half-Markov jump system, and the fault detection is carried out on a traffic signal lamp to prevent the traffic jam from occurring.
1.2, constructing a state space model of the urban road system:
Figure BDA0003092518370000021
y(t)＝C(rt)x(t)+D(rt)w(t)+F(rt)f(t), (1)
wherein x (t) ═ x1(t),x2(t),...,xn(t)]T∈RnNumber of vehicles, x, entering the intersection at time tj(t) is the number of vehicles on the jth road at the moment t, wherein j is more than or equal to 1 and less than or equal to n, and n represents the number of main roads. y (t) ε RpP represents the dimension of y (t) as the number of vehicles exiting a portion of the intersection at time t,
Figure BDA0003092518370000022
is an immeasurable external disturbance factor causing traffic jam (such as occurrence of traffic accident, sudden increase of traffic flow in rush hour, and the like), and m is the number of branches.
Figure BDA0003092518370000023
Is a fault signal causing traffic congestion and q represents the number of traffic lights. When the traffic signal lamp breaks down, the orderly circulation of the traffic flow can not be guided normally at the moment. r istRepresents a half-Markov jump process, where J e N is set in a finite set S1, 2+An internal value. A (r)t),B(rt),C(rt),D(rt),E(rt),F(rt) Is a known system matrix. For convenience, let rtI, i ∈ S, the system matrix can be denoted as ai,Bi,Ci,Di,Ei,Fi. Assume matrix AiIs a matrix of Metzler's,
Figure BDA0003092518370000031
Rn,
Figure BDA0003092518370000032
N+,Rn×nrespectively representing an n-dimensional vector, an n-dimensional non-negative vector, a positive integer, and an nxn-dimensional euclidean matrix space.
1.3 design half Markov jump signal rtIts transition probability λij(h) Satisfies the following conditions:
Figure BDA0003092518370000033
wherein h > 0, withΔ goes to 0 and (Δ)/Δ goes to 0, where Δ represents an independent variable and o (Δ) represents the higher order infinity of Δ. For each i ∈ S, i ≠ j there is λij(h) Is greater than 0 and
Figure BDA0003092518370000034
where N represents the number of subsystems.
Step 2, establishing an event triggering condition of the urban road system traffic flow, wherein the construction form is as follows:
||m(t)‖1＞β||y(t)‖1， (3)
wherein the constant 0 < beta < 1, m (t) is the measured traffic flow error,
Figure BDA0003092518370000035
wherein
Figure BDA0003092518370000036
Figure BDA0003092518370000037
Representing a natural number, which represents the time tιThe number of vehicles exiting the intersection, y (t), is the number of vehicles exiting the intersection at time t.
Step 3, establishing an event trigger filter model, wherein the structural form is as follows:
Figure BDA0003092518370000038
Figure BDA0003092518370000039
wherein x isf(t) represents the state signal of the filter, rf(t) denotes a residual signal, Afi,Bfi,Cfi,DfiIs the filter matrix to be designed.
Step 4, constructing a fault detection model of the traffic signal lamp of the urban road system:
Figure BDA00030925183700000310
Figure BDA00030925183700000311
wherein the content of the first and second substances,
Figure BDA00030925183700000312
e(t)＝rf(t)-f(t)，
Figure BDA00030925183700000313
Figure BDA00030925183700000314
i denotes an identity matrix having compatible dimensions.
Step 5, introducing a threshold alarm fault detection mechanism:
Figure BDA00030925183700000315
wherein T represents the evaluation time, E { } represents the mathematical expectation, L1[0, ∞) denotes L1Norm space, Jr(T) denotes a residual evaluation function, JthRepresents a threshold value, when Jr(T)＞JthWhen the alarm is in use, the alarm is generated.
Step 6, designing an event trigger fault detection filter of a traffic signal lamp in an urban road:
the event-triggered failure detection filter system matrix designed by 6.1 is as follows:
Figure BDA0003092518370000041
wherein alpha is greater than 0, Rn(Vector)
Figure BDA00030925183700000412
Rp(Vector)
Figure BDA00030925183700000417
μ, v are intermediate variables for designing the filter, 1nRepresenting an n-dimensional vector with elements all being 1,
Figure BDA0003092518370000042
an n-dimensional vector representing that the μ -th element is 1 and the remaining elements are 0, and q is the number of traffic lights.
6.2 design constants alpha > 0, beta > 0, gamma > 0, sigma > 0, Rn(Vector)
Figure BDA00030925183700000413
Rp(Vector)
Figure BDA00030925183700000414
Such that the following inequality:
Figure BDA0003092518370000043
Figure BDA0003092518370000044
Figure BDA0003092518370000045
Figure BDA0003092518370000046
Figure BDA0003092518370000047
Figure BDA0003092518370000048
Figure BDA0003092518370000049
Figure BDA00030925183700000415
for each μ 1,2,., n, ν 1, 2., q, this holds true with the filter designed in step 6.1, where α is an intermediate variable that proves that the fault detection system is in use, β is a coefficient in the event trigger condition, γ is L1Gain performance index, σ is an intermediate variable that ensures stable use of the fault detection system, Z1＝I-β1p×p，Z2＝I+β1p×p，1p×pIs a full 1 matrix of p rows and p columns,
Figure BDA00030925183700000416
is a half Markov process transition probability λij(h) The upper bound of (c).
6.3 according to the first three conditions of step 2, step 6.1 and step 6.2, obtaining a condition for ensuring that the fault detection system is positive:
Figure BDA0003092518370000051
Figure BDA0003092518370000052
wherein the content of the first and second substances,
Figure BDA0003092518370000053
6.4 consider the influence of various external uncertain factors on road vehicles on the urban traffic network, and consider the following constraint performance:
Figure BDA0003092518370000054
6.5 obtaining the conditions for ensuring the random stability of the fault detection system according to the step 2 and the step 6.1:
Figure BDA0003092518370000055
wherein the content of the first and second substances,
Figure BDA0003092518370000056
Figure BDA0003092518370000057
6.6 design random Lyapunov function
Figure BDA0003092518370000058
Wherein
Figure BDA0003092518370000059
Its weak infinitesimal small operator:
Figure BDA00030925183700000510
Figure BDA00030925183700000511
according to the conditions in step 6.2, one can obtain:
Figure BDA00030925183700000512
the failure detection system is L under the designed event triggered filter as illustrated by step 6.61And (4) random stabilization.
The invention provides a method for detecting faults of traffic signal lamps of an urban road system. TheThe method provides a set of fault detection scheme of the traffic system aiming at the problems of traffic jam and accidents caused by overlarge traffic flow or traffic signal lamp faults and various external interference factors in the urban road system, and can timely avoid long-time jam of the road when the traffic signal lamp is in fault. Aiming at the influence of overlarge traffic flow at an intersection of an urban traffic system, various external uncertain interference factors, faults of traffic lights and the like on a traffic network, the method utilizes a positive half Markov jump system to model the system, and establishes a state space model of the system. 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 flow chart of the present invention.
Detailed Description
The invention will be further explained with reference to the drawings.
As shown in fig. 1, a dynamic model of the traffic flow of the urban traffic system is established by taking the traffic flow of the incoming and outgoing vehicles at the node of the annular intersection of the urban road system as a research object, the traffic flow of the incoming intersection as a control input and the traffic flow of the outgoing vehicle at the intersection as an output.
Step 1, establishing a state space model of an urban road system, wherein the specific method comprises the following steps:
1.1, the actual traffic network is described by collecting input and output data of an urban road system:
considering the annular crossing of the urban road system, the annular crossing of the urban road system consists of four main roads, four branch roads and traffic lights for guiding vehicles, and the annular crossing is shown in a schematic diagram (see the attached drawing of the specification) in figure 1. Fig. 1 shows the relationship between the main roads, branch roads and traffic lights in the circular intersection, and the driving direction of the vehicles on each road is marked in the figure. Traffic signal lamps at each intersection in fig. 1 can play a role in regulating traffic flow of each road segment in an annular traffic network, and play a vital role in preventing vehicle congestion or traffic accidents. It is known that the time for switching traffic lights is generally fixed, however, the road conditions in the urban road system are quite complex, and congestion is easily caused when the traffic flow at the intersection is very large, for example, in fig. 1, when the main road R1 and R3 are green lights, at this time, c1 goes straight from the main road R1 to the main road R3, d1 from the branch R1 turns right, c2 from the main road R2 and d2 from the branch R2 turn right and merge into the straight traffic flow, so that traffic congestion is easily caused when vehicles from different intersections converge together, at this time, the event generator detects that the traffic flow is too large, the system switches to the working mode of prolonging the green light time of congestion and prolonging the red light time of non-congestion intersections, and when the traffic flow is normal, the system switches to the normal working mode. When the traffic signal lamp has a fault, an alarm can be sent out in time to inform related staff to process the fault. Considering that the traffic flow at a road intersection is not fixed, has randomness and is non-negative, the positive half-Markov hopping system is used for modeling, and fault detection is carried out on a traffic signal lamp, so that the traffic jam is prevented.
1.2, constructing a state space model of the urban road system:
Figure BDA0003092518370000061
y(t)＝C(rt)x(t)+D(rt)w(t)+F(rt)f(t),
wherein x (t) ═ x1(t),x2(t),...,xn(t)]T∈RnNumber of vehicles, x, entering the intersection at time tj(t) is the number of vehicles on the jth road at the moment t, wherein j is more than or equal to 1 and less than or equal to n, and n represents the number of main roads. y (t) ε RpP represents the dimension of y (t) as the number of vehicles exiting a portion of the intersection at time t,
Figure BDA0003092518370000062
is an immeasurable external disturbance factor causing traffic jam (such as occurrence of traffic accident, sudden increase of traffic flow in rush hour, and the like), and m is the number of branches.
Figure BDA0003092518370000063
Is a fault signal causing traffic congestion and q represents the number of traffic lights. When the traffic signal lamp breaks down, the orderly circulation of the traffic flow can not be guided normally at the moment. r istRepresents a half-Markov jump process, where J e N is set in a finite set S1, 2+An internal value. A (r)t),B(rt),C(rt),D(rt),E(rt),F(rt) Is a known system matrix. For convenience, let rtI, i ∈ S, the system matrix can be denoted as ai,Bi,Ci,Di,Ei,Fi. Assume matrix AiIs a matrix of Metzler's,
Figure BDA0003092518370000071
Rn,
Figure BDA0003092518370000072
N+,Rn×nrespectively representing an n-dimensional vector, an n-dimensional non-negative vector, a positive integer, and an nxn-dimensional euclidean matrix space.
1.3 design half Markov jump signal rtIts transition probability λij(h) Satisfies the following conditions:
Figure BDA0003092518370000073
where h > 0, (o (Δ)/Δ) goes to 0 as Δ goes to 0, where Δ represents an argument and o (Δ) represents the higher order infinitesimal of Δ. For each i ∈ S, i ≠ j there is λij(h) Is greater than 0 and
Figure BDA0003092518370000074
where N represents the number of subsystems.
Step 2, establishing an event triggering condition of the urban road system traffic flow, wherein the construction form is as follows:
||m(t)‖1＞β||y(t)‖1，
wherein the constant 0 < beta < 1, m (t) is the measured traffic flow errorThe difference is that the number of the first and second,
Figure BDA0003092518370000075
wherein
Figure BDA0003092518370000076
Figure BDA0003092518370000077
Representing a natural number, which represents the time tιThe number of vehicles exiting the intersection, y (t), is the number of vehicles exiting the intersection at time t.
Step 3, establishing an event trigger filter model, wherein the structural form is as follows:
Figure BDA0003092518370000078
Figure BDA0003092518370000079
wherein x isf(t) represents the state signal of the filter, rf(t) denotes a residual signal, Afi,Bfi,Cfi,DfiIs the filter matrix to be designed.
Step 4, constructing a fault detection model of the traffic signal lamp of the urban road system:
Figure BDA00030925183700000710
Figure BDA00030925183700000711
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00030925183700000712
e(t)＝rf(t)-f(t)，
Figure BDA00030925183700000713
Figure BDA00030925183700000714
i denotes an identity matrix having compatible dimensions.
Step 5, introducing a threshold alarm fault detection mechanism:
Figure BDA00030925183700000715
wherein T represents the evaluation time, E { } represents the mathematical expectation, L1[0, ∞) denotes L1Norm space, Jr(T) denotes a residual evaluation function, JthRepresents a threshold value, when Jr(T)＞JthWhen the alarm is in use, the alarm is generated.
Step 6, designing an event trigger fault detection filter of a traffic signal lamp in an urban road:
the event-triggered failure detection filter system matrix designed by 6.1 is as follows:
Figure BDA0003092518370000081
Figure BDA0003092518370000082
wherein alpha is greater than 0, Rn(Vector)
Figure BDA00030925183700000812
Rp(Vector)
Figure BDA00030925183700000813
μ, v are intermediate variables for designing the filter, 1nRepresenting an n-dimensional vector with elements all being 1,
Figure BDA0003092518370000083
an n-dimensional vector representing that the μ -th element is 1 and the remaining elements are 0, and q is the number of traffic lights.
6.2 design constants alpha > 0, beta > 0, gamma > 0, sigma > 0, Rn(Vector)
Figure BDA00030925183700000814
Rp(Vector)
Figure BDA00030925183700000815
Such that the following inequality:
Figure BDA0003092518370000084
Figure BDA0003092518370000085
Figure BDA0003092518370000086
Figure BDA0003092518370000087
Figure BDA0003092518370000088
Figure BDA0003092518370000089
Figure BDA00030925183700000810
Figure BDA00030925183700000816
for each μ 1,2,., n, ν 1, 2., q, this holds true with the filter designed in step 6.1, where α is an intermediate variable that proves that the fault detection system is in use, β is a coefficient in the event trigger condition, γ is L1Gain performance index, σ is an intermediate variable that ensures stable use of the fault detection system, Z1＝I-β1p×p，Z2＝I+β1p×p，1p×pIs a full 1 matrix of p rows and p columns,
Figure BDA00030925183700000811
is a half Markov process transition probability lambdaij(h) The upper bound of (c).
6.3 according to the first three conditions of step 2, step 6.1 and step 6.2, obtaining a condition for ensuring that the fault detection system is positive:
Figure BDA0003092518370000091
Figure BDA0003092518370000092
wherein the content of the first and second substances,
Figure BDA0003092518370000093
6.4 the influence of various external uncertain factors on road vehicles on the urban traffic network is considered, and the following constraint performances are considered:
Figure BDA0003092518370000094
6.5 obtaining the conditions for ensuring the random stability of the fault detection system according to the step 2 and the step 6.1:
Figure BDA0003092518370000095
Figure BDA0003092518370000096
wherein the content of the first and second substances,
Figure BDA0003092518370000097
Figure BDA0003092518370000098
6.6 design random Lyapunov function
Figure BDA0003092518370000099
Wherein
Figure BDA00030925183700000910
Its weak infinitesimal small operator:
Figure BDA00030925183700000911
Figure BDA00030925183700000912
according to the conditions in step 6.2, one can obtain:
Figure BDA00030925183700000913
the fault detection system is L under the designed event triggered filter as illustrated by step 6.61And (4) random stabilization.

Claims (1)

1. A method for detecting faults of traffic lights of an urban road system is characterized in that data acquisition is carried out on the randomly generated traffic flow on a road based on a positive half Markov jump system model, an event triggering strategy and a filter, so that fault detection is effectively carried out on the traffic lights, and the problems of traffic accidents and traffic paralysis caused by vehicle blockage and crowd on the urban road are solved, and the method specifically comprises the following steps:
step 1, establishing a state space model of an urban road system;
step 2, establishing event triggering conditions of the traffic flow of the urban road system;
step 3, establishing an event trigger filter model;
step 4, constructing a fault detection model of the traffic signal lamp of the urban road system;
step 5, introducing a threshold alarm fault detection mechanism;
step 6, designing an event trigger fault detection filter of a traffic signal lamp in an urban road;
the step 1 is specifically realized as follows:
1.1, the actual traffic network is described by collecting input and output data of an urban road system:
considering the annular crossing of the urban road system, the annular crossing of the urban road system consists of four main roads, four branch roads and traffic lights for guiding vehicles; the traffic signal lamps at each intersection can play a role in regulating the traffic flow of each road section in the annular traffic network, and play a vital role in preventing vehicle congestion or traffic accidents; modeling by using a positive half-Markov jump system, and detecting faults of traffic lights to prevent traffic jam;
1.2, constructing a state space model of the urban road system:
Figure FDA0003532048050000011
y(t)＝C(rt)x(t)+D(rt)w(t)+F(rt)f(t), (1)
wherein x (t) ═ x1(t),x2(t),…,xn(t)]T∈RnNumber of vehicles, x, entering the intersection at time tj(t) the number of vehicles on the jth road at the moment t, wherein j is more than or equal to 1 and less than or equal to n, and n represents the number of main roads；y(t)∈RpP represents the dimension of y (t) as the number of vehicles exiting a portion of the intersection at time t,
Figure FDA0003532048050000012
the method is an immeasurable external disturbance factor causing traffic jam, and m is the number of branches;
Figure FDA0003532048050000013
is a fault signal causing traffic congestion, q represents the number of traffic lights; when the traffic signal lamp breaks down, the traffic flow cannot be guided to circulate orderly at the moment; r istRepresents a half-Markov jump process, where J e N is set in a finite set S1, 2+Internal value taking; a (r)t),B(rt),C(rt),D(rt),E(rt),F(rt) Is a known system matrix; for convenience, let rtI, i ∈ S, the system matrix can be denoted as ai,Bi,Ci,Di,Ei,Fi(ii) a Assume matrix AiIs a Metzler matrix, Bi≥0,Ci≥0,Di≥0,Ei≥0,Fi≥0；Rn,
Figure FDA0003532048050000014
N+,Rn×nRespectively representing n-dimensional vectors, n-dimensional non-negative vectors, positive integers and n multiplied by n dimensional Euclidean matrix spaces;
1.3 design half Markov jump signal rtIts transition probability λij(h) Satisfies the following conditions:
Figure FDA0003532048050000021
where h > 0, and (o (Δ)/Δ) tends to 0 as Δ tends to 0, where Δ represents an independent variable and o (Δ) represents the higher order infinitesimal of Δ; for each i ∈ S, i ≠ j has λij(h) Is greater than 0 and
Figure FDA0003532048050000022
wherein N represents the number of subsystems;
the event triggering condition for establishing the urban road system traffic flow in the step 2 has the following structural form:
||m(t)‖1＞β||y(t)‖1， (3)
wherein the constant 0 < beta < 1, m (t) is the measured traffic error,
Figure FDA0003532048050000023
wherein
Figure FDA0003532048050000024
t∈[tι,tι+1),
Figure FDA0003532048050000025
Figure FDA0003532048050000026
Representing a natural number, which represents the time tιThe number of vehicles exiting the intersection, wherein y (t) is the number of vehicles exiting the intersection at time t;
the establishment of the event-triggered filter model in step 3 has the following construction form:
Figure FDA0003532048050000027
Figure FDA0003532048050000028
wherein x isf(t) represents the state signal of the filter, rf(t) denotes a residual signal, Afi,Bfi,Cfi,DfiIs the filter matrix to be designed;
the method for constructing the fault detection model of the traffic signal lamp of the urban road system comprises the following specific steps:
Figure FDA0003532048050000029
Figure FDA00035320480500000210
wherein the content of the first and second substances,
Figure FDA00035320480500000211
e(t)＝rf(t)-f(t)，
Figure FDA00035320480500000212
i represents an identity matrix with compatible dimensions;
the introduction of the threshold alarm fault detector in step 5 is specifically realized as follows:
Figure FDA00035320480500000213
wherein T represents the evaluation time, E { } represents the mathematical expectation, L1[0, ∞) denotes L1Norm space, Jr(T) denotes a residual evaluation function, JthRepresents a threshold value, when Jr(T)＞JthWhen the alarm is in use, the alarm is generated;
the event triggering fault detection filter for the traffic signal lamp in the designed urban road is specifically realized as follows:
the event-triggered failure detection filter system matrix designed by 6.1 is as follows:
Figure FDA0003532048050000031
Figure FDA0003532048050000032
wherein alpha is greater than 0, RnVector hi＞0,δui＞0,ξvi＞0,RpVector ηui＞0,ζvi> 0, mu, v are intermediate variables for designing the filter, 1nRepresenting an n-dimensional vector with elements all being 1,
Figure FDA0003532048050000033
n-dimensional vectors representing that the mu-th element is 1 and the other elements are 0, and q is the number of traffic lights;
6.2 design constants alpha > 0, beta > 0, gamma > 0, sigma > 0, RnVector gi＞0,hi＞0,gj＞0,hj＞0,δi＞0,δui＞0,ξvi＞0,RpVector ηi＞0,ηui＞0,ζvi> 0 makes the following inequality:
Figure FDA0003532048050000034
Figure FDA0003532048050000035
Figure FDA0003532048050000036
Figure FDA0003532048050000037
Figure FDA0003532048050000038
Figure FDA0003532048050000039
Figure FDA00035320480500000310
δui＜δi,ηui＜ηi,α≥nσ, (9)
for each μ 1,2,., n, ν 1, 2., q, this holds true with the filter designed in step 6.1, where α is an intermediate variable that proves that the fault detection system is in use, β is a coefficient in the event trigger condition, γ is L1Gain performance index, σ is an intermediate variable that ensures stable use of the fault detection system, Z1＝I-β1p×p，Z2＝I+β1p×p，1p×pIs a full 1 matrix of p rows and p columns,
Figure FDA00035320480500000311
is a half Markov process transition probability lambdaij(h) The upper bound of (c);
6.3 according to the first three conditions of step 2, step 6.1 and step 6.2, obtaining the condition for ensuring the fault detection system is positive:
Figure FDA00035320480500000312
Figure FDA00035320480500000313
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003532048050000041
C i＝(DfiZ1Ci Cfi),D i＝(DfiZ1Di DfiZ1Fi-I).
6.4 consider the influence of various external uncertain factors on road vehicles on the urban traffic network, and consider the following constraint performance:
Figure FDA0003532048050000042
6.5 obtaining the conditions for ensuring the random stability of the fault detection system according to the step 2 and the step 6.1:
Figure FDA0003532048050000043
wherein the content of the first and second substances,
Figure FDA0003532048050000044
Figure FDA0003532048050000045
6.6 design random Lyapunov function
Figure FDA0003532048050000046
Wherein
Figure FDA0003532048050000047
Its weak infinitesimal small operator:
Figure FDA0003532048050000048
according to the conditions in step 6.2, we obtain:
Figure FDA0003532048050000049
the fault detection system is L under the designed event triggered filter as illustrated by step 6.61And (4) random stabilization.
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