CN105978725B - 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, are related to a kind of non-fragility based on sensor network
Distributed fault method of estimation, it is the Fault Estimation that a kind of non-linear and sensor of random generation occurs stochastic gain change
Method, Fault Estimation of the present invention suitable for non-linear complex dynamic systems.
Background technology
With developing rapidly for modern science and technology level, the scale and complexity of control system are increasingly improved, system
In sensor, controller and actuator quantity greatly increases.Among this complicated control system, traditional is point-to-point special
Line transmission design can not meet the requirement of the aspects such as its cost benefit, flexibility and maintainability.Therefore, it is necessary to by communication network
Control system is incorporated into, with the different parts that network comes in connection control system as carrier.But the introducing of communication network and other
Part increases the generation that increased failure again, therefore, Fault Estimation be it is a kind of important in control system study a question, flying
Extensively application is obtained in the Signal estimation task in field such as the formation of row device, Global localization system, Target Tracking System.
But, at present existing Fault Estimation method can not simultaneously process the non-linear and distributed sensor of random generation
Change in gain, and then affect Fault Estimation performance.
The content of the invention
In order to solve the problems, such as techniques as described above, the present invention proposes that a kind of non-fragility based on sensor network is distributed
Formula Fault Estimation method, it is the Fault Estimation side that a kind of non-linear and sensor of random generation occurs stochastic gain change
Method.Which solving existing Fault Estimation method in control system can not be while processes the non-linear and distributed sensing of random generation
Device change in gain, and then affect the problem of 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, using sensor network from control system, extract fault data and simultaneously pre-process；
Step 2, the data based on pretreatment, set up and carry random generation change in gain and random generation non-linear phenomena
Time-varying system uncatalyzed coking distributed fault estimator dynamic model；
Step 3, the uncatalyzed coking distributed fault estimator to the nonlinear and time-varying system with random generation change in gain
Dynamic model carry out Fault Estimation
Step 4, the uncatalyzed coking point with the random nonlinear and time-varying system that change in gain occurs set up according to step 3
Cloth fault approximator dynamic model, calculates Fault Estimation error：
Step 5, the Fault Estimation error obtained according to step 4, obtain Fault Estimation augmented system；
Step 6, using Fault Estimation augmented system, by constructor and using known constraints, analyze failure
Whether estimator meets average behavior constraint
If step 7, step 6 meet performance constraints, fault approximator parameter matrix is calculated, realized to 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 and non-linear being present in occurs at random simultaneously
Impact of the Discrete Time-Varying Systems to Fault Estimation performance, using constraints and stochastic analysis versatility random generation is considered
The effective information of change in gain, compared with the Fault Estimation method of existing non-linear complex dynamic systems, the failure of the present invention
Method of estimation can simultaneously process the change in gain of the non-linear and random generation of random generation, obtain based on linear matrix not
The Fault Estimation method of equation solution, reaches the purpose of anti-nonlinear disturbance, and has the advantages that to be easy to solve and realize.
Description of the drawings
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 the estimation schematic diagram of fault-signal and sensor node to fault-signal.
Specific embodiment
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
Site preparation is described, it is clear that described embodiment a part of embodiment only of the invention, rather than the embodiment of whole.Base
Embodiment in the present invention, those of ordinary skill in the art obtained under the premise of creative work is not made it is all its
His embodiment, belongs to 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 ranks reality squares
The set of battle array.I and 0 represents respectively unit matrix, null matrix.Matrix P>0 represents that P is real symmetric tridiagonal matrices, E { x } and E x |
Y } mathematic expectaion of stochastic variable x under the conditions of the mathematic expectaion and y of stochastic variable x is represented respectively.The Europe of | | x | | representation vector x
Norm is obtained in several.diag{A1,A2,…,AnRepresent that diagonal blocks are matrix As1,A2,…,AnBlock diagonal matrix, symbol * is symmetrical
The omission of symmetrical item is represented in block matrix.If M is a symmetrical matrix, λmax(M) eigenvalue of maximum of M is represented.Symbol
Represent Kronecker multiplication.If somewhere does not have clear and definite specified matrix dimension in text, assume that its dimension is adapted to the algebraically of matrix
Computing.
Proposed by the present invention is that one kind has random generation change in gain under sensor network environment and occurs at random 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 dotted line is the Fault Estimation of sensor node 1 in figure
Error, with the Fault Estimation error that asterisk solid line is sensor node 2, chain-dotted line is the Fault Estimation error of sensor node 3,
It is the Fault Estimation error of sensor node 4 with five-pointed star solid line, misses with Fault Estimation of the cross solid line for sensor node 5
Difference.Fig. 3 is the estimation schematic diagram of fault-signal and sensor node to fault-signal, and solid line is fault-signal in figure, and dotted line is
The Fault Estimation of sensor node 1, with the Fault Estimation that asterisk solid line is sensor node 2, chain-dotted line is sensor node 3
Fault Estimation, is the Fault Estimation of sensor node 4 with five-pointed star solid line, is estimated with failure of the cross solid line for sensor node 5
Meter.
A kind of non-fragility distributed fault method of estimation based on sensor network, the method is comprised the following steps：
Step one, using sensor network from control system, extract fault data and simultaneously pre-process；
Step 2, the data based on pretreatment, set up and carry random generation change in gain and random generation non-linear phenomena
Time-varying system uncatalyzed coking distributed fault estimator dynamic model；
Step 3, the uncatalyzed coking distributed fault estimator to the nonlinear and time-varying system with random generation change in gain
Dynamic model carry out Fault Estimation
Step 4, the uncatalyzed coking point with the random nonlinear and time-varying system that change in gain occurs set up according to step 3
Cloth fault approximator dynamic model, calculates Fault Estimation error：
Step 5, the Fault Estimation error obtained according to step 4, obtain Fault Estimation augmented system；
Step 6, using Fault Estimation augmented system, by constructor and using known constraints, analyze failure
Whether estimator meets average behavior constraint
If step 7, step 6 meet performance constraints, fault approximator parameter matrix is calculated, realized to random generation
The uncatalyzed coking distributed fault estimator design of the nonlinear and time-varying system of change in gain.
Wherein, tool is specially set up based on the step two in the non-fragility distributed fault method of estimation of sensor network
There is 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)
Fault approximator nodeiModel expression be：
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
Need the failure of detection.For fault approximator nodeiThe measurement output for obtaining, v (k) ∈ l2[0, N) it is that outside is disturbed
It is dynamic.A (k), D (k), G (k), Ci(k), Ei(k) and HiK () is the real-time change matrix of known appropriate dimension.Wherein stochastic variableFor describing the non-linear phenomena of random generation, the white sequence distribution of Bernoulli Jacob is obeyed.K ∈ [0, N], [0, N]=0,
1 ..., N } it 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 is the known real matrix with corresponding dimension to Ω.
It is specially to random based on the step three in the non-fragility distributed fault method of estimation of sensor network
The dynamic model of 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 formulaBe fault approximator node i state estimation vector, aijIt 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
The parameter matrix that needs are tried to achieve, stochastic variable σ1k、σ2kThere is the probability of change in gain in control fault approximator, mathematic expectaion isVariance isΔKij(k) and Δ HijK () represents the change in gain that fault approximator is produced, Δ Kij(k)
=Kij(k)HaFa(k)Ea, Δ Hij(k)=Hij(k)HbFb(k)Eb, wherein Ha Hb EaAnd EbIt is the suitable square of known dimension
Battle array, Fa(k) and FbK () is unknown matrix and satisfactionI is unit matrix.NiRepresent
The set of sensor node.
It is specially based on the step four in the non-fragility distributed fault method of estimation of sensor network：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
Calculate Fault Estimation error：
Residual error deducts failure and obtains Fault Estimation error equation：
In formula,For the Fault Estimation error at k moment,It is the output residual error of fault approximator,
To need the failure of detection.
It is specially based on the step five in the non-fragility distributed fault method of estimation of sensor network：According to step 4
The Fault Estimation error of acquisition, obtains Fault Estimation augmented system；
In above formula, The form of formula (5) matrix is：
WhereinFor known constant.WhenWhen, aij=0, matrixIt is sparse square
Battle array,
It is specially based on the step six in the non-fragility distributed fault method of estimation of sensor network：Estimated using failure
Meter augmented system, by constructor and using known constraints, whether analysis fault approximator meets average H∞Performance
Constraint；
Using formula：
It is assumed 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 vectorial ξ (k) non-zero, parameter K is judgedij(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 be a given positive scalar, Si>0 (i=1,2 ..., n) be a series of positive definite matrixes, { 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 ETAnd square
Battle array XTProduct.Represent Euclidean n-space,Represent that n × m ties up the set of real matrix.Represent the mathematics phase of x
Hope,Represent the mathematic expectaion of the x under conditions of y.Kronecker product is represented, | | x | | represents Euclid's model of x
Number.
It is specially based on the step seven in the non-fragility distributed fault method of estimation of sensor network：If step 6 expires
Sufficient performance constraints, calculate fault approximator parameter matrix Kij(k)Hij(k)LijK () (i, j) ∈ ε, realize to random generation
The uncatalyzed coking distributed fault estimator design of the nonlinear and time-varying system of change in gain.
Further, there is provided another kind based on sensor network non-fragility distributed fault method of estimation, its with it is upper
The method difference of stating is：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 indexForOriginal state,For fault approximator Initial state estimation vector, e (0) is initial estimation error,ForTurn
Put.
Emulated using the method for the invention：
Systematic parameter：
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), initial shape x (0) of system=
[0.26 -0.2]T, the original state of estimator is
Formula (6), formula (7) and formula (8) are solved, and obtain fault approximator parameter matrix Kij(k)、Hij(k) and
LijK () meets average H∞Performance constraints.
Fault Estimation gain is solved：
According to step 7, fault approximator parameter matrix K is obtainedij(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 failure of fault-signal and sensor node is estimated
Meter schematic diagram.
From Fig. 2, Fig. 3, for there is change in gain and the random time-varying system that non-linear phenomena occurs with random,
The uncatalyzed coking distributed fault estimator method for designing invented can effectively estimate dbjective state.
A kind of non-fragility distributed fault method of estimation based on sensor network proposed by the present invention, its be it is a kind of with
There is the Fault Estimation method of stochastic gain change in the non-linear and sensor that machine occurs, be related to occur at random change in gain and with
There is the design of nonlinear time-varying system uncatalyzed coking distributed fault estimator in machine.The present invention solves the distributed event of uncatalyzed coking
Random generation change in gain and non-linear two kinds of phenomenons occur at random while being present in that barrier estimation problem is not also solved so far
Discrete Time-Varying Systems, and then a difficult problem for Fault Estimation performance is affected, the present invention is first uncatalyzed coking distributed fault estimation problem
It is introduced in the nonlinear and time-varying system under sensor network environment.Using L2Gain theory and stochastic analysis technology obtain abundant bar
Part, it is ensured that the presence of required distributed fault estimator, compared with existing linearity failure method of estimation, the failure of the present invention
Method of estimation can simultaneously process the uncertainty of random generation and the random non-linear phenomena for occurring, and reach anti-nonlinear disturbance
Purpose, the present invention suitable for non-linear complex dynamic systems Fault Estimation.
As described above, method proposed by the present invention has clearly been describe in detail.Although the preferred embodiments of the present invention are detailed
The present invention is carefully described and explains, 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, various modifications can be made in form and details.
Claims (1)
1. a kind of non-fragility distributed fault method of estimation based on sensor network, the method is comprised the following steps：
Step one, using sensor network from control system, extract fault data and simultaneously pre-process；
Step 2, the data based on pretreatment, set up with it is random occur change in gain and it is random occur non-linear phenomena when
The dynamic model of the uncatalyzed coking distributed fault estimator of change system；
Step 3, moving to the uncatalyzed coking distributed fault estimator 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, calculates Fault Estimation error；
Step 5, the Fault Estimation error obtained according to step 4, obtain Fault Estimation augmented system；
Step 6, using Fault Estimation augmented system, by constructor and using known constraints, analyze Fault Estimation
Whether device meets average behavior constraint；
If step 7, step 6 meet average behavior constraint, fault approximator parameter matrix is calculated, realized to random generation
The uncatalyzed coking distributed fault estimator design of the nonlinear and time-varying system of change in gain.
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| CN107563103B (en) * | 2017-10-16 | 2020-11-10 | 东北石油大学 | Consistency filter design method based on local conditions |
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| CN108445759B (en) * | 2018-03-13 | 2020-01-07 | 江南大学 | Random fault detection method for networked system under sensor saturation constraint |
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| CN108732926A (en) * | 2018-06-05 | 2018-11-02 | 东北石油大学 | Networked system method for estimating state based on insufficient information |
| CN108959808B (en) * | 2018-07-23 | 2022-05-03 | 哈尔滨理工大学 | Optimized distributed state estimation method based on sensor network |
| CN110262334B (en) * | 2019-06-17 | 2021-05-28 | 江南大学 | Finite time domain H-infinity control method of state saturation system under random communication protocol |
| CN112051737B (en) * | 2020-08-28 | 2021-05-28 | 江南大学 | Finite time domain H-infinity control method of nonlinear time-varying wind energy generator system under dynamic scheduling protocol |
| CN112255917B (en) * | 2020-10-19 | 2022-06-07 | 东北石油大学 | Positioning driving control method, positioning driving control device, positioning driving control system, electronic equipment and storage medium |
| CN113008290B (en) * | 2021-03-08 | 2022-04-01 | 清华大学 | Sensor composite fault detection and separation method, storage medium and electronic device |
| CN113204193B (en) * | 2021-05-06 | 2022-10-25 | 北京航空航天大学 | Fault-tolerant control method and device for aircraft and electronic equipment |
| CN116339355B (en) * | 2023-03-03 | 2023-10-20 | 新兴际华(北京)智能装备技术研究院有限公司 | Underwater vehicle and formation tracking control method and device thereof |
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