CN112180899B - State estimation method of system under intermittent anomaly measurement detection - Google Patents

State estimation method of system under intermittent anomaly measurement detection Download PDF

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CN112180899B
CN112180899B CN202011058827.XA CN202011058827A CN112180899B CN 112180899 B CN112180899 B CN 112180899B CN 202011058827 A CN202011058827 A CN 202011058827A CN 112180899 B CN112180899 B CN 112180899B
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CN112180899A (en
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邹磊
王子栋
白星振
赵忠义
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Shandong University of Science and Technology
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    • 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
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    • 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
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Abstract

The invention discloses a state estimation method of a system under intermittent anomaly measurement detection, which is based on l2‑l∞The estimation technology specifically comprises the following steps: establishing a system state space model; a method for detecting an intermittent abnormal signal is established,detecting all abnormal signals of the system in the operation process; calculating l according to the detection result of abnormal signal in system output2‑l∞The parameters of the estimator in turn calculate an estimate of the system state. The method can effectively solve the estimation problem under the interference of the bounded noise of the external energy, thereby ensuring better estimation effect. In addition, the invention also considers the influence of abnormal signals intermittently generated in the actual industrial process, establishes the abnormal signal detection method, can effectively detect all system outputs interfered by the abnormal signals, and can avoid using the outputs interfered by the abnormal signals in the design of the estimator, so that the designed estimator can accurately obtain the state estimation value of the system, and the application requirements of the actual industry can be further met.

Description

State estimation method of system under intermittent anomaly measurement detection
Technical Field
The present invention relates to a state estimation method, and more particularly, to a state estimation method for a system under intermittent abnormal measurement detection.
Background
With the development of science and technology, the structure of modern industrial systems tends to be complex, and the manufacturing cost is higher and higher, so that the guarantee of the safe operation of the system is particularly important. The operating conditions of the system are fully reflected by their state. However, due to physical limitations and the like, it is generally difficult to obtain all the state information of a system by means of measurement and the like, and therefore, the state estimation technique plays an important role in an industrial system. State estimation is one of the basic research subjects in the control field, and the basic idea thereof is to obtain an estimated value of a system state satisfying a specific performance by using received output information of a system and combining a model of the system.
On the one hand, systems in industrial environments are often disturbed by ambient noise, and ambient energy-bounded noise has an impact on the performance of the system and on the estimation of the state of the system. On the other hand, in an actual industrial system, there are often intermittently generated interference signals, which have a larger amplitude than external noise, and if appropriate processing is not performed, the estimation effect of the system state is greatly affected, and the estimation accuracy is greatly affected. Therefore, it is necessary to establish a detection mechanism for intermittent abnormal signals in order to identify the system output affected by the abnormal interference signal.
Disclosure of Invention
The invention aims to provide a system state estimation method under intermittent abnormal measurement detection, which fully considers the influence of intermittent abnormal signals and energy-bounded external noise and effectively ensures the estimation precision of an estimator.
In order to achieve the purpose, the invention adopts the following technical scheme:
a state estimation method of a system under intermittent abnormal measurement detection comprises the following steps:
s1, establishing a state space model of a system, as shown in a formula (1);
Figure GDA0003100215390000011
wherein the subscript k denotes the sampling instant, xkIs the state of the system, ykAs an output of the system, zkRepresenting the signal to be estimated, ωkRepresenting energy bounded process noise, vkThe measurement noise is indicative of the energy being bounded,
Figure GDA0003100215390000012
indicating an abnormal signal;
a represents a system matrix, B represents an influence matrix of process noise on the system state and the output, C represents a measurement matrix, D represents an influence matrix of the measurement noise on the system state and the output, and M represents a relation matrix of a signal to be estimated and the system state;
the above matrices A, B, C, D, M are all known matrices;
for practical industrial systems, the process noise ωkAnd measuring noise vkThe magnitude is bounded and the following condition is satisfied:
Figure GDA0003100215390000013
in the formula (I), the compound is shown in the specification,
Figure GDA0003100215390000021
represents an upper bound on the magnitude of the process noise,
Figure GDA0003100215390000022
an upper bound representing the magnitude of the measurement noise;
s2, establishing an intermittent abnormal signal detection method, and detecting all abnormal signals of the system in the operation process;
firstly, giving out conditions met by the occurrence time, duration and signal amplitude of an abnormal signal;
abnormal signal of intermittent occurrence
Figure GDA0003100215390000023
Expressed as:
Figure GDA0003100215390000024
wherein Γ (·) represents a step function,t iindicating an abnormal signal
Figure GDA0003100215390000025
The time of occurrence of the i-th time,
Figure GDA0003100215390000026
indicating an abnormal signal
Figure GDA0003100215390000027
The moment of disappearance of the i-th time,
Figure GDA0003100215390000028
indicating an abnormal signal
Figure GDA0003100215390000029
The magnitude of amplitude of (d);
order to
Figure GDA00031002153900000210
Indicating the interval time between the appearance time of the i +1 th abnormal signal and the disappearance time of the i-th abnormal signal,
Figure GDA00031002153900000211
abnormal signal indicating i-th occurrence
Figure GDA00031002153900000212
The duration of (d) then being:
Figure GDA00031002153900000213
wherein the content of the first and second substances,
Figure GDA00031002153900000224
a symbol representing the definition of the variable,
Figure GDA00031002153900000214
representing the time interval between the initial operating moment of the system and the moment of the first occurrence of an abnormal signal disturbance,t 1indicating the occurrence time of the 1 st abnormal signal;
formula (3) reflects the intermittent occurrence characteristic of the abnormal signal interfering with the system output;
for the abnormal signals which occur intermittently, the following relational expression is satisfied for any i ≧ 1:
Figure GDA00031002153900000215
Figure GDA00031002153900000216
Figure GDA00031002153900000217
wherein the content of the first and second substances,T，
Figure GDA00031002153900000218
oall represent known normal numbers;
formula (4) indicates that the time interval between the disappearance time of any abnormal signal and the appearance time of the next abnormal signal is not less than a positive integerT；
The formula (5) shows that the duration of any abnormal signal is not more than a positive integer
Figure GDA00031002153900000219
Equation (6) shows that the amplitude of the abnormal signal is not less than the normal numbero；
The sequence of the occurrence time and the disappearance time of the abnormal signal at the ith time is defined as shown in equations (7) and (8), respectively:
Figure GDA00031002153900000220
Figure GDA00031002153900000221
in the formula (I), the compound is shown in the specification,τ iand
Figure GDA00031002153900000222
respectively representing the ith abnormal signal
Figure GDA00031002153900000223
N represents the dimension of the system state; f. of0(k) A detection function indicating the occurrence time of the abnormal signal; f. ofj(τ i) A detection function for the disappearance moment of the abnormal signal;
Figure GDA0003100215390000031
is a parameter associated with the system parameter and the abnormal signalT、
Figure GDA0003100215390000032
oA relevant detection threshold;
by detecting function f0(k)、fj(τ i) And a detection threshold
Figure GDA0003100215390000033
Comparing, namely judging whether a certain specific moment is the appearance moment or disappearance moment of the abnormal signal; the specific judgment process is as follows:
when the abnormal signal occurring intermittently at the ith time in the running process of the system is detected, the detection condition is met
Figure GDA0003100215390000034
The minimum time k is the ith occurrence time of the abnormal signal, and the occurrence time is detectedτ iThen, the detection condition is satisfied
Figure GDA0003100215390000035
The minimum time j +τ iNamely the disappearance moment of the abnormal signal intermittently occurring in the ith time in the system operation process;
wherein, the detection function f of the abnormal signal occurrence time0(k) Disappearance time detection function fj(τ i) And a detection threshold
Figure GDA0003100215390000036
The calculation processes of (2) are respectively shown in formulas (9), (10) and (11):
Figure GDA0003100215390000037
Figure GDA0003100215390000038
Figure GDA0003100215390000039
wherein the content of the first and second substances,
Figure GDA00031002153900000310
is the system output at time k, yk-n+iThe system output at the time of k-n + i;
Figure GDA00031002153900000322
is j +τ iThe output of the system at the time of day,
Figure GDA00031002153900000323
is composed ofτ i-system output at time n + i;
Figure GDA00031002153900000311
wherein, variable
Figure GDA00031002153900000312
And
Figure GDA00031002153900000313
the calculation is respectively obtained through iterative calculation according to the following formula:
Figure GDA00031002153900000314
Figure GDA00031002153900000315
wherein the initial conditions are
Figure GDA00031002153900000316
And
Figure GDA00031002153900000317
and is
Figure GDA00031002153900000318
And
Figure GDA00031002153900000319
is a constant value;
α0represents a given initial value, which is a constant value;
αiis the coefficient of the characteristic polynomial of the system matrix a, i ═ 1, 2, …, n-1; a has a characteristic polynomial of
Figure GDA00031002153900000320
Wherein z represents a variable of a characteristic polynomial, and I represents an identity matrix;
b1，b2，…，bnby the formula
Figure GDA00031002153900000321
Calculated, wherein:
Figure GDA0003100215390000041
F＝[(An-1)TCT(An-2)TCT…CT]T；
if conditions can be detected
Figure GDA0003100215390000042
If the requirement is met, all intermittent abnormal measurements appearing in the whole operation process of the system can be detected, and the sequence of appearance time and disappearance time of all abnormal signals can be obtainedt i}i≥0And
Figure GDA0003100215390000043
s3, calculating according to the result of intermittent abnormal measurement and detection
Figure GDA00031002153900000419
The parameters of the state estimator are specifically shown in equation (12):
Figure GDA0003100215390000044
wherein, L (theta)k) An estimator parameter representing a detection result depending on the abnormal signal;
when theta iskWhen 0, it means that no abnormal signal is detected from the system output at time k, and at this time,
Figure GDA00031002153900000422
the parameter of the state estimator takes L (theta)k) The values of the parameter K will be given below; when theta iskWhen 1, it indicates that an abnormal signal is detected from the system output at time k, and at this time, the abnormal signal is detected
Figure GDA00031002153900000421
Parameter L (theta) of the state estimatork) Setting zero;
parameter K is represented by
Figure GDA0003100215390000045
Given, among them, positive definite matrix P and matrix
Figure GDA0003100215390000046
Optimization problem constrained by a linear matrix inequality having
Figure GDA0003100215390000047
The solution of (a) gives:
Figure GDA0003100215390000048
Figure GDA0003100215390000049
Figure GDA00031002153900000410
wherein the content of the first and second substances,
Figure GDA00031002153900000411
Figure GDA00031002153900000412
a transpose of a matrix representing a symmetric position in the matrix inequality;
0＜μ1＜1，μ2> 0 is satisfied
Figure GDA00031002153900000413
The given parameter of (a);
optimization parameters in equation (15)
Figure GDA00031002153900000414
The suppression capability of the designed estimator on external noise is described, and parameters are optimized
Figure GDA00031002153900000415
Is a normal number; when optimizing the parameters
Figure GDA00031002153900000416
When the maximum value is reached, the designed estimator has the strongest capacity of inhibiting external noise;
solving based on the above formula to obtain positive definite matrix P and matrix
Figure GDA00031002153900000417
Normal number
Figure GDA00031002153900000418
And
Figure GDA00031002153900000420
the state estimator parameter L (θ)k)；
S4. construction
Figure GDA00031002153900000518
The state estimator, as shown in equation (16), compares L (θ)k) Substituting the calculated state estimate；
Figure GDA0003100215390000051
In the formula (I), the compound is shown in the specification,
Figure GDA0003100215390000052
represents the system state xkIs determined by the estimated value of (c),
Figure GDA0003100215390000053
representing the signal z to be estimatedkIs determined by the estimated value of (c),
Figure GDA0003100215390000054
representing an estimate of the state of the system at the initial operating time,
Figure GDA0003100215390000055
indicating setting
Figure GDA00031002153900000517
An initial value of a state estimator;
Figure GDA00031002153900000519
the state estimator uses the system output ykIteratively calculating an estimated value of the system state, wherein the initial value of the system state during iteration is
Figure GDA00031002153900000520
Estimator parameter L (theta) used in iterationk) And system output ykThe detection result of the abnormal signal in (1) is correlated;
specifically, at time k, when no abnormal signal is detected from the system output, the estimator parameter is L (θ)k) K; conversely, when an abnormal signal is detected in the system output at time k, the estimator parameter L (θ)k) Setting zero;
Figure GDA00031002153900000521
the state estimator can guarantee zkIs estimated error of
Figure GDA0003100215390000056
The index is stable, and the index is stable,
Figure GDA0003100215390000057
at the same time satisfy
Figure GDA0003100215390000058
Performance, namely when noise energy is bounded, the estimation error amplitude of a signal to be estimated is bounded;
by construction of
Figure GDA00031002153900000522
And the state estimator is used for estimating the state of the system to obtain a state estimation value of the system.
The invention has the following advantages:
as described above, the present invention relates to a method for estimating the state of a system under intermittent abnormal measurement detection, which considers the influence and detection of an abnormal signal occurring intermittently and the suppression of the external energy bounded noise at the same time, and utilizes
Figure GDA00031002153900000523
The estimation technology and the linear matrix inequality technology design the method which meets the requirements of exponential stability and linear matrix inequality while detecting abnormal signals
Figure GDA0003100215390000059
A state estimator of the performance. The invention does not need the statistical properties such as mathematical expectation and variance of noise and can better meet the application requirements of actual industry.
Drawings
FIG. 1 is a schematic flow chart illustrating a method for estimating a state of a system under intermittent abnormal measurement detection according to an embodiment of the present invention;
FIG. 2 is a diagram of an exception signal in an embodiment of the present invention
Figure GDA00031002153900000510
With a binary detection function thetakA track graph;
FIG. 3 shows the estimation error generated by the method of the present invention and a conventional Luneberg estimator
Figure GDA00031002153900000511
Amplitude of
Figure GDA00031002153900000512
A comparison graph of (A);
FIG. 4 is a diagram of actual state traces in an embodiment of the present invention
Figure GDA00031002153900000513
And its estimated trajectory
Figure GDA00031002153900000514
A comparison graph of (A);
FIG. 5 is a diagram of actual state traces in an embodiment of the present invention
Figure GDA00031002153900000515
And its estimated trajectory
Figure GDA00031002153900000516
A comparative graph of (a).
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
examples
As shown in fig. 1, a method for estimating the state of a system under intermittent abnormal measurement detection includes the following steps:
s1, establishing a state space model of a system, which is shown in the following formula (1);
Figure GDA0003100215390000061
wherein the subscript k denotes the sampling instant, xkIs the state of the system, ykAs an output of the system, zkRepresenting the signal to be estimated, ωkProcess noise, v, representing energy boundingkThe measurement noise is indicative of the energy being bounded,
Figure GDA0003100215390000062
indicating an abnormal signal.
A represents a system matrix, B represents an influence matrix of process noise on the system state and the output, C represents a measurement matrix, D represents an influence matrix of the measurement noise on the system state and the output, and M represents a relation matrix of a signal to be estimated and the system state.
The above matrix A, B, C, D, M is a known matrix.
For practical industrial systems, the process noise ωkAnd measuring noise vkThe magnitude is bounded and the following condition is satisfied:
Figure GDA0003100215390000063
in the formula (I), the compound is shown in the specification,
Figure GDA0003100215390000064
represents an upper bound on the magnitude of the process noise,
Figure GDA0003100215390000065
representing an upper bound on the magnitude of the measurement noise.
For an actual industrial system, it satisfies an observable rank criterion (only if the criterion is satisfied, the state estimation can be performed on the system, and an actual system can generally satisfy the criterion), that is:
rank[(An-1)TCT(An-2)TCT…CT)]n; where n represents the dimension of the system state.
S2, establishing an intermittent abnormal signal detection method, and detecting all abnormal signals of the system in the operation process.
Firstly, giving out conditions met by the occurrence time, duration and signal amplitude of an abnormal signal;
abnormal signal of intermittent occurrence
Figure GDA0003100215390000066
Expressed as:
Figure GDA0003100215390000067
wherein Γ (·) represents a step function,t iindicating an abnormal signal
Figure GDA0003100215390000068
The time of occurrence of the i-th time,
Figure GDA0003100215390000069
indicating an abnormal signal
Figure GDA00031002153900000610
The moment of disappearance of the i-th time,
Figure GDA00031002153900000611
indicating an abnormal signal
Figure GDA00031002153900000612
The magnitude of (c).
Order to
Figure GDA00031002153900000613
Indicating the interval time between the appearance time of the i +1 th abnormal signal and the disappearance time of the i-th abnormal signal,
Figure GDA00031002153900000614
abnormal signal indicating i-th occurrence
Figure GDA00031002153900000615
The duration of (d) then being:
Figure GDA00031002153900000616
wherein the content of the first and second substances,
Figure GDA00031002153900000617
a symbol representing the definition of the variable,
Figure GDA00031002153900000618
representing the time interval between the initial operating moment of the system and the moment of the first occurrence of an abnormal signal disturbance,t 1indicating the occurrence of the 1 st anomaly signal.
Equation (3) reflects the characteristics of intermittent occurrence of an abnormal signal that interferes with the system output.
For the abnormal signals which occur intermittently, the following relational expression is satisfied for any i ≧ 1:
Figure GDA0003100215390000071
Figure GDA0003100215390000072
Figure GDA0003100215390000073
wherein the content of the first and second substances,T，
Figure GDA0003100215390000074
oall represent known normal numbers;
formula (4) indicates that the time interval between the disappearance time of any abnormal signal and the appearance time of the next abnormal signal is not less than a positive integerT；
The formula (5) shows that the duration of any abnormal signal is not more than a positive integer
Figure GDA0003100215390000075
Equation (6) shows that the amplitude of the abnormal signal is not less than the normal numbero。
The sequence of the occurrence time and the disappearance time of the abnormal signal at the ith time is defined as shown in equation (7) and equation (8), respectively:
Figure GDA0003100215390000076
Figure GDA0003100215390000077
in the formula (I), the compound is shown in the specification,τ iand
Figure GDA0003100215390000078
respectively representing the ith abnormal signal
Figure GDA0003100215390000079
The occurrence time and the disappearance time of (c); f. of0(k) A detection function indicating the occurrence time of the abnormal signal; f. ofj(. cndot.) is a detection function of the moment when the abnormal signal disappears.
Figure GDA00031002153900000710
Is a parameter associated with the system parameter and the abnormal signalT、
Figure GDA00031002153900000711
oThe relevant detection threshold.
By detecting function f0(k)、fjAnd detection threshold
Figure GDA00031002153900000712
And comparing to judge whether a certain specific moment is the appearance moment or disappearance moment of the abnormal signal. The specific judgment process is as follows:
when the abnormal signal occurring intermittently at the ith time in the running process of the system is detected, the detection condition is met
Figure GDA00031002153900000713
At a minimum time k, i.eDetecting the occurrence time of the ith occurrence time of the abnormal signalτ iThen, the detection condition is satisfied
Figure GDA00031002153900000714
The minimum time j +τ iNamely the disappearance moment of the abnormal signal intermittently occurring in the ith time in the system operation process;
function f for detecting occurrence time of abnormal signal0(k) Disappearance time detection function fj(τ i) And a detection threshold
Figure GDA00031002153900000715
The calculation processes of (2) are respectively shown in formulas (9), (10) and (11):
Figure GDA00031002153900000716
Figure GDA00031002153900000717
Figure GDA00031002153900000718
wherein the content of the first and second substances,
Figure GDA00031002153900000719
is the system output at time k, yk-n+iIs the system output at time k-n + i,
Figure GDA00031002153900000720
is j +τ iThe output of the system at the time of day,
Figure GDA00031002153900000721
is composed ofτ i-system output at time n + i;
Figure GDA0003100215390000081
wherein, variable
Figure GDA0003100215390000082
And
Figure GDA0003100215390000083
the calculation is respectively obtained through iterative calculation according to the following formula:
Figure GDA0003100215390000084
Figure GDA0003100215390000085
wherein the initial conditions are
Figure GDA0003100215390000086
And
Figure GDA0003100215390000087
and is
Figure GDA0003100215390000088
And
Figure GDA0003100215390000089
is a constant value;
α0represents a given initial value, which is a constant value;
αiis the coefficient of the characteristic polynomial of the system matrix a, i ═ 1, 2, …, n-1; a has a characteristic polynomial of
Figure GDA00031002153900000810
Wherein z represents a variable of a characteristic polynomial, and I represents an identity matrix;
b1，b2，…，bncan be represented by formula
Figure GDA00031002153900000811
The calculation gives, where:
Figure GDA00031002153900000812
F＝[(An-1)TCT(An-2)TCT…CT]T；
if conditions can be detected
Figure GDA00031002153900000813
If the requirement is met, all intermittent abnormal measurements appearing in the whole operation process of the system can be detected, and the sequence of appearance time and disappearance time of all abnormal signals can be obtainedt i}i≥0And
Figure GDA00031002153900000814
s3, calculating according to the result of the intermittent abnormal measurement detection
Figure GDA00031002153900000818
The parameters of the state estimator, as shown in equation (12):
Figure GDA00031002153900000815
wherein, L (theta)k) Representing estimator parameters that depend on the anomaly signal detection result.
θ k0 indicates that no abnormal signal is detected from the system output at time k, at which time
Figure GDA00031002153900000819
The parameter of the state estimator takes L (theta)k) K, the estimator has better anti-interference capability. The values of the parameter K will be given later in the description.
θ k1 indicates that an abnormal signal is detected in the system output at time k, at which time
Figure GDA00031002153900000820
Parameter L (theta) of the state estimatork) And setting zero to avoid the abnormal signal from influencing the estimation effect of the estimator.
Parameter K is represented by
Figure GDA00031002153900000816
Given, among them, positive definite matrix P and matrix
Figure GDA00031002153900000817
Optimization problem constrained by a linear matrix inequality having
Figure GDA0003100215390000091
The solution of (a) gives:
Figure GDA0003100215390000092
Figure GDA0003100215390000093
Figure GDA0003100215390000094
wherein the content of the first and second substances,
Figure GDA0003100215390000095
Figure GDA0003100215390000096
a transpose of a matrix representing a symmetric position in the matrix inequality;
0＜μ1＜1，μ2> 0 is satisfied
Figure GDA0003100215390000097
Given parameters of (1).
Formula (II)(15) Middle optimization parameter
Figure GDA00031002153900000923
Designed by carving
Figure GDA00031002153900000924
The suppression capability of the estimator to the external noise and the optimization parameter
Figure GDA0003100215390000098
Is a normal number; when optimizing the parameters
Figure GDA0003100215390000099
At maximum, indicates what was designed
Figure GDA00031002153900000925
The estimator has the strongest capacity of suppressing the external noise.
Solving based on the above formula to obtain positive definite matrix P and matrix
Figure GDA00031002153900000910
Normal number
Figure GDA00031002153900000911
And
Figure GDA00031002153900000926
the state estimator parameter L (θ)k)。
S4. construction
Figure GDA00031002153900000927
The state estimator, as shown in equation (16), compares L (θ)k) Substituting the estimated value of the calculation state;
Figure GDA00031002153900000912
in the formula (I), the compound is shown in the specification,
Figure GDA00031002153900000913
presentation systemState xkIs determined by the estimated value of (c),
Figure GDA00031002153900000914
representing the signal z to be estimatedkIs determined by the estimated value of (c),
Figure GDA00031002153900000915
which represents the initial state of the system and,
Figure GDA00031002153900000916
indicating setting
Figure GDA00031002153900000928
Initial values of the state estimator.
Figure GDA00031002153900000929
The state estimator uses the system output ykIteratively calculating an estimated value of the system state, wherein the initial value of the system state during iteration is
Figure GDA00031002153900000917
Estimator parameters and system output y used in iterationkThe detection result of the abnormal signal in (1) is correlated;
wherein at time k, no abnormal signal is detected from the system output, at which time
Figure GDA00031002153900000930
The state estimator parameter L (θ)k) K; conversely, when an abnormal signal is detected in the system output at time k, this time
Figure GDA00031002153900000931
The state estimator parameters are zeroed out.
Designed by
Figure GDA00031002153900000932
The state estimator can guarantee zkIs estimated error of
Figure GDA00031002153900000918
Stable index while satisfying
Figure GDA00031002153900000919
When the performance, namely the noise energy, is bounded, the estimation error amplitude of the signal to be estimated is bounded, namely:
Figure GDA00031002153900000920
wherein the content of the first and second substances,
Figure GDA00031002153900000921
gamma is the optimized interference rejection level (when optimizing the parameters)
Figure GDA00031002153900000922
At maximum, the parameter γ is minimum).
By construction of
Figure GDA00031002153900000933
And the state estimator is used for estimating the state of the system to obtain a state estimation value of the system.
The method of the invention aims at the state estimation problem of the industrial system influenced by the external noise and the intermittent abnormal signals, establishes the method for detecting the abnormal signals in the output of the system, can accurately detect all the abnormal signals contained in the output, and can construct the abnormal signals related to the detection result
Figure GDA00031002153900001013
And when the system output contains the abnormal signal, the parameter of the estimator is set to zero, so that the influence of the abnormal signal on the state estimation is avoided.
The method for estimating the state of the system under intermittent anomaly measurement provided by the invention is described below by combining experiments to verify the effectiveness of the method provided by the invention. During the experiment: and taking the experimental step length as 150, adding an abnormal signal to a semi-physical simulation platform capable of acquiring the real-time state of the system, and inputting the system output given by the platform to a computer as the input of an estimator.
The estimation algorithm provided by the invention is used for generating an estimation value, and the estimation value is compared with a real value of the system state provided by the platform.
Inputting the abnormal signal sequence added to the system output into a computer, and drawing the sequence by using MATLAB software, wherein the details are shown in FIG. 2 (a); according to the method provided by the invention, MATLAB software is used for calculating the detection function theta of the abnormal signalkAt time 1-150 and an image of the function is plotted, as shown in fig. 2 (b).
Wherein FIG. 2(a) is an abnormal measurement value
Figure GDA00031002153900001014
FIG. 2(b) is a graph corresponding to θkA trajectory diagram of (a); FIG. 2 shows that the applied abnormal signals can be detected completely by using the method of the present invention, thereby verifying the effectiveness of the detection method of the present invention;
in addition, the method of the present invention is compared to the estimation method based on the lunberg estimator, as shown in fig. 3.
In fig. 3, the solid line represents the estimation error of the signal to be estimated based on the method of the present invention, and the dotted line represents the estimation error of the signal to be estimated based on the roberg estimator.
As can be seen from fig. 3, the estimation error of the signal to be estimated obtained by the method of the present invention is significantly smaller than the estimation error of the signal to be estimated obtained based on the luneberg estimator, which indicates that the method of the present invention has higher estimation accuracy.
In addition, the invention also provides a state estimation track obtained by the method
Figure GDA0003100215390000101
Track of actual state
Figure GDA0003100215390000102
By contrast, as shown in FIG. 4, the solid line in FIG. 4 is the actual state trace
Figure GDA0003100215390000103
The dotted line is the state estimation trajectory
Figure GDA0003100215390000104
As can be seen from FIG. 4, the state estimation trajectory obtained by the method of the present invention
Figure GDA0003100215390000105
Track of actual state
Figure GDA0003100215390000106
The goodness of fit is high.
The invention also provides a state estimation track obtained by the method
Figure GDA0003100215390000107
Track of actual state
Figure GDA0003100215390000108
In contrast, as in fig. 5, the solid line in fig. 5 is the actual state trajectory
Figure GDA0003100215390000109
The dotted line is the state estimation trajectory
Figure GDA00031002153900001010
As can be seen from FIG. 5, the state estimation trajectory obtained by the method of the present invention
Figure GDA00031002153900001011
Track of actual state
Figure GDA00031002153900001012
The goodness of fit is high.
The effectiveness of the method is shown through the experiments, and the method has high estimation precision.
It should be understood, however, that the description herein of specific embodiments is not intended to limit the invention to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1. A method for estimating the state of a system under intermittent abnormal measurement detection is characterized by comprising the following steps:
s1, establishing a state space model of a system, as shown in a formula (1);
Figure FDA0003135224800000011
wherein the subscript k denotes the sampling instant, xkIs the state of the system, ykAs an output of the system, zkRepresenting the signal to be estimated, ωkProcess noise, v, representing energy boundingkThe measurement noise is indicative of the energy being bounded,
Figure FDA00031352248000000114
indicating an abnormal signal;
a represents a system matrix, B represents an influence matrix of process noise on the system state and the output, C represents a measurement matrix, D represents an influence matrix of the measurement noise on the system state and the output, and M represents a relation matrix of a signal to be estimated and the system state;
the above matrices A, B, C, D, M are all known matrices;
for practical industrial systems, the process noise ωkAnd measuring the noise vkThe magnitude is bounded and the following condition is satisfied:
Figure FDA00031352248000000115
in the formula (I), the compound is shown in the specification,
Figure FDA00031352248000000116
represents an upper bound on the magnitude of the process noise,
Figure FDA00031352248000000117
an upper bound representing the magnitude of the measurement noise;
s2, establishing an intermittent abnormal signal detection method, and detecting all abnormal signals of the system in the operation process;
firstly, giving out conditions met by the occurrence time, duration and signal amplitude of an abnormal signal;
abnormal signal of intermittent occurrence
Figure FDA00031352248000000118
Expressed as:
Figure FDA0003135224800000012
wherein Γ (·) represents a step function,t iindicating an abnormal signal
Figure FDA0003135224800000013
The time of occurrence of the i-th time,
Figure FDA0003135224800000014
indicating an abnormal signal
Figure FDA0003135224800000015
The moment of disappearance of the i-th time,
Figure FDA0003135224800000016
indicating an abnormal signal
Figure FDA0003135224800000017
The magnitude of amplitude of (d);
order to
Figure FDA0003135224800000018
Indicating the interval time between the appearance time of the i +1 th abnormal signal and the disappearance time of the i-th abnormal signal,
Figure FDA0003135224800000019
abnormal signal indicating i-th occurrence
Figure FDA00031352248000000110
The duration of (d) then being:
Figure FDA00031352248000000111
wherein the content of the first and second substances,
Figure FDA00031352248000000112
a symbol representing the definition of the variable,
Figure FDA00031352248000000113
representing the time interval between the initial operating moment of the system and the moment of the first occurrence of an abnormal signal disturbance,t 1indicating the occurrence time of the 1 st abnormal signal;
formula (3) reflects the intermittent occurrence characteristic of the abnormal signal interfering with the system output;
for the abnormal signals which occur intermittently, the following relational expression is satisfied for any i ≧ 1:
Figure FDA0003135224800000021
Figure FDA0003135224800000022
Figure FDA0003135224800000023
wherein the content of the first and second substances,T，
Figure FDA0003135224800000024
oall represent known normal numbers;
formula (4) indicates that the time interval between the disappearance time of any abnormal signal and the appearance time of the next abnormal signal is not less than a positive integerT；
The formula (5) shows that the duration of any abnormal signal is not more than a positive integer
Figure FDA0003135224800000025
Equation (6) shows that the amplitude of the abnormal signal is not less than the normal numbero；
The sequence of the occurrence time and the disappearance time of the abnormal signal at the ith time is defined as shown in equations (7) and (8), respectively:
Figure FDA0003135224800000026
Figure FDA0003135224800000027
in the formula (I), the compound is shown in the specification,τ iand
Figure FDA0003135224800000028
respectively representing the ith abnormal signal
Figure FDA0003135224800000029
N represents the dimension of the system state; f. of0(k) A detection function indicating the occurrence time of the abnormal signal; f. ofj(τ i) When abnormal signals disappearA test function of the scale;
Figure FDA00031352248000000210
is a parameter associated with the system parameter and the abnormal signalT、
Figure FDA00031352248000000211
oA relevant detection threshold;
by detecting function f0(k)、fj(τ i) And a detection threshold
Figure FDA00031352248000000212
Comparing, namely judging whether a certain specific moment is the appearance moment or disappearance moment of the abnormal signal; the specific judgment process is as follows:
when the abnormal signal occurring intermittently at the ith time in the running process of the system is detected, the detection condition is met
Figure FDA00031352248000000213
The minimum time k is the ith occurrence time of the abnormal signal, and the occurrence time is detectedτ iThen, the detection condition is satisfied
Figure FDA00031352248000000214
The minimum time j +τ iNamely the disappearance moment of the abnormal signal intermittently occurring in the ith time in the system operation process;
wherein, the detection function f of the abnormal signal occurrence time0(k) Disappearance time detection function fj(τ i) And a detection threshold
Figure FDA00031352248000000215
The calculation processes of (2) are respectively shown in formulas (9), (10) and (11):
Figure FDA00031352248000000216
Figure FDA00031352248000000217
Figure FDA00031352248000000218
wherein the content of the first and second substances,
Figure FDA00031352248000000219
ykis the system output at time k, yk-n+iThe system output at the time of k-n + i;
Figure FDA00031352248000000221
is j +τ iThe output of the system at the time of day,
Figure FDA00031352248000000222
is composed ofτ i-system output at time n + i;
Figure FDA00031352248000000220
wherein, variable
Figure FDA0003135224800000031
And
Figure FDA0003135224800000032
the calculation is respectively obtained through iterative calculation according to the following formula:
Figure FDA0003135224800000033
Figure FDA0003135224800000034
wherein the initial conditions are
Figure FDA0003135224800000035
And
Figure FDA0003135224800000036
and is
Figure FDA0003135224800000037
And
Figure FDA0003135224800000038
is a constant value;
α0represents a given initial value, which is a constant value;
αiis the coefficient of the characteristic polynomial of the system matrix a, i ═ 1, 2, …, n-1; a has a characteristic polynomial of
Figure FDA0003135224800000039
Wherein z represents a variable of a characteristic polynomial, and I represents an identity matrix;
b1，b2，...，bnby the formula
Figure FDA00031352248000000310
Calculated, wherein:
Figure FDA00031352248000000311
F＝[(An-1)TCT (An-2)TCT … CT]T；
if conditions can be detected
Figure FDA00031352248000000312
If the system is satisfied, the system isAll intermittent abnormal measurements appearing in the whole operation process can be detected, namely a sequence of appearance time and disappearance time of all abnormal signalst i}i≥0And
Figure FDA00031352248000000313
s3, calculating l according to the result of intermittent anomaly measurement detection2-l∞The parameters of the state estimator are specifically shown in equation (12):
Figure FDA00031352248000000315
wherein, L (theta)k) An estimator parameter representing a detection result depending on the abnormal signal;
when theta iskWhen 0, it means that no abnormal signal is detected from the system output at time k, and in this case, l2-l∞The parameter of the state estimator takes L (theta)k) The values of the parameter K will be given below; when theta iskWhen 1 indicates that an abnormal signal is detected from the system output at time k, l is set2-l∞Parameter L (theta) of the state estimatork) Setting zero;
the parameter K is represented by the formula K ═ P-1
Figure FDA00031352248000000320
Given, among them, positive definite matrix P and matrix
Figure FDA00031352248000000319
Optimization problem constrained by a linear matrix inequality having
Figure FDA00031352248000000318
The solution of (a) gives:
Figure FDA0003135224800000041
Figure FDA0003135224800000042
Figure FDA0003135224800000043
wherein the content of the first and second substances,
Figure FDA0003135224800000044
Figure FDA0003135224800000045
a transpose of a matrix representing a symmetric position in the matrix inequality;
0＜μ1＜1，μ2> 0 is satisfied
Figure FDA0003135224800000046
The given parameter of (a);
optimization parameters in equation (15)
Figure FDA00031352248000000425
The suppression capability of the designed estimator on external noise is described, and parameters are optimized
Figure FDA0003135224800000047
Is a normal number; when optimizing the parameters
Figure FDA0003135224800000048
When the maximum value is reached, the designed estimator has the strongest capacity of inhibiting external noise;
solving based on the above formula to obtain positive definite matrix P and matrix
Figure FDA0003135224800000049
Normal number
Figure FDA00031352248000000410
And l2-l∞The state estimator parameter L (θ)k)；
S4. construction of2-l∞The state estimator, as shown in equation (16), compares L (θ)k) Substituting the estimated value of the calculation state;
Figure FDA00031352248000000413
in the formula (I), the compound is shown in the specification,
Figure FDA00031352248000000414
represents the system state xkIs determined by the estimated value of (c),
Figure FDA00031352248000000415
representing the signal z to be estimatedkIs determined by the estimated value of (c),
Figure FDA00031352248000000416
representing an estimate of the state of the system at the initial operating time,
Figure FDA00031352248000000417
indicates a set2-l∞An initial value of a state estimator;
l2-l∞the state estimator uses the system output ykIteratively calculating an estimated value of the system state, wherein the initial value of the system state during iteration is
Figure FDA00031352248000000420
Estimator parameter L (theta) used in iterationk) And system output ykThe detection result of the abnormal signal in (1) is correlated;
specifically, at time k, when no abnormal signal is detected from the system output, the estimator parameter is L (θ)k) K; on the contrary, at the momentk, when an abnormal signal is detected in the system output, the estimator parameter L (theta)k) Setting zero;
l2-l∞the state estimator can guarantee zkIs estimated error of
Figure FDA00031352248000000422
The index is stable, and the index is stable,
Figure FDA00031352248000000423
at the same time satisfy
Figure FDA00031352248000000426
Performance, namely when noise energy is bounded, the estimation error amplitude of a signal to be estimated is bounded;
using constructed l2-l∞And the state estimator is used for estimating the state of the system to obtain a state estimation value of the system.
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