CN105978725A - Non-fragile distributed fault estimation method based on sensor network - Google Patents
Non-fragile distributed fault estimation method based on sensor network Download PDFInfo
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Abstract
The invention proposes a non-fragile distributed fault estimation method based on a sensor network, and the method is a fault estimation method for random nonlinearity and random gain changes of a sensor. The invention relates to the design of a random gain change and random nonlinear time-varying system non-fragile distributed fault estimator. The method introduces a non-fragile distributed fault estimation problem into a nonlinear time-varying system in a sensor network environment at first. The method obtains sufficient conditions through employing the L2 gain theory and the random analysis technology, and guarantees the existing of a needed distributed fault estimator. Compared with a conventional linear fault estimation method, the method can process random uncertainty and random nonlinear phenomena at the same time, and achieves a purpose of nonlinear disturbance resistance.
Description
Technical field
The invention belongs to fault diagnosis and active tolerant control field, relate to a kind of non-fragility based on sensor network
Distributed fault method of estimation, it is the non-linear of a kind of random generation and the Fault Estimation of sensor generation stochastic gain change
Method, the present invention is applicable to the Fault Estimation of non-linear complex dynamic systems.
Background technology
Along with developing rapidly of modern science and technology level, scale and the complexity of control system improve day by day, system
In sensor, controller and executor's quantity be greatly increased.Among the control system of this complexity, traditional point-to-point specially
Line transmission design can not meet the requirement of the aspects such as its cost benefit, motility and maintainability.Therefore, it is necessary to by communication network
It is incorporated into control system, carrys out the different parts in connection control system with network for carrier.But the introducing of communication network and other
The increase of parts adds again the generation of fault, and therefore, Fault Estimation is a kind of important studying a question in control system, is flying
The Signal estimation task in the field such as the formation of row device, Global localization system, Target Tracking System obtains extensively application.
But, current existing Fault Estimation method can not process the non-linear and distributed sensor of random generation simultaneously
Change in gain, and then affect Fault Estimation performance.
Summary of the invention
In order to solve techniques as described above problem, the present invention proposes the distribution of a kind of non-fragility based on sensor network
Formula Fault Estimation method, it is the non-linear of a kind of random generation and the Fault Estimation side of sensor generation stochastic gain change
Method.The existing Fault Estimation method in control system which solves can not process the non-linear and distributed sensing of random generation simultaneously
Device change in gain, and then the problem affecting Fault Estimation performance.
According to technical scheme, a kind of non-fragility distributed fault method of estimation bag based on sensor network
Include following steps:
Step one, use sensor network, from control system, extract fault data pretreatment；
Step 2, data based on pretreatment, set up and change in gain occur with random and non-linear phenomena occurs at random
The dynamic model of uncatalyzed coking distributed fault estimator of time-varying system；
Step 3, to the uncatalyzed coking distributed fault estimator with the random nonlinear and time-varying system that change in gain occurs
Dynamic model carry out Fault Estimation
Step 4, the uncatalyzed coking with the random nonlinear and time-varying system that change in gain occurs set up according to step 3 divide
Cloth fault approximator dynamic model, calculating Fault Estimation error:
Step 5, the Fault Estimation error obtained according to step 4, it is thus achieved that Fault Estimation augmented system；
Step 6, utilize Fault Estimation augmented system, by constructor with utilize known constraints, analyze fault
Whether estimator meets average behavior constraint
If step 7 step 6 meets Performance Constraints, calculate fault approximator parameter matrix, it is achieved to having random generation
The uncatalyzed coking distributed fault estimator design of the nonlinear and time-varying system of change in gain.
The Fault Estimation method of the present invention considers random generation change in gain simultaneously and non-linear being present in occurs at random
The Discrete Time-Varying Systems impact on Fault Estimation performance, utilizes constraints and stochastic analysis versatility to consider random generation
The effective information of change in gain, compared with the Fault Estimation method of existing non-linear complex dynamic systems, the fault of the present invention
Method of estimation can process the change in gain of the non-linear and random generation of random generation simultaneously, has obtained based on linear matrix not
The Fault Estimation method of equation solution, reaches the purpose of anti-nonlinear disturbance, and has the advantage being prone to solve and realize.
Accompanying drawing explanation
Fig. 1 is the method for the invention schematic flow sheet；
Fig. 2 is the Fault Estimation error schematic diagram of sensor node；
Fig. 3 is fault-signal and the sensor node estimation schematic diagram to fault-signal.
Detailed description of the invention
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Describe, it is clear that described embodiment is only a part of embodiment of the present invention rather than whole embodiments wholely.Base
Embodiment in the present invention, those of ordinary skill in the art obtained under not making creative work premise all its
His embodiment, broadly falls into the scope of protection of the invention.
Symbol description:
Herein, MTThe transposition of representing matrix M.RnRepresent Euclidean n-space, Rn×mRepresent all n × m rank reality square
The set of battle array.I and 0 representation unit matrix, null matrix respectively.Matrix P > 0 represents that P is real symmetric tridiagonal matrices, E{x} and E{x |
Y} represents the mathematic expectaion of stochastic variable x under the conditions of the mathematic expectaion of stochastic variable x and y respectively.The Europe of | | x | | representation vector x
Norm is obtained in several.diag{A1,A2,…,AnRepresent that diagonal blocks is matrix A1,A2,…,AnBlock diagonal matrix, symbol * is in symmetry
Block matrix represents the omission of symmetrical item.If M is symmetrical matrix, then a λmax(M) eigenvalue of maximum of M is represented.Symbol
Represent Kronecker multiplication.If somewhere does not has clear and definite specified matrix dimension in literary composition, then suppose that its dimension is suitable for the algebraically of matrix
Computing.
What the present invention proposed is that one has random generation change in gain under sensor network environment and random generation is non-
The time-varying system uncatalyzed coking distributed fault method of estimation of linear phenomena, as Figure 1-3.Fig. 1 is the method for the invention stream
Journey schematic diagram.Fig. 2 is the Fault Estimation error schematic diagram of sensor node, and in figure, dotted line is the Fault Estimation of sensor node 1
Error, band asterisk solid line is the Fault Estimation error of sensor node 2, and chain-dotted line is the Fault Estimation error of sensor node 3,
With the Fault Estimation error that five-pointed star solid line is sensor node 4, band cross solid line is that the Fault Estimation of sensor node 5 is missed
Difference.Fig. 3 is fault-signal and the sensor node estimation schematic diagram to fault-signal, and in figure, solid line is fault-signal, and dotted line is
The Fault Estimation of sensor node 1, band asterisk solid line is the Fault Estimation of sensor node 2, and chain-dotted line is sensor node 3
Fault Estimation, band five-pointed star solid line is the Fault Estimation of sensor node 4, and band cross solid line is that the fault of sensor node 5 is estimated
Meter.
A kind of non-fragility distributed fault method of estimation based on sensor network, the method comprises the following steps:
Step one, use sensor network, from control system, extract fault data pretreatment；
Step 2, data based on pretreatment, set up and change in gain occur with random and non-linear phenomena occurs at random
The dynamic model of uncatalyzed coking distributed fault estimator of time-varying system；
Step 3, to the uncatalyzed coking distributed fault estimator with the random nonlinear and time-varying system that change in gain occurs
Dynamic model carry out Fault Estimation
Step 4, the uncatalyzed coking with the random nonlinear and time-varying system that change in gain occurs set up according to step 3 divide
Cloth fault approximator dynamic model, calculating Fault Estimation error:
Step 5, the Fault Estimation error obtained according to step 4, it is thus achieved that Fault Estimation augmented system；
Step 6, utilize Fault Estimation augmented system, by constructor with utilize known constraints, analyze fault
Whether estimator meets average behavior constraint
If step 7 step 6 meets Performance Constraints, calculate fault approximator parameter matrix, it is achieved to having random generation
The uncatalyzed coking distributed fault estimator design of the nonlinear and time-varying system of change in gain.
Wherein, the step 2 in non-fragility distributed fault method of estimation based on sensor network specially sets up tool
Having the dynamic model of the uncatalyzed coking distributed fault estimator of the random nonlinear and time-varying system that change in gain occurs, its state is empty
Between form be:
X (k+1)=A (k) x (k)+α (k) h (x (k))+D (k) w (k)+G (k) f (k) (1)
The model expression of fault approximator node i is:
yi(k)=Ci(k)x(k)+Ei(k)v(k)+Hi(k) f (k) i=1,2 ..., n (2)
In formula,The state vector of expression system,It is the input nonlinearities of system,
For needing the fault of detection.The measurement output obtained for fault approximator node i, v (k) ∈ l2[0, N) be outside
Portion's disturbance.A (k), D (k), G (k), Ci(k), Ei(k) and HiK () is the real-time bending moment battle array of known suitable dimension.The most random
VariableIt is used for describing the non-linear phenomena of random generation, obeys the distribution of Bernoulli Jacob's white sequence.K ∈ [0, N], [0, N]=
0,1 ..., N} is a finite time-domain space.Nonlinear Vector value functionH (0)=0 meets [h (x)-h
(y)-Ψ(x-y)]T[h (x)-h (y)-Ω (x-y)]≤0, Ψ to Ω is the known real matrix with corresponding dimension.
Step 3 in non-fragility distributed fault method of estimation based on sensor network is specially having random
The dynamic model that the uncatalyzed coking distributed fault estimator of the nonlinear and time-varying system of change in gain occurs carries out Fault Estimation；
Set up fault approximator model as follows:
In formulaIt is the state estimation vector of fault approximator node i, aijIt it is sensor node connection weight system
Number,It is the output residual error of fault approximator node i, Kij(k), Hij(k) and LijK () is fault approximator node i institute
Need the parameter matrix tried to achieve, stochastic variable σ1k、σ2kControlling the probability of fault approximator generation change in gain, mathematic expectaion isVariance is△Kij(k) and △ HijK () represents the change in gain that fault approximator produces, △ Kij(k)
=Kij(k)HaFa(k)Ea, △ Hij(k)=Hij(k)HbFb(k)Eb, wherein Ha Hb EaAnd EbIt is the square that known dimension is suitable
Battle array, Fa(k) and FbK () is unknown matrix and meets Fa T(k)Fa(k)≤I,Fb T(k)FbK ()≤I, I are unit matrix.NiTable
Show the set of sensor node.
Step 4 in non-fragility distributed fault method of estimation based on sensor network is particularly as follows: according to step 3
The uncatalyzed coking distributed fault estimator dynamic model with the random nonlinear and time-varying system that change in gain occurs set up, meter
Calculation Fault Estimation error:
Residual error deducts fault and obtains Fault Estimation error equation:
In formula,For the Fault Estimation error in k moment,It is the output residual error of fault approximator,For needing the fault of detection.
Step 5 in non-fragility distributed fault method of estimation based on sensor network is particularly as follows: according to step 4
The Fault Estimation error obtained, it is thus achieved that Fault Estimation augmented system；
In above formula, The form of formula (5) matrix is:
WhereinFor known constant.WhenTime, aij=0, matrixIt it is sparse square
Battle array,
Step 6 in non-fragility distributed fault method of estimation based on sensor network is particularly as follows: utilize fault to estimate
Meter augmented system, by the known constraints of constructor and utilization, analyzes whether fault approximator meets average H∞Performance
Constraint；
Utilize formula:
Assuming that the parameter matrix K of fault approximatorij(k), Hij(k) and LijK () is it is known that pass through constructor (7):
J (k)=ηT(k+1)P(k+1)η(k+1)-ηT(k)P(k)η(k)(7)
In the case of vector ξ (k) non-zero, it is judged that parameter Kij(k), Hij(k) and LijK whether () meet average H∞Performance
Constraint；Matrix concrete form in formula (6):
I2=[I 0], I1=[I 0]T
γ > 0 is a given positive scalar, Si> 0 (i=1,2 ..., n) it is a series of positive definite matrix, { P (k) }0≤k≤N+1
It is a series of positive definite matrixes.Diag{...} represents diagonal matrix, and X is matrix, ETFor the transposition of matrix E, ETXTFor matrix ETWith
Matrix XTProduct.Represent Euclidean n-space,Represent the set of n × m dimension real matrix.E{x} represents the number of x
Term hopes, E{x | y} represents the mathematic expectaion of x under conditions of y.Representing Kronecker product, | | x | | represents the Euclid of x
Norm.
If the step 7 in non-fragility distributed fault method of estimation based on sensor network is particularly as follows: step 6 is full
Foot Performance Constraints, calculates fault approximator parameter matrix Kij(k)Hij(k)Lij(k) (i, j) ∈ ε, it is achieved to having random generation
The uncatalyzed coking distributed fault estimator design of the nonlinear and time-varying system of change in gain.
Further, it is provided that another kind of non-fragility distributed fault method of estimation based on sensor network, it is with upper
The method difference of stating is: the constraints described in step 6 is:
Wherein:
R=diag{S1,S2,...,Sn}
In formula,For Fault Estimation error, ξ (k) is non-vanishing vector, given AF panel index γ > 0,ForOriginal state,For fault approximator Initial state estimation vector, e (0) is initial estimation error,For's
Transposition.
The method of the invention is used to emulate:
Systematic parameter:
D (k)=[0.2 0.6]T, G (k)=[0.5 0.8]T
Nonlinear function is:
The parameter of sensor node is:
C1(k)=[0.5 0.1sin (2k)], C2(k)=[0.4 0.2], C3(k)=[0.6 0.4sin (2k)],
C4(k)=[0.3sin (4k) 0], C5(k)=[0.2sin (3k) 0.1sin (2k)], E1(k)=0.1,
E2(k)=0.31, E3(k)=0.23, E4(k)=0.2, E5(k)=0.11, H1(k)=0.6, H2(k)=0.8, H3
(k)=0.7, H4(k)=0.9, H5(k)=0.4,Hb=1,Eb=0.3
Additionally, the probability of stochastic variable α (k) is 0.8, external disturbance ω (k)=exp (-k),
Fault-signal isPositive definite matrix Si=diag{2,2} (i=1,2 ..., 5), the initial shape x (0) of system=
[0.26 -0.2]T, the original state of estimator is
Formula (6), formula (7) and formula (8) solve, and obtain fault approximator parameter matrix Kij(k)、Hij(k) and
LijK () meets average H∞Performance Constraints.
Fault Estimation gain solves:
According to step 7, obtain fault approximator parameter matrix Kij(k)、Hij(k) and LijK () is following form:
Fault approximator effect:
Fig. 2 is the Fault Estimation error schematic diagram of sensor node, and Fig. 3 is that the fault of fault-signal and sensor node is estimated
Meter schematic diagram.
From Fig. 2, Fig. 3, for having the random time-varying system that change in gain and random generation non-linear phenomena occur,
The uncatalyzed coking distributed fault estimator method for designing invented can estimate dbjective state effectively.
The present invention propose a kind of based on sensor network non-fragility distributed fault method of estimation, its be one with
The Fault Estimation method of the non-linear and sensor generation stochastic gain change that machine occurs, relate to occurring at random change in gain and
The random design that nonlinear time-varying system uncatalyzed coking distributed fault estimator occurs.It is distributed that the present invention solves uncatalyzed coking
There are non-linear two kinds of phenomenons simultaneously in the random generation change in gain that Fault Estimation problem does not the most solve with random
In Discrete Time-Varying Systems, and then affecting the difficult problem of Fault Estimation performance, the present invention estimates that uncatalyzed coking distributed fault ask first
Topic introduces in the nonlinear and time-varying system under sensor network environment.Utilize L2Gain theory and stochastic analysis technology obtain fully
Condition, it is ensured that the existence of required distributed fault estimator, compared with existing linearity failure method of estimation, the event of the present invention
Barrier method of estimation can process the uncertainty of generation at random and the random non-linear phenomena occurred simultaneously, reaches to resist non-linear disturbing
Dynamic purpose, the present invention is applicable to the Fault Estimation of non-linear complex dynamic systems.
As above-mentioned, the most clearly describe in detail the method that the present invention proposes.Although the preferred embodiments of the present invention are detailed
Carefully describe and explain the present invention, but those skilled in the art is appreciated that fixed without departing substantially from claims
In the case of the spirit and scope of the present invention of justice, multiple amendment can be made in form and details.
Claims (8)
1. a non-fragility distributed fault method of estimation based on sensor network, the method comprises the following steps:
Step one, use sensor network, from control system, extract fault data pretreatment；
Step 2, data based on pretreatment, set up with random occur change in gain and random occur non-linear phenomena time
The dynamic model of the uncatalyzed coking distributed fault estimator of change system；
Step 3, to uncatalyzed coking distributed fault estimator dynamic with the random nonlinear and time-varying system that change in gain occurs
States model carries out Fault Estimation
Step 4, the uncatalyzed coking with the random nonlinear and time-varying system that change in gain occurs set up according to step 3 are distributed
Fault approximator dynamic model, calculating Fault Estimation error:
Step 5, the Fault Estimation error obtained according to step 4, it is thus achieved that Fault Estimation augmented system；
Step 6, utilize Fault Estimation augmented system, by constructor with utilize known constraints, analyze Fault Estimation
Whether device meets average behavior constraint
If step 7 step 6 meets Performance Constraints, calculate fault approximator parameter matrix, it is achieved to having, gain occurs at random
The uncatalyzed coking distributed fault estimator design of the nonlinear and time-varying system of change.
2. according to the non-fragility distributed fault method of estimation based on sensor network of claim 1, it is characterised in that
Step 2 is specially the uncatalyzed coking distributed fault of the nonlinear and time-varying system that foundation has random generation change in gain and estimates
The dynamic model of gauge, its state space form is:
X (k+1)=A (k) x (k)+α (k) h (x (k))+D (k) w (k)+G (k) f (k) (1)
The model expression of fault approximator node i is:
yi(k)=Ci(k)x(k)+Ei(k)v(k)+Hi(k) f (k i=1,2 ..., n (2)
In formula,The state vector of expression system,It is the input nonlinearities of system,For needs
The fault of detection.The measurement output obtained for fault approximator node i, v (k) ∈ l2[0, N) it is external disturbance.
A (k), D (k), G (k), Ci(k), Ei(k) and HiK () is the real-time bending moment battle array of known suitable dimension.Wherein stochastic variableIt is used for describing the non-linear phenomena of random generation, obeys the distribution of Bernoulli Jacob's white sequence.K ∈ [0, N], [0, N]=0,
1 ..., N} is a finite time-domain space.Nonlinear Vector value functionH (0)=0 meet [h (x)-h (y)-
Ψ(x-y)]T[h (x)-h (y)-Ω (x-y)]≤0, Ψ to Ω is the known real matrix with corresponding dimension.
3. according to the non-fragility distributed fault method of estimation based on sensor network of claim 1, it is characterised in that
The uncatalyzed coking distributed fault that step 3 is specially having the random nonlinear and time-varying system that change in gain occurs is estimated
The dynamic model of device carries out Fault Estimation；
Set up fault approximator model as follows:
In formulaIt is the state estimation vector of fault approximator node i, aijIt is sensor node connection weight coefficient,It is the output residual error of fault approximator node i, Kij(k), Hij(k) and LijK () is fault approximator node i needed for
Parameter matrix to be tried to achieve, stochastic variable σ1k、σ2kControlling the probability of fault approximator generation change in gain, mathematic expectaion isVariance isΔKij(k) and Δ HijK () represents the change in gain that fault approximator produces, Δ Kij(k)
=Kij(k)HaFa(k)Ea, Δ Hij(k)=Hij(k)HbFb(k)Eb, wherein Ha Hb EaAnd EbIt is the square that known dimension is suitable
Battle array, Fa(k) and FbK () is unknown matrix and meets Fa T(k)Fa(k)≤I,Fb T(k)FbK ()≤I, I are unit matrix.NiTable
Show the set of sensor node.
4. according to the non-fragility distributed fault method of estimation based on sensor network of claim 1, it is characterised in that
Step 4 is particularly as follows: the uncatalyzed coking with the random nonlinear and time-varying system that change in gain occurs set up according to step 3
Distributed fault estimator dynamic model, calculating Fault Estimation error:
Residual error deducts fault and obtains Fault Estimation error equation:
In formula,For the Fault Estimation error in k moment,It is the output residual error of fault approximator,For needing
Fault to be detected.
5. according to the non-fragility distributed fault method of estimation based on sensor network of claim 1, it is characterised in that step
Rapid five particularly as follows: according to step 4 obtain Fault Estimation error, it is thus achieved that Fault Estimation augmented system；
In above formula, The form of formula (5) matrix is:
WhereinFor known constant.WhenTime, aij=0, matrixIt is sparse matrix,
6. according to the non-fragility distributed fault method of estimation based on sensor network of claim 1, it is characterised in that
Step 6, particularly as follows: utilize Fault Estimation augmented system, by the known constraints of constructor and utilization, analyzes event
Whether barrier estimator meets average H∞Performance Constraints；
Utilize formula:
Assuming that the parameter matrix K of fault approximatorij(k), Hij(k) and LijK () is it is known that pass through constructor (7):
J (k)=ηT(k+1)P(k+1)η(k+1)-ηT(k)P(k)η(k) (7)
In the case of vector ξ (k) non-zero, it is judged that parameter Kij(k), Hij(k) and LijK whether () meet average H∞Performance Constraints；
Matrix concrete form in formula (6):
I2=[I 0], I1=[I 0]T
γ > 0 is a given positive scalar, Si> 0 (i=1,2 ..., n) it is a series of positive definite matrix, { P (k) }0≤k≤N+1It is one
Series positive definite matrix.Diag{...} represents diagonal matrix, and X is matrix, ETFor the transposition of matrix E, ETXTFor matrix ETWith matrix XT
Product.Represent Euclidean n-space,Represent the set of n × m dimension real matrix.E{x} represents the mathematic expectaion of x, E
X | y} represents the mathematic expectaion of x under conditions of y.Representing Kronecker product, | | x | | represents the Euclid norm of x.
7. according to the non-fragility distributed fault method of estimation based on sensor network of claim 1, it is characterised in that
If step 7 is particularly as follows: step 6 meets Performance Constraints, calculate fault approximator parameter matrix Kij(k), Hij(k), Lij
(k) (i, j) ∈ ε, it is achieved the uncatalyzed coking distributed fault with the random nonlinear and time-varying system that change in gain occurs is estimated
Device designs.
8. according to the non-fragility distributed fault method of estimation based on sensor network of claim 1, it is characterised in that
Step 6 is particularly as follows: the constraints described in step 6 is:
Wherein:
R=diag{S1,S2,...,Sn}
In formula,For Fault Estimation error, ξ (k) is non-vanishing vector, given AF panel index γ > 0,ForJust
Beginning state,For fault approximator Initial state estimation vector, e (0) is initial estimation error,ForTransposition.
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