CN114740826B - Multi-vehicle tracking system fault detection method based on optimal variable order observer - Google Patents
Multi-vehicle tracking system fault detection method based on optimal variable order observer Download PDFInfo
- Publication number
- CN114740826B CN114740826B CN202210418435.2A CN202210418435A CN114740826B CN 114740826 B CN114740826 B CN 114740826B CN 202210418435 A CN202210418435 A CN 202210418435A CN 114740826 B CN114740826 B CN 114740826B
- Authority
- CN
- China
- Prior art keywords
- tracking system
- faults
- residual
- observer
- vehicle tracking
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000001514 detection method Methods 0.000 title claims abstract description 39
- 230000007246 mechanism Effects 0.000 claims abstract description 29
- 230000005540 biological transmission Effects 0.000 claims abstract description 22
- 230000035945 sensitivity Effects 0.000 claims abstract description 22
- 238000000034 method Methods 0.000 claims abstract description 14
- 239000011159 matrix material Substances 0.000 claims description 55
- 230000003044 adaptive effect Effects 0.000 claims description 16
- 239000013598 vector Substances 0.000 claims description 10
- 238000005259 measurement Methods 0.000 claims description 8
- 230000009467 reduction Effects 0.000 claims description 8
- 238000005516 engineering process Methods 0.000 claims description 6
- 230000002708 enhancing effect Effects 0.000 claims description 6
- 230000008569 process Effects 0.000 claims description 6
- 238000000354 decomposition reaction Methods 0.000 claims description 3
- 238000013461 design Methods 0.000 claims description 3
- 229910052739 hydrogen Inorganic materials 0.000 claims description 3
- 230000008685 targeting Effects 0.000 claims description 3
- 238000010276 construction Methods 0.000 claims description 2
- 238000004891 communication Methods 0.000 abstract description 5
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 8
- 230000000694 effects Effects 0.000 description 8
- 238000001914 filtration Methods 0.000 description 4
- 230000008901 benefit Effects 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 230000003247 decreasing effect Effects 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000003745 diagnosis Methods 0.000 description 2
- 238000011156 evaluation Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 239000000654 additive Substances 0.000 description 1
- 230000000996 additive effect Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 230000001960 triggered effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/20—Pc systems
- G05B2219/24—Pc safety
- G05B2219/24065—Real time diagnostics
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Filters That Use Time-Delay Elements (AREA)
- Mobile Radio Communication Systems (AREA)
Abstract
The invention provides a fault detection method of a multi-vehicle tracking system based on an optimal variable order observer, and belongs to the technical field of fault detection. The problem that the observer residual error has low sensitivity to system faults under the triggering of events is solved. The technical proposal is as follows: and reducing unnecessary communication transmission of the system through an event triggering mechanism, designing a variable order observer for residual error generation, solving performance indexes to obtain an optimal post filter to enhance the robustness of the residual error to disturbance and the sensitivity to faults, and finally designing fault decision logic by adopting a method based on central symmetry multicellular bodies. The beneficial effects of the invention are as follows: according to the invention, under a self-adaptive mixed event triggering mechanism, the loss caused by unnecessary network data transmission of the multi-vehicle tracking system can be effectively reduced, the flexibility of the observation order is improved by the variable order observer, the balance of robustness of residual error to unknown disturbance and sensitivity to faults is realized, and the optimal fault detection of the multi-vehicle tracking system is finally realized.
Description
Technical Field
The invention relates to the technical field of fault detection, in particular to a fault detection method of a multi-vehicle tracking system based on an optimal variable order observer.
Background
The continuous upgrading of automobile machine systems and network communication technologies of automobiles promotes the rapid development of automatic driving technologies, and a multi-automobile tracking system is taken as a key component in the automatic driving technologies, so that the safety problem of the multi-automobile tracking system is considered to be important. Because once the multi-car tracking system fails, a huge economic loss is caused and even the life safety of drivers and passengers is threatened.
In the running process of the multi-vehicle tracking system, a large amount of data needs to be transmitted, a large amount of redundant information is generated by a traditional fixed-period transmission mechanism, unnecessary loss of network resources is further caused, and in order to avoid the phenomenon, a popular event triggering mechanism is generated. In addition, in the method for detecting whether the tracking system has faults by constructing residual errors, the diagnosis observer with online fault detection capability and flexible orders is not popularized because the parameter matrix of the diagnosis observer needs to meet the Luenberger condition, and the robustness of the existing residual errors to disturbance and the sensitivity to faults can be further improved. Therefore, aiming at a multi-vehicle tracking system, the research on the fault detection method based on the optimal variable order observer has important practical significance and application value.
With the development of multi-vehicle tracking systems, a multi-vehicle tracking system fault detection method based on an optimal variable order observer is proposed to solve the above problems.
Disclosure of Invention
The invention aims to provide a fault detection method of a multi-vehicle tracking system 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 a self-adaptive mixed event triggering mechanism, and realize the balance of robustness of residual error on unknown disturbance and sensitivity on faults while improving the flexibility of the observation order of the variable order observer, thereby finally realizing the optimal fault detection of the multi-vehicle tracking system.
The invention is characterized in that: firstly, constructing a multi-vehicle tracking system model containing unknown disturbance, sensor measurement noise and controller faults; secondly, in order to realize the full utilization of the limited network resources, a self-adaptive mixed event triggering mechanism is designed to restrict the data transmission; then, constructing a variable order observer parameter matrix generation algorithm with a combination of numerical values and algebra, and enhancing the sensitivity of the generated residual error to faults and the robustness to unknown disturbance by designing and solving performance balance indexes aiming at an optimal post filter; then, constructing an error dynamic system without faults, and obtaining residual error central symmetry multicellular bodies constrained by the order of the reduction operator according to central symmetry multicellular bodies corresponding to all components of the residual error; finally, 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; according to the method, under a self-adaptive mixed event triggering mechanism, loss caused by unnecessary network data transmission of the multi-vehicle tracking system can be effectively reduced, the flexibility of the observation order of the variable order observer is improved, meanwhile, the balance of robustness of residual error on unknown disturbance and sensitivity on faults is realized, and finally the optimal fault detection of the multi-vehicle tracking system is realized.
In order to achieve the aim of the invention, the invention adopts the technical scheme that: a fault detection method of a multi-vehicle tracking system based on an optimal variable order observer specifically comprises the following steps:
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. and setting residual error threshold values according to upper and lower boundaries corresponding to the 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.
Further, the multi-vehicle tracking system model including unknown disturbance, sensor measurement noise and controller failure is constructed in the 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)
wherein ,
the unknown but bounded states in the multi-vehicle tracking system, the actual control inputs of the system, the unknown disturbances, the fault signals and the measured outputs are represented, respectively. 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+.n. Meanwhile, the (A, B) pair is controllable, and the (A, C) pair is observable.
Further, in the step b, in order to fully utilize the limited network resources, an event trigger mechanism for designing an adaptive hybrid event trigger mechanism to restrict data transmission is as follows:
wherein ,ki+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) And < 1 is an adaptive trigger threshold. Resolution y (k) = [ y ] 1 (k),...,y g (k),...,y m (k)] T ，δ(k)＝diag{δ 1 (k),...,δ g (k),...,δ m (k)}。
Further, in the step c, the algorithm for generating the parameter matrix of the variable order observer by combining the construction value and algebra is used for enhancing the sensitivity of the generated residual error to faults and the robustness to unknown disturbance by designing and solving performance balance indexes aiming at the optimal post filter. The corresponding variable order observer structure is as follows:
wherein ,
state vector (s.gtoreq.n-m+1) representing the variable order 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 matrix T to be introduced in the variable order observation process represent variable order observer parameter matrices to be designed, and in order for the residual generated by the observer to meet the basic residual generation conditions, the parameter matrices to be designed must meet the well-known Luenberger conditions.
In order to make the above parameter matrix to be designed meet the Luenberger condition, the numerical and algebraic combined variable order observer parameter matrix generation algorithm constructed herein 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 design will be generated as follows. First, solve the parameter matrix W to satisfy
wherein ,
and represents the zero matrix of C. Next, the parameter matrices V and Q are solved according to the following two equations.
V＝WTC T (CC T ) -1
Q＝VD w
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:
further, in the step d, the error dynamic system is constructed when no fault exists, and the residual central symmetry multicellular body constrained by the order of the reduced operator is obtained according to the central symmetry multicellular body corresponding to each component of the residual, and the process mainly 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 initial value x (0) of state variable of multi-vehicle tracking systemThe actual control input u (k), the unknown disturbance d (k) satisfies the inequality
Is a constraint of (a). 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->
Initial state of the device
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 ,
setting proper order xs by using the definition of Minkowski sum and the existence of central symmetry multicellular body, and using the reduction operator kappa s (. Cndot.) constraint
Corresponding to the error system without fault, the new estimated error at time k+1 can be obtained
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 (. Cndot.) the new matrix is constructed by directly selecting the first xs columns of the set constraint order in the order of decreasing Euclidean norms of the constraint matrix.
Further, in the step e, a residual threshold is set according to the upper and lower bounds corresponding to the residual centrosymmetric multicellular bodies, so as to enhance the practicability of the centrosymmetric multicellular body fault detection algorithm, thereby ensuring that faults in the multi-vehicle tracking system can be timely detected, and the method comprises the following steps:
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 ,ns 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.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the fault detection method, unnecessary network resource loss is restrained by designing a self-adaptive mixed event trigger mechanism, a variable order observer and a parameter matrix generation algorithm thereof are designed under the framework of the event trigger mechanism to construct a residual error, and the robustness and the sensitivity of the residual error are improved according to an optimal solution form of a ratio type performance index, so that the optimal fault detection of the multi-vehicle tracking system is realized.
(2) The variable order observer is adopted to generate residual errors, and the performance index is constructed to calculate the form of the optimal post filter, so that the robustness and sensitivity of the residual errors are effectively improved, and the fault detection capability of the system is enhanced.
(3) And the self-adaptive mixed event triggering mechanism is adopted to restrict unnecessary network communication loss, so that the transmission of a large amount of redundant information is effectively reduced.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is a schematic diagram of a multiple vehicle tracking system according to the present invention.
Fig. 2 is a flowchart of a fault detection method of a multi-vehicle tracking system based on an optimal variable order observer.
Fig. 3 is a graph comparing the effects of residual r (k) before and after filtering in the present invention.
FIG. 4 is a diagram of event triggered intervals for a multiple vehicle tracking system in accordance with the present invention.
FIG. 5 is a residual R in the present invention 1 (k) And a corresponding fault detection effect diagram.
FIG. 6 is a residual R in the present invention 2 (k) And a corresponding fault detection effect diagram.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. Of course, the specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
Examples
Referring to fig. 1 to 6, the invention provides a method for detecting faults of a multi-vehicle tracking system based on an optimal variable order observer, which specifically comprises the following steps:
constructing a multi-vehicle tracking system model containing unknown disturbance, sensor measurement noise and controller faults;
specifically, a multi-vehicle tracking system model is constructed that contains unknown disturbances, sensor measurement noise, and controller faults:
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 ,
the unknown but bounded states in the multi-vehicle tracking system, the actual control inputs of the system, the unknown disturbances, the fault signals and the measured outputs are represented, respectively. 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+.n. Meanwhile, the (A, B) pair is controllable, and the (A, C) pair is observable.
Step 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;
specifically, the full utilization of the limited network resources is realized, and an event trigger mechanism for restricting the data transmission by designing a self-adaptive mixed event trigger mechanism is as follows:
wherein ,ki+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) And < 1 is an adaptive trigger threshold. Resolution y (k) = [ y ] 1 (k),...,y g (k),...,y m (k)] T ，δ(k)＝diag{δ 1 (k),...,δ g (k),...,δ m (k)}。
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 aiming at an optimal post filter;
specifically, a variable order observer parameter matrix generation algorithm with numerical value and algebraic combination is constructed, and 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 an optimal post filter. The corresponding variable order observer structure is as follows:
wherein ,
state vector (s.gtoreq.n-m+1) representing the variable order 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 matrix T to be introduced in the variable order observation process represent variable order observer parameter matrix to be designed, and the residual generated by the observer meets basic residual generation conditions, and the matrix T is used for generating the residualThe parameter matrix to be designed must satisfy the well-known Luenberger condition.
After the variable order observer structure is given, in order to enable the parameter matrix to be designed to meet the luneberger condition, a numerical value and algebraic combination type variable order observer parameter matrix generation algorithm constructed in the text 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 design will be generated as follows. First, solve the parameter matrix W to satisfy
wherein ,
and represents the zero matrix of C. Next, the parameter matrices V and Q are solved according to the following two equations.
V＝WTC T (CC T ) -1
Q＝VD w
After the parameter matrix is generated, 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 an optimal post filter, and the corresponding performance balance indexes are as follows:
after the performance index is constructed, the optimal post filter 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
wherein ,
x is a stable solution of the following discrete Riccati equation:
step 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;
specifically, by introducing a new residual state variable x r (k) Defining event transmission errors
Utilizing the adaptive mixingThe event triggering mechanism and the variable order observer construct an error system without faults:
wherein ,
after the error system is built, the system actually controls the input u (k) by assuming the initial value x (0) of the state variable of the multi-vehicle tracking system, and the unknown disturbance d (k) meets the inequality
Is a constraint of (a). 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.
When the initial value of the state variable of the system is known, the system actually controls the input u (k), and after the unknown disturbance d (k) is respectively limited to the centrosymmetric multicellular bodies, the new estimation error is assumed
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 ,
when an event is transmitted
When the central symmetry multicellular bodies are also known, the definition of Minkowski sum and the existence of central symmetry multicellular bodies are used to set proper order xs, and the order-reducing operator kappa is used s (. About.) constraint->
Corresponding to the error system without fault, 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 (. Cndot.) the new matrix is constructed by directly selecting the first xs columns of the set constraint order in the order of decreasing Euclidean norms of the constraint matrix.
Step e: and setting residual error threshold values according to upper and lower boundaries corresponding to the 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.
Specifically, the central symmetry multicellular body corresponding to the residual error r (k) is used for generating a matrix H 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 ,ns 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.
In the environment of Matlab2016b, taking a single-lane tracking system of three automobiles as an example, the simulation time is set to 100 sampling periods (sampling period T t =0.1 s), the method designed by the present invention was verified, and the model of the tracking system was set 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 ,
representing state variables +.>
Representing the deviation (++) of the actual speed of i-vehicle from the reference speed>
Indicating the reference speed of i car)>
Representing the deviation (++1) of the actual distance between the j car and the j+1 car from the reference distance between the car and the car>
Representing the reference distance between j car and j+1 workshop), -j +>
Representing the control variable of the controller, R L Evaluation function +.>
Weights corresponding to control variables, Q L Weights for state variables corresponding to the performance trade-off evaluation function J +.>
Is algebraic equation->
D (k) represents the unknown disturbance matrix (++>
Representing random disturbance values), f (k) represents a fault matrix in the form of:
further, the respective system parameter matrices of the model are set as follows:
setting constraint order xs=12 of a reduction operator, and setting silence time h in an adaptive mixed time trigger mechanism k =1, maximum trigger interval τ max =5, setting the event trigger parameter as
Setting the order s=4 < n of the variable order observer, realizing reduced order observation, setting a set of vectors g= [0.5,0,0,0], and setting a set of left zero 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 gamma is obtained d 12.8179 and the remaining variable order observer parameter matrix:
can obtain the L corresponding to the optimal post-filter o and Mo The matrix is as follows:
the results illustrate:
fig. 1 shows a schematic diagram of the operation of a single lane tracking system for three vehicles.
FIG. 2 shows a flow chart of a fault detection method of the multi-vehicle tracking system based on an optimal variable order observer, which can be divided into two parts of system initialization and cycle detection, and the logic operation system according to the flow chart can realize effective fault detection of the multi-vehicle tracking system.
FIG. 3 shows a comparison of the effects of residual r (k) before and after filtering, as can be seen from the graph, the residual r after filtering by the post-filter 1 (k) The effect of the change in (c) is not significant because the preset controller additive fault pair r 1 (k) Is less influential and residual r 2 (k) The change effect is obvious after the filtering by the post filter. Residual r 2 (k) Filtered to be residual R 2 (k) As can be seen, the filtered residual R 2 (k) The robustness to unknown disturbance is stronger, the sensitivity to faults is stronger, the robustness of the residual error to the unknown disturbance and the sensitivity to faults can be enhanced by the optimal post filter, and the variable order observer can effectively generate the residual error r (k) is also illustrated.
Fig. 4 shows an event triggering interval diagram of the multi-vehicle tracking system, and it can be seen that the adaptive hybrid event triggering mechanism effectively reduces unnecessary network communication loss and can timely transmit data at a fault location for fault detection. As can also be seen from fig. 4, the minimum event trigger interval is greater than the preset silence time 1, which can effectively avoid the "gano phenomenon"; the maximum event triggering interval is a preset maximum triggering interval 5, which indicates that the self-adaptive hybrid event triggering mechanism can effectively operate, and the information of the multi-vehicle tracking system can be effectively prevented from being lost for a long time through the preset maximum triggering interval.
FIG. 5 shows the residual R 1 (k) The corresponding fault detection effect diagram has the advantage that the threshold value at the fault is increased because the residual central symmetry multicellular body is influenced by the central symmetry multicellular body of the event transmission error, so as to avoid the event transmission error from influencing the fault detection.
FIG. 6 shows the residual R 2 (k) The corresponding fault detection effect diagram can be used for detecting faults in time. Experiments prove that the method not only can reduce unnecessary network communication loss of the multi-vehicle tracking system under a self-adaptive mixed event triggering mechanism, but also can realize the balance of robustness of residual error to unknown disturbance and sensitivity to faults while improving the flexibility of the observation order of the variable order observer, and finally realize optimal fault detection of the multi-vehicle tracking system.
In summary, the invention overcomes the limited network resource constraint on the basis of the networked data transmission and fault detection research of the multi-vehicle tracking system, and provides the fault detection method of the multi-vehicle tracking system based on the optimal variable order observer, wherein the diagnostic observer parameter matrix must meet the Luenberger condition and the problem that the residual error has low sensitivity to faults. Finally, taking a single-lane tracking system of three automobiles as an example, the validity of the proposed method is verified.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the 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 ,ki+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 ,ns 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. />
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210418435.2A CN114740826B (en) | 2022-04-20 | 2022-04-20 | Multi-vehicle tracking system fault detection method based on optimal variable order observer |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210418435.2A CN114740826B (en) | 2022-04-20 | 2022-04-20 | Multi-vehicle tracking system fault detection method based on optimal variable order observer |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114740826A CN114740826A (en) | 2022-07-12 |
| CN114740826B true CN114740826B (en) | 2023-05-16 |
Family
ID=82284602
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210418435.2A Active CN114740826B (en) | 2022-04-20 | 2022-04-20 | Multi-vehicle tracking system fault detection method based on optimal variable order observer |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114740826B (en) |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110377921A (en) * | 2018-04-12 | 2019-10-25 | 哈尔滨工业大学 | A kind of failure determination threshold value calculation method based on the more cell spaces of central symmetry |
| US11635734B2 (en) * | 2019-01-10 | 2023-04-25 | Dalian University Of Technology | Interval error observer-based aircraft engine active fault tolerant control method |
| CN110161882B (en) * | 2019-06-12 | 2020-09-18 | 江南大学 | Fault detection method of networked system based on event trigger mechanism |
| CN113848876B (en) * | 2021-08-13 | 2022-04-22 | 南通大学 | Low-communication and low-calculation-consumption fault detection method for multi-AGV distance cruise system |
-
2022
- 2022-04-20 CN CN202210418435.2A patent/CN114740826B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN114740826A (en) | 2022-07-12 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Li et al. | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication | |
| WO2021077727A1 (en) | Electric truck steer-by-wire system and network uncertainty control method therefor | |
| CN104076687B (en) | A kind of Active suspension and the decoupling control method of electric power steering integrated system | |
| CN110673474B (en) | Intrusion-tolerant control method of networked motion control system based on event triggering | |
| CN113391616B (en) | Mining trolley bus safety state estimation method based on event trigger mechanism | |
| CN110826054A (en) | Vehicle-mounted CAN bus intrusion detection method based on message data field characteristics | |
| CN106864436A (en) | A kind of automatic driving vehicle brakes and braking method | |
| CN114740826B (en) | Multi-vehicle tracking system fault detection method based on optimal variable order observer | |
| CN107585207A (en) | A kind of vehicle line traffic control four-wheel steering system and its control method | |
| CN101377657A (en) | Power-assisted steering system with robust stability | |
| CN210478602U (en) | Gateway and car | |
| CN111221311A (en) | Complex network distributed pulse synchronization method and system based on parameter variational method | |
| CN102336189A (en) | Decoupling control method applied to automobile AFS (Active Front Steering) and ESP (Electronic Stability Program) integrated system | |
| JP4069481B2 (en) | Vehicle behavior estimation device | |
| CN102736517A (en) | Direct adaptive reconstruction control method for three-degree-of-freedom helicopter | |
| Shah et al. | An analysis of CAN-based steer-by-wire system performance in vehicle | |
| Yu et al. | Zonotope-based asynchronous fault detection for Markov jump systems subject to deception attacks via dynamic event-triggered communication | |
| Zeng et al. | Event-triggered controller design for active suspension systems: An adaptive backstepping method with error-dependent gain | |
| Jin et al. | Event-triggered fault detection and diagnosis for networked systems with sensor and actuator faults | |
| CN115167131A (en) | Adaptive event trigger estimation method of sewage treatment system based on disturbance observer | |
| Holzmann et al. | Vehicle dynamics simulation based on hybrid modeling | |
| CN110957952B (en) | Direct current motor system anti-interference control method based on event trigger mechanism | |
| CN103158763A (en) | Wheel speed velocity variation scaling system | |
| Latrach et al. | H∞ fuzzy networked control for vehicle lateral dynamics | |
| CN114578795B (en) | Self-adaptive fault compensation control method with transient performance guarantee for electric automobile EPS |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |