CN105978725B - Non-fragile distributed fault estimation method based on sensor network - Google Patents

Abstract

The present invention proposes a non-fragile distributed fault estimation method based on a sensor network, which is a fault estimation method for randomly occurring nonlinearity and random gain changes of sensors, involving random gain changes and random nonlinearity Design of nonfragile distributed fault estimators for variable systems. The invention first introduces the non-fragile distributed fault estimation problem into the nonlinear time-varying system under the sensor network environment. Using the _L2 gain theory and stochastic analysis techniques to obtain sufficient conditions ensures the existence of the required distributed fault estimator. Compared with the existing linear fault estimation method, the fault estimation method of the present invention can simultaneously deal with random occurrence of uncertainties Non-linear phenomena that occur randomly and randomly, to achieve the purpose of resisting nonlinear disturbances.

Description

A Nonfragile Distributed Fault Estimation Method Based on Sensor Networks

technical field

The invention belongs to the field of fault diagnosis and active fault-tolerant control, and relates to a non-fragile distributed fault estimation method based on a sensor network. Fault estimation for nonlinear complex dynamic systems.

Background technique

With the rapid development of modern science and technology, the scale and complexity of control systems are increasing day by day, and the number of sensors, controllers and actuators in the system has increased greatly. In this complex control system, the traditional point-to-point dedicated line transmission design cannot meet the requirements of cost-effectiveness, flexibility and maintainability. Therefore, it is necessary to introduce the communication network into the control system, and use the network as a carrier to connect different components in the control system. However, the introduction of the communication network and the increase of other components have increased the occurrence of faults. Therefore, fault estimation is an important research problem in the control system. In the signal estimation tasks in the fields of aircraft formation, global positioning system, and target tracking system Get widely used.

However, current existing fault estimation methods cannot simultaneously handle randomly occurring nonlinear and distributed sensor gain variations, which in turn affect fault estimation performance.

Contents of the invention

In order to solve the above-mentioned technical problems, the present invention proposes a non-vulnerable distributed fault estimation method based on sensor networks, which is a fault estimation method with randomly occurring nonlinearity and random gain changes of sensors. It solves the problem that the existing fault estimation methods in the control system cannot simultaneously deal with randomly occurring nonlinear and distributed sensor gain changes, thereby affecting the performance of fault estimation.

According to the technical solution of the present invention, a non-vulnerable distributed fault estimation method based on sensor networks includes the following steps:

Step 1. Use the sensor network to extract fault data from the control system and preprocess it;

Step 2. Based on the preprocessed data, a dynamic model of a non-fragile distributed fault estimator for a time-varying system with randomly occurring gain changes and randomly occurring nonlinear phenomena is established;

Step 3. Fault estimation for a dynamic model of a non-fragile distributed fault estimator for nonlinear time-varying systems with stochastically occurring gain changes

Step 4. Calculate the fault estimation error according to the non-fragile distributed fault estimator dynamic model of nonlinear time-varying system with stochastic gain changes established in step 3:

Step 5. Obtain the fault estimation augmentation system according to the fault estimation error obtained in step 4;

Step 6. Use the fault estimation augmentation system to analyze whether the fault estimator satisfies the average performance constraints by constructing functions and using known constraints

Step 7. If step 6 satisfies the performance constraints, calculate the parameter matrix of the fault estimator to realize the design of a non-fragile distributed fault estimator for nonlinear time-varying systems with randomly occurring gain changes.

The fault estimation method of the present invention takes into account the influence of random gain changes and stochastic nonlinearities on the performance of fault estimation in discrete time-varying systems, and fully considers the effective information of random gain changes by using constraint conditions and stochastic analysis techniques. Compared with the existing fault estimation methods for nonlinear complex dynamic systems, the fault estimation method of the present invention can simultaneously deal with randomly occurring nonlinear and randomly occurring gain changes, and obtains a fault estimation method based on linear matrix inequality solutions, achieving anti- The purpose of nonlinear disturbance, and has the advantage of being easy to solve and implement.

Description of drawings

Fig. 1 is a schematic flow chart of the method of the present invention;

Fig. 2 is a schematic diagram of a fault estimation error of a sensor node;

Fig. 3 is a schematic diagram of the fault signal and the estimation of the fault signal by sensor nodes.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Symbol Description:

Herein, ^MT denotes the transpose of matrix M. R ⁿ represents the n-dimensional Euclidean space, and R ^n×m represents the collection of all n×m order real matrices. I and 0 represent the identity matrix and the zero matrix, respectively. The matrix P>0 means that P is a real symmetric positive definite matrix, and E{x} and E{x|y} respectively represent the mathematical expectation of the random variable x and the mathematical expectation of the random variable x under the condition of y. ||x|| represents the Euclidean norm of the vector x. diag{A ₁ ,A ₂ ,…,A _n } indicates that the diagonal block is a block diagonal matrix of the matrix A ₁ ,A ₂ ,…,A _n , and the symbol * indicates omission of symmetric items in the symmetric block matrix. If M is a symmetric matrix, then λ _max (M) represents the largest eigenvalue of M. symbol denotes the Kronecker product. Where the dimension of a matrix is not explicitly specified somewhere in the text, its dimension is assumed to be suitable for the algebraic operations on the matrix.

The present invention proposes a non-fragile distributed fault estimation method for a time-varying system with random gain changes and random nonlinear phenomena in a sensor network environment, as shown in Figures 1-3. Fig. 1 is a schematic flow chart of the method of the present invention. Figure 2 is a schematic diagram of the fault estimation error of sensor nodes. The dotted line in the figure is the fault estimation error of sensor node 1, the solid line with asterisks is the fault estimation error of sensor node 2, and the dotted line is the fault estimation error of sensor node 3. The solid line of the five-pointed star is the fault estimation error of sensor node 4, and the solid line with a cross is the fault estimation error of sensor node 5. Figure 3 is a schematic diagram of the fault signal and the estimation of the fault signal by sensor nodes. The solid line in the figure is the fault signal, the dotted line is the fault estimation of sensor node 1, the solid line with asterisks is the fault estimation of sensor node 2, and the dotted line is the sensor The fault estimation of node 3, the solid line with a five-pointed star is the fault estimation of sensor node 4, and the solid line with a cross is the fault estimation of sensor node 5.

A non-fragile distributed fault estimation method based on sensor networks, the method includes the following steps:

Step 1. Use the sensor network to extract fault data from the control system and preprocess it;

Step 2. Based on the preprocessed data, a dynamic model of a non-fragile distributed fault estimator for a time-varying system with randomly occurring gain changes and randomly occurring nonlinear phenomena is established;

Step 3. Fault estimation for a dynamic model of a non-fragile distributed fault estimator for nonlinear time-varying systems with stochastically occurring gain changes

Step 4. Calculate the fault estimation error according to the non-fragile distributed fault estimator dynamic model of nonlinear time-varying system with stochastic gain changes established in step 3:

Step 5. Obtain the fault estimation augmentation system according to the fault estimation error obtained in step 4;

Step 6. Use the fault estimation augmentation system to analyze whether the fault estimator satisfies the average performance constraints by constructing functions and using known constraints

Step 7. If step 6 satisfies the performance constraints, calculate the parameter matrix of the fault estimator to realize the design of a non-fragile distributed fault estimator for nonlinear time-varying systems with randomly occurring gain changes.

Among them, the second step in the sensor network-based non-fragile distributed fault estimation method is specifically to establish a dynamic model of a non-fragile distributed fault estimator for a nonlinear time-varying system with random gain changes, and 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 for fault estimator node _i is:

y _i (k)=C _i (k)x(k)+E _i (k)v(k)+H _i (k)f(k)i=1,2,...,n (2)

In the formula, represents the state vector of the system, is the input disturbance of the system, for the faults to be detected. is the measurement output obtained by fault estimator node _i , v(k)∈l ₂ [0,N) is the external disturbance. A(k), D(k), G(k), C _i (k), E _i (k) and H _i (k) are known real-time varying matrices of appropriate dimensions. where the random variable It is used to describe randomly occurring nonlinear phenomena and obeys the Bernoulli white sequence distribution. k∈[0,N], [0,N]={0,1,...,N} is a finite time domain space. nonlinear vector-valued function h(0)=0 satisfies [h(x)-h(y)-Ψ(xy)] ^T [h(x)-h(y)-Ω(xy)]≤0, Ψ and Ω have corresponding dimensions The known real matrix of numbers.

The third step in the non-fragile distributed fault estimation method based on the sensor network is specifically to perform fault estimation on the dynamic model of the non-fragile distributed fault estimator of the nonlinear time-varying system with randomly occurring gain changes;

The fault estimator model is established as follows:

In the formula is the state estimation vector of fault estimator node i, a _ij is the sensor node connection weight coefficient, is the output residual of fault estimator node i, K _ij (k), H _ij (k) and L _ij (k) are the parameter matrix required by fault estimator node i, random variables σ _1k , σ _2k control The probability of a gain change of the fault estimator, the mathematical expectation is variance is ΔK _ij (k) and ΔH _ij (k) represent the gain variation produced by the fault estimator, ΔK _ij (k)=K _ij (k)H _a F _a (k)E _a , ΔH _ij (k)=H _ij ( k)H _b F _b (k)E _b , where H _a H _b E _a and E _b are matrices with known dimensions, F _a (k) and F _b (k) are unknown matrices and satisfy I is the identity matrix. N _i represents a collection of sensor nodes.

The fourth step in the non-fragile distributed fault estimation method based on sensor networks is specifically: according to the non-fragile distributed fault estimator dynamic model of the nonlinear time-varying system with random gain changes established in step 3, calculate the fault estimation error :

Subtracting the fault from the residual gives the fault estimation error equation:

In the formula, is the fault estimation error at time k, is the output residual of the fault estimator, for the faults to be detected.

The fifth step in the sensor network-based non-fragile distributed fault estimation method is specifically: according to the fault estimation error obtained in step four, an augmented fault estimation system is obtained;

In the above formula, The form of the matrix of formula (5) is:

in is a known constant. when When , a _ij =0, the matrix is a sparse matrix,

Step six in the non-fragile distributed fault estimation method based on sensor networks is specifically: using the fault estimation augmentation system, by constructing functions and using known constraints, analyzing whether the fault estimator satisfies the average H _∞ performance constraint;

Use the formula:

Assuming that the parameter matrices K _ij (k), H _ij (k) and L _ij (k) of the fault estimator are known, by constructing the function (7):

J(k)= ^ηT (k+1)P(k+1)η(k+1) ^-ηT (k)P(k)η(k) (7)

When the vector ξ(k) is non-zero, judge whether the parameters K _ij (k), H _ij (k) and L _ij (k) satisfy the average H _∞ performance constraint; the specific form of the matrix in formula (6):

I ₂ =[I 0]I ₁ =[I 0] ^T

γ>0 is a given positive scalar, S _i >0 (i=1,2,…,n) is a series of positive definite matrices, {P(k)} _0≤k≤N+1 is a series of positive definite matrices . diag{…} represents a diagonal matrix, X is a matrix, E ^T is the transpose of matrix E, and E ^T X ^T is the product of matrix E ^T and matrix X ^T. represents n-dimensional Euclidean space, Represents a collection of n×m dimensional real matrices. represents the mathematical expectation of x, Indicates the mathematical expectation of x conditional on y. Represents the Kronecker product, and ||x|| represents the Euclidean norm of x.

Step seven in the non-fragile distributed fault estimation method based on sensor networks is specifically: if step six meets the performance constraints, calculate the fault estimator parameter matrix K _ij (k)H _ij (k)L _ij (k)(i, j) ∈ε, enabling the design of non-fragile distributed fault estimators for nonlinear time-varying systems with randomly occurring gain changes.

Further, another sensor network-based non-vulnerable distributed fault estimation method is provided, which is different from the above method in that the constraints described in step six are:

in:

R＝diag{S ₁ ,S ₂ ,…,S _n }

In the formula, is the fault estimation error, ξ(k) is a non-zero vector, and the given interference suppression index for initial state, is the initial state estimation vector of the fault estimator, e(0) is the initial estimation error, for transpose.

Adopt method described in the present invention to carry out emulation:

System parameters:

The nonlinear function is:

The parameters of the sensor nodes are:

C ₁ (k)=[0.5 0.1 sin(2k)], C ₂ (k)=[0.4 0.2], C ₃ (k)=[0.6 0.4 sin(2k)],

C ₄ (k)=[0.3sin(4k) 0], C ₅ (k)=[0.2sin(3k) 0.1sin(2k)], E ₁ (k)=0.1,

E ₂ (k)=0.31, E ₃ (k)=0.23, E ₄ (k)=0.2, E ₅ (k)=0.11, H ₁ (k)=0.6, H ₂ (k)=0.8, H ₃ (k) = 0.7,

H ₄ (k)=0.9, H ₅ (k)=0.4, _Hb = 1, _Eb = 0.3

In addition, the probability of the random variable α(k) is 0.8, the external disturbance ω(k)=exp(-k), The fault signal is Positive definite matrix S _i =diag{2,2}(i=1,2,…,5), the initial state of the system x(0)=[0.26 -0.2] ^T , the initial state of the estimator is

Formula (6), formula (7) and formula (8) are solved, and the fault estimator parameter matrices K _ij (k), H _ij (k) and L _ij (k) are obtained to satisfy the average H _∞ performance constraint.

Fault estimation gain solution:

According to step seven, the fault estimator parameter matrices K _ij (k), H _ij (k) and L _ij (k) are obtained as follows:

Fault estimator effect:

Fig. 2 is a schematic diagram of fault estimation errors of sensor nodes, and Fig. 3 is a schematic diagram of fault signals and fault estimation of sensor nodes.

It can be seen from Fig. 2 and Fig. 3 that for time-varying systems with random gain changes and random nonlinear phenomena, the invented non-fragile distributed fault estimator design method can effectively estimate the target state.

A non-vulnerable distributed fault estimation method based on sensor networks proposed by the present invention is a fault estimation method for randomly occurring nonlinearity and random gain changes of sensors, involving stochastic gain changes and random nonlinearity Design of nonfragile distributed fault estimators for time-varying systems. The present invention solves the non-fragile distributed fault estimation problem that has not been solved so far. The two phenomena of random gain change and random nonlinearity exist in the discrete time-varying system at the same time, and then affect the performance of fault estimation. The present invention combines the non-fragile The distributed fault estimation problem is introduced into the nonlinear time-varying system under the sensor network environment. Using the _L2 gain theory and stochastic analysis techniques to obtain sufficient conditions ensures the existence of the required distributed fault estimator. Compared with the existing linear fault estimation method, the fault estimation method of the present invention can simultaneously deal with random occurrence of uncertainties Non-linear phenomena that occur randomly and randomly, and achieve the purpose of resisting nonlinear disturbances. The invention is suitable for fault estimation of nonlinear complex dynamic systems.

As above, the method proposed by the present invention has been described clearly and in detail. While the preferred embodiment of the invention has been described and explained in detail, it will be understood by those skilled in the art that changes in form and details may be made without departing from the spirit and scope of the invention as defined by the appended claims. Make various modifications.

Claims (1)

1. A non-fragile distributed fault estimation method based on sensor network, the method may further comprise the steps: Step 1. Use the sensor network to extract fault data from the control system and preprocess it; Step 2. Based on the preprocessed data, a dynamic model of a non-fragile distributed fault estimator for a time-varying system with randomly occurring gain changes and randomly occurring nonlinear phenomena is established; Step 3, performing fault estimation on the dynamic model of the non-fragile distributed fault estimator of the nonlinear time-varying system with randomly occurring gain changes; Step 4. Calculate the fault estimation error according to the non-fragile distributed fault estimator dynamic model of the nonlinear time-varying system with randomly occurring gain changes established in step 3; Step 5. Obtain the fault estimation augmentation system according to the fault estimation error obtained in step 4; Step 6. Utilize the fault estimation augmentation system to analyze whether the fault estimator satisfies the average performance constraint by constructing functions and using known constraints; Step 7. If step 6 satisfies the average performance constraint, calculate the fault estimator parameter matrix to realize the non-fragile distributed fault estimator design for nonlinear time-varying systems with randomly occurring gain changes.