CN112180899A - 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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CN112180899A
CN112180899A CN202011058827.XA CN202011058827A CN112180899A CN 112180899 A CN112180899 A CN 112180899A CN 202011058827 A CN202011058827 A CN 202011058827A CN 112180899 A CN112180899 A CN 112180899A
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state
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CN112180899B (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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    • 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
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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; establishing an intermittent abnormal signal detection method for detecting all abnormal signals in the running process of the system; 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 BDA0002711609090000011
wherein, the lower partThe index 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 BDA0002711609090000012
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 BDA0002711609090000013
in the formula (I), the compound is shown in the specification,
Figure BDA0002711609090000021
represents an upper bound on the magnitude of the process noise,
Figure BDA0002711609090000022
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 BDA0002711609090000023
Expressed as:
Figure BDA0002711609090000024
wherein (·) represents a step function,t iindicating an abnormal signal
Figure BDA0002711609090000025
The time of occurrence of the i-th time,
Figure BDA0002711609090000026
indicating an abnormal signal
Figure BDA0002711609090000027
The moment of disappearance of the i-th time,
Figure BDA0002711609090000028
indicating an abnormal signal
Figure BDA0002711609090000029
The magnitude of amplitude of (d);
order to
Figure BDA00027116090900000210
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 BDA00027116090900000211
abnormal signal indicating i-th occurrence
Figure BDA00027116090900000212
The duration of (d) then being:
Figure BDA00027116090900000213
wherein the content of the first and second substances,
Figure BDA00027116090900000223
a symbol representing the definition of the variable,
Figure BDA00027116090900000214
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 BDA00027116090900000215
Figure BDA00027116090900000216
Figure BDA00027116090900000217
wherein, T is the sum of the total weight of the components,
Figure BDA00027116090900000218
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 BDA00027116090900000219
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 BDA00027116090900000220
Figure BDA00027116090900000224
in the formula (I), the compound is shown in the specification,τ iand
Figure BDA00027116090900000221
respectively representing the ith abnormal signal
Figure BDA00027116090900000222
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 BDA0002711609090000031
is a parameter associated with the system parameter and the abnormal signalT、
Figure BDA0002711609090000032
oA relevant detection threshold;
by detecting function f0(k)、fj(τ i) And a detection threshold
Figure BDA0002711609090000033
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 BDA0002711609090000034
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 BDA0002711609090000035
Minimum time of dayj+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 BDA0002711609090000036
The calculation processes of (2) are respectively shown in formulas (9), (10) and (11):
Figure BDA0002711609090000037
Figure BDA0002711609090000038
Figure BDA0002711609090000039
wherein the content of the first and second substances,
Figure BDA00027116090900000310
ykis the system output at time k, yk-n+iThe system output at the time of k-n + i;
Figure BDA00027116090900000311
is j +τ iThe output of the system at the time of day,
Figure BDA00027116090900000312
is composed ofτ i-system output at time n + i;
Figure BDA00027116090900000313
wherein, variable
Figure BDA00027116090900000314
And
Figure BDA00027116090900000315
the calculation is respectively obtained through iterative calculation according to the following formula:
Figure BDA00027116090900000316
Figure BDA00027116090900000317
wherein the initial conditions are
Figure BDA00027116090900000318
And
Figure BDA00027116090900000319
and is
Figure BDA00027116090900000320
And
Figure BDA00027116090900000321
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 BDA00027116090900000322
Wherein z represents a variable of a characteristic polynomial, and I represents an identity matrix;
b1，b2，…，bnby the formula
Figure BDA00027116090900000323
Calculated, wherein:
Figure BDA0002711609090000041
F＝[(An-1)TCT(An-2)TCT…CT]T；
if conditions can be detected
Figure BDA0002711609090000042
If the requirement is met, all intermittent abnormal measurements appearing in the whole operation process of the system (1) can be detected, and a sequence of appearance time and disappearance time of all abnormal signals can be obtainedt i}i≥0And
Figure BDA0002711609090000043
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 BDA0002711609090000044
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;
parameter K is represented by
Figure BDA0002711609090000045
Given, among them, positive definite matrix P and matrix
Figure BDA0002711609090000046
Optimization problem constrained by a linear matrix inequality having
Figure BDA0002711609090000047
The solution of (a) gives:
Figure BDA0002711609090000048
Figure BDA0002711609090000049
Figure BDA00027116090900000410
wherein the content of the first and second substances,
Figure BDA00027116090900000411
Figure BDA00027116090900000412
a transpose of a matrix representing a symmetric position in the matrix inequality;
0＜μ1＜1，μ2> 0 is satisfied
Figure BDA00027116090900000413
The given parameter of (a);
optimization parameters in equation (15)
Figure BDA00027116090900000414
The suppression capability of the designed estimator on external noise is described, and parameters are optimized
Figure BDA00027116090900000415
Is a normal number; when optimizing the parameters
Figure BDA00027116090900000416
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 BDA00027116090900000417
Normal number
Figure BDA00027116090900000418
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 BDA0002711609090000051
in the formula (I), the compound is shown in the specification,
Figure BDA0002711609090000052
represents the system state xkIs determined by the estimated value of (c),
Figure BDA0002711609090000053
representing the signal z to be estimatedkIs determined by the estimated value of (c),
Figure BDA0002711609090000054
representing an estimate of the state of the system at the initial operating time,
Figure BDA0002711609090000055
indicates a set2-l∞An initial value of a state estimator (16);
l2-l∞the state estimator (16) 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 BDA0002711609090000056
Estimator parameter L (theta) used in iterationk) And system output ykThe detection result of the abnormal signal in (1) is correlated;
specifically, when no abnormal signal is detected from the system output at time k, at this time, the estimation is performedThe counter parameter is L (theta)k) K; conversely, when an abnormal signal is detected in the system output at time k, the estimator parameter L (θ)k) Setting zero;
l2-l∞the state estimator can guarantee zkIs estimated error of
Figure BDA0002711609090000057
The index is stable, and the index is stable,
Figure BDA0002711609090000058
at the same time satisfy
Figure BDA0002711609090000059
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 (16) estimates 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 l2-l∞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 BDA00027116090900000510
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 BDA00027116090900000511
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 BDA00027116090900000512
Amplitude of
Figure BDA00027116090900000513
A comparison graph of (A);
FIG. 4 is a diagram of actual state traces in an embodiment of the present invention
Figure BDA00027116090900000514
And its estimated trajectory
Figure BDA00027116090900000515
A comparison graph of (A);
FIG. 5 is a diagram of actual state traces in an embodiment of the present invention
Figure BDA00027116090900000516
And its estimated trajectory
Figure BDA00027116090900000517
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 BDA0002711609090000061
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 energyBounded process noise, vkThe measurement noise is indicative of the energy being bounded,
Figure BDA0002711609090000062
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 BDA0002711609090000063
in the formula (I), the compound is shown in the specification,
Figure BDA0002711609090000064
represents an upper bound on the magnitude of the process noise,
Figure BDA0002711609090000065
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 BDA0002711609090000066
Expressed as:
Figure BDA0002711609090000067
wherein (·) represents a step function,t iindicating an abnormal signal
Figure BDA0002711609090000068
The time of occurrence of the i-th time,
Figure BDA0002711609090000069
indicating an abnormal signal
Figure BDA00027116090900000610
The moment of disappearance of the i-th time,
Figure BDA00027116090900000611
indicating an abnormal signal
Figure BDA00027116090900000612
The magnitude of (c).
Order to
Figure BDA00027116090900000613
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 BDA00027116090900000614
abnormal signal indicating i-th occurrence
Figure BDA00027116090900000615
The duration of (d) then being:
Figure BDA00027116090900000616
wherein the content of the first and second substances,
Figure BDA00027116090900000617
a symbol representing the definition of the variable,
Figure BDA00027116090900000618
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 BDA0002711609090000071
Figure BDA0002711609090000072
Figure BDA0002711609090000073
wherein the content of the first and second substances,T，
Figure BDA0002711609090000074
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 BDA0002711609090000075
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 BDA0002711609090000076
Figure BDA0002711609090000077
in the formula (I), the compound is shown in the specification,τ iand
Figure BDA0002711609090000078
respectively representing the ith abnormal signal
Figure BDA0002711609090000079
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 BDA00027116090900000710
Is a parameter associated with the system parameter and the abnormal signalT、
Figure BDA00027116090900000711
oThe relevant detection threshold.
By detecting function f0(k)、fjAnd detection threshold
Figure BDA00027116090900000712
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 BDA00027116090900000713
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 BDA00027116090900000714
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 BDA00027116090900000715
The calculation processes of (2) are respectively shown in formulas (9), (10) and (11):
Figure BDA00027116090900000716
Figure BDA00027116090900000717
Figure BDA00027116090900000718
wherein the content of the first and second substances,
Figure BDA00027116090900000719
ykis the system output at time k, yk-n+iIs the system output at time k-n + i,
Figure BDA00027116090900000720
is j +τ iThe output of the system at the time of day,
Figure BDA00027116090900000721
is ti-system output at time n + i;
Figure BDA0002711609090000081
wherein, variable
Figure BDA0002711609090000082
And
Figure BDA0002711609090000083
the calculation is respectively obtained through iterative calculation according to the following formula:
Figure BDA0002711609090000084
Figure BDA0002711609090000085
wherein the initial conditions are
Figure BDA0002711609090000086
And
Figure BDA0002711609090000087
and is
Figure BDA0002711609090000088
And
Figure BDA0002711609090000089
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 BDA00027116090900000810
Wherein z represents a variable of a characteristic polynomial, and I represents an identity matrix;
b1，b2，…，bncan be represented by formula
Figure BDA00027116090900000811
The calculation gives, where:
Figure BDA00027116090900000812
F＝[(An-1)TCT (An-2)TCT … CT]T；
if conditions can be detected
Figure BDA00027116090900000817
If the requirement is met, all intermittent abnormal measurements appearing in the whole operation process of the system (1) can be detected, and a sequence of appearance time and disappearance time of all abnormal signals can be obtainedt i}i≥0And
Figure BDA00027116090900000813
s3, calculating l according to the result of intermittent abnormal measurement detection2-l∞The parameters of the state estimator, as shown in equation (12):
Figure BDA00027116090900000814
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, when l2-l∞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, when l2-l∞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 BDA00027116090900000815
Given, among them, positive definite matrix P and matrix
Figure BDA00027116090900000816
Optimization problem constrained by a linear matrix inequality having
Figure BDA0002711609090000091
The solution of (a) gives:
Figure BDA0002711609090000092
Figure BDA0002711609090000093
Figure BDA0002711609090000094
wherein the content of the first and second substances,
Figure BDA0002711609090000095
Figure BDA0002711609090000096
a transpose of a matrix representing a symmetric position in the matrix inequality;
0＜μ1＜1，μ2> 0 is satisfied
Figure BDA0002711609090000097
Given parameters of (1).
Optimization parameters in equation (15)
Figure BDA0002711609090000098
Depicting the designed l2-l∞The suppression capability of the estimator to the external noise and the optimization parameter
Figure BDA0002711609090000099
Is a normal number; when optimizing parametersNumber of
Figure BDA00027116090900000910
At maximum, represents the designed l2-l∞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 BDA00027116090900000911
Normal number
Figure BDA00027116090900000912
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 BDA00027116090900000913
in the formula (I), the compound is shown in the specification,
Figure BDA00027116090900000914
represents the system state xkIs determined by the estimated value of (c),
Figure BDA00027116090900000915
representing the signal z to be estimatedkIs determined by the estimated value of (c),
Figure BDA00027116090900000916
which represents the initial state of the system and,
Figure BDA00027116090900000917
indicates a set2-l∞Initial values for a state estimator (16).
The estimator (16) 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 BDA00027116090900000918
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 l2-l∞The state estimator parameter L (θ)k) K; conversely, when an abnormal signal is detected in the system output at time k, at which time l2-l∞The state estimator parameters are zeroed out.
Design of2-l∞The state estimator can guarantee zkIs estimated error of
Figure BDA00027116090900000919
Stable index while satisfying
Figure BDA00027116090900000920
When the performance, namely the noise energy, is bounded, the estimation error amplitude of the signal to be estimated is bounded, namely:
Figure BDA00027116090900000921
wherein the content of the first and second substances,
Figure BDA00027116090900000922
gamma is the optimized interference rejection level (when optimizing the parameters)
Figure BDA00027116090900000923
At maximum, the parameter γ is minimum).
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.
Aiming at the state estimation problem of the industrial system influenced by external noise and abnormal signals intermittently generated, the method 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 l related to the detection result of the abnormal signals2-l∞EstimatingWhen the system output contains abnormal signals, the estimator can ensure a good suppression effect on the bounded noise of the external energy, and realize more accurate state estimation.
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 BDA0002711609090000101
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 BDA0002711609090000102
Track of actual state
Figure BDA0002711609090000103
By contrast, as shown in FIG. 4, the solid line in FIG. 4 is the actual state trace
Figure BDA0002711609090000104
The dotted line is the state estimation trajectory
Figure BDA0002711609090000105
As can be seen from FIG. 4, the state estimation trajectory obtained by the method of the present invention
Figure BDA0002711609090000106
Track of actual state
Figure BDA0002711609090000107
The goodness of fit is high.
The invention also provides a state estimation track obtained by the method
Figure BDA0002711609090000108
Track of actual state
Figure BDA0002711609090000109
In contrast, as in fig. 5, the solid line in fig. 5 is the actual state trajectory
Figure BDA00027116090900001010
The dotted line is the state estimation trajectory
Figure BDA00027116090900001011
As can be seen from fig. 5, the present inventionState estimation trajectory obtained by bright method
Figure BDA00027116090900001012
Track of actual state
Figure BDA00027116090900001013
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 FDA0002711609080000011
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 FDA0002711609080000012
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 FDA0002711609080000013
in the formula (I), the compound is shown in the specification,
Figure FDA0002711609080000014
represents an upper bound on the magnitude of the process noise,
Figure FDA0002711609080000015
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 FDA0002711609080000016
Expressed as:
Figure FDA0002711609080000017
wherein (·) represents a step function,t iindicating an abnormal signal
Figure FDA0002711609080000018
The time of occurrence of the i-th time,
Figure FDA0002711609080000019
indicating an abnormal signal
Figure FDA00027116090800000110
The moment of disappearance of the i-th time,
Figure FDA00027116090800000111
indicating an abnormal signal
Figure FDA00027116090800000112
The magnitude of amplitude of (d);
order to
Figure FDA00027116090800000113
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 FDA00027116090800000114
abnormal signal indicating i-th occurrence
Figure FDA00027116090800000115
The duration of (d) then being:
Figure FDA00027116090800000116
wherein the content of the first and second substances,
Figure FDA00027116090800000117
a symbol representing the definition of the variable,
Figure FDA00027116090800000118
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 FDA0002711609080000021
Figure FDA0002711609080000022
Figure FDA0002711609080000023
wherein the content of the first and second substances,T，
Figure FDA0002711609080000024
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 FDA0002711609080000025
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 FDA0002711609080000026
Figure FDA0002711609080000027
in the formula (I), the compound is shown in the specification,τ iand
Figure FDA0002711609080000028
respectively representing the ith abnormal signal
Figure FDA0002711609080000029
N represents the dimension of the system state; f. of0(k) A detection function indicating the occurrence time of the abnormal signal; f. ofi(τ i) A detection function for the disappearance moment of the abnormal signal;
Figure FDA00027116090800000210
is a parameter associated with the system parameter and the abnormal signalT、
Figure FDA00027116090800000211
oA relevant detection threshold;
by detecting function f0(k)、fj(τ i) And a detection threshold
Figure FDA00027116090800000212
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 FDA00027116090800000213
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 FDA00027116090800000214
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 FDA00027116090800000215
The calculation processes of (2) are respectively shown in formulas (9), (10) and (11):
Figure FDA00027116090800000216
Figure FDA00027116090800000217
Figure FDA00027116090800000218
wherein the content of the first and second substances,
Figure FDA00027116090800000219
ykis the system output at time k, yk-n+iThe system output at the time of k-n + i;
Figure FDA00027116090800000220
is j +τ iThe output of the system at the time of day,
Figure FDA00027116090800000221
is composed ofτ i-system output at time n + i;
Figure FDA00027116090800000222
wherein, variable
Figure FDA0002711609080000031
And
Figure FDA0002711609080000032
the calculation is respectively obtained through iterative calculation according to the following formula:
Figure FDA0002711609080000033
Figure FDA0002711609080000034
wherein the initial conditions are
Figure FDA0002711609080000035
And
Figure FDA0002711609080000036
and is
Figure FDA0002711609080000037
And
Figure FDA0002711609080000038
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 FDA0002711609080000039
Wherein z represents a variable of a characteristic polynomial, and I represents an identity matrix;
b1，b2，…，bnby the formula
Figure FDA00027116090800000310
Calculated, wherein:
Figure FDA00027116090800000311
F＝[(An-1)TCT (An-2)TCT…CT]T；
if conditions can be detected
Figure FDA00027116090800000312
If the requirement is met, all intermittent abnormal measurements appearing in the whole operation process of the system (1) can be detected, and a sequence of appearance time and disappearance time of all abnormal signals can be obtainedt i}i≥0And
Figure FDA00027116090800000313
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 FDA00027116090800000314
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;
parameter K is represented by
Figure FDA00027116090800000315
Given, among them, positive definite matrix P and matrix
Figure FDA00027116090800000316
Advantage constrained by a linear matrix inequality havingProblem of chemical conversion
Figure FDA00027116090800000317
The solution of (a) gives:
Figure FDA0002711609080000041
Figure FDA0002711609080000042
Figure FDA0002711609080000043
wherein the content of the first and second substances,
Figure FDA0002711609080000044
Figure FDA0002711609080000045
a transpose of a matrix representing a symmetric position in the matrix inequality;
0＜μ1＜1，μ2> 0 is satisfied
Figure FDA0002711609080000046
The given parameter of (a);
optimization parameters in equation (15)
Figure FDA0002711609080000047
The suppression capability of the designed estimator on external noise is described, and parameters are optimized
Figure FDA0002711609080000048
Is a normal number; when optimizing the parameters
Figure FDA0002711609080000049
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 FDA00027116090800000410
Normal number
Figure FDA00027116090800000411
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 FDA00027116090800000412
in the formula (I), the compound is shown in the specification,
Figure FDA00027116090800000413
represents the system state xkIs determined by the estimated value of (c),
Figure FDA00027116090800000414
representing the signal z to be estimatedkIs determined by the estimated value of (c),
Figure FDA00027116090800000415
representing an estimate of the state of the system at the initial operating time,
Figure FDA00027116090800000416
indicates a set2-l∞An initial value of a state estimator (16);
l2-l∞the state estimator (16) 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 FDA00027116090800000417
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;
l2-l∞the state estimator can guarantee zkIs estimated error of
Figure FDA00027116090800000418
The index is stable, and the index is stable,
Figure FDA00027116090800000419
at the same time satisfy
Figure FDA00027116090800000420
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 (16) estimates the state of the system to obtain a state estimation value of the system.
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