CN110161882A - A kind of fault detection method of the networked system based on event trigger mechanism - Google Patents

Abstract

The invention discloses a fault detection method for a networked system based on an event-triggered mechanism, and belongs to the field of networked systems. Firstly, a continuous-time networked system model is established under the conditions of sensor saturation, disturbance and fault, and an effective event-triggered communication transmission is introduced. The strategy solves the problem of limited bandwidth of the actual network, and then designs the fault detection filter, and introduces the residual evaluation mechanism to judge whether the system fails. Using the Lyapunov stability theory and the linear matrix inequality analysis method, the asymptotic stability and fault detection of the filter error system are obtained. A sufficient condition for the existence of the filter; the optimization problem is solved by using the Matlab LMI toolbox, and the optimal fault detection filter parameters are obtained as The method of the invention takes into account the fact that the network bandwidth is limited, the sensor is constrained by saturation and faults in the actual situation, and is suitable for general fault detection and has good universality.

Description

A fault detection method for networked systems based on event-triggered mechanism

technical field

The invention belongs to the field of networked systems, and relates to a fault detection method of a networked system based on an event trigger mechanism.

Background technique

A networked control system is a closed-loop control system formed by a shared communication network connection between the controlled object and other components. Compared with the traditional control system, the networked control system has the advantages of simple connection, strong flexibility, easy expansion, and easy maintenance. However, due to the introduction of the network, it inevitably brings a series of new problems, such as information transmission delay, data packet loss, quantization error and bandwidth limitation, etc., which lead to the performance degradation of the system, and in severe cases, the system will become unstable. Fault detection is to judge whether the system fails, and it is an important basis for the establishment of the early warning mechanism for the safe operation of the system. Due to the introduction of the communication network, the traditional fault detection method is difficult to be directly applied to the networked control system. Therefore, for the non-ideal network factors, the research on the fault detection method of the networked system has important theoretical significance and application value.

Fault detection is to establish a threshold and evaluation function related to measurable signals (such as status, output, etc.), and detect whether a fault occurs by comparing the evaluation function value and the threshold. When the evaluation function value is greater than the threshold, the system detects the fault and issues an alarm Signal. However, most scholars choose discrete systems when they study the problem of fault detection in networked systems. For the transmission mode in communication networks, traditional periodic triggering mechanisms with equal time intervals are mostly used. In the case of limited network bandwidth in practice Network congestion is inevitable, unnecessary computation is added, and a lot of energy and network resources are wasted.

SUMMARY OF THE INVENTION

In view of the above problems in the prior art, the present invention provides a fault detection method for a networked system based on an event-triggered mechanism. Considering that the networked system has sensor saturation constraints and the actual network bandwidth is limited, a fault detection filter is designed, so that the networked system can not only maintain asymptotic stability under the constraints of the above conditions, but also can satisfy the H _∞ performance index, Faults are effectively detected through the residual evaluation mechanism.

Technical scheme of the present invention:

A fault detection method for a networked system based on an event-triggered mechanism, comprising the following steps:

1) Establish a mathematical model of a networked system with limited communication bandwidth and sensor saturation constraints:

in: is the state vector, is the derivative of the state vector; is the measurement output vector with sensor saturation; and are the measurement noise and the unknown fault signal, respectively, and satisfy L ₂ [0,∞). A, B _w , B _f , C and D _w are constant matrices of known appropriate dimensions; is the nonlinear part under sensor saturation, belonging to [L ₁ , L ₂ ], and is a diagonal matrix, and L=L ₂ -L ₁ is a symmetric positive definite matrix. For the network environment with limited communication bandwidth, the trigger mechanism and network detection are as follows:

where: σ∈[0,1), is a positive definite weighting matrix, the sampler collects the output signal with a fixed period h, τ(t) is the time-varying delay of network transmission, e _k (t) is the error vector, is the input of the filter, and the trigger sends the data at i ₀ h, i ₁ h,…, i _k h,…, is the delay of the _ith trigger.

2) Design a fault detection filter:

where: x _F (t) is the filter state, is the filter input, r _F (t) is the residual signal; _AF , _BF , _CF and _DF are the filter parameters to be designed.

The residual evaluation mechanism is used to detect whether the fault occurs, and the residual evaluation function J(t) and the threshold J _th are respectively expressed as follows:

where: T _d denotes the finite evaluation time length.

Whether the system fails is judged by the rules of formula (6):

3) The sufficient conditions for the asymptotic stability of the system and the existence of the fault detection filter are as follows:

where * denotes a symmetric matrix block, and

Θ ₁₁ =-XX ^T , Θ ₁₂ =-YZ ^T , Θ ₂₂ =-ZZ ^T , Θ ₇₇ =-2I+σΩ,

is the intermediate variable,

is the intermediate variable,

Ω is a positive definite weighting matrix, Q, R, is an unknown positive definite matrix, X, Y, Z, is the unknown matrix of appropriate dimension, and the performance index γ, other variables are known, I is the identity matrix and 0 is the zero matrix.

Given a scalar λ>0 and 0<σ<1, use the Matlab LMI toolbox to solve the linear matrix inequality (7). When there is a feasible solution to the inequality (7), there are positive definite matrices Ω, Q, R, and matrices X,Y, and the performance index γ, then the system is asymptotically stable and satisfies the H _∞ performance index, and thus the parameters of the fault detection filter can be obtained, and step 4 can be continued); when there is no feasible solution to inequality (7), it cannot be obtained. The parameters of the fault detection filter, do not go to step 4), and end.

4) Calculate the optimal fault detection filter parameters

according to Find the performance index γ, and apply the Matlab LMI toolbox to solve the convex optimization problem (8):

where e(t)=r _F (t)-f(t) is the residual error signal,

When equation (8) has a solution, the optimal H _∞ performance index is γ _min , and the optimal fault detection filter parameters are obtained as follows:

in: is a nonsingular matrix.

5) Logical decision to determine whether the fault occurs or not

Based on the event trigger mechanism, the input of the filter is obtained through network transmission The residual signal r _F (t) is obtained from the fault detection filter formula (3), and then the current value J(t) and the threshold value at the time t of the residual evaluation are calculated by the residual evaluation mechanism formula (4) and formula (5). J _th , and finally through the logic of formula (6) to judge whether the fault occurs.

Compared with the prior art, the beneficial effects of the present invention are as follows: for the network environment with limited communication bandwidth and sensor saturation constraints, the present invention provides a fault detection method in the network environment by introducing an effective transmission strategy based on an event-triggered mechanism. Compared with the traditional periodic triggering mechanism that uses equal time interval triggering, the filter design method has more practical application value, and can effectively reduce the amount of data transmission and save network resources.

Description of drawings

FIG. 1 is a flow chart of a networked system fault detection method based on an event-triggered mechanism.

Figure 2 is a structural block diagram of a networked system fault detection method based on an event-triggered mechanism.

Fig. 3 is the residual signal diagram when w(t)≠0, σ=0.1, λ=0.15 fault exists.

FIG. 4 is a graph of the residual evaluation function when w(t)≠0, σ=0.1, and λ=0.15.

FIG. 5 is a graph of the event trigger time and trigger interval when w(t)≠0, σ=0.1, and λ=0.15.

Detailed ways

The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

Referring to Figure 1, a fault detection method for a networked system based on an event-triggered mechanism, comprising the following steps:

Step 1: Build a mathematical model of a networked system with limited communication bandwidth and sensor saturation constraints

The state space expression of the networked system based on the event-triggered mechanism is as follows:

Consider the case of the sensor saturation constraint, and the saturation function sat( ): Belonging to [L ₁ , L ₂ ], L ₁ and L ₂ are diagonal matrices, and L=L ₂ -L ₁ is a symmetric positive definite matrix.

For ease of processing, we divide sat(Cx(t)) into a linear part and a nonlinear part:

The non-line part The following conditions are met:

Step 2: Design the Fault Detection Filter

Considering that the network transmission is constrained by the actual bandwidth and sensor saturation, in order to reduce the number of triggering control signals and the burden of sharing the network, an event triggering mechanism is selected, and the triggering conditions are assumed as follows:

The fault detection filter formula (3) is designed, and combined with the event trigger mechanism and the sensor saturation constraint, the fault detection filter input transmitted through the network is:

Considering equations (10), (3) and (14) comprehensively, the filter error system (15) can be obtained by the method of state augmentation:

where: e(t)=r _F (t)-f(t), H=[I 0],

It can be seen that the filter error system (15) incorporates network transmission delay, sensor saturation constraint parameters, event trigger parameters, measurement noise and unknown fault signals. The fault detection problem of the original system is transformed into the H _∞ filtering problem with unknown parameter error system. The following specific problem becomes to find the filter parameters _{AF , BF , CF and DF so that the} filter error system satisfies the following conditions:

(i) when , the filtered error system (15) is asymptotically stable.

(ii) Under zero initial conditions, for any non-zero vector The filtered error vector e(t) is full Among them, γ is the H _∞ performance index, which reflects the suppression level of the residual signal to the external disturbance signal.

The residual evaluation function J(t) and the threshold value J _th are constructed as formula (4) and formula (5) respectively, and whether the system fails is judged by formula (6). When the residual evaluation function value is greater than the threshold, a fault occurs and an alarm occurs; otherwise, no fault occurs.

Step 3: The system is asymptotically stable and a sufficient condition for the existence of a fault detection filter

The Lyapunov function is constructed as:

Using the Lyapunov stability theory and the free weight matrix theory, the sufficient conditions (17) for the filter error system (15) to satisfy (i) and (ii) are obtained:

where * denotes a symmetric matrix block, and

θ ₄₄ = -2I+σΩ, θ ₄₆ =σΩκ, θ ₆₆ = -γI+σκ ^T Ωκ, κ = [0 0D _w ], Σ ₁₂ (1) = λM, Σ ₁₂ (2) = λN, Γ=[-MH MN N 0 0 0].

Given positive scalars λ>0 and 0<σ<1, when there are scalars γ>0 and matrices Ω>0, Q>0, R>0, P>0, and matrices M, N of appropriate dimensions such that (17 ), then the filtered error system (15) satisfies (i) and (ii).

Although equation (17) gives the conditions that the filter error system (15) satisfies (i) and (ii), unfortunately there is a coupled nonlinear term in equation (17), which cannot be solved directly by MATLAB's LMI toolbox . Next, by introducing an additional matrix G for decoupling, the new filter error system (15) satisfies the sufficient conditions (18) of (i) and (ii):

where * denotes a symmetric matrix block, and

Λ ₁ =diag{0,Γ+Γ ^T ,0},

From Expression (18), the following establishes sufficient conditions for system stability and the existence of a fault detection filter.

For convenience, first decompose the matrix G into the following form:

For contract transformation, it is assumed here that the matrices G ₂₁ and G ₂₂ are invertible, and define an invertible matrix

For further simplification, the following expressions are given:

Multiply both sides of equation (18) by and J ₂ to carry out contract transformation, the sufficient conditions (7) for the asymptotic stability of the system and the existence of the fault detection filter can be obtained.

Given a scalar λ>0 and 0<σ<1, use the Matlab LMI toolbox to solve the linear matrix inequality (7). and matrices X, Y, Z, and the performance index γ, then the system is asymptotically stable and satisfies the H _∞ performance index, and the parameters of the fault detection filter can be obtained from this, and step 4 can be continued; when there is no feasible solution to formula (7), the fault cannot be obtained. Detect filter parameters, do not go to step 4, end.

Step 4: Calculate optimal fault detection filter parameters

For Equation (15), use the Matlab LMI toolbox to solve the convex optimization problem Equation (8). When equation (8) has a solution, the optimal H _∞ performance index is γ _min and the optimal fault detection filter parameter expression (9). When equation (8) has no solution, the optimal fault detection filter cannot be obtained.

Step 5: Logical decision to determine whether the failure occurred or not

Based on the event trigger mechanism, the input of the filter is obtained through network transmission The residual signal r _F (t) is obtained from the fault detection filter formula (3), and then the current value J(t) and the threshold value at the time t of the residual evaluation are calculated by the residual evaluation mechanism formula (4) and formula (5). J _th , and finally through the logic of formula (6) to judge whether the fault occurs.

Example:

By adopting the fault detection method of the networked system based on the event-triggered mechanism proposed by the present invention, the system is asymptotically stable in the absence of external disturbances and faults. when When the above method is used to detect the fault in the system. The specific implementation method is as follows:

The mathematical model of a networked motor stirring system is formula (10), where the system parameters are:

Suppose the sensor saturation function sat(Cx(t)) can be expressed as follows:

where the saturation value is

Based on the event-triggered mechanism and considering sensor saturation constraints, assuming h=0.1, λ=0.15, σ=0.1, By solving the convex optimization problem (8), the optimal H _∞ performance index can be obtained as γ _min =1.2105 and the corresponding trigger parameter matrix and obtain the optimal fault detection filter parameters

C _F =[0.0627 0.0144-0.0464], D _F =[0.0050 0.0257].

Note that the H _∞ performance index is very important, reflecting the level of rejection of the residual signal to external disturbance signals, and its value is affected by trigger conditions, network delays, and sensor saturation constraints. It can be seen from Table 1 and Table 2 that as the parameters σ and λ increase, the value of γ _min also increases accordingly. In addition, Table 3 shows that the optimal performance index _γmin is affected by the change of sensor saturation constraints.

Table 1 Optimal performance index γ _min with parameter σ

Table 2 The optimal performance index γ _min with the change of parameter λ

Table 3 Optimal performance index γ _min with parameters L ₁ , L ₂

Table 4 Fault detection time as a function of parameter σ

In order to further verify the effectiveness of the above fault detection filter, it is assumed that the interference noise signal w(t) is a random signal obeying a uniform distribution on [0,1], and the fault signal is assumed to have the following form

Under the zero initial condition, the change of residual signal with time can be obtained using MATLAB as shown in Figure 3, and Figure 4 shows the residual evaluation function J ( t) Curves over time. According to the threshold expression (5) of the residual evaluation mechanism, selecting the evaluation time length T _d =200s, the threshold J _th =0.2586 can be obtained. From the expression (4) of the residual evaluation function, J(t)| _t=55.4 =0.2615>0.2586 can be obtained through calculation and comparison, that is, the fault is detected within 5.4s. Using the same method, the variation of the time length of fault detection with the parameter σ can be obtained as shown in Table 4. In addition, FIG. 5 shows the event trigger time and trigger interval when the parameter σ=0.1. In the evaluation time of 200s, the number of sampling is 2001, and the number of sensor sending is 853, which means that the data sending rate of the event trigger mechanism is only 42.63%, which greatly reduces the network burden and reduces network congestion.

It can be seen that the designed fault detection filter can quickly make a judgment and detect the fault after the fault occurs; and the transmission strategy based on the event trigger mechanism can reduce the amount of data transmission and save network resources, which shows that the proposed method is very effective. meaningful.

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,B_w,B_f, C and D_wFor 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, e_kIt (t) is error vector,For filter input, trigger sends the data moment as i₀h, i₁h,…,i_kH ...,It is i-th_kThe time delay of secondary triggering；

2) design error failure Fault detection filter:

Wherein: x_FIt (t) is filter status,For filter input, r_FIt (t) is residual signals；A_F,B_F,C_FAnd D_FIt 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 J_thRespectively indicate as Under:

Wherein: T_dIndicate 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-X^T, Θ₁₂=-Y-Z^T,Θ₂₂=-Z-Z^T, 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)=r_F(t)-f (t) is residual error error signal,

When formula (8) has solution, optimal H is obtained_∞Performance indicator is γ_min, 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 r_F(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 J_th, whether occur finally by formula (6) logic judgment failure.