CN113325822A - Network control system fault detection method based on dynamic event trigger mechanism and sensor nonlinearity - Google Patents
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Abstract
The invention discloses a network control system fault detection method based on a dynamic event trigger mechanism and sensor nonlinearity, which comprises the steps of establishing a sensor nonlinear system model, setting the dynamic event trigger mechanism, establishing a sensor output quantization strategy, designing a fault detection filter and a weighted fault model, finally establishing a fault detection model of a networked system, and detecting the faults of the networked system by constructing a residual error evaluation mechanism. The invention greatly improves the robustness of the fault detection model to external disturbance and the sensitivity to system faults, and the application of the dynamic event trigger mechanism and the signal quantization strategy can effectively improve the utilization rate of network resources and save the network resources.
Description
Technical Field
The invention relates to the technical field of network control system fault detection, in particular to a network control system fault detection method based on a dynamic event trigger mechanism and sensor nonlinearity.
Background
Due to the advantages of low installation and maintenance costs, high reliability and safety, flexible communication and the like, network control systems have gained continuous attention in the industrial production process. The problem of fault detection in network controller systems is becoming an important area of research, due to the need for safety, stability and high performance requirements, which place higher demands on the network control systems.
Due to the characteristics of the network control system, the existence of sensor nonlinearity is inevitable, and more new problems and challenges are brought to the control system. At present, most of research results of network control systems mainly aim at a design method of a controller and a filter provided for communication delay, data packet loss, data confusion and limited bandwidth, and relatively few researches on the problem of fault detection of the system are carried out. Therefore, the method has important significance and very wide practical application prospect in the research of the fault detection problem of the sensor nonlinear network control system.
In the existing literature, most of the methods of time triggering or static event triggering are used for data transmission, and in practical engineering application, not all data need to be transmitted, so that the time triggering easily causes resource waste, and further deepens various problems caused by the network. An "event" in event triggering is defined as a trigger condition that depends on the system state and trigger thresholds that determine when and how to trigger the event. The smaller the trigger threshold, the easier it is for an event to trigger, and the more data that is transferred. The static event trigger mechanism does not reflect the relationship between the event trigger and the system state. Therefore, the real-time adjustment of the threshold parameter according to the dynamic environment is very needed in practical application, which results in the dynamic event trigger mechanism provided by the invention, and the trigger threshold can be dynamically adjusted, thereby realizing more effective saving of limited network resources and conforming to the development trend of network control system fault detection.
In a network control system, due to the accuracy limitation of the sensor itself, the signal must be quantized before being transmitted to the communication network. The introduction of the quantizer can solve the problem that part of digital signals are not easy to be coded on one hand, and on the other hand, because the transmission capacity of a transmission channel is very limited, the data is quantized before transmission, so that the size of a data packet can be reduced, and the pressure of network bandwidth is relieved. In a network control system, the quantization precision cannot be too high, which can cause a data packet to influence the network too much, but cannot be too low, otherwise, a lot of important information of the network control system can be lost. Therefore, it is very interesting to quantify the impact on the performance of network control systems.
Disclosure of Invention
Aiming at the technical problem, the invention provides a network control system fault detection method based on a dynamic event trigger mechanism and sensor nonlinearity.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a network control system fault detection method based on a dynamic event trigger mechanism and sensor nonlinearity under the condition of limited network communication comprises the following steps:
s100, establishing a mathematical model of a networked system containing system faults, external disturbance and output sensor nonlinearity;
s200, setting a dynamic event trigger mechanism;
s300, establishing a sensor output quantification model;
s400, establishing a fault detection model;
and S500, evaluating the fault detection performance of the networked system.
Compared with the prior art, the invention has the following beneficial effects:
(1) the method comprises the steps of establishing a sensor nonlinear system model, setting a dynamic event trigger mechanism, establishing a sensor output quantization strategy, establishing a fault detection filter and a weighted fault model, finally establishing a fault detection model of a networked system, and constructing a residual error evaluation mechanism to detect the faults of the networked system. The invention greatly improves the robustness of the fault detection model to external disturbance and the sensitivity to system faults, and the application of the dynamic event trigger mechanism and the signal quantization strategy can effectively improve the utilization rate of network resources and save the network resources.
(2) The invention is based on a new dynamic event trigger communication mechanism, judges whether the signal needs to be transmitted through the network according to the trigger condition, and improves the utilization efficiency of network resources.
(3) Aiming at a linearized network control model, the invention considers the influence of the nonlinearity and the quantization error of a system output sensor on the system, provides a corresponding solution and is more suitable for practical engineering application occasions.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention.
FIG. 2 is a diagram illustrating residual error output based on dynamic event triggering conditions according to an embodiment of the present invention.
Fig. 3 is a schematic diagram illustrating residual evaluation output based on dynamic event triggering conditions according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of transmission time and transmission interval of data based on a dynamic event trigger condition according to an embodiment of the present invention.
Detailed Description
The present invention is further illustrated by the following figures and examples, which include, but are not limited to, the following examples.
Examples
As shown in fig. 1 to 4, the method for detecting a fault of a network control system based on a dynamic event trigger mechanism and sensor nonlinearity includes the following steps:
1) establishing a mathematical model of a networked system comprising system faults, external disturbance and sensor output nonlinearity:
wherein,
a state vector representing the state of the system,
the output of the system is represented by,
and
representing external disturbances and system faults, psi (-) representing sensor non-linearity constraints, A, C, E1,E2,F1,F2A known matrix with appropriate dimensions.
The non-linear function in the above system is set to satisfy the following sector conditions:
wherein the matrix K1> 0 and K2＞0(K2＞K1) Is a symmetrical positive definite real matrix.
For technical processing convenience, the non-linear function is decomposed into a linear part and a non-linear part:
ψ(ξ)＝ψs(ξ)+K1ξ
wherein the non-linear part ψs(xi) is the given set Ψs(xi) and is expressed as:
2) setting dynamic event trigger mechanisms
To alleviate network burden and conserve communication resources, a novel dynamic event triggering mechanism is used to determine when to send data to a communication network. To clearly explain this dynamic event triggering mechanism, a trigger time series of 0 ≦ k is defined0≤k1≤…≤kt… and an event trigger function v (·, ·), as follows:
wherein,
k∈[ki,ki+1)，kifor the latest event trigger time, y (k)i) Is the measured output at that time instant, and δ and ε are two given positive scalars. ζ is an internal dynamic variable that satisfies the following condition:
where θ ∈ (0,1) is a given constant, and ζ ≧ 0 is an initial value. As long as the condition v (phi (k), zeta, epsilon) ≧ 0 is satisfied, an event is triggered and the data at that time needs to be transmitted through the network to the fault detection filter. The order of the event trigger times is determined in the following manner:
wherein,
representing non-negative real numbers.
3) Establishing sensor output quantification model
Considering the limited capacity of the communication channel between the network system and the filter, the output signal needs to be quantized by a quantizer g (-) before it is transmitted.
Quantizer g (·) is defined as g (y) ═ g1(y1),g2(y2),…,gp(yp)]T，gi(yi) (1 ≦ i ≦ p) as a logarithmic quantizer and the quantization level is set to
Quantized density 0 < etagi< 1 is a given scalar and
associated quantizer gi(yi) Is defined as
Wherein σgi＝(1-ηgi)/(1+ηgi)(0＜ηgi< 1), define Δg＝diag{Δg1,Δg2,…,ΔgpWhere Δgi∈[-σgi,σgi](i ═ 1,2, …, p), according to the sector constraint method, g (y) is expressed as:
g(y)＝(I+Δg)y。
4) establishing a fault detection model
Fault detection is performed by constructing a residual system, typically consisting of a filter or an observer, and designing a residual merit function. And then, designing a fault detection filter, and constructing a residual signal based on the fault detection filter to judge whether the system has faults or not. The fault detection filter is of the form:
wherein,
is the state vector of the filter and is,
is the constructed residual output vector and is,
is the input vector of the filter, matrix Af,Bf,Cf,DfIs the filtering to be designedA matrix of device parameters.
Input signal of filter
Is defined as
Here is constructed as one
A weighted fault model is shown to improve detection performance, where w (z) is a weighting matrix. Weighted fault models are generally considered to be linear systems that can quickly and accurately detect faults when the system fails. The minimum implementation form of the weighted fault model is as follows:
wherein x isw(k) State variables representing the model, f (k) a system fault signal,
representing a weighted fault signal, Aw,Bw,Cw,DwRepresenting a known parameter matrix.
In summary, the following fault detection models are obtained:
wherein,
θ(k)＝[dT(k) fT(k)]T，
based on the above procedure, the fault detection problem to be solved can be described as follows: under the zero initial condition, a fault detection model is constructed by designing a fault detection filter and a dynamic event trigger mechanism to meet the following conditions:
when theta (k) is 0, the fault detection model is gradually stable;
for all non-zero θ (k), the presence of the constant γ > 0 makes the fault detection model satisfy the following inequality:
||re(k)||2≤γ||θ(k)||2
to facilitate the subsequent certification, the following two arguments are introduced,
theory of quotation 1 (schur's theorem of complement)
Given the following symmetric matrix
Wherein S11∈Rr×rThe following three inequalities are equivalent:
(1)S＜0；
(2)
(3)
The matrices D, E, F are matrices of appropriate dimensions and satisfy | | | F | | | ≦ 1, for any variable ε > 0, the following inequality holds:
DEF+ETFTD≤ε-1DDT+εETE
next, we prove that the fault detection model designed by the method satisfies the progressive stability and the expected fault detection performance by the following theorem.
Theorem 1: networked control systems taking into account the non-linearity of the presence sensor, for a given constant λ > 0, ε > 0,0 < θ < 1, θ ε ≧ 1, if there is a matrix of appropriate dimensions
AF,BF,CF,DFAnd the event trigger related parameters satisfy the following inequality:
wherein,
JF＝[0 0 0 0 0 0 BF BF DF 0]
and (3) proving that: by constructing the following Lyapunov function:
W(k)＝W1(k)+W2(k)
W1(k)＝ηT(k)Pη(k)
ΔW(k)＝ΔW1(k)+ΔW2(k)
ΔW1(k)＝W1(k+1)-W1(k)
ΔW2(k)＝W2(k+1)-W2(k),k∈(ki,ki+1)
definition of
By combining the dynamic event trigger mechanism and the quantitative constraint provided by the method, the method can obtain
Wherein,
order to
And define
To Ψ left and right multiplication T respectivelyTAnd T, wherein
T＝diag{I,I,I,I,I,G,I,G5}，
Due to-GTP-1G＜P-G-GT，
The following inequality holds:
definition of
And F ═ diag { T, I, T, I }, and to left-and right-multiplication matrices F, respectively, of the above formula ΨTAnd F, and define new variables
U＝G1,
CF＝CfY,DF＝Df，
Depending on the quantization mechanism, Ψ can be written as:
by way of introduction 2, the following inequality is found to hold:
by factoring 1, Ψ < Ψ ≦ xi < 0, and Δ w (k) ≦ 0 when θ (k) is 0, it may be deduced that the fault detection model is asymptotically stable; when θ (k) ≠ 0, pair
The left side and the right side are sequentially accumulated from 0 to N to obtain:
since W (∞) > 0 and W (0) ═ 0 under the zero initial condition, it is possible to obtain:
5) fault detection and evaluation mechanism of networked system
Constructing a residual evaluation function chi (k) and an evaluation threshold chith(k) To evaluate the fault detection performance of the fault detection filter when χ (k) > χth(k) Then the system is deemed to have failed. The form of the residual merit function is as follows:
wherein k is1Denotes an initial evaluation time, r (k) denotes a residual output, and N denotes a residual evaluation time period.
The selected residual evaluation threshold values were as follows:
whether the system fails or not can be timely and accurately detected through the following logical relations:
according to an input signal of a fault detection filter obtained when the networked system actually operates, a residual signal is obtained by the fault detection filter, then a residual evaluation function and a threshold value are obtained through calculation, and whether a fault of the network control system occurs or not is judged. As shown in fig. 2-4.
The method comprises the steps of establishing a sensor nonlinear system model, setting a dynamic event trigger mechanism, establishing a sensor output quantization strategy, designing a fault detection filter and a weighted fault model, finally establishing a fault detection model of a networked system, and detecting faults of the networked system by constructing a residual error evaluation mechanism. The invention greatly improves the robustness of the fault detection model to external disturbance and the sensitivity to system faults, and the application of the dynamic event trigger mechanism and the signal quantization strategy can effectively improve the utilization rate of network resources and save the network resources.
The above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, but all changes that can be made by applying the principles of the present invention and performing non-inventive work on the basis of the principles shall fall within the scope of the present invention.
Claims (1)
1. A network control system fault detection method based on a dynamic event trigger mechanism and sensor nonlinearity is characterized by comprising the following steps:
s100, establishing a mathematical model of a networked system containing system faults, external disturbances and output sensor nonlinearity:
wherein,
a state vector representing the state of the system,
the output of the system is represented by,
and
respectively representing external disturbance signals and system fault signals, psi (-) representing sensor non-linearity constraints, A, C, E1,E2,F1,F2Is a known matrix;
the non-linear function in the networked system is set to meet the following sector conditions:
wherein the matrix K1> 0 and K2＞0(K2＞K1) Is a symmetrical positive definite real matrix;
and decomposing the non-linear function into a linear part and a non-linear part:
ψ(ξ)＝ψs(ξ)+K1ξ
wherein the non-linear part ψs(xi) is the given set Ψs(xi) and is expressed as:
s200, setting a dynamic event trigger mechanism:
defining trigger time sequence 0 ≦ k0≤k1≤…≤kt… and an event trigger function v (·, ·), as follows:
wherein,
kifor the latest event trigger time, y (k)i) Is the measurement output at that time, and δ and ε are two given positive scalars; ζ is an internal dynamic variable that satisfies the following condition:
wherein theta is an initial value, theta is an initial constant (0, 1); when the condition v (φ (k), ζ, ε) ≧ 0 is satisfied, an event is triggered at which time data is transmitted through the network to the fault detection filter, the order of event trigger times being determined in the following manner:
wherein,
representing a non-negative real number,
s300, establishing a sensor output quantification model:
the output signal is quantized by a quantizer g (-) prior to its transmission, to match the limited capacity of the communication channel between the communication-based system and the filter,
quantizer g (·) is defined as g (y) ═ g1(y1),g2(y2),…,gp(yp)]T，gi(yi) (1 ≦ i ≦ p) as a logarithmic quantizer and the quantization level is set to
Quantized density 0 < etagi< 1 is a given scalar and
associated quantizer gi(yi) Is defined as
Wherein σgi＝(1-ηgi)/(1+ηgi)(0＜ηgi< 1), define Δg＝diag{Δg1,Δg2,…,ΔgpWhere Δgi∈[-σgi,σgi](i ═ 1,2, …, p), according to the sector constraint method, g (y) is expressed as:
g(y)＝(I+Δg)y；
s400, establishing a fault detection model:
one form of fault detection filter is designed as follows:
wherein,
is the state vector of the filter and is,
is the constructed residual output vector and is,
is the input vector of the filter, matrix Af,Bf,Cf,DfIs a filter parameter matrix to be solved;
input signal of filter
Is defined as
And is constructed to
A weighted fault model is represented to improve fault detection performance, where w (z) is a weighting matrix;
the minimum implementation form of the weighted fault model is as follows:
wherein x isw(k) State variables representing the model, f (k) a system fault signal,
representing a weighted fault signal, Aw,Bw,Cw,DwRepresenting a known parameter matrix;
the following fault detection model is thus obtained:
wherein,
θ(k)＝[dT(k) fT(k)]T，
s500, a networked system fault detection performance evaluation mechanism:
detecting whether faults of the networked system occur or not by using a residual evaluation mechanism, and evaluating a residual evaluation function x (k) and a threshold xth(k) When χ (k) > χth(k) Then the system is deemed to have failed.
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| CN116160455B (en) * | 2023-04-03 | 2023-12-19 | 中国矿业大学 | Dynamic event triggering and quantization control method for single-arm manipulator under multi-channel attack |
| CN116628862A (en) * | 2023-07-19 | 2023-08-22 | 浙江大学海南研究院 | Dynamic positioning event triggering robust H of mass-switching unmanned ship ∞ Filtering method |
| CN116628862B (en) * | 2023-07-19 | 2024-04-02 | 浙江大学海南研究院 | Dynamic positioning event triggering robust H of mass-switching unmanned ship ∞ Filtering method |
| CN117221075A (en) * | 2023-10-16 | 2023-12-12 | 哈尔滨理工大学 | Discrete networking system fault detection method based on self-adaptive event trigger mechanism |
| CN117221075B (en) * | 2023-10-16 | 2024-03-19 | 哈尔滨理工大学 | Discrete networking system fault detection method based on self-adaptive event trigger mechanism |
| CN118296811A (en) * | 2024-03-25 | 2024-07-05 | 海南大学 | Fault detection observer design method based on simulated annealing algorithm |
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