CN117221075B - Discrete networking system fault detection method based on self-adaptive event trigger mechanism - Google Patents
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Abstract
The invention discloses a discrete networking system fault detection method based on a self-adaptive event trigger mechanism, which comprises the following steps: 1. establishing a discrete networked system model containing uncertainty factors, randomly generated nonlinear phenomena, external disturbance and system fault signals; 2. establishing a signal continuous packet loss model; 3. setting an adaptive event triggering mechanism; 4. establishing a fault detection filter model; 5. based on Lyapunov stability theorem, the system is randomly stable in a limited time and meets H ∞ Judging basis of performance index constraint; 6. and setting a fault detection mechanism of the discrete networking system. The invention can avoid unnecessary triggering events when the system is inactive or the demand is low, thereby saving calculation and communication resources, reducing energy consumption, and triggering events in real time according to the system demand, thereby responding to changes more quickly, improving the response speed of the system and detecting the occurrence of faults in time.
Description
Technical Field
The invention relates to a fault detection method of a discrete networking system, in particular to a fault detection method of a discrete networking system based on a self-adaptive event trigger mechanism.
Background
Networking systems have been widely used in the critical fields of aerospace, industrial automation, electricity and energy, and we enjoyed unprecedented convenience and efficiency. However, as networked systems continue to evolve, so too does the complexity and technical challenges. One of the most attractive challenges is the problem of fault detection.
In a discrete networked system, information transmission is affected by multiple factors including uncertainty factors, randomly occurring nonlinearities, network attacks, signal quantization, communication time lags, and interference of network-induced phenomena such as packet loss. Among these network-induced phenomena, uncertainty factors, random non-linearities, and continuous packet loss often occur, which makes the conventional failure detection method frustrating. Thus, it becomes particularly important to study the design of fault detection filters for discrete networked systems with random non-linearities and uncertainties in the case of continuous packet loss.
In the prior art, conventional fault detection methods generally adopt a static event trigger mechanism or a time trigger mode for checking, and the methods can greatly increase network transmission pressure, waste network resources and lack enough flexibility to cope with challenges caused by system complexity.
Disclosure of Invention
The invention provides a discrete networking system fault detection method based on a self-adaptive event triggering mechanism, which aims to solve the problem that the existing method can not simultaneously process the fault detection of an uncertainty discrete networking system under the conditions of random nonlinear phenomenon and continuous packet loss. According to the method, a more accurate fault detection filter system is established by considering uncertainty factors, randomly generated nonlinear phenomena and continuous packet loss possibly occurring in actual transmission in a discrete networked system, so that the false alarm rate is reduced, the occurrence of faults can be more accurately detected, and the cost and risk of system maintenance are reduced. Meanwhile, the invention applies the self-adaptive event triggering mechanism to the fault detection process, and the mechanism can respond to the change of the system state in real time without depending on static rules or preset time intervals, thereby reducing the total amount of network transmission data, effectively reducing the total amount of network transmission data, saving network resources, accurately detecting faults and improving the accuracy and efficiency of fault detection.
The invention aims at realizing the following technical scheme:
a discrete network system fault detection method based on an adaptive event trigger mechanism comprises the following steps:
step one, establishing a discrete networked system model containing uncertainty factors, randomly-occurring nonlinear phenomena, external disturbance and system fault signals:
wherein x is k A state vector representing the system at time k; x is x k+1 A state vector representing the system at time k+1; y is k Representing the measurement output obtained by the system at the time k; g (x) k ) Representing a non-linear function, where k.epsilon.0, N]N is a positive integer; w (w) k And f k Respectively representing external disturbance and fault signals at the time k; a, C, D 1 ,D 2 ,E 1 ,E 2 As a constant matrix, ΔA is the parameter uncertainty, α k Is a bernoulli random variable;
step two, establishing a signal continuous packet loss model:
wherein y is k-1 Representing the measured output obtained by the system at time k-1, the variable ε k Is a Bernoulli random variable;
step three, setting a self-adaptive event triggering mechanism:
step three, definitionWherein->And->Respectively representing the measured value transmitted at the last self-adaptive event triggering moment and the measured output sampled at the current moment, and psi k Representing the transmission error between the measured value transmitted at the last self-adaptive event triggering moment and the measured output sampled at the current moment;
step three, defining an event generator function:
wherein Ω=Ω T > 0 is a given event weighting matrix; delta k Is an event trigger threshold; if the condition phi (phi) k ,δ k ) The measurement output sampled at the current moment is transmitted to the fault detection filter side through a network; transmission signal y k Is defined as:
wherein, the event trigger time sequence 0 is less than or equal to k 0 ＜k 1 ＜…＜k t < … is determined by the following trigger conditions:
k t+1 ＝inf{k∈[0,N]|k＞k t ,Φ(ψ k ,δ k )＞0}
k t+1 representing the next event trigger time;
step four, establishing a fault detection filter model:
step four, according to the actually received measurement output y k A fault detection filter model is constructed of the form:
wherein,r is the state vector of the fault detection filter at time k k As residual signal, A F ,B F ,D F ,E F A filter parameter matrix of appropriate dimension to be designed;
step IV, bySum phi k Defining, the fault detection filter model is rewritten as follows:
step IV, definitionAccording to the discrete networked system model in the first step and the fault detection filter model in the fourth step, the system is subjected to augmentation treatment to obtain the following fault detection filter residual error system:
the matrix elements therein are as follows:
fourth, through designing the self-adaptive event triggering mechanism and the fault detection filter model, the obtained fault detection filtering residual error system meets the following conditions:
(1) When v k =0, given matrix W > 0, scalar c 1 ,c 2 Satisfy constraint 0 < c 1 ＜c 2 When the following formula holds:
the fault detection filtering residual error system is randomly stable for a limited time;
(2) When v k With a value of not equal to 0, under zero initial conditions,the following constraints are satisfied:
wherein, gamma is a positive scalar, and the fault detection filtering residual error system satisfies H ∞ Performance index constraints;
step five, based on Lyapunov stability theorem, obtaining random stability of the system in a limited time and meeting H ∞ The basis for judging the performance index constraint is as follows:
λ 0 W＜P＜λ 1 W
λ 1 c 1 ≤χ -N λ 0 c 2
wherein,
step six, setting a fault detection mechanism of the discrete networking system:
step six, constructing a residual error evaluation function J for realizing fault detection of the discrete networking system k And a detection threshold J th ：
Step six, detecting whether the discrete networking system has faults according to the following judging standards:
compared with the prior art, the invention has the following advantages:
1. aiming at the discrete networking system with uncertainty factors and random nonlinear phenomena, the invention provides the fault detection of the discrete networking system based on the self-adaptive event triggering mechanism under the condition of continuous packet loss, and simultaneously considers the influence of the random nonlinear phenomena and the continuous packet loss on the system performance, thereby better processing the problem of repeated data in the data transmission process, reducing the network transmission pressure and improving the data transmission efficiency. Different from the traditional static event triggering mechanism, the fault detection method of the invention simultaneously processes the fault detection problems of uncertainty factors, random nonlinear phenomena and continuous packet loss phenomena in a limited time, adopts the self-adaptive event triggering mechanism to judge whether data are transmitted or not, and the triggering condition depends on the measurement output sampled at the current moment, the measurement value transmitted at the last self-adaptive event triggering moment and the triggering threshold value, wherein the triggering threshold value is adjusted in real time according to the current system state instead of the fixed threshold value parameter, thus avoiding unnecessary triggering events when the system is inactive or the demand is lower, saving calculation and communication resources, reducing energy consumption, and triggering events in real time according to the system demand, thereby responding to changes more quickly and improving the response speed of the system.
2. The invention analyzes by means of Lyapunov stability theorem, solves the parameters of the fault detection filter in the form of LMI linear matrix inequality, considers the system to meet H ∞ The performance index constraint condition can ensure that the system is randomly stable in a limited time. Compared with a static event trigger mechanism transmission mode, the data quantity transmitted in the same time period is reduced by 40%. This means that the network communication is more efficient, more bandwidth can be reserved for other important tasks, the failure detection efficiency is improved, and the stability of the system can be ensured under the condition of continuous packet loss.
Drawings
FIG. 1 is a flow chart of a method of discrete networked system failure detection under an adaptive event triggering mechanism.
Fig. 2 is a schematic diagram of residual signal output of a discrete networked motor stirring system in an embodiment.
FIG. 3 is a residual evaluation function output schematic of a discrete networked motor stirring system in an embodiment.
Fig. 4 is a schematic diagram of trigger thresholds under adaptive event based trigger conditions in an embodiment.
Fig. 5 is a schematic diagram of stability of a fault detection filter residual system in an embodiment.
Fig. 6 is a diagram of data transmission timing and event trigger intervals based on an adaptive event trigger condition in an embodiment.
Fig. 7 is a diagram of data transmission timing and event trigger intervals based on a static event trigger condition in an embodiment.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a discrete networking system fault detection method based on a self-adaptive event trigger mechanism, as shown in fig. 1, the method comprises the following steps:
step one, a discrete networked system model comprising uncertainty factors, randomly generated nonlinear phenomena, external disturbance and system fault signals is established.
In this step, the discrete networked system model is as follows:
in the method, in the process of the invention,a state vector of the system at the time k is represented, and n represents an n-dimensional vector; />A state vector representing the system at time k+1; />Representing the measurement output obtained by the system at the moment k, wherein m represents an m-dimensional vector; />Representing a non-linear function, where k.epsilon.0, N]N is a positive integer; />And->Respectively represent the external disturbance and fault signals at time k, which belong to l 2 [0,N]S represents an s-dimensional vector, l represents an l-dimensional vector, l 2 [0,N]Represent [0, N ]]A space of squarable sum vector functions; a, C, D 1 ,D 2 ,E 1 ,E 2 Deltaa is the parameter uncertainty, a constant matrix of appropriate dimensions.
Considering the system parameter uncertainty, ΔA should satisfy the following constraints:
ΔA＝HFL
where H, L is a known constant matrix of appropriate dimension, F is an unknown matrix satisfying constraint F T F≤I。
Assume that the nonlinear function satisfies the following Lipschitz condition:
||g(x k )|| 2 ≤μ k ||Mx k || 2
wherein mu k > 0 is a known positive scalar and M is a positive definite matrix of appropriate dimension.
The randomly occurring nonlinear phenomenon can be represented by the Bernoulli random variable alpha k To describe, it satisfies the following probability distribution:
wherein,is a positive scalar, ++>Representing parameter uncertainty, satisfying constraint conditionsIs a known positive scalar.
And step two, establishing a signal continuous packet loss model.
Consider that a sensor may experience continuous packet loss during the acquisition of measurement signals. This network-induced phenomenon can be expressed in the following form:
wherein y is k-1 Representing the measured output obtained by the system at time k-1, the variable ε k Also a Bernoulli random variable, satisfies the following probability distribution:
wherein,is also a known positive scalar, < >>Representing parameter uncertainty, satisfying constraint +.>Beta is a known positive scalar. If epsilon k =1, sensor data transmission was successful; otherwiseThe sensor will continue to lose packets. It should be noted that α k And epsilon k Are random variables independent of each other.
Step three, setting a self-adaptive event triggering mechanism.
In order to save energy, an adaptive event triggering mechanism is used to decide whether the measurement output at the current sampling instant can be transmitted to the fault detection filter side. To better explain the adaptive event trigger mechanism, first defineWherein->And->Respectively representing the measured value transmitted at the last self-adaptive event triggering moment and the measured output sampled at the current moment, and psi k Representing the transmission error between the measured value transmitted at the last self-adaptive event triggering time and the measured output sampled at the current time. An event generator function is then defined, as shown in the following equation:
wherein Ω=Ω T > 0 is a given event weighting matrix; delta k Is an event trigger threshold that satisfies the following adaptive control law:
wherein ρ is 1 And ρ 2 Are defined parameters which satisfy the constraint 0 < ρ 1 ≤ρ 2 < 1; the positive scalar k is the adjustment function ||ψ k || 2 Is a high sensitivity. If the condition phi (phi) k ,δ k ) The measurement output sampled at the current moment is transmitted to the networkA fault detection filter side. Transmitting signalsIs defined as:
wherein, the event trigger time sequence 0 is less than or equal to k 0 ＜k 1 ＜…＜k t < … is determined by the following trigger conditions:
k t+1 ＝inf{k∈[0,N]|k＞k t ,Φ(ψ k ,δ k )＞0}
k t+1 representing the next event trigger time.
And step four, establishing a fault detection filter model.
Based on the measured output actually receivedA fault detection filter model is constructed in the form of:
wherein,r is the state vector of the fault detection filter at time k k As residual signal, A F ,B F ,D F ,E F A matrix of filter parameters of appropriate dimensions to be designed. By->Sum phi k Defining, the fault detection filter model is rewritten as follows:
definition of the definitionAccording to the discrete networking system model in the first step and the fault detection filter model in the first step, the system is subjected to augmentation treatment to obtain the following fault detection filter residual error system:
the matrix elements therein are as follows:
from the foregoing, the problem of fault detection to be solved can be described as follows: by designing a self-adaptive event triggering mechanism and a fault detection filter model, the obtained fault detection filter residual error system meets the following conditions:
(1) When v k =0, given matrix W > 0, scalar c 1 ,c 2 Satisfy constraint 0 < c 1 ＜c 2 When the following formula holds:
the fault detection filter residual system is randomly stable for a limited time.
(2) When v k With a value of not equal to 0, under zero initial conditions,the following constraints are satisfied:
wherein, gamma is a positive scalar, and the fault detection filtering residual error system satisfies H ∞ Performance index constraints.
Step five, based on Lyapunov stability theorem, obtaining random stability of the system in a limited time and meeting H ∞ And judging the basis of the performance index constraint.
In the step, the fault detection filtering residual error system is randomly stable in a limited time and meets H ∞ The basis for judging the performance index constraint is as follows:
consider an uncertain discrete networking system in the presence of randomly occurring non-linear phenomena and continuous packet loss, for a given positive scalar kappa, χ > 1,0 < c 1 ＜c 2 ,0＜ρ 1 ≤ρ 2 When gamma > 0, if positive definite symmetric matrix P exists, matrix X, K of proper dimension 2 Positive scalar iota, lambda 0 ,λ 1 The following formula is satisfied:
λ 0 W＜P＜λ 1 W
λ 1 c 1 ≤χ -N λ 0 c 2
wherein,
can ensure that the system is randomly stable for a limited time and meets H ∞ Performance index constraints.
In the step, when the stability judging condition is obtained, the Lyapunov stability theorem is used, and the constructed Lyapunov function is as follows: v (V) k ＝η k T Pη k At the same time define E { DeltaV k }＝E{V k+1 -χV k }。
Step six, setting a fault detection mechanism of the discrete networking system.
To achieve fault detection for discrete networked systems, a residual evaluation function J is constructed k And a detection threshold J th . The residual evaluation function is used for detecting a fault signal in time when a system breaks down; the detection threshold is that when the system has no fault signal, the maximum value of the residual evaluation function is taken as the detection threshold. The specific expression is as follows:
whether the discrete networking system fails or not can be accurately detected according to the following judging standard:
examples:
in this embodiment, taking a discrete networked motor stirring system with parameter modeling uncertainty of random nonlinear and continuous packet loss as an example, the following simulation is performed by adopting the method of the present invention:
matrix parameters of the discrete networked motor stirring system with random nonlinear and continuous packet loss parameter modeling uncertainty are respectively as follows:
the relevant parameters of the uncertainty factor are:L＝[0.30.2]. The relevant parameters of the nonlinear function are: />μ k ＝1，/> The related parameters of the continuous packet loss phenomenon are as follows: />Beta=0.1. Determining whether data is to be transmitted using an adaptive event triggering mechanism, assuming +.>ρ 1 ＝0.2，ρ 2 =0.7, κ=50. The initial values of the other relevant parameters are: w=i, c 1 ＝0.3，c 2 ＝7，χ＝1.001，N＝30，γ＝1.05。
To verify the validity of the designed fault detection filter model, it is assumed that the external disturbance is denoted w k ＝1.2sin(1.5k)ω k ，ω k Indicated in the interval [ -0.4,0.4]Noise uniformly distributed in the inner part, and the fault signal is assumed to be:
solving a linear matrix inequality by using an LMI tool kit of Matlab, solving a feasible solution, and calculating a fault detection filter parameter matrix as follows:
D F ＝[0.09450.2577],E F ＝[-0.05300.0892]
given system initial stateThe sensitivity of the fault detection filter to fault signals and the speed of fault detection when the system is affected by external disturbance are shown in fig. 2 and 3, and when faults occur, the fault detection filter can rapidly and accurately detect the faults. The threshold of the adaptive event triggering mechanism adjusts adaptively as the state of the system changes, as shown in fig. 4. As can be seen from fig. 5, when v k When=0, the fault detection filter residual system in this embodiment is randomly stable for a finite time. FIGS. 6 and 7 illustrate the use of an adaptive event trigger mechanism and a static event trigger mechanism, respectivelyTwo different data transmission modes are manufactured, and the data transmission requirement is reduced under the self-adaptive event triggering mechanism, so that the network resource is saved, and the data transmission efficiency of the networked system is improved. It follows that the adaptive event triggering method proposed by the present invention is very significant.
Claims (1)
1. A discrete networking system fault detection method based on an adaptive event trigger mechanism is characterized by comprising the following steps:
step one, establishing a discrete networked system model containing uncertainty factors, randomly-occurring nonlinear phenomena, external disturbance and system fault signals:
wherein x is k A state vector representing the system at time k; x is x k+1 A state vector representing the system at time k+1; y is k Representing the measurement output obtained by the system at the time k; g (x) k ) Representing a non-linear function, where k.epsilon.0, N]N is a positive integer; w (w) k And f k Respectively representing external disturbance and fault signals at the time k; a, C, D 1 ,D 2 ,E 1 ,E 2 As a constant matrix, ΔA is the parameter uncertainty, α k Is a bernoulli random variable;
considering the system parameter uncertainty, ΔA satisfies the following constraint:
ΔA＝HFL
where H, L is a known constant matrix and F is an unknown matrix satisfying constraint F T F≤I；
Nonlinear function g (x k ) The following Lipschitz conditions are satisfied:
||g(x k )|| 2 ≤μ k ||Mx k || 2
wherein mu k > 0 is a known positive scalar, M is a positive definite matrix of appropriate dimension;
bernoulli random variable alpha k The following probability distribution is satisfied:
wherein,is a positive scalar, ++>Representing parameter uncertainty, satisfying constraint conditions Is a known positive scalar;
step two, establishing a signal continuous packet loss model:
wherein y is k-1 Representing the measured output obtained by the system at time k-1, the variable ε k Is a Bernoulli random variable;
variable epsilon k The following probability distribution is satisfied:
wherein,is a known positive scalar, +.>Representing parameter uncertainty, satisfying constraint +.>Beta is a known positive scalar; if epsilon k =1, sensor data transmission was successful; otherwise, the sensor will continue to lose packets; alpha k And epsilon k Is a random variable independent of each other;
step three, setting a self-adaptive event triggering mechanism:
step three, definitionWherein->And->Respectively representing the measured value transmitted at the last self-adaptive event triggering moment and the measured output sampled at the current moment, and psi k Representing the transmission error between the measured value transmitted at the last self-adaptive event triggering moment and the measured output sampled at the current moment;
step three, defining an event generator function:
wherein Ω=Ω T > 0 is a given event weightingA matrix; delta k Is an event trigger threshold; if the condition phi (phi) k ,δ k ) The measurement output sampled at the current moment is transmitted to the fault detection filter side through a network; transmitting signalsIs defined as:
wherein, the event trigger time sequence 0 is less than or equal to k 0 ＜k 1 ＜…＜k t < … is determined by the following trigger conditions:
k t+1 ＝inf{k∈[0,N]|k＞k t ,Φ(ψ k ,δ k )＞0}
k t+1 representing the next event trigger time;
δ k the following adaptive control rules are satisfied:
wherein ρ is 1 And ρ 2 Are defined parameters which satisfy the constraint 0 < ρ 1 ≤ρ 2 < 1; the positive scalar k is the adjustment function ||ψ k || 2 Sensitivity of (2);
step four, establishing a fault detection filter model:
step four, according to the actually received measurement outputA fault detection filter model is constructed in the form of:
wherein,r is the state vector of the fault detection filter at time k k As residual signal, A F ,B F ,D F ,E F A filter parameter matrix of appropriate dimension to be designed;
step IV, bySum phi k Defining, the fault detection filter model is rewritten as follows:
step IV, definitionAccording to the discrete networked system model in the first step and the fault detection filter model in the fourth step, the system is subjected to augmentation treatment to obtain the following fault detection filter residual error system:
the matrix elements therein are as follows:
fourth, through designing the self-adaptive event triggering mechanism and the fault detection filter model, the obtained fault detection filtering residual error system meets the following conditions:
(1) When v k =0, given matrix W > 0, scalar c 1 ,c 2 Satisfy constraint 0 < c 1 ＜c 2 When the following formula holds:
the fault detection filtering residual error system is randomly stable for a limited time;
(2) When v k With a value of not equal to 0, under zero initial conditions,the following constraints are satisfied:
wherein, gamma is a positive scalar, and the fault detection filtering residual error system satisfies H ∞ Performance index constraints;
step five, based on Lyapunov stability theorem, obtaining random stability of the system in a limited time and meeting H ∞ The basis for judging the performance index constraint is as follows:
λ 0 W＜P＜λ 1 W
λ 1 c 1 ≤χ -N λ 0 c 2
wherein,
step six, setting a fault detection mechanism of the discrete networking system:
step six, constructing a residual error evaluation function J for realizing fault detection of the discrete networking system k And a detection threshold J th ：
Step six, detecting whether the discrete networking system has faults according to the following judging standards:
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