CN112965461B - Motor system fault estimation method based on minimum conservative interval filtering - Google Patents

Motor system fault estimation method based on minimum conservative interval filtering Download PDF

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CN112965461B
CN112965461B CN202110174617.5A CN202110174617A CN112965461B CN 112965461 B CN112965461 B CN 112965461B CN 202110174617 A CN202110174617 A CN 202110174617A CN 112965461 B CN112965461 B CN 112965461B
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fault
motor
interval
motor system
moment
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CN112965461A (en
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王子赟
张梦迪
王艳
张梓蒙
纪志成
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Jiangnan University
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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
    • 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
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/34—Testing dynamo-electric machines
    • 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

Abstract

The invention discloses a motor system fault estimation method based on minimum conservative interval filtering, and belongs to the technical field of fault estimation. The method has the advantages that the unknown and bounded noise is represented by the fully-symmetrical multi-cell body, so that the practicability and the accuracy rate of the method are increased; designing a dynamic interval observer according to the reconstructed motor model, and designing the dynamic gain of the interval observer by minimizing the state conservatism of the system to realize the estimation of the observer fault interval with the minimum conservatism; designing a set inverse shrinkage filtering problem of the fault, and further shrinking an observer fault estimation interval by utilizing vector Boolean operation and fractal dimension sequential operation to be closer to a filtering fault estimation interval of a real fault value; meanwhile, the computational complexity of the solution method of the integrated inverse shrinkage filtering problem is obviously less than that of the most widely used solution method at present; compared with the existing fault estimation method, the method can more efficiently estimate the more compact fault interval in real time, and provides guarantee for the performance supervision of the motor system.

Description

Motor system fault estimation method based on minimum conservative interval filtering
Technical Field
The invention relates to a motor system fault estimation method based on minimum conservative interval filtering, and belongs to the technical field of fault estimation.
Background
For increasingly integrated control systems, the occurrence of faults can have a serious impact on production and life. Therefore, the method has important theoretical and practical significance for the research of system faults. Fault estimation is used to reflect the severity of a fault and is an important component of the fault diagnosis task.
Due to various uncertain factors such as noise and the like existing in the actual operation of the system, an accurate system model or the statistical characteristics of the noise cannot be obtained, and further the fault estimation result is inaccurate. The method for filtering the set members uses geometric bodies such as intervals, ellipsoids, multicellular bodies and the like to describe the uncertain parts in the system, thereby effectively solving the problem. However, such methods tend to have low accuracy or high computational complexity.
And setCompared with the member filtering method, the interval observer has higher calculation efficiency and is widely applied to various systems. For the study of interval observers, most methods are through coordinate transformation, H∞The interval estimation value is obtained by the criterion and the like, and the conservative property of the estimation result is large and cannot be ignored.
Disclosure of Invention
In order to estimate a more compact fault interval in real time more efficiently, the invention provides a motor system fault estimation method based on minimum conservative interval filtering, which comprises the following steps:
the method comprises the following steps: establishing a discrete model of a motor system;
step two: obtaining a reconstructed motor model without a fault value according to the discrete model of the motor system;
step three: designing a minimum conservative interval observer, and acquiring an observer state estimation interval and an observer fault estimation interval of the motor system at the moment k;
step four: designing a set inverse shrinkage filtering problem of a fault according to output data obtained under the actual operation condition of the motor at the moment k +1 and an observer state estimation interval of a motor system at the moment k; the output data obtained under the actual operation condition of the motor system at the moment of k +1 is a vector consisting of the motor angular position, the motor rotating speed and the armature current which are obtained by actual measurement;
step five: and solving the problem of inverse shrinkage filtering of the fault set, and obtaining a filtering fault estimation interval of the motor system at the moment k.
Optionally, the discrete model of the motor system established in the first step is as follows:
Figure BDA0002935154610000011
wherein the content of the first and second substances,
Figure BDA0002935154610000021
the state vector of the motor system at the moment k is represented, and the state vector of the motor system at the moment k is a vector formed by a real motor angular position, a motor rotating speed and an armature current;
Figure BDA0002935154610000022
the input vector of the motor system at the moment k is represented, and the input vector of the motor system at the moment k is a voltage value applied to the motor at the moment k;
Figure BDA0002935154610000023
the output vector of the motor system at the moment k is represented, and the output vector of the motor system at the moment k is a vector consisting of a motor angular position, a motor rotating speed and an armature current which are obtained through measurement respectively;
a represents a state space matrix, B represents an input matrix, C represents an output matrix, D represents a process noise action matrix, E represents a measurement noise action matrix, and F represents a fault action matrix;
wk∈<0,W>representing an unknown but bounded process noise vector of the motor system at time k, W representing a cutoff value of the process noise vector; v. ofk∈<0,V>An unknown but bounded measurement noise vector representing the motor system at time k, V representing the cutoff value of the measurement noise vector;
Figure BDA0002935154610000024
indicating an additive failure of the motor system at time k.
Optionally, the second step: obtaining a reconstructed motor model without fault values from a discrete model of the motor system comprises:
obtaining additive fault f of motor system at moment k according to formula (2)kExpression (c):
fk＝Of(yk+1-C(Axk+Buk+Dwk)-Evk+1) (3)
wherein the intermediate variable Of＝((CF)TCF)-1(CF)T；
Substituting the formula (3) into the formula (2) to obtain a reconstructed motor model without a fault value as follows:
Figure BDA0002935154610000025
wherein the content of the first and second substances,
Figure BDA0002935154610000026
optionally, the third step: designing a minimum conservative interval observer, and acquiring an observer state estimation interval and an observer fault estimation interval of the motor system at the moment k comprises the following steps:
designing a dynamic interval observer according to equation (4):
Figure BDA0002935154610000027
wherein the content of the first and second substances,
Figure BDA0002935154610000028
represents the observed state of the motor system at time k, LkRepresenting the observer gain of the motor system at time k;
determining the state error e of the motor system at the moment k +1 according to the formula (4) and the formula (5)k+1：
Figure BDA0002935154610000029
ek+1Using a holosymmetric multicellular body<0,Hk+1>Denotes, a fully symmetrical multicellular body<0,Hk+1>Generating matrix Hk+1Expressed as:
Figure BDA00029351546100000210
e0the state error of the motor system at the initial moment is represented by a full-symmetrical multi-cell body<0,H0>Is represented by H0Representing a fully symmetric multicellular body<0,H0>Generating a matrix;
of observer state estimation interval of motor system at time k +1Conservative conxk+1Expressed as:
Figure BDA0002935154610000031
solving the optimization problem shown in equation (9):
Lk＝argminconxk+1 (9)
obtaining the minimum conservative observer gain L of the motor system at the moment kkComprises the following steps:
Figure BDA0002935154610000032
determining an observer state estimation interval of the motor system at the time k according to the equations (5), (6) and (7)
Figure BDA00029351546100000318
Upper and lower bounds of (c):
Figure BDA0002935154610000033
wherein the content of the first and second substances,
Figure BDA0002935154610000034
represents the upper bound of the observer state estimation interval of the electric machine system at time k,
Figure BDA0002935154610000035
represents the lower bound of the observer state estimation interval of the electric machine system at time k,
Figure BDA0002935154610000036
an upper bound representing the state error of the motor system at time k,e ka lower bound representing a state error of the motor system at time k;
additive failure f of the motor system at time k according to equation (3)kExpressed as:
Figure BDA0002935154610000037
wherein the content of the first and second substances,
Figure BDA0002935154610000038
represents a fault observation of the motor system at time k,
Figure BDA0002935154610000039
representing the fault error of the motor system at the moment k;
fault error of motor system at time k
Figure BDA00029351546100000310
Composed of a plurality of cells in full symmetry
Figure BDA00029351546100000311
Shows, a full symmetry of the multicellular
Figure BDA00029351546100000312
Generating matrix of
Figure BDA00029351546100000313
Expressed as:
Figure BDA00029351546100000314
Figure BDA00029351546100000315
the fault error of the motor system at the initial moment is represented by a full-symmetrical multi-cell body
Figure BDA00029351546100000316
Represents;
determining observer fault estimation interval of motor system at time k according to equation (12) and equation (13)
Figure BDA00029351546100000317
Upper and lower bounds of (c):
Figure BDA0002935154610000041
wherein the content of the first and second substances,
Figure BDA0002935154610000042
represents the upper bound of the observer fault estimation interval of the electric machine system at time k,
Figure BDA0002935154610000043
represents the upper bound of the observer fault estimation interval of the electric machine system at time k,
Figure BDA0002935154610000044
an upper bound representing the fault error of the motor system at time k,
Figure BDA0002935154610000045
representing the lower bound of the fault error of the motor system at time k.
Optionally, the fourth step: according to output data obtained under the actual operation condition of the motor at the moment k +1 and an observer state estimation interval of a motor system at the moment k, designing a set of inverse shrinkage filtering problems of faults comprises the following steps:
designing a set inverse shrinkage filtering problem of a fault:
Figure BDA0002935154610000046
wherein the content of the first and second substances,
Figure BDA0002935154610000047
and represents a filtering fault estimation interval of the motor system at the moment k, wherein O is CF,
Figure BDA0002935154610000048
yk+1represents the output vector of the motor system at the time k +1, [ w ]k]Represents the process noise interval of the motor system at time k, [ v ]k+1]And the measurement noise interval of the motor system at the moment k +1 is shown.
Optionally, the fifth step: solving the problem of inverse shrinkage filtering of a fault set, and acquiring a filtering fault estimation interval of the motor system at the moment k comprises the following steps:
observer fault estimation interval of motor system at selected k time
Figure BDA0002935154610000049
As the initial interval box, it is expressed in the form of a row vector and is written as
Figure BDA00029351546100000410
Using the test function shown in the following equation (16)
Figure BDA00029351546100000411
Searching a solution set:
Figure BDA00029351546100000412
wherein in, out and eps represent Boolean vectors, and when the specified condition is satisfied, the values thereof take 1, and when the specified condition is not satisfied, the values thereof take 0,
Figure BDA00029351546100000413
to represent
Figure BDA00029351546100000414
Vectors formed by the maximum widths of the represented interval boxes, wherein epsilon represents the precision of the solution set;
Figure BDA00029351546100000415
vector groups composed of row vector forms representing interval boxes belonging to the solution set;
Figure BDA00029351546100000416
vector groups composed of row vector forms representing interval boxes not belonging to the solution set;
Figure BDA00029351546100000417
the vector group is composed of row vector forms of interval boxes which have partial intersection with the solution set and have the maximum width smaller than the precision epsilon;
Figure BDA00029351546100000418
the vector group is composed of row vector forms of interval boxes which have partial intersection with the solution set and have the maximum width larger than the precision epsilon;
cyclic search, to search each time
Figure BDA0002935154610000051
The corresponding interval boxes are divided into new interval boxes along the first dimension two, and all the new interval boxes form a new vector group
Figure BDA0002935154610000052
When in use
Figure BDA0002935154610000053
When the vector is empty, all vectors searched in the whole process are grouped
Figure BDA0002935154610000054
Form a new set of vectors
Figure BDA0002935154610000055
If additive failure of the motor system fkIs equal to 1, and is,
Figure BDA0002935154610000056
the corresponding interval box is a filtering fault estimation interval at the time of k;
if additive failure of the motor system fkIs greater than 1, and the dimension m of (a),
Figure BDA0002935154610000057
the corresponding interval box is the first dimension fault estimation interval at the moment k, the rootTest function shown by
Figure BDA0002935154610000058
Figure BDA0002935154610000059
Continuing along the ith dimension in turn
Figure BDA00029351546100000510
Searching solution set in corresponding interval box to obtain vector group
Figure BDA00029351546100000511
The corresponding interval box is the filter fault estimation interval at time k, where i is 2,3, …, m.
The fault estimation system comprises a computer, a current sensing amplifier and an incremental encoder, wherein the current sensing amplifier is used for measuring armature current when the direct current servo motor operates, and the incremental encoder is used for measuring the angular position and the rotating speed of the motor.
Optionally, when the fault estimation system performs fault estimation on the motor, firstly, the current sensing amplifier measures the armature current of the dc servo motor during operation, the incremental encoder measures the angular position of the motor and the rotational speed of the motor at the same time to form an output vector of the motor, and the dc voltmeter obtains the voltage value applied to the motor as the input vector of the motor.
Optionally, the fault estimation system is configured to detect an additive fault of the electric machine.
Optionally, when the fault estimation system performs fault estimation on the motor, the problem of set inverse shrinkage filtering of the fault is designed, and the fault estimation interval of the observer is further shrunk by using a vector boolean operation and a fractal dimension sequential operation method.
The invention has the beneficial effects that:
the unknown and bounded noise is represented by adopting the full-symmetry multilocular body, so that the practicability and the accuracy of the fault estimation method are improved; designing a dynamic interval observer according to the reconstructed motor model, and designing the dynamic gain of the interval observer by minimizing the state conservatism of the system to realize the estimation of the observer fault interval with the minimum conservatism; designing a set inverse shrinkage filtering problem of the fault, and further shrinking an observer fault estimation interval by using a vector Boolean operation and a dimension-division sequential operation method to be closer to a filtering fault estimation interval of a real fault value; the computational complexity of the solution method for the set inverse shrinkage filtering problem provided by the application is obviously less than that of the most widely used solution method at present, and the computational power requirement on a hardware processor is reduced; compared with the existing fault estimation method, the method can more efficiently estimate the more compact fault interval in real time, and provides guarantee for the performance supervision of the motor system.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flowchart of a method for estimating a fault of a motor system based on minimum conservative interval filtering, disclosed in an embodiment of the present invention.
Fig. 2 is a schematic diagram of the fault estimation result of the motor applying the fault signal and adopting the method of the present invention compared with the fault estimation result of the existing method in one embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The first embodiment is as follows:
the embodiment provides a motor system fault estimation method based on minimum conservative interval filtering, and with reference to fig. 1, the method includes:
the method comprises the following steps: establishing a discrete model of a motor system;
step two: obtaining a reconstructed motor model without a fault value according to the discrete model of the motor system;
step three: designing a minimum conservative interval observer, and acquiring an observer state estimation interval and an observer fault estimation interval of the motor system at the moment k;
step four: designing a set inverse shrinkage filtering problem of a fault according to output data obtained under the actual operation condition of the motor at the moment k +1 and an observer state estimation interval of a motor system at the moment k; the output data obtained under the actual operation condition of the motor system at the moment of k +1 is a vector consisting of the motor angular position, the motor rotating speed and the armature current which are obtained by actual measurement;
step five: solving the problem of inverse shrinkage filtering of a fault set, and obtaining a filtering fault estimation interval of the motor system at the moment k; when the problem of inverse contraction filtering of the fault set is solved, the fault estimation interval of the observer is further contracted by utilizing a vector Boolean operation method and a dimension-division sequential operation method, and the filtering fault estimation interval is closer to the filtering fault estimation interval of a real fault value.
Example two
The embodiment provides a motor system fault estimation method based on minimum conservative interval filtering, which is applied to a direct-current servo motor as an example, and the method comprises the following steps:
the method comprises the following steps: acquiring armature current, a motor angular position and motor rotating speed when the direct current servo motor operates; establishing a system model of the direct current servo motor;
specifically, the MAX472 current sensing amplifier is used for measuring the armature current when the DC servo motor operates, and the incremental encoder is used for simultaneously measuring the angular position of the motor and the rotating speed of the motor.
The control computer is connected with the current sensor, the encoder and the direct current servo motor through the special I/O board and the power interface, and a system model of the direct current servo motor is established:
Figure BDA0002935154610000071
where u denotes a voltage value of a voltage source applied to the dc servomotor, i denotes an armature current, v denotes a motor rotation speed, θ denotes a dc servomotor angular position, J denotes an armature moment of inertia, b denotes a friction coefficient, K denotes a torque constant and a back electromotive force constant of the dc servomotor, L denotes an inductance, and R denotes a resistance.
And (3) utilizing MATLAB to carry out parameter identification to obtain: j is 0.0985kg m2B is 0.1482N · m · s, K is 0.4901V · s/rad, L is 1.3726H, R is 0.0062 Ω, and the sampling time T issTaking 0.1s, discretizing by utilizing a forward Euler method to obtain a discrete model of the direct current servo motor:
Figure BDA0002935154610000072
wherein the content of the first and second substances,
Figure BDA0002935154610000073
the state vector of the motor at the moment k is represented, and the state vector of the motor at the moment k is a vector formed by a real motor angular position, a motor rotating speed and an armature current;
Figure BDA0002935154610000074
the input vector of the motor at the moment k is represented, and the input vector of the motor at the moment k is a voltage value applied to the motor at the moment k;
Figure BDA0002935154610000075
the method comprises the steps that an output vector of a motor at the moment k is represented, and the output vector of the motor at the moment k is a vector formed by a motor angular position, a motor rotating speed and an armature current which are obtained through measurement; a represents a state space matrix, B represents an input matrix, C represents an output matrix, D represents a process noise action matrix, E represents a measurement noise action matrix, F represents a fault action matrix, wk∈<0,W>Representing an unknown but bounded process noise vector, v, of the motor system at time kk∈<0,V>Unknown but bounded representation of a motor system at time kThe measured noise vector of (a) is,
Figure BDA0002935154610000076
indicating an additive failure.
Step two: according to the discrete model of the direct current servo motor established in the step one, the motor fault f at the moment k is obtainedkExpression (c):
fk＝Of(yk+1-C(Axk+Buk+Dwk)-Evk+1) (3)
wherein, Of＝((CF)TCF)-1(CF)T(ii) a T represents transposition;
substituting formula (3) into formula (2) to obtain a reconstructed motor model without fault values:
Figure BDA0002935154610000081
wherein the content of the first and second substances,
Figure BDA0002935154610000082
step three: designing a dynamic interval observer according to equation (4):
Figure BDA0002935154610000083
wherein the content of the first and second substances,
Figure BDA0002935154610000084
indicating the observed state of the motor at time k, LkAn observer gain representing the motor at time k;
determining the state error e of the motor at the moment k +1 according to the formula (4) and the formula (5)k+1：
Figure BDA0002935154610000085
ek+1Using a holosymmetric multicellular body<0,Hk+1>It is shown that,wherein
Figure BDA0002935154610000086
e0Representing the state error of the motor at the initial moment, consisting of a fully symmetrical multi-cell body<0,H0>Represents;
conservative conx of observer state estimation interval at time k +1k+1Expressed as:
Figure BDA0002935154610000087
solving an optimization problem:
Lk＝argminconxk+1 (9)
get the minimum conservative observer gain:
Figure BDA0002935154610000088
determining an observer state estimation interval of the motor at the time k according to the formula (5), the formula (6) and the formula (7)
Figure BDA0002935154610000089
Upper and lower bounds of (c):
Figure BDA00029351546100000810
wherein the content of the first and second substances,
Figure BDA00029351546100000811
represents the upper bound of the observer state estimation interval,
Figure BDA00029351546100000812
represents the lower bound of the observer state estimation interval,
Figure BDA00029351546100000813
indicating a stateThe upper bound of the error is the upper bound,e ka lower bound representing a state error;
according to equation (3), motor failure at time kkCan be expressed as:
Figure BDA00029351546100000814
wherein the content of the first and second substances,
Figure BDA0002935154610000091
indicating the fault observation at time k,
Figure BDA0002935154610000092
indicating a fault error at time k;
fault at time k
Figure BDA0002935154610000093
Error is composed of multiple cells
Figure BDA0002935154610000094
Is shown in which
Figure BDA0002935154610000095
Figure BDA0002935154610000096
Indicating the fault error at the initial moment, from a fully symmetrical multicellular body
Figure BDA0002935154610000097
Represents;
determining observer fault estimation interval at k-time according to equations (12) and (13)
Figure BDA0002935154610000098
Upper and lower bounds of (c):
Figure BDA0002935154610000099
wherein the content of the first and second substances,
Figure BDA00029351546100000910
represents an upper bound on the observer fault estimation interval,
Figure BDA00029351546100000911
represents an upper bound on the observer fault estimation interval,
Figure BDA00029351546100000912
an upper bound for the fault error is indicated,
Figure BDA00029351546100000913
a lower bound representing a fault error;
step four: according to output data obtained under the actual operation condition of the motor at the moment k +1 and a state estimation interval of an observer at the moment k, designing an inverse shrinkage filtering problem of a fault:
Figure BDA00029351546100000914
wherein the content of the first and second substances,
Figure BDA00029351546100000915
a filter failure estimation interval representing the time k, O ═ CF,
Figure BDA00029351546100000916
yk+1represents the output vector of the motor at time k +1, [ w ]k]Represents the process noise interval at time k, [ v ]k+1]Represents the measurement noise interval at time k + 1.
Step five: solving the problem of inverse shrinkage filtering of the fault set in the step four;
observer fault estimation interval of k moments is selected
Figure BDA00029351546100000923
As initial interval box, expressed in the form of row vectorIs marked as
Figure BDA00029351546100000917
Using a test function as shown below
Figure BDA00029351546100000918
Searching a solution set:
Figure BDA00029351546100000919
wherein in, out and eps represent Boolean vectors, and when the specified condition is met, the values of the Boolean vectors are 1, and when the specified condition is not met, the values of the Boolean vectors are 0;
Figure BDA00029351546100000920
to represent
Figure BDA00029351546100000921
Vectors formed by the maximum widths of the represented interval boxes, wherein epsilon represents the precision of the solution set;
Figure BDA00029351546100000922
vector groups composed of row vector forms representing interval boxes belonging to the solution set;
Figure BDA0002935154610000101
vector groups composed of row vector forms representing interval boxes not belonging to the solution set;
Figure BDA0002935154610000102
the vector group is composed of row vector forms of interval boxes which have partial intersection with the solution set and have the maximum width smaller than the precision epsilon;
Figure BDA0002935154610000103
is shown andthe solution sets are vector groups formed by row vector forms of interval boxes with partial intersection and the maximum width larger than the precision epsilon;
cyclic search, to search each time
Figure BDA0002935154610000104
The corresponding interval boxes are divided into new interval boxes along the first dimension two to form a new vector group
Figure BDA0002935154610000105
When in use
Figure BDA0002935154610000106
When the vector is empty, all vectors searched in the whole process are grouped
Figure BDA0002935154610000107
Form a new set of vectors
Figure BDA0002935154610000108
E.g. if the motor fails fkIs equal to 1, and is,
Figure BDA0002935154610000109
the corresponding interval box is a filtering fault estimation interval at the time of k;
if the motor fails fkIs greater than 1, and the dimension m of (a),
Figure BDA00029351546100001010
the corresponding interval box is a first-dimension fault estimation interval at the moment k, and a test function shown in the following formula is used
Figure BDA00029351546100001011
Figure BDA00029351546100001012
Sequentially continuing along the i (i) 2, m) dimension
Figure BDA00029351546100001013
Searching solution set in corresponding interval box to obtain vector group
Figure BDA00029351546100001014
And the corresponding interval box is a filtering fault estimation interval at the moment k.
In order to verify that the method can effectively diagnose the fault, MATLAB software is specially adopted to simulate the fault diagnosis experiment of the direct current servo motor:
if the motor system has a fault of
Figure BDA00029351546100001015
Namely, the motor system fails at the moment when k is 101 and continues until the moment when k is 200; and in a preset time range, after the first step to the fifth step are executed, obtaining a fault estimation interval of the motor at each moment in the preset time range, and realizing fault estimation.
FIG. 2 shows the result of fault estimation using the method of the present invention and the prior art method using H∞A simulation diagram of the Fault Estimation result of the Fault Estimation method (refer to C.Martini nez Garc i a, V.Puig, C.M.Astorga-Zaragoza, et al.Robust Fault Estimation based on intersval Takagi-Sugeno Unknown Input observer.2018,51(24):508 and 514.).
As can be seen from FIG. 2, the prior art uses H∞The method for fault estimation by the criterion design interval observer and the method provided by the invention can realize interval estimation of the fault of the motor system, and the upper and lower boundaries of the estimated fault estimation interval always surround the true value of the fault no matter whether the fault occurs or not. But with the prior use of H∞Compared with the fault estimation interval obtained by the method for fault estimation by the criterion design interval observer, the width of the fault estimation interval obtained by the method provided by the invention is far smaller than that of the existing method, and the accuracy is improved by 77.4-89.1%.
In addition, the computational complexity of the solution method of the set inverse shrinkage filtering problem proposed by the present application is
Figure BDA0002935154610000111
The complexity is obviously less than 2N +1 (refer to Jaulin L, Walter E.set inversion via intersection-analysis for non-linear bound-optimization [ J ] for the most widely used solving method at present].Automatica,1993,29(4):1053-1064.)，
Figure BDA0002935154610000112
Is the total number of halves of the interval box, NiIs the number of halves of the interval box along the ith dimension,
Figure BDA0002935154610000113
is greater than and closest to NiThe integral multiple of 2 of +1, i is 1.
Some steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (8)

1. A motor system fault estimation method based on minimum conservative interval filtering is characterized by comprising the following steps:
the method comprises the following steps: establishing a discrete model of a motor system;
step two: obtaining a reconstructed motor model without a fault value according to the discrete model of the motor system;
step three: designing a minimum conservative interval observer, and acquiring an observer state estimation interval and an observer fault estimation interval of the motor system at the moment k;
step four: designing a set inverse shrinkage filtering problem of a fault according to output data obtained under the actual operation condition of the motor at the moment k +1 and an observer state estimation interval of a motor system at the moment k; the output data obtained under the actual operation condition of the motor system at the moment of k +1 is a vector consisting of the motor angular position, the motor rotating speed and the armature current which are obtained by actual measurement;
step five: solving the problem of inverse shrinkage filtering of a fault set, and obtaining a filtering fault estimation interval of the motor system at the moment k;
the discrete model of the motor system established in the first step is as follows:
Figure FDA0003387308340000011
wherein the content of the first and second substances,
Figure FDA0003387308340000012
the state vector of the motor system at the moment k is represented, and the state vector of the motor system at the moment k is a vector formed by a real motor angular position, a motor rotating speed and an armature current;
Figure FDA0003387308340000013
the input vector of the motor system at the moment k is represented, and the input vector of the motor system at the moment k is a voltage value applied to the motor at the moment k;
Figure FDA0003387308340000014
the output vector of the motor system at the moment k is represented, and the output vector of the motor system at the moment k is a vector consisting of a motor angular position, a motor rotating speed and an armature current which are obtained through measurement respectively;
a represents a state space matrix, B represents an input matrix, C represents an output matrix, D represents a process noise action matrix, E represents a measurement noise action matrix, and F represents a fault action matrix;
wk∈<0,W>representing an unknown but bounded process noise vector of the motor system at time k, W representing a cutoff value of the process noise vector; v. ofk∈<0,V>An unknown but bounded measurement noise vector representing the motor system at time k, V representing the cutoff value of the measurement noise vector;
Figure FDA0003387308340000015
indicating additive faults of the motor system at the moment k;
the second step is as follows: obtaining a reconstructed motor model without fault values from a discrete model of the motor system comprises:
obtaining additive fault f of motor system at moment k according to formula (2)kExpression (c):
fk＝Of(yk+1-C(Axk+Buk+Dwk)-Evk+1) (3)
wherein the intermediate variable Of＝((CF)TCF)-1(CF)T；
Substituting the formula (3) into the formula (2) to obtain a reconstructed motor model without a fault value as follows:
xk+1＝Axk+Buk+Fyk+1+Dwk-FEvk+1 (4)
wherein A is A-FOfCA，B＝B-FOfCB，D＝D-FOfCD，F＝FOf。
2. The method of claim 1, wherein the step three: designing a minimum conservative interval observer, and acquiring an observer state estimation interval and an observer fault estimation interval of the motor system at the moment k comprises the following steps:
designing a dynamic interval observer according to equation (4):
Figure FDA0003387308340000021
wherein the content of the first and second substances,
Figure FDA0003387308340000022
represents the observed state of the motor system at time k, LkMotor for indicating k timeObserver gain of the system;
determining the state error e of the motor system at the moment k +1 according to the formula (4) and the formula (5)k+1：
Figure FDA0003387308340000023
ek+1Using a holosymmetric multicellular body<0,Hk+1>Denotes, a fully symmetrical multicellular body<0,Hk+1>Generating matrix Hk+1Expressed as:
Hk+1＝[(A-LkC)Hk DW -LkEV -FEV] (7)
e0the state error of the motor system at the initial moment is represented by a full-symmetrical multi-cell body<0,H0>Is represented by H0Representing a fully symmetric multicellular body<0,H0>Generating a matrix;
conservative conx of observer state estimation interval of motor system at time k +1k+1Expressed as:
Figure FDA0003387308340000024
solving the optimization problem shown in equation (9):
Lk＝argminconxk+1 (9)
obtaining the minimum conservative observer gain L of the motor system at the moment kkComprises the following steps:
Figure FDA0003387308340000025
determining an observer state estimation interval of the motor system at the time k according to the equations (5), (6) and (7)
Figure FDA0003387308340000026
Upper and lower bounds of (c):
Figure FDA0003387308340000031
wherein the content of the first and second substances,
Figure FDA0003387308340000032
represents the upper bound of the observer state estimation interval of the electric machine system at time k,
Figure FDA0003387308340000033
represents the lower bound of the observer state estimation interval of the electric machine system at time k,
Figure FDA0003387308340000034
an upper bound representing the state error of the motor system at time k,e ka lower bound representing a state error of the motor system at time k;
additive failure f of the motor system at time k according to equation (3)kExpressed as:
Figure FDA0003387308340000035
wherein the content of the first and second substances,
Figure FDA0003387308340000036
represents a fault observation of the motor system at time k,
Figure FDA0003387308340000037
representing the fault error of the motor system at the moment k;
fault error of motor system at time k
Figure FDA0003387308340000038
Composed of a plurality of cells in full symmetry
Figure FDA0003387308340000039
Shows, a full symmetry of the multicellular
Figure FDA00033873083400000310
Generating matrix of
Figure FDA00033873083400000311
Expressed as:
Figure FDA00033873083400000312
Figure FDA00033873083400000313
the fault error of the motor system at the initial moment is represented by a full-symmetrical multi-cell body
Figure FDA00033873083400000314
Represents;
determining observer fault estimation interval [ f ] of motor system at time k according to equation (12) and equation (13)k o]Upper and lower bounds of (c):
Figure FDA00033873083400000315
wherein the content of the first and second substances,
Figure FDA00033873083400000316
represents the upper bound of the observer fault estimation interval of the electric machine system at time k,f k orepresents the lower bound of the observer fault estimation interval of the electric machine system at time k,
Figure FDA00033873083400000317
an upper bound representing the fault error of the motor system at time k,e k frepresenting the lower bound of the fault error of the motor system at time k.
3. The method of claim 2, wherein said step four: according to output data obtained under the actual operation condition of the motor at the moment k +1 and an observer state estimation interval of a motor system at the moment k, designing a set of inverse shrinkage filtering problems of faults comprises the following steps:
designing a set inverse shrinkage filtering problem of a fault:
[fk s]＝O-1[Πk] (15)
wherein, [ f ]k s]And represents a filtering fault estimation interval of the motor system at the moment k, wherein O is CF,
Figure FDA0003387308340000041
yk+1represents the output vector of the motor system at the time k +1, [ w ]k]Represents the process noise interval of the motor system at time k, [ v ]k+1]And the measurement noise interval of the motor system at the moment k +1 is shown.
4. The method of claim 3, wherein step five: solving the problem of inverse shrinkage filtering of a fault set, and acquiring a filtering fault estimation interval of the motor system at the moment k comprises the following steps:
selecting an observer fault estimation interval [ f ] of a motor system at the moment kk o]The initial interval box is expressed by a row vector and is marked as L 1 _；
Using a test function [ t ] shown in the following formula (16)](L1) Searching a solution set:
Figure FDA0003387308340000042
wherein in, out, eps represent Boolean vectors, and when the specified condition is satisfied, their values are 1, and when the specified condition is not satisfied, their values are 0, W (L)1) Represents L1Vectors formed by the maximum widths of the represented interval boxes, wherein epsilon represents the precision of the solution set;
L1(in) a vector group consisting of row vector forms of interval boxes belonging to the solution set;
L1(out) a set of vectors in the form of row vectors representing interval boxes not belonging to the solution set;
Figure FDA0003387308340000043
the vector group is composed of row vector forms of interval boxes which have partial intersection with the solution set and have the maximum width smaller than the precision epsilon;
Figure FDA0003387308340000044
the vector group is composed of row vector forms of interval boxes which have partial intersection with the solution set and have the maximum width larger than the precision epsilon;
cyclic search, to search each time
Figure FDA0003387308340000045
The corresponding interval boxes are divided into new interval boxes along the first dimension two, and all the new interval boxes form a new vector group L1；
When L is1When the vector is empty, all the vectors searched in the whole process are grouped into a group L1(in)、
Figure FDA0003387308340000046
Form a new vector set L2If additive failure of the motor system fkDimension m of equal to 1, L2The corresponding interval box is a filtering fault estimation interval at the time of k;
if additive failure of the motor system fkM is greater than 1, L2The corresponding interval box is a first-dimension fault estimation interval at the moment k, and a test function [ t ] shown in the following formula](Li)，
Figure FDA0003387308340000051
Sequentially continuing at L along the ith dimensioniSearching solution set in corresponding interval box to obtain directionQuantity group LmThe corresponding interval box is the filter fault estimation interval at time k, where i is 2,3, …, m.
5. A fault estimation system for fault estimation using the fault estimation method of any one of claims 1 to 4, the fault estimation system comprising a computer, a current sense amplifier for measuring armature current when the DC servo motor is running, and an incremental encoder for measuring motor angular position and motor speed.
6. The fault estimation system according to claim 5, wherein when the fault estimation system is used for estimating the fault of the motor, firstly, the armature current of the direct current servo motor during operation is measured through the current sensing amplifier, the angular position of the motor and the rotating speed of the motor are simultaneously measured through the incremental encoder to form an output vector of the motor, and a voltage value applied to the motor is obtained through the direct current voltmeter to serve as an input vector of the motor.
7. The fault estimation system of claim 5, wherein the fault estimation system is configured to detect an additive fault of the electric machine.
8. The fault estimation system according to claim 5, wherein when the fault estimation system is used for fault estimation of the motor, a set of inverse shrinkage filtering problems of faults are designed, and a fault estimation interval of the observer is further shrunk by using a vector Boolean operation method and a fractal dimension sequential operation method.
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