CN114740826B - A Fault Detection Method for Multi-vehicle Tracking System Based on Optimal Variable-order Observer - Google Patents

Abstract

The invention provides a multi-vehicle tracking system fault detection method based on an optimal variable-order observer, which belongs to the technical field of fault detection. The problem that the observer residuals are not sensitive to system faults under event triggering is solved. Its technical solution is: reduce the unnecessary communication transmission of the system through the event trigger mechanism, design a variable-order observer for residual error generation, and solve the performance index to obtain the optimal post-filter to enhance the robustness and stability of the residual error to disturbance. For the sensitivity to faults, the fault decision logic is designed based on the method of centrosymmetric polytope. The beneficial effects of the present invention are: the present invention can effectively reduce the loss caused by the unnecessary network data transmission of the multi-vehicle tracking system under the adaptive hybrid event trigger mechanism, and realize it while the variable-order observer improves the flexibility of the observation order The balance between robustness to unknown disturbances and sensitivity to faults of the residual is achieved, and the optimal fault detection for multi-vehicle tracking system is finally realized.

Description

A Fault Detection Method for Multi-vehicle Tracking System Based on Optimal Variable-order Observer

Technical Field

The invention relates to the technical field of fault detection, and in particular to a multi-vehicle tracking system fault detection method based on an optimal variable-order observer.

Background Art

The continuous upgrading of vehicle computer systems and network communication technologies has led to the rapid development of autonomous driving technology. As a key component of autonomous driving technology, the safety of multi-vehicle tracking systems should be taken seriously. Once a multi-vehicle tracking system fails, it will lead to huge economic losses and even threaten the lives of drivers and passengers.

During the operation of multi-vehicle tracking systems, a large amount of data needs to be transmitted. The traditional periodic transmission mechanism will cause a large amount of redundant information, which will lead to unnecessary loss of network resources. To avoid this phenomenon, the popular event trigger mechanism has emerged. In addition, in the method of detecting whether there is a fault in the tracking system by constructing residuals, the diagnostic observer with online fault detection capability and flexible order has not been promoted because its parameter matrix needs to satisfy the Luenberger condition, and the robustness of the existing residuals to disturbances and the sensitivity to faults can be further improved. Therefore, for multi-vehicle tracking systems, it is of great practical significance and application value to carry out research on fault detection methods based on optimal variable-order observers.

With the development of multi-vehicle tracking systems, a fault detection method for multi-vehicle tracking systems based on optimal variable-order observer is proposed to solve the above problems.

Summary of the invention

The purpose of the present invention is to provide a multi-vehicle tracking system fault detection method based on an optimal variable-order observer, which can effectively reduce the loss caused by unnecessary network data transmission of the multi-vehicle tracking system under an adaptive hybrid event trigger mechanism, and while the variable-order observer improves the flexibility of the observation order, it achieves a trade-off between the robustness of the residual to unknown disturbances and the sensitivity to faults, and ultimately achieves optimal fault detection of the multi-vehicle tracking system.

The inventive concept of the present invention is as follows: first, a multi-vehicle tracking system model including unknown disturbances, sensor measurement noise and controller failure is constructed; second, in order to fully utilize limited network resources, an adaptive hybrid event trigger mechanism is designed to constrain data transmission; then, a variable-order observer parameter matrix generation algorithm combining numerical and algebraic is constructed, and the sensitivity of the generated residual to faults and the robustness to unknown disturbances are enhanced by designing and solving a performance trade-off index with the optimal post-filter as the target; then, an error dynamic system is constructed in the absence of faults, and the centrosymmetric polyhedron corresponding to each component of the residual is obtained. The residual centrosymmetric polyhedron is constrained by the order of the reduced-order operator; finally, the residual threshold is set according to the upper and lower bounds corresponding to the residual centrosymmetric polyhedron to enhance the practicality of the fault detection algorithm based on the centrosymmetric polyhedron, thereby ensuring that the faults in the multi-vehicle tracking system can be detected in time; this method can effectively reduce the loss caused by unnecessary network data transmission in the multi-vehicle tracking system under the adaptive hybrid event trigger mechanism, and while improving the flexibility of the observation order of the variable-order observer, it achieves a trade-off between the robustness of the residual to unknown disturbances and the sensitivity to faults, ultimately achieving optimal fault detection for the multi-vehicle tracking system.

In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a multi-vehicle tracking system fault detection method based on an optimal variable-order observer, which specifically includes the following steps:

a. Construct a multi-vehicle tracking system model that includes unknown disturbances, sensor measurement noise, and controller failures;

b. To fully utilize limited network resources, an adaptive hybrid event triggering mechanism is designed to constrain data transmission;

c. Construct a variable-order observer parameter matrix generation algorithm that combines numerical and algebraic methods, and enhance the sensitivity of the generated residual to faults and the robustness to unknown disturbances by designing and solving performance trade-off indicators with the optimal post-filter as the target;

d. Construct the error dynamic system in the absence of faults, and obtain the residual centrosymmetric polyhedron constrained by the order of the reduced-order operator based on the centrosymmetric polyhedron corresponding to each component of the residual;

e. The residual threshold is set according to the upper and lower bounds corresponding to the residual centrosymmetric polyhedron to enhance the practicality of the fault detection algorithm based on the centrosymmetric polyhedron, thereby ensuring that the faults in the multi-vehicle tracking system can be detected in time.

Furthermore, the multi-vehicle tracking system model including unknown disturbances, sensor measurement noise and controller failure is constructed in step a as follows:

x(k+1)＝Ax(k)+B _u u(k)+E _d d(k)+E _f f(k)

y(k)＝Cx(k)+D _u u(k)+F _d d(k)+F _f f(k)

分别表示多车跟踪系统中未知但有界的状态，系统的实际控制输入，未知扰动、故障信号和测量输出。此外，A,B_u,E_d,E_f,C,D_u,F_d,F_f均是具有适应维数的多车跟踪系统矩阵，并且满足rank(C)＝m≤n。同时，(A,B)对是可控的，(A,C)对是可观测的。in,

They represent the unknown but bounded state in the multi-vehicle tracking system, the actual control input of the system, the unknown disturbance, the fault signal and the measured output. In addition, A, _Bu , _Ed , _Ef , C, _Du , _Fd , _Ff are all matrices of the multi-vehicle tracking system with adaptive dimensions and satisfy rank(C) = m≤n. At the same time, the (A, B) pair is controllable and the (A, C) pair is observable.

Furthermore, in step b, in order to fully utilize limited network resources, an adaptive hybrid event trigger mechanism is designed to constrain the event trigger mechanism of data transmission as follows:

Wherein, k _i+1 is the time when the event is about to be triggered, k _i is the time when the last event was triggered, k _inf = k _i + h _k represents the lower limit of the trigger time, h _k is the adaptive silent time, k _sup = k _i + τ _max represents the upper limit of the trigger time, τ _max represents the maximum trigger interval, I = {1, ..., m} represents a set containing m numbers, Δ _g (k) = y _g (k) - y _g (k _i ), 0 < δ _g (k) < 1 is the adaptive trigger threshold. Split y(k) = [y ₁ (k), ..., y _g (k), ..., y _m (k)] ^T , δ(k) = diag {δ ₁ (k), ..., δ _g (k), ..., δ _m (k)}.

Furthermore, the variable order observer parameter matrix generation algorithm combining numerical and algebraic construction in step c is constructed, and the sensitivity of the generated residual to faults and the robustness to unknown disturbances are enhanced by designing and solving the performance trade-off index with the optimal post-filter as the target. The corresponding variable order observer structure is as follows:

表示可变阶观测器的状态向量(s≥n-m+1)，

表示生成的残差信号，

表示y(k_i)经零阶保持器处理后的值，R(k)表示待求的最优后置滤波器，“*”表示卷积符号。G,H,L,V,W,Q和变阶观测过程中需要引入的矩阵T表示待设计的可变阶观测器参数矩阵，并为使得观测器生成的残差满足基本的残差生成条件，这些待设计的参数矩阵必须满足著名的Luenberger条件。in,

represents the state vector of the variable-order observer (s≥n-m+1),

represents the generated residual signal,

represents the value of y(k _i ) after being processed by the zero-order holder, R(k) represents the optimal post-filter to be sought, and “*” represents the convolution symbol. G, H, L, V, W, Q and the matrix T that needs to be introduced in the variable-order observation process represent the variable-order observer parameter matrix to be designed, and in order to make the residual generated by the observer meet the basic residual generation conditions, these parameter matrices to be designed must meet the famous Luenberger conditions.

In order to make the above-mentioned parameter matrix to be designed satisfy the Luenberger condition, the numerical and algebraic variable-order observer parameter matrix generation algorithm constructed in this paper is as follows:

First, solve a set of left null spaces _vs = [ _{vs,0 vs,1} ... _vs,s ] to satisfy the equation

Then set a set of vectors g = [g ₁ g ₂ … g _s ] to ensure the stability of the matrix G

Then the remaining parameter matrices T, H, and L in the variable-order observer can be generated in sequence according to the following formulas:

The design of the parameter matrix V, W, Q is generated in the following steps. First, solve the parameter matrix W to satisfy

表示C的零矩阵。其次，依据如下两个等式求解出参数矩阵V和Q。in,

Denotes the zero matrix of C. Secondly, the parameter matrices V and Q are solved according to the following two equations.

V＝WTC ^T (CC ^T ) ^-1

Q＝ _VDw

The sensitivity of the generated residual to faults and the robustness to unknown disturbances are enhanced by designing and solving the performance trade-off index with the optimal post-filter as the target. The corresponding performance trade-off index is as follows:

The optimal post-filter form solved by the mutual internal and external decomposition technique is as follows:

R(z)＝M _o -M _o W(zI-G+L _o W) ^-1 L _o

in,

X is a stable solution of the following discrete Riccati equation:

Furthermore, in the step d, the error dynamic system is constructed when there is no fault, and the residual central symmetric polyhedron constrained by the order of the reduced-order operator is obtained according to the central symmetric polyhedron corresponding to each component of the residual, and the process mainly includes the following steps:

利用所述自适应混合事件触发机制和可变阶观测器构造无故障时的误差系统：By introducing a new residual state variable x _r (k), the event transmission error is defined as

The error system in the absence of faults is constructed using the adaptive hybrid event triggering mechanism and the variable order observer:

in,

的约束。可知系统状态变量的初值，系统实际控制输入u(k)，未知扰动d(k)分别界于如下的中心对称多胞体：By assuming that the initial value of the state variable x(0) of the multi-vehicle tracking system, the actual control input u(k) of the system, and the unknown disturbance d(k) satisfy the inequality

It is known that the initial values of the system state variables, the actual control input u(k) of the system, and the unknown disturbance d(k) are bounded by the following centrally symmetric polytopes:

x(0)∈Y _x ＝<p ₀ ,H _x >,u(k)∈Y _u ＝<0,H _u >,d(k)∈Y _d ＝<0,H _d >

且

和

为已知向量。in,

and

and

is a known vector.

属于中心对称多胞体

及其初始状态

属于中心对称多胞体

并依据所述自适应混合事件触发机制可知事件传输误差

界于如下中心对称多胞体：By assuming a new estimated error

Centrosymmetric polytope

and its initial state

Centrosymmetric polytope

According to the adaptive hybrid event triggering mechanism, the event transmission error

Bounded by the following centrosymmetric polytope:

in,

的阶次，则对应所述无故障时的误差系统，可得k+1时刻新估计误差

和残差r(k)对应的中心对称多胞体：Using the definition of Minkowski sum and the existence of centrosymmetric polytopes, we set a suitable order xs and constrain the reduced-order operator κ _s (·)

The order of the error system when there is no fault is:

The centrosymmetric polytope corresponding to the residual r(k):

r(k+1)∈Υ _r (k+1)＝<P _r (k+1),H _r (k+1)>

in,

The reduction operator κ _s (·) constructs a new matrix by directly selecting the first xs columns of the set constraint order from the constraint matrix in descending order of the Euclidean norm.

Furthermore, in the step e, the residual threshold is set according to the upper and lower bounds corresponding to the residual centrosymmetric polyhedron to enhance the practicality of the fault detection algorithm based on the centrosymmetric polyhedron, thereby ensuring that the faults in the multi-vehicle tracking system can be detected in time, including the following steps:

Through the centrosymmetric polytope corresponding to the residual r(k), the upper and lower bounds of the centrosymmetric polytope generation matrix H _r (k) are solved, and the following fault decision logic is constructed, thereby avoiding a large computational load and improving the practicability of the algorithm in the multi-vehicle tracking system.

q(k)是故障标志，q(k)＝0表示多车跟踪系统中无故障，q(k)＝1表示多车跟踪系统中有故障。Where _ns represents the number of columns in H _r (k), _ri (k) represents the i-th element in r (k), and Hi _,l (k) represents the i-th row and l-th column element in the matrix H _r (k).

q(k) is a fault flag, q(k)=0 indicates that there is no fault in the multi-vehicle tracking system, and q(k)=1 indicates that there is a fault in the multi-vehicle tracking system.

Compared with the prior art, the present invention has the following beneficial effects:

(1) This fault detection method constrains unnecessary network resource loss by designing an adaptive hybrid event trigger mechanism. Under the framework of the event trigger mechanism, a variable-order observer and its parameter matrix generation algorithm are designed to construct the residual. The robustness and sensitivity of the residual are improved based on the optimal solution form of the ratio-type performance indicator, thereby achieving optimal fault detection for the multi-vehicle tracking system.

(2) A variable-order observer is used to generate residuals, and performance indicators are constructed to find the optimal post-filter form, which effectively improves the robustness and sensitivity of the residuals and enhances the fault detection capability of the system.

(3) An adaptive hybrid event trigger mechanism is used to constrain unnecessary network communication losses, effectively reducing the transmission of a large amount of redundant information.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

FIG. 1 is a schematic diagram of a multi-vehicle tracking system according to the present invention.

FIG2 is a flow chart of a multi-vehicle tracking system fault detection method based on an optimal variable-order observer provided by the present invention.

FIG3 is a comparison diagram of the effects before and after filtering of the residual r(k) in the present invention.

FIG. 4 is a diagram showing event triggering intervals of the multi-vehicle tracking system of the present invention.

FIG5 is a diagram showing the fault detection effect corresponding to the residual R ₁ (k) in the present invention.

FIG6 is a diagram showing the fault detection effect corresponding to the residual R ₂ (k) in the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

Example

Referring to FIG. 1 to FIG. 6 , the present invention provides a technical solution, which provides a multi-vehicle tracking system fault detection method based on an optimal variable-order observer, specifically comprising the following steps:

Step a: construct a multi-vehicle tracking system model including unknown disturbances, sensor measurement noise and controller failure;

Specifically, a multi-vehicle tracking system model with unknown disturbances, sensor measurement noise, and controller failure is constructed:

x(k+1)＝Ax(k)+B _u u(k)+E _d d(k)+E _f f(k)

y(k)＝Cx(k)+D _u u(k)+F _d d(k)+F _f f(k)

分别表示多车跟踪系统中未知但有界的状态，系统的实际控制输入，未知扰动、故障信号和测量输出。此外，A,B_u,E_d,E_f,C,D_u,F_d,F_f均是具有适应维数的多车跟踪系统矩阵，并且满足rank(C)＝m≤n。同时，(A,B)对是可控的，(A,C)对是可观测的。in,

They represent the unknown but bounded state in the multi-vehicle tracking system, the actual control input of the system, the unknown disturbance, the fault signal and the measured output. In addition, A, _Bu , _Ed , _Ef , C, _Du , _Fd , _Ff are all matrices of the multi-vehicle tracking system with adaptive dimensions and satisfy rank(C) = m≤n. At the same time, the (A, B) pair is controllable and the (A, C) pair is observable.

Step b: To fully utilize limited network resources, an adaptive hybrid event triggering mechanism is designed to constrain data transmission;

Specifically, to fully utilize limited network resources, an adaptive hybrid event trigger mechanism is designed to constrain the event trigger mechanism of data transmission as follows:

Wherein, k _i+1 is the time when the event is about to be triggered, k _i is the time when the last event was triggered, k _inf = k _i + h _k represents the lower limit of the trigger time, h _k is the adaptive silent time, k _sup = k _i + τ _max represents the upper limit of the trigger time, τ _max represents the maximum trigger interval, I = {1, ..., m} represents a set containing m numbers, Δ _g (k) = y _g (k) - y _g (k _i ), 0 < δ _g (k) < 1 is the adaptive trigger threshold. Split y(k) = [y ₁ (k), ..., y _g (k), ..., y _m (k)] ^T , δ(k) = diag {δ ₁ (k), ..., δ _g (k), ..., δ _m (k)}.

Step c: construct a variable-order observer parameter matrix generation algorithm that combines numerical and algebraic methods, and enhance the sensitivity of the generated residual to faults and the robustness to unknown disturbances by designing and solving a performance trade-off indicator with the optimal post-filter as the target;

Specifically, a variable-order observer parameter matrix generation algorithm combining numerical and algebraic methods is constructed, and the sensitivity of the generated residual to faults and the robustness to unknown disturbances are enhanced by designing and solving the performance trade-off index with the optimal post-filter as the target. The corresponding variable-order observer structure is as follows:

表示可变阶观测器的状态向量(s≥n-m+1)，

表示生成的残差信号，

表示y(k_i)经零阶保持器处理后的值，R(k)表示待求的最优后置滤波器，“*”表示卷积符号。G,H,L,V,W,Q和变阶观测过程中需要引入的矩阵T表示待设计的可变阶观测器参数矩阵，并为使得观测器生成的残差满足基本的残差生成条件，这些待设计的参数矩阵必须满足著名的Luenberger条件。in,

represents the state vector of the variable-order observer (s≥n-m+1),

represents the generated residual signal,

represents the value of y(k _i ) after being processed by the zero-order holder, R(k) represents the optimal post-filter to be sought, and “*” represents the convolution symbol. G, H, L, V, W, Q and the matrix T that needs to be introduced in the variable-order observation process represent the variable-order observer parameter matrix to be designed, and in order to make the residual generated by the observer meet the basic residual generation conditions, these parameter matrices to be designed must meet the famous Luenberger conditions.

When the variable-order observer structure is given, in order to make the above-mentioned parameter matrix to be designed satisfy the Luenberger condition, the numerical and algebraic combination variable-order observer parameter matrix generation algorithm constructed in this paper is as follows:

First, solve a set of left null spaces _vs = [ _{vs,0 vs,1} ... _vs,s ] to satisfy the equation

Then set a set of vectors g = [g ₁ g ₂ … g _s ] to ensure the stability of the matrix G

Then the remaining parameter matrices T, H, and L in the variable-order observer can be generated in sequence according to the following formulas:

The design of the parameter matrix V, W, Q is generated in the following steps. First, solve the parameter matrix W to satisfy

表示C的零矩阵。其次，依据如下两个等式求解出参数矩阵V和Q。in,

Denotes the zero matrix of C. Secondly, the parameter matrices V and Q are solved according to the following two equations.

V＝WTC ^T (CC ^T ) ^-1

Q＝ _VDw

After the above parameter matrix is generated, the sensitivity of the generated residual to faults and the robustness to unknown disturbances are enhanced by designing and solving the performance trade-off index with the optimal post-filter as the target. The corresponding performance trade-off index is as follows:

After the performance index is constructed, the optimal post-filter form is solved by applying the mutual internal and external decomposition technology as follows:

R(z)＝M _o -M _o W(zI-G+L _o W) ^-1 L _o

in,

X is a stable solution of the following discrete Riccati equation:

Step d: construct an error dynamic system when there is no fault, and obtain the residual central symmetric polyhedron constrained by the order of the reduced-order operator based on the central symmetric polyhedron corresponding to each component of the residual;

利用所述自适应混合事件触发机制和可变阶观测器构造无故障时的误差系统：Specifically, we first introduce a new residual state variable x _r (k) and define the event transmission error

The error system in the absence of faults is constructed using the adaptive hybrid event triggering mechanism and the variable order observer:

in,

的约束。可知系统状态变量的初值，系统实际控制输入u(k)，未知扰动d(k)分别界于如下的中心对称多胞体：After the above error system is established, by assuming that the initial value of the state variable x(0) of the multi-vehicle tracking system, the actual control input u(k) of the system, and the unknown disturbance d(k) satisfy the inequality

It is known that the initial values of the system state variables, the actual control input u(k) of the system, and the unknown disturbance d(k) are bounded by the following centrally symmetric polytopes:

x(0)∈Y _x ＝<p ₀ ,H _x >,u(k)∈Y _u ＝<0,H _u >,d(k)∈Y _d ＝<0,H _d >

且

和

为已知向量。in,

and

and

is a known vector.

属于中心对称多胞体

及其初始状态

属于中心对称多胞体

并依据所述自适应混合事件触发机制可知事件传输误差

界于如下中心对称多胞体：When the initial values of the system state variables, the actual control input u(k) of the system, and the unknown disturbance d(k) are bounded by the central symmetric polyhedron, the new estimated error is assumed to be

Centrosymmetric polytope

and its initial state

Centrosymmetric polytope

According to the adaptive hybrid event triggering mechanism, the event transmission error

Bounded by the following centrosymmetric polytope:

in,

界于的中心对称多胞体也已知时，利用闵可夫斯基和的定义及中心对称多胞体存在的性质，设定合适阶次xs，用降阶算子κ_s(·)约束

的阶次，则对应所述无故障时的误差系统，可得k+1时刻新估计误差

和残差r(k)对应的中心对称多胞体：When the event transmission error

When the centrosymmetric polytope bounded by is also known, we use the definition of the Minkowski sum and the existence of centrosymmetric polytopes, set a suitable order xs, and use the reduction operator κ _s (·) to constrain

The order of the error system when there is no fault is:

The centrosymmetric polytope corresponding to the residual r(k):

r(k+1)∈Υ _r (k+1)＝<P _r (k+1),H _r (k+1)>

in,

The reduction operator κ _s (·) constructs a new matrix by directly selecting the first xs columns of the set constraint order from the constraint matrix in descending order of the Euclidean norm.

Step e: Set the residual threshold according to the upper and lower bounds corresponding to the residual centrosymmetric polyhedron to enhance the practicality of the centrosymmetric polyhedron-based fault detection algorithm, thereby ensuring that faults in the multi-vehicle tracking system can be detected in a timely manner.

Specifically, the upper and lower bounds of the centrosymmetric polyhedron generation matrix H _r (k) are solved through the centrosymmetric polyhedron corresponding to the residual r(k), and the following fault decision logic is constructed, thereby avoiding a large computational load and improving the practicability of the algorithm in the multi-vehicle tracking system.

q(k)是故障标志，q(k)＝0表示多车跟踪系统中无故障，q(k)＝1表示多车跟踪系统中有故障。Where _ns represents the number of columns in H _r (k), _ri (k) represents the i-th element in r (k), and Hi _,l (k) represents the i-th row and l-th column element in the matrix H _r (k).

q(k) is a fault flag, q(k)=0 indicates that there is no fault in the multi-vehicle tracking system, and q(k)=1 indicates that there is a fault in the multi-vehicle tracking system.

In the environment of Matlab2016b, the present invention takes a single lane tracking system of three vehicles as an example, and the simulation time is set to 100 sampling cycles (sampling cycle T _t = 0.1s) to verify the method designed by the present invention. The model setting of the tracking system is as follows:

x(k+1)＝Ax(k)+B _u u(k)+E _d d(k)+E _f f(k)

y(k)＝Cx(k)+D _u u(k)+F _d d(k)+F _f f(k)

表示状态变量，

表示i车的实际车速与参考车速偏差(

表示i车的参考车速)，

表示j车与j+1车间实际距离与车间参考距离的偏差(

表示j车与j+1车间参考距离)，

表示控制器的控制变量，R_L为性能权衡评价函数

对应控制变量的权重，Q_L为性能权衡评价函数J对应状态变量的权重，

是代数等式

的实对称常数矩阵解，d(k)表示未知扰动矩阵(

表示随机扰动值)，f(k)表示故障矩阵，其形式为：in,

represents the state variable,

Indicates the deviation between the actual speed of vehicle i and the reference speed (

represents the reference speed of vehicle i),

represents the deviation between the actual distance between vehicle j and vehicle j+1 and the reference distance between the vehicles (

represents the reference distance between vehicle j and vehicle j+1),

represents the control variable of the controller, and _RL is the performance trade-off evaluation function

The weight corresponding to the control variable, Q _L is the weight corresponding to the state variable of the performance trade-off evaluation function J,

is an algebraic equation

The real symmetric constant matrix solution of , d(k) represents the unknown perturbation matrix (

represents the random disturbance value), f(k) represents the fault matrix, which is in the form of:

In addition, the system parameter matrices of the model are set as follows:

Set the constraint order of the reduction operator xs = 12, set the silent time h _k = 1 in the adaptive hybrid time trigger mechanism, set the maximum trigger interval τ _max = 5, and set the event trigger parameters to

Set the order of the variable-order observer s = 4 < n to achieve reduced-order observation, set a set of vectors g = [0.5, 0, 0, 0], and set a set of left null spaces:

v _s =[v _s,0 ,v _s,1 ,v _s,2 ,v _s,3 ,v _s,4 ],v _s,0 =[-0.4432,-0.1564]

v _s,1 = [0.6060,0.1937], v _s,2 = [0.1090,0.2398]

v _s,3 =[0.0119,-0.4141],v _s,4 =[-0.3364,0.1420]

Then we can get γ _d = 12.8179 and the remaining variable order observer parameter matrix:

The L _o and M _o matrices corresponding to the optimal post-filter are as follows:

Result description:

Figure 1 shows a schematic diagram of the single lane tracking system operation of three vehicles.

Figure 2 shows the flow chart of the fault detection method for a multi-vehicle tracking system based on the optimal variable-order observer, which can be divided into two parts: system initialization and cyclic detection. Running the system according to the logic of the flowchart can achieve effective fault detection of the multi-vehicle tracking system.

Figure 3 shows the effect comparison of residual r(k) before and after filtering. It can be seen from the figure that the change effect of residual r ₁ (k) after filtering by the post filter is not obvious. This is because the effect of the preset controller additive fault on r ₁ (k) is weak, while the change effect of residual r ₂ (k) after filtering by the post filter is obvious. The residual r ₂ (k) is the residual R ₂ (k) after filtering. It can be seen from the figure that the residual R ₂ (k) after filtering is more robust to unknown disturbances and more sensitive to faults. This verifies that the optimal post filter can enhance the robustness of the residual to unknown disturbances and enhance the sensitivity to faults, and also shows that the variable order observer can effectively generate residual r(k).

Figure 4 shows the event trigger interval diagram of the multi-vehicle tracking system. It can be seen from the figure that the adaptive hybrid event trigger mechanism effectively reduces unnecessary network communication losses and can transmit data in time at the fault location for fault detection. It can also be seen from Figure 4 that the minimum event trigger interval is greater than the preset silent time 1, which can effectively avoid the "Zeno phenomenon"; the maximum event trigger interval is the preset maximum trigger interval 5, indicating that the adaptive hybrid event trigger mechanism can operate effectively and can effectively avoid the long-term loss of information of the multi-vehicle tracking system through the preset maximum trigger interval.

FIG5 shows the fault detection effect diagram corresponding to the residual R ₁ (k). The increase in the threshold at the fault location is because the residual centrosymmetric polyhedron is affected by the event transmission error centrosymmetric polyhedron. This is to avoid the event transmission error affecting fault detection.

Figure 6 shows the fault detection effect diagram corresponding to the residual R ₂ (k). It can be seen from the figure that the fault can be detected in time. Through experiments, it is verified that the proposed method can not only reduce the unnecessary network communication loss of the multi-vehicle tracking system under the adaptive hybrid event trigger mechanism, but also achieve a trade-off between the robustness of the residual to unknown disturbances and the sensitivity to faults while improving the flexibility of the observation order of the variable-order observer, and finally achieve the optimal fault detection of the multi-vehicle tracking system.

In summary, based on the research on networked data transmission and fault detection of multi-vehicle tracking system, the present invention overcomes the problem of limited network resource constraints, the parameter matrix of the diagnostic observer must satisfy the Luenberger condition and the low sensitivity of the residual to faults, and proposes a multi-vehicle tracking system fault detection method based on the optimal variable-order observer. Finally, a single-lane tracking system with three vehicles is taken as an example to verify the effectiveness of the proposed method.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. The fault detection method of the multi-vehicle tracking system based on the optimal variable order observer is characterized by comprising the following steps of:

a. constructing a multi-vehicle tracking system model containing unknown disturbance, sensor measurement noise and controller faults;

b. in order to realize the full utilization of the limited network resources, an adaptive mixed event triggering mechanism is designed to restrict the data transmission;

c. constructing a variable order observer parameter matrix generation algorithm with a combination of numerical values and algebra, and enhancing the sensitivity of generated residual errors to faults and the robustness to unknown disturbance by designing and solving performance balance indexes targeting an optimal post filter;

d. constructing an error dynamic system without faults, and obtaining residual error central symmetry multicellular bodies constrained by the order of a reduction operator according to central symmetry multicellular bodies corresponding to each component of the residual error;

e. setting residual error threshold values according to upper and lower boundaries corresponding to residual error central symmetry multicellular bodies so as to enhance the practicability of a central symmetry multicellular body fault detection algorithm, thereby ensuring that faults in a multi-vehicle tracking system can be timely detected;

in the step a, a multi-vehicle tracking system model containing unknown disturbance, sensor measurement noise and controller faults is constructed as follows:

x(k+1)＝Ax(k)+B _u u(k)+E _d d(k)+E _f f(k)

y(k)＝Cx(k)+D _u u(k)+F _d d(k)+F _f f(k)

wherein ,

respectively representing unknown but bounded states in the multi-vehicle tracking system, actual control input of the system, unknown disturbance, fault signals and measurement output; in addition, A, B _u ,E _d ,E _f ,C,D _u ,F _d ,F _f Are all multi-car tracking system matrices with adaptive dimensions and satisfy rank (C) =m.ltoreq.n, while the (a, B) pairs are controllable and the (a, C) pairs are observable;

the step b specifically comprises the following steps:

in order to realize the full utilization of the limited network resources, an event trigger mechanism for designing a self-adaptive mixed event trigger mechanism to restrict data transmission is as follows:

wherein ,k_i+1 For instant of impending trigger, k _i K is the time of last event trigger _inf ＝k _i +h _k Represents the lower bound of the trigger time, h _k To adapt silence time, k _sup ＝k _i +τ _max Represents the upper bound of the trigger time τ _max Indicating the maximum trigger interval, i= {1,..m } indicates a set containing m numbers, Δ _g (k)＝y _g (k)-y _g (k _i )，0＜δ _g (k) < 1 is an adaptive trigger threshold, split y (k) = [ y ] ₁ (k),...,y _g (k),...,y _m (k)] ^T ，δ(k)＝diag{δ ₁ (k),...,δ _g (k),...,δ _m (k)}；

In the step c:

the variable order observer parameter matrix generation algorithm combining the construction values and algebra is used for enhancing the sensitivity of generated residual errors to faults and the robustness to unknown disturbance by designing and solving performance balance indexes targeting an optimal post filter, and the corresponding variable order observer structure is as follows:

wherein ,

representing the state vector of the variable order observer, s.gtoreq.n-m+1,/for the observer>

Representing the generated residual signal->

Represents y (k) _i ) The value processed by the zero-order keeper, R (k) represents the optimal post-filter to be solved, and "+" represents the convolution symbol; g, H, L, V, W, Q and a matrix T which needs to be introduced in the variable order observation process represent variable order observer parameter matrices to be designed, and in order to enable residuals generated by an observer to meet basic residual generation conditions, the parameter matrices to be designed need to meet the well-known Luenberger conditions;

in order to make the parameter matrix to be designed meet the Luenberger condition, the constructed numerical value and algebraic combination type variable order observer parameter matrix generation algorithm is as follows:

first solve a group of left zero spaces v _s ＝[v _s,0 v _s,1 ... v _s,s ]So that it satisfies the equation

A set of vectors g= [ g ] is reset ₁ g ₂ … g _s ]Ensuring the stability of the matrix G

The remaining parameter matrix T, H, L in the variable order observer may be generated sequentially as follows:

for the parameter matrix V, W, Q, the design is generated by the following steps, firstly, solving the parameter matrix W to satisfy

wherein ,

a zero matrix representing C; secondly, solving a parameter matrix V and a parameter matrix Q according to the following two equations;

V＝WTC ^T (CC ^T ) ^-1

Q＝VD _u ,

the sensitivity of the generated residual error to faults and the robustness to unknown disturbance are enhanced by designing and solving performance balance indexes aiming at the optimal post filter, and the corresponding performance balance indexes are as follows:

the optimal post filter solved by the mutual internal and external decomposition technology is as follows:

R(z)＝M _o -M _o W(zI-G+L _o W) ^-1 L _o

wherein ,

x is a stable solution of the following discrete Riccati equation:

in the step d, an error dynamic system without faults is constructed, and residual central symmetry multicellular bodies constrained by the order of a reduction operator are obtained according to the central symmetry multicellular bodies corresponding to all components of the residual, and the process specifically comprises the following steps:

by introducing a new residual state variable x _r (k) Defining event transmission errors

Constructing an error system without faults by utilizing the self-adaptive mixed event triggering mechanism and a variable order observer:

wherein ,

by assuming an initial value x (0) of a state variable of the multi-vehicle tracking system, the system actually controls the input u (k), and the unknown disturbance d (k) meets the inequality

Is a constraint of (2); the initial value of the system state variable can be known, the system actually controls the input u (k), and the unknown disturbance d (k) is respectively defined by the following centrosymmetric multicellular bodies:

x(0)∈Υ _x ＝<p ₀ ,H _x >,u(k)∈Υ _u ＝<0,H _u >,d(k)∈Υ _d ＝<0,H _d >

wherein ,

and->

and

Is a known vector;

by assuming a new estimation error

Belongs to the central symmetry multicellular body->

And its initial state->

Belongs to the central symmetry multicellular body->

And based on the adaptive hybrid event trigger mechanism, the event transmission error is known>

Is bound to the following centrosymmetric multicellular bodies:

wherein ,

by using the definition of Minkowski sum and the existence of central symmetry multicellular body, it is provided thatDetermining the proper order xs by using a reduction operator kappa _s (. Cndot.) constraint

Corresponding to the error system without fault to obtain new estimated error +.>

Central symmetry multicellular body corresponding to residual r (k):

r(k+1)∈Υ _r (k+1)＝<P _r (k+1),H _r (k+1)>

wherein ,

wherein, the order operator kappa is reduced _s (.) selecting the front xs columns of the constraint orders to form a new matrix by arranging the constraint matrices in descending order of European norms;

the specific content of the step e is as follows:

generating a matrix H by the central symmetry multicellular bodies corresponding to the residual error r (k) _r (k) The upper and lower bounds of the algorithm are solved, and the following fault decision logic is constructed, so that a larger operation load is avoided, and the practicability of the algorithm on a multi-vehicle tracking system is improved;

wherein ,n_s Represents H _r (k) The number of columns, r _i (k) The ith element, H, representing r (k) _i,l (k) Representation matrix H _r (k) In the actual detection of the elements of the ith row and the first column

q (k) is a fault flag, q (k) =0 indicates no fault in the multi-car tracking system, and q (k) =1 indicates a fault in the multi-car tracking system. />

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