CN110161882A - A kind of fault detection method of the networked system based on event trigger mechanism - Google Patents
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Abstract
The present invention discloses a kind of fault detection method of networked system based on event trigger mechanism, belongs to networked system field；Initially set up there are sensor saturation, disturbance and fault condition under Continuous Network system model, solve the problems, such as that real network bandwidth is limited by introducing effective event triggering communication transfer strategy, fault Detection Filter is redesigned, introduces residual error evaluation mechanism to judge whether system breaks down；With Lyapunov Theory of Stability and linear matrix inequality analysis method, adequate condition existing for filtering error system Asymptotic Stability and fault Detection Filter is obtained；Optimization problem is solved using the tool box Matlab LMI, obtaining Optimal Fault Detection Filter parameter isThe method of the present invention considers under actual conditions that there are network bandwidths in system limited, sensor is suitable for general fault detection, has preferable universality by constraint of saturation and failure.
Description
Technical field
The invention belongs to networked system fields, are related to a kind of failure inspection of networked system based on event trigger mechanism
Survey method.
Background technique
Network control system is to be formed between controlled device and other component by shared communication network connection
Closed-loop control system.Compared to traditional control system, network control system have simple connection, strong flexibility, be easy extension,
The advantages that convenient for safeguarding.But due to the introducing of network, a series of new problems are also inevitably brought, when such as information transmission
Prolong, data-bag lost, quantization error and Bandwidth-Constrained etc., declines so as to cause the performance of system, system unstability can be made when serious.
Fault detection is to judge whether system breaks down, it is the important evidence that system safety operation early warning mechanism is established.Due to logical
The introducing for interrogating network causes traditional fault detection method to be difficult to directly apply to network control system, therefore is directed to unreasonably
Think network factors, the fault detection method for studying networked system has important theory significance and application value.
Fault detection is to establish a threshold value relevant to that can survey signal (such as state, output) and valuation functions, is passed through
Whether comparative assessment functional value and threshold value, detection failure occur, and when valuation functions value is greater than threshold value, system detection is out of order simultaneously
Issue alarm signal.However the most of scholar research object selected when study networking system failure detection problem for from
Dissipate system, for the transmission mode in communication network mostly use be constant duration traditional period trigger mechanism, in reality
Network congestion is inevitably generated in the limited situation of network bandwidth, increases unnecessary calculating, is wasted a large amount of
The energy and Internet resources.
Summary of the invention
For above-mentioned problems of the prior art, the present invention provides a kind of networkings based on event trigger mechanism
The fault detection method of system.Consider that networked system has that sensor is limited by constraint of saturation and real network bandwidth
Under, fault Detection Filter is devised, so that networked system can not only keep Asymptotic Stability under above-mentioned condition constraint, and
And satisfiable H∞Performance indicator is effectively detected by residual error evaluation mechanism and is out of order.
Technical solution of the present invention:
A kind of fault detection method of the networked system based on event trigger mechanism, comprising the following steps:
1) there are the limited mathematical models with the networked system of sensor constraint of saturation of communication bandwidth for foundation:
Wherein:For state vector,For the derivative of state vector；For the survey of belt sensor saturation
Measure output vector；WithIt is measurement noise and unknown failure signal respectively, and meets L2[0,∞)。A,Bw,
Bf, C and DwFor the constant matrices of known appropriate dimension；It is the non-linear partial under sensor saturation, belongs to [L1,
L2],WithIt is diagonal matrix, and L=L2-L1It is symmetric positive definite matrix.For the limited net of communication bandwidth
Network environment, trigger mechanism and network detection are as follows:
Wherein: σ ∈ [0,1),It is positive definite weighting matrix, sampler acquires output signal, τ with fixed cycle h
It (t) is the time-vary delay system of network transmission, ekIt (t) is error vector,For filter input, the trigger transmission data moment is
i0h,i1h,…,ikH ...,It is i-thkThe time delay of secondary triggering.
2) design error failure Fault detection filter:
Wherein: xFIt (t) is filter status,For filter input, rFIt (t) is residual signals；AF,BF,CFAnd DFFor to
The filter parameter of design.
Whether occurred using residual error evaluation mechanism detection failure, and residual error valuation functions J (t) and threshold value JthIt respectively indicates
It is as follows:
Wherein: TdIndicate limited assessment time span.
Whether system breaks down, and is judged by the rule of formula (6):
3) adequate condition existing for system Asymptotic Stability and fault Detection Filter is as follows:
Wherein * indicates symmetrical matrix block, and
Θ11=-X-XT, Θ12=-Y-ZT,Θ22=-Z-ZT, Θ77=-2I+ σ Ω,
It is intermediate variable,
It is intermediate variable,
Ω is positive definite weighting matrix, Q, R,It is unknown positive definite matrix, X, Y, Z,It is appropriate
The unknown matrix and performance indicator γ of dimension, dependent variable be all it is known, I is unit matrix, and 0 is null matrix.
The given < σ of scalar lambda > 0 and 0 < 1 solves linear matrix inequality (7) using the tool box Matlab LMI, when not
When equation (7) has feasible solution, there are positive definite matrix Ω, Q, R,With matrix X, Y,And
Performance indicator γ then system is asymptotically stable, and meets H∞Performance indicator, and thus, it is possible to obtain fault Detection Filter
Parameter can continue to carry out step 4)；When inequality (7) is without feasible solution, fault Detection Filter parameter can not be obtained, no longer
Step 4) is carried out, is terminated.
4) Optimal Fault Detection Filter parameter is calculated
According toPerformance indicator γ is found out, and is asked using the tool box Matlab LMI
Solve convex optimization problem (8):
Wherein, e (t)=rF(t)-f (t) is residual error error signal,
When formula (8) has solution, optimal H is obtained∞Performance indicator is γmin, and acquire Optimal Fault Detection Filter parameter
It is as follows:
Wherein:It is nonsingular matrix.
5) whether logical decision determines that failure occurs
Based on event trigger mechanism, the input of filter is obtained by network transmissionBy fault Detection Filter formula
(3) residual signals r is obtainedF(t), the current of residual error assessment t moment then by residual error evaluation mechanism formula (4) and formula (5) is calculated
Value J (t) and threshold value Jth, whether occur finally by formula (6) logic judgment failure.
Compared with prior art, beneficial effects of the present invention: for the limited net with sensor constraint of saturation of communication bandwidth
Network environment, the present invention are given under the network environment by introducing a kind of effectively transmission strategy based on event trigger mechanism
The design method of fault Detection Filter, compared to traditional period trigger mechanism using constant duration triggering, this method is more
With practical application value, data traffic volume can be effectively reduced, saves Internet resources.
Detailed description of the invention
Fig. 1 is the flow chart of the networked system fault detection method based on event trigger mechanism.
Fig. 2 is the structural block diagram of the networked system fault detection method based on event trigger mechanism.
Fig. 3 is w (t) ≠ 0, the residual signals figure in the presence of the failure of σ=0.1, λ=0.15.
Fig. 4 is w (t) ≠ 0, residual error valuation functions figure when σ=0.1, λ=0.15.
Fig. 5 is w (t) ≠ 0, event triggering moment and trigger interval figure when σ=0.1, λ=0.15.
Specific embodiment
The following further describes the specific embodiments of the present invention with reference to the drawings.
Referring to attached drawing 1, a kind of fault detection method of the networked system based on event trigger mechanism, including following step
It is rapid:
Step 1: there are the limited mathematical models with the networked system of sensor constraint of saturation of communication bandwidth for foundation
The state-space expression of networked system based on event trigger mechanism is as follows:
The case where considering sensor constraint of saturation, and saturation function sat ():Belong to [L1, L2], L1And L2
It is diagonal matrix, and L=L2-L1It is symmetric positive definite matrix.
For the ease of processing, sat (Cx (t)) is divided into linear segment and non-linear partial:
Wherein non-thread partIt is as follows to meet condition:
Step 2: design error failure Fault detection filter
Consider network transmission by actual bandwidth limit with sensor constraint of saturation, in order to reduce the number of Trig control signal
With the burden of shared network, event trigger mechanism is selected, it is assumed that trigger condition is as follows:
Design error failure Fault detection filter formula (3), and binding events trigger mechanism and sensor constraint of saturation, are passed by network
Defeated fault Detection Filter input are as follows:
Comprehensively consider formula (10), (3) and (14), pass through the available filtering error system (15) of the method for state augmentation:
Wherein: e (t)=rF(t)-f (t), H=[I 0],
It can be seen that filtering error system (15) have merged network transfer delay, sensor constraint of saturation parameter, event touching
Parameter is sent out, noise and unknown failure signal are measured.The fault detection problem of original system is translated into unknown parameter error system
The H of system∞Filtering problem.Specific problem becomes to find filter parameter A belowF,BF,CFAnd DFSo that filtering error system is full
The following condition of foot:
(i) whenWhen, filtering error system (15) is asymptotically stable.
(ii) under zero initial condition, to any non-vanishing vectorFiltering error vector e (t) is fullWherein γ is H∞Performance indicator, suppression level of the reflection residual signals to external disturbing signal.
Construct residual error valuation functions J (t) and threshold value JthRespectively formula (4) and formula (5), whether system, which breaks down, is used formula
(6) judged.It when residual error valuation functions value is greater than threshold value, then breaks down and alarms, otherwise indicate that there is no events
Barrier.
Step 3: adequate condition existing for system Asymptotic Stability and fault Detection Filter
Construct Lyapunov function are as follows:
It is theoretical using Lyapunov Theory of Stability and free-form curve and surface, obtain filtering error system (15) meet (i) and
(ii) adequate condition (17):
Wherein * indicates symmetrical matrix block, and
θ44=-2I+ σ Ω, θ46=σ Ω κ, θ66=-γ I+ σ κTΩ κ, κ=[0 0Dw], Σ12(1)=λ M, Σ12
(2)=λ N, Γ
=[- MH M-N N 00 0].
The positive < σ of scalar lambda > 0 and 0 < 1 is given, when there are scalar γ > 0 and matrix Ω > 0, Q > 0, R > 0, P > 0, with
And appropriate dimension matrix M, N make formula (17), then filtering error system (15) meets (i) and (ii).
Although formula (17) gives the condition that filtering error system (15) meet (i) and (ii), regrettably in formula (17)
There are the nonlinear terms of coupling, can not directly be solved using the tool box LMI of MATLAB.Below by introducing added martix
G releases coupling, obtains the adequate condition (18) that new filtering error system (15) meets (i) and (ii):
Wherein * indicates symmetrical matrix block, and
Λ1=diag
{0,Γ+ΓT, 0 },
According to expression formula (18), adequate condition existing for system stabilization and fault Detection Filter is established below.
For convenience, matrix G is first resolved into following form:
In order to carry out contragradient transformation, it is assumed here that matrix G21And G22It is reversible, and defines invertible matrix
In order to be further simplified, it is given below expression formula:
To formula (18) both sides respectively multiplied byAnd J2Contragradient transformation is carried out, system Asymptotic Stability and fault detection filtering can be obtained
Adequate condition existing for device (7).
The given < σ of scalar lambda > 0 and 0 < 1 solves linear matrix inequality (7) using the tool box Matlab LMI, works as formula
(7) when having feasible solution, there are positive definite matrix Ω, Q, R,With matrix X, Y, Z,And performance
Index γ then system is asymptotically stable, and meets H∞Performance indicator, and it is hereby achieved that fault Detection Filter is joined
Number can continue to carry out step 4；When formula (7) is without feasible solution, fault Detection Filter parameter can not be obtained, is no longer walked
Rapid 4, terminate.
Step 4: calculating Optimal Fault Detection Filter parameter
For formula (15), convex optimization problem formula (8) is solved using the tool box Matlab LMI.When formula (8) has solution, obtain most
Excellent H∞Performance indicator is γminWith Optimal Fault Detection Filter parameter expression (9).When formula (8) is without solution, then can not obtain
Optimal Fault Detection Filter.
Step 5: whether logical decision determines that failure occurs
Based on event trigger mechanism, the input of filter is obtained by network transmissionBy fault Detection Filter formula
(3) residual signals r is obtainedF(t), the current of residual error assessment t moment then by residual error evaluation mechanism formula (4) and formula (5) is calculated
Value J (t) and threshold value Jth, whether occur finally by formula (6) logic judgment failure.
Embodiment:
Using the fault detection method of the networked system proposed by the present invention based on event trigger mechanism, in no external world
In the case where disturbance and failure, system is asymptotically stable.WhenWhen, the failure in system is carried out by the above method
Detection.Concrete methods of realizing is as follows:
The mathematical model of certain networking motor stirring system is formula (10), wherein system parameter are as follows:
Assuming that sensor saturation function sat (Cx (t)) can be expressed as follows:
Wherein saturation value is
Based on event trigger mechanism and consider sensor constraint of saturation, it is assumed that h=0.1, λ=0.15, σ=0.1,By solving convex optimization problem (8), optimal H can be obtained∞Performance indicator is
γmin=1.2105 and corresponding trigger parameter matrixAnd obtain Optimal Fault Detection Filter
Parameter
CF=[0.0627 0.0144-0.0464], DF=[0.0050 0.0257].
Notice H∞Performance indicator is extremely important, reflect residual signals to the suppression level of external disturbing signal, it
Value will receive trigger condition, the influence of network delay and sensor constraint of saturation.As can be seen from Table 1 and Table 2, with parameter σ
With the increase of λ, γminValue also increasing accordingly.In addition, table 3 gives optimal performance index γminBy sensor constraint of saturation
The influence of condition variation.
The optimal performance index γ that table 1 changes with parameter σmin
The optimal performance index γ that table 2 changes with parameter lambdamin
Table 3 is with parameter L1, L2The optimal performance index γ of variationmin
The failure detection time that table 4 changes with parameter σ
In order to further verify the validity of above-mentioned fault Detection Filter, it is assumed that interfering noise signal w (t) is [0,1]
Upper obedience uniformly distributed random signal, and assume that fault-signal has following form
Under zero initial condition, changed over time as shown in Fig. 3 using the available residual signals of MATLAB, also,
Attached drawing 4 shows that the residual error valuation functions J (t) for having fault-free that two kinds of situations occur under event trigger mechanism in system becomes at any time
The curve of change.According to the threshold expression (5) of residual error evaluation mechanism, assessment time span T is chosend=200s, can be in the hope of threshold
Value Jth=0.2586.Again by the expression formula (4) of residual error valuation functions, J (t) can be obtained by comparing by calculating |T=55.4=0.2615 >
It detects and is out of order within 0.2586, i.e. 5.4s.Using the time span of the available fault detection of same method with parameter σ's
Situation of change is as shown in table 4.In addition, event triggering moment and trigger interval figure when attached drawing 5 gives parameter σ=0.1.It is commenting
Estimate time 200s, the number of sampling is 2001 times, and the number that sensor is sent is 853 times, it is meant that event trigger mechanism number
Only have 42.63% according to transmission rate, this greatly reduces network burden, reduces network congestion.
It can be seen that designed fault Detection Filter can be judged quickly after the failure occurred detects event
Barrier；Also, the transmission strategy based on event trigger mechanism can reduce data traffic volume, save Internet resources, illustrate to be mentioned
Method is significantly out.
Claims (1)
1. a kind of fault detection method of the networked system based on event trigger mechanism, which comprises the following steps:
1) there are the limited mathematical models with the networked system of sensor constraint of saturation of communication bandwidth for foundation:
Wherein:For state vector,For the derivative of state vector；Measurement for belt sensor saturation is defeated
Outgoing vector；WithIt is measurement noise and unknown failure signal respectively, and meets L2[0,∞)；A,Bw,Bf, C and
DwFor the constant matrices of known appropriate dimension；It is the non-linear partial under sensor saturation, belongs to [L1, L2],WithIt is diagonal matrix, and L=L2-L1It is symmetric positive definite matrix；For the limited network rings of communication bandwidth
Border, trigger mechanism and network detection are as follows:
Wherein: σ ∈ [0,1),It is positive definite weighting matrix, sampler acquires output signal with fixed cycle h, and τ (t) is net
The time-vary delay system of network transmission, ekIt (t) is error vector,For filter input, trigger sends the data moment as i0h,
i1h,…,ikH ...,It is i-thkThe time delay of secondary triggering；
2) design error failure Fault detection filter:
Wherein: xFIt (t) is filter status,For filter input, rFIt (t) is residual signals；AF,BF,CFAnd DFIt is to be designed
Filter parameter；
Whether occurred using residual error evaluation mechanism detection failure, and residual error valuation functions J (t) and threshold value JthRespectively indicate as
Under:
Wherein: TdIndicate limited assessment time span；
Whether system breaks down, and is judged by the rule of formula (6):
3) adequate condition existing for system Asymptotic Stability and fault Detection Filter is as follows:
Wherein * indicates symmetrical matrix block, and
Θ11=-X-XT, Θ12=-Y-ZT,Θ22=-Z-ZT, Θ77=-2I+ σ Ω, It is intermediate variable, It is intermediate variable,
Ω is positive definite weighting matrix, Q, R,It is unknown positive definite matrix, X, Y, Z,It is appropriate dimension
Unknown matrix and performance indicator γ, dependent variable be all it is known, I is unit matrix, and 0 is null matrix；
The given < σ of scalar lambda > 0 and 0 < 1 solves linear matrix inequality (7) using the tool box Matlab LMI, works as inequality
(7) when having feasible solution, there are positive definite matrix Ω, Q, R,With matrix X, Y, Z,And property
Energy index γ, then system is asymptotically stable, and meets H∞Performance indicator, and thus, it is possible to obtain fault Detection Filter ginseng
Number can continue to carry out step 4)；When inequality (7) is without feasible solution, fault Detection Filter parameter can not be obtained, no longer into
Row step 4) terminates；
4) Optimal Fault Detection Filter parameter is calculated
According toPerformance indicator γ is found out, and the solution of the application tool box Matlab LMI is convex
Optimization problem (8):
Wherein, e (t)=rF(t)-f (t) is residual error error signal,
When formula (8) has solution, optimal H is obtained∞Performance indicator is γmin, and acquire Optimal Fault Detection Filter parameter such as
Under:
Wherein:It is nonsingular matrix；
5) whether logical decision determines that failure occurs
Based on event trigger mechanism, the input of filter is obtained by network transmissionIt is obtained by fault Detection Filter formula (3)
To residual signals rF(t), the current value J (t) of residual error assessment t moment then by residual error evaluation mechanism formula (4) and formula (5) is calculated
With threshold value Jth, whether occur finally by formula (6) logic judgment failure.
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