CN112305418B - Motor system fault diagnosis method based on mixed noise double filtering - Google Patents

Motor system fault diagnosis method based on mixed noise double filtering Download PDF

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CN112305418B
CN112305418B CN202011088531.2A CN202011088531A CN112305418B CN 112305418 B CN112305418 B CN 112305418B CN 202011088531 A CN202011088531 A CN 202011088531A CN 112305418 B CN112305418 B CN 112305418B
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CN112305418A (en
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王子赟
张梦迪
王艳
纪志成
张梓蒙
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Jiangnan University
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Abstract

The invention discloses a motor system fault diagnosis method based on mixed noise double filtering, and belongs to the technical field of fault diagnosis. According to the method, unknown but bounded noise is represented by a full-symmetry multicellular body, random noise is represented by Gaussian noise, a dynamic state observer of a motor system is designed by minimizing the derivative of an F norm and a covariance matrix trace of a full-symmetry multicellular body generating matrix, an optimal weight solution at each moment is obtained based on signal average power, and the dynamic gain of a state estimator is designed, so that the accuracy and the conservation of a state estimation interval are effectively reduced. Further, a confidence interval of the fault detection index is calculated based on the residual probability distribution function, so that efficient fault detection, fault identification and fault interval estimation of the actuator fault are realized; compared with the existing diagnosis method, the method has the advantages that the detection efficiency is higher, the occurrence of the fault can be detected more quickly, the condition of missed diagnosis does not occur, and the fault detection accuracy is higher.

Description

Motor system fault diagnosis method based on mixed noise double filtering
Technical Field
The invention relates to a motor system fault diagnosis method based on mixed noise double filtering, and belongs to the technical field of fault diagnosis.
Background
With the development of science and technology, highly integrated automation equipment can be widely applied to production and life, and a motor plays a vital role as an important component of the automation equipment. In order to ensure the normal operation of the automation equipment, the motor needs to be subjected to real-time and accurate fault diagnosis.
In the conventional fault diagnosis method, noise existing in the operation process of a motor system is generally assumed to be random in the diagnosis process and meet certain probability distribution, for example, methods such as kalman filtering and extended kalman filtering assume that the noise is zero mean gaussian white noise. However, it is difficult to obtain accurate statistical characteristics of the noise of the motor system in a complex actual operating environment, which results in inaccurate fault diagnosis results by using the conventional fault diagnosis method.
In order to solve the problem, researchers use the collective filtering method to describe system state data, measurement data and noise by space geometry such as intervals, ellipsoids, multicellular bodies and the like on the assumption that the system noise is unknown but bounded. But this approach to approximate description does not accurately represent the size of the feasible set. As the amount of calculation increases, the accumulation of errors reduces the susceptibility of the fault diagnosis method to motor faults.
In order to overcome the limitations of the filtering method, researches on the hybrid noise double filtering technology combining random and collective features are increasingly paid attention to in the field of fault diagnosis of motor systems. At present, some fault diagnosis researches on double filtering search a feasible set for describing a system state through a convex optimization problem and the like, but many optimization problems do not belong to or cannot be converted into the convex optimization problem, so that a situation of no solution may occur, and therefore the methods cannot be widely applied. In addition, some fault diagnosis researches related to double filtering are carried out, the same weight is selected in the diagnosis process to process mixed noise of various random and collective members, but various random noise and collective member noise in a complex actual operation environment cannot be the same, so that the diagnosis result of the fault diagnosis method is inaccurate.
Disclosure of Invention
In order to solve the problem of fault diagnosis by combining random and collective mixed noise double filtering, the invention provides a motor system fault diagnosis method based on mixed noise double filtering, which comprises the following steps:
the method comprises the following steps: establishing an unknown discrete motor model mixed with bounded noise and Gaussian noise;
step two: designing a dynamic state interval observer, and acquiring a state estimation interval of the motor system at the moment k;
step three: acquiring a measurement residual interval at the moment k according to an output vector obtained under the actual operation condition of the motor at the moment k; the output vector is a vector formed by the angular position of the motor, the rotating speed of the motor and the armature current obtained by measurement;
step four: acquiring upper and lower boundaries of a fault detection factor at the k moment according to the measurement residual interval at the k moment;
step five: and detecting whether the motor system has a fault according to the upper and lower bounds of the fault detection factor.
Optionally, the method further includes: and when the motor system is detected to be in fault, calculating a fault estimation interval at the moment k and judging the fault type of the motor system in fault.
Optionally, the discrete motor model of unknown but bounded noise mixed with gaussian noise established in the first step is:
Figure BDA0002721250250000021
wherein the content of the first and second substances,
Figure BDA0002721250250000022
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 BDA0002721250250000023
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 BDA0002721250250000024
motor for indicating k timeThe output vector of the motor at the moment k is a vector consisting of a motor angular position, a motor rotating speed and an armature current which are respectively and actually measured by a speed sensor, a position sensor and a current sensor;
a denotes a state space matrix, B denotes an input matrix, C denotes an output matrix, F denotes a malfunction matrix, wk∈<0,W>Representing an unknown but bounded process noise vector, v, of the motor system at time kk∈<0,V>An unknown but bounded measurement noise vector representing the motor system at time k,
Figure BDA0002721250250000025
a gaussian-distributed process noise vector representing the motor system at time k,
Figure BDA0002721250250000026
a gaussian-distributed measurement noise vector representing the motor system at time k,
Figure BDA0002721250250000027
indicating an additive failure.
Optionally, the second step: designing a dynamic state interval observer, and acquiring a state estimation interval of the motor system at the moment k comprises the following steps:
2.1 constructing a dynamic state interval observer:
Figure BDA0002721250250000028
wherein the content of the first and second substances,
Figure BDA0002721250250000029
indicating the observed state at time k, GkAn observer gain representing time k;
determining the state error at the time k +1 according to equations (3) and (4):
Figure BDA00027212502500000210
wherein z isk+1Representing the state error of an unknown but bounded portion of time k +1, from a fully symmetric multicellular body<0,Hk+1>Represents, generates a matrix Hk+1Comprises the following steps:
Hk+1＝[(A-GkC)Hk W -GkV] (6)
z0representing state errors of unknown but bounded parts of the initial moment, by a fully symmetrical multicellular body<0,H0>Is represented by H0A generator matrix representing a fully symmetric multicellular body;
gk+1indicating that the k +1 time obeys a Gaussian distribution
Figure BDA0002721250250000031
Partial state error, covariance matrix Pk+1Comprises the following steps:
Figure BDA0002721250250000032
g0indicating that the initial time obeys a Gaussian distribution
Figure BDA0002721250250000033
Partial state error, P0Representing a covariance matrix;
obtaining an optimum criterion J according to (6) and (7)kComprises the following steps:
Figure BDA0002721250250000034
wherein eta iskAn optimal weight coefficient representing the k time;
unknown but bounded noise wkAnd vkIs a bounded signal with average power equal to the sum of the squares of the respective signals, using a fully symmetric multi-cell body respectively<0,WWT>、<0,VVT>Represents; gaussian noise dkAnd ekThe average power of (a) is the respective covariance matrix;
the state error of the unknown but bounded portion is at time k ═ 1:
z1＝Az0+w0 (9)
wherein, w0Representing an unknown but bounded process noise vector of the motor system at the initial moment, the state error mean power of the unknown but bounded part being Pz1∈<0,Z1>Generating a matrix of
Figure BDA0002721250250000035
The state error of the gaussian uncertainty part is:
g1＝Ag0+d0 (10)
wherein d is0Representing the process noise vector of the motor system at the initial moment and obeying Gaussian distribution, and the state error average power of the Gaussian uncertain part is equal to the covariance matrix P of the state error average powerG1＝AP0AT+R；
The optimal weight coefficient at the moment when k is 1 is:
Figure BDA0002721250250000036
according to equation (6) and equation (7), the optimal weight coefficient at the time when k >1 is:
Figure BDA0002721250250000037
solving (8) to obtain observer gain Gk：
Figure BDA0002721250250000038
Wherein the content of the first and second substances,
Figure BDA0002721250250000039
Qηk＝(1-ηk)VVT+ηkQ；
2.2 determining the observer State estimation interval at the time k according to equations (4) and (5)
Figure BDA00027212502500000310
The upper and lower bounds of (A) are:
Figure BDA00027212502500000311
wherein the content of the first and second substances,
Figure BDA00027212502500000312
andz krespectively representing the upper and lower bounds of an unknown but bounded state error interval,
Figure BDA00027212502500000313
andg krepresenting the upper and lower bounds of the gaussian state error confidence interval, respectively.
Optionally, the third step: obtaining a measurement residual interval at the moment k according to a state vector obtained under the actual operation condition of the motor at the moment k, wherein the measurement residual interval comprises the following steps:
determining a measurement residual interval at time k:
[rk]＝yk-C[xk] (15)
wherein [ r ]k]Denotes the measurement residual interval at time k, ykAnd the state vector obtained under the actual operation condition of the motor at the moment k is shown.
Optionally, the fourth step: acquiring the upper and lower bounds of the fault detection factor at the k moment according to the measurement residual interval at the k moment, wherein the method comprises the following steps:
defining the fault detection factor at the moment k as:
Figure BDA0002721250250000041
wherein, p (r)k|fk) Representing the probability density function at the time of failure, p (r)k|fk0) represents the probability density function without failure;
from equations (3) and (5), the measurement residual at time k is expressed as:
Figure BDA0002721250250000042
wherein the content of the first and second substances,
Figure BDA0002721250250000043
central value, Γ, representing the measurement residual at time kk＝(A-Gk-1C)Γk-1+F，
Figure BDA0002721250250000044
Representing the unknown but bounded portion of the measurement residual at time k,
Figure BDA0002721250250000045
representing the Gaussian distribution obeying to the measured residual at the k time
Figure BDA0002721250250000046
Part of, covariance matrix
Figure BDA0002721250250000047
The measurement residuals at time k follow a gaussian distribution:
Figure BDA0002721250250000048
the upper bound of the fault detection factor is obtained from equations (14) and (15):
Figure BDA0002721250250000049
the lower bound is:
Figure BDA0002721250250000051
wherein the content of the first and second substances,
Figure BDA0002721250250000052
represents the upper bound of the measurement residual interval at time k, krrepresents the lower bound of the measurement residual interval at time k,
Figure BDA0002721250250000053
represents the upper bound of the fault estimation interval at time k,f krepresenting the lower bound of the fault estimation interval at the moment k;
solving an optimization problem:
Figure BDA0002721250250000054
obtaining an optimal solution of an upper boundary and a lower boundary of a fault estimation interval:
Figure BDA0002721250250000055
wherein the content of the first and second substances,
Figure BDA0002721250250000056
Figure BDA0002721250250000057
Figure BDA0002721250250000058
obtaining upper and lower bounds of the fault detection factor at the time k according to the formula (19), the formula (20) and the formula (22):
Figure BDA0002721250250000059
optionally, the fifth step: whether the motor system breaks down or not is detected according to the upper and lower bounds of the fault detection factor, and the method comprises the following steps:
calculating the midpoint of the fault detection factor interval
Figure BDA00027212502500000510
When the middle point of the fault detection factor interval at continuous Q moments meets
Figure BDA00027212502500000511
When the motor system is always in the right state, the motor system is judged to have a fault from the k-Q moment to the k moment, wherein lambdathrIs given a threshold value.
Optionally, when a fault of the motor system is detected, calculating a fault estimation interval at time k and determining a fault type of the fault of the motor system includes:
obtaining a fault interval of the motor system at the moment k according to the formula (22), wherein k < l, and l is the length of a given sliding window;
when k is larger than l, the fault interval of the motor system obtained by adopting a sliding window filtering method is as follows:
Figure BDA0002721250250000061
and searching for the type of the fault value within the fault estimation interval in the known fault types, and determining the fault type of the motor system.
The invention also provides a fault diagnosis system which adopts the fault diagnosis method to carry out fault diagnosis.
Optionally, the fault diagnosis system is provided with a speed sensor, a position sensor and a current sensor to measure the angular position of the motor, the rotating speed of the motor and the armature current.
The invention has the beneficial effects that:
according to the fault diagnosis method for the mixed noise motor system, through double filtering, unknown but bounded noise is represented by the full-symmetry multi-cell body, random noise is represented by Gaussian noise, a dynamic state observer of the motor system is designed by minimizing the derivative of the F norm and covariance matrix trace of a full-symmetry multi-cell body generating matrix, the optimal weight solution of each moment is obtained based on the signal average power, and the dynamic gain of the state estimator is designed, so that the estimated state interval is closer to the real state of the motor, and the accuracy and the conservation of the state estimation interval are effectively reduced. Further, a confidence interval of the fault detection index is calculated based on the residual probability distribution function, so that fault detection, fault identification and fault interval estimation of the actuator with high efficiency are realized; compared with the existing diagnosis method combining random and collective mixed noise double filtering, the method has the advantages of higher detection efficiency, capability of more quickly detecting the occurrence of the fault, no diagnosis missing condition and higher fault detection accuracy.
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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 diagnosing a fault of a motor system based on a mixed noise double filtering according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of the comparison between the fault detection result of the motor using the method of the present invention after applying a fault signal according to an embodiment of the present invention and the fault detection result of the conventional method.
Fig. 3 is a schematic diagram of a projection of a fault estimation interval on an X-Y plane during a motor fault diagnosis process disclosed in an embodiment of the present invention, wherein the fault type 1 is identified by using a double filtering algorithm of the present invention.
Fig. 4 is a schematic diagram of a projection of a fault estimation interval on an X-Z plane during a motor fault diagnosis process disclosed in an embodiment of the present invention, where the double filtering algorithm of the present invention is used to identify a fault type 1.
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 present embodiment provides a motor system fault diagnosis method based on mixed noise double filtering, please refer to fig. 1, the method includes:
the method comprises the following steps: establishing an unknown discrete motor model mixed with bounded noise and Gaussian noise;
step two: designing a dynamic state interval observer, and acquiring a state estimation interval of the motor system at the moment k;
step three: acquiring a measurement residual interval at the moment k according to an output vector obtained under the actual operation condition of the motor at the moment k; the output vector is a vector formed by the angular position of the motor, the rotating speed of the motor and the armature current obtained by measurement;
step four: acquiring upper and lower boundaries of a fault detection factor at the k moment according to the measurement residual interval at the k moment;
step five: detecting whether the motor system has faults according to the upper and lower bounds of the fault detection factor
Step six: and if the motor system fails, calculating a failure estimation interval at the moment k and judging the type of the failure of the motor system.
Example two:
in this embodiment, the method for diagnosing a fault of a motor system based on dual filtering of mixed noise provided by the present invention is described as an example when applied to a dc servo motor, and the method includes:
the method comprises the following steps: the armature current when the DC servo motor runs is measured by a MAX472 current sensing amplifier, and the angular position of the motor and the rotating speed of the motor are simultaneously measured by an incremental encoder. 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 BDA0002721250250000071
where u denotes a voltage value of a voltage source applied to the dc servomotor, i denotes an armature current, θ denotes an angular position of the dc servomotor, J denotes an armature moment of inertia, b denotes a friction coefficient, K denotes a torque constant and a counter electromotive force constant of the dc servomotor, L denotes an inductance, R denotes a resistance, and t denotes a time.
Before the discretization process, t represents a continuous time, and after the discretization, k represents a sampling time.
The state vector x defining the motor system model is composed of the motor angular position, the motor speed, and the armature current, i.e., x ═ θ, v, i]TThe input data is a voltage source u applied to the motor.
The system model of the dc servo motor in equation (1) is converted into:
Figure BDA0002721250250000081
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 · srad, L is 1.3726H, R is 0.0062 Ω, and the interval T between sampling times is taken after the formula (2) is substitutedsAnd (3) discretizing by using a forward Euler method to obtain a discrete model of the direct current servo motor, wherein the discretization is 0.1 s:
Figure BDA0002721250250000082
wherein the content of the first and second substances,
Figure BDA0002721250250000083
representing a state vector of the motor at the moment k;
Figure BDA0002721250250000084
an input vector representing the motor at the moment k, namely a voltage value applied to the motor;
Figure BDA0002721250250000085
the output vector of the motor at the moment k is represented, namely the measured angular position of the motor at the moment k, the motor rotating speed and the armature current; a represents a state space matrix, B represents an input matrix, C represents an output matrix, and F represents a fault action matrix.
In the motor system, with wk∈<0,W>Representing an unknown but bounded process noise vector, vk∈<0,V>Representing an unknown but bounded measurement noise vector,
Figure BDA0002721250250000086
representing a process noise vector that obeys a gaussian distribution,
Figure BDA0002721250250000087
representing a measured noise vector that obeys a gaussian distribution,
Figure BDA0002721250250000088
indicating an additive failure.
Step two: constructing a dynamic state interval observer according to the discrete model of the direct current servo motor established in the first step:
Figure BDA0002721250250000089
wherein the content of the first and second substances,
Figure BDA00027212502500000810
indicating the observed state at time k, GkAn observer gain representing time k;
determining the state error at the time k +1 according to equations (3) and (4):
Figure BDA00027212502500000811
wherein z isk+1Representing the state error of an unknown but bounded portion of time k +1, from a fully symmetric multicellular body<0,Hk+1>Represents, generates a matrix Hk+1Comprises the following steps:
Hk+1＝[(A-GkC)Hk W -GkV] (6)
z0representing state errors of unknown but bounded parts of the initial moment, by a fully symmetrical multicellular body<0,H0>Is represented by H0A generator matrix representing a fully symmetric multicellular body.
gk+1Indicating that the k +1 time obeys a Gaussian distribution
Figure BDA0002721250250000091
Partial state error, covariance matrix Pk+1Comprises the following steps:
Figure BDA0002721250250000092
g0indicating that the initial time obeys a Gaussian distribution
Figure BDA0002721250250000093
Partial state error, P0A covariance matrix is represented.
Obtaining an optimum criterion J according to (6) and (7)kComprises the following steps:
Figure BDA0002721250250000094
wherein eta iskAn optimal weight coefficient representing the k time;
unknown but bounded noise wkAnd vkAre bounded signals whose average power is equal to the sum of the squares of the signals, each with a fully symmetric multi-cell body<0,WWT>、<0,VVT>And (4) showing. Gaussian noise dkAnd ekAre the respective covariance matrices.
The state error of the unknown but bounded portion is at time k ═ 1:
z1＝Az0+w0 (9)
wherein, w0Representing an unknown but bounded process noise vector of the motor system at the initial moment, the average power of the state error of the unknown but bounded part being Pz1∈<0,Z1>Generating a matrix of
Figure BDA0002721250250000095
The state error of the gaussian uncertainty part is:
g1＝Ag0+d0 (10)
wherein d is0Representing the process noise vector of the motor system at the initial moment and obeying Gaussian distribution, and the state error average power of the Gaussian uncertain part is equal to the covariance matrix P of the state error average powerG1＝AP0AT+R。
The optimal weight coefficient at the moment when k is 1 is:
Figure BDA0002721250250000096
according to equation (6) and equation (7), the optimal weight coefficient at the time when k >1 is:
Figure BDA0002721250250000097
solving (8) to obtain observer gain Gk：
Figure BDA0002721250250000098
Wherein the content of the first and second substances,
Figure BDA0002721250250000099
Qηk＝(1-ηk)VVT+ηkQ；
determining an observer state estimation interval at the k time according to equations (4) and (5)
Figure BDA00027212502500000910
The upper and lower bounds of (A) are:
Figure BDA0002721250250000101
wherein the content of the first and second substances,
Figure BDA0002721250250000102
andz krespectively representing the upper and lower bounds of an unknown but bounded state error interval,
Figure BDA0002721250250000103
andg krespectively representing an upper bound and a lower bound of a gaussian state error confidence interval;
step three: determining a measurement residual interval at the moment k according to an output vector obtained under the actual operation condition of the motor at the moment k:
[rk]＝yk-C[xk] (15)
wherein [ r ]k]Denotes the measurement residual interval at time k, ykRepresenting an output vector obtained under the actual running condition of the motor at the moment k;
step four: defining a fault detection factor lambda at time kkComprises the following steps:
Figure BDA0002721250250000104
wherein, p (r)k|fk) Representing the probability density function at the time of failure, p (r)k|fk0) represents the probability density function without failure;
from equations (3) and (5), the measurement residual at time k is expressed as:
Figure BDA0002721250250000105
wherein the content of the first and second substances,
Figure BDA0002721250250000106
central value, Γ, representing the measurement residual at time kk＝(A-Gk-1C)Γk-1+F，
Figure BDA0002721250250000107
Representing the unknown but bounded portion of the measurement residual at time k,
Figure BDA0002721250250000108
representing the Gaussian distribution obeying to the measured residual at the k time
Figure BDA0002721250250000109
Part of, covariance matrix
Figure BDA00027212502500001010
The measurement residuals at time k follow a gaussian distribution:
Figure BDA00027212502500001011
the upper bound of the fault detection factor is obtained from equations (14) and (15):
Figure BDA0002721250250000111
the lower bound is:
Figure BDA0002721250250000112
wherein the content of the first and second substances,
Figure BDA0002721250250000113
represents the upper bound of the measurement residual interval at time k, krrepresents the lower bound of the measurement residual interval at time k,
Figure BDA0002721250250000114
represents the upper bound of the fault estimation interval at time k,f krepresenting the lower bound of the fault estimation interval at the moment k;
solving an optimization problem:
Figure BDA0002721250250000115
obtaining an optimal solution of an upper boundary and a lower boundary of a fault estimation interval:
Figure BDA0002721250250000116
wherein the content of the first and second substances,
Figure BDA0002721250250000117
Figure BDA0002721250250000118
Figure BDA0002721250250000119
obtaining upper and lower bounds of the fault detection factor at the time k according to the formula (19), the formula (20) and the formula (22):
Figure BDA0002721250250000121
step five: and detecting whether the motor system has a fault according to the upper and lower bounds of the fault detection factor.
Calculating the midpoint of the fault detection factor interval
Figure BDA0002721250250000122
When the middle point of the fault detection factor interval at continuous Q moments meets
Figure BDA0002721250250000123
When the motor system is always in the right state, the motor system is judged to have a fault from the k-Q moment to the k moment, wherein lambdathrIs given a threshold value.
Step six: if the motor system fails, obtaining a failure interval of the motor system at the moment k (k is less than l) according to a formula (22);
when k is larger than l, the fault interval of the motor system obtained by adopting a sliding window filtering method is as follows:
Figure BDA0002721250250000124
where l is the given sliding window length.
And searching for the type of the fault value within the fault estimation interval in the known fault types, and determining the fault type of the motor system.
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 type 1 fault, the method comprises the following steps
Figure BDA0002721250250000125
Namely, the motor system has a fault at the moment when k is 100 and continues; and within a preset time range, after the first step to the sixth step are executed, obtaining a fault signal and a fault estimation interval of the motor at each moment within the preset time range, and realizing fault diagnosis.
FIG. 2 is a simulation diagram of the fault detection result of the method of the present invention and the fault detection result of the conventional method (refer to the Extended Zonotopic and Gaussian Kalman Filter (EZGKF) aggregation set-membership and storage characteristics: aware non-linear filtering and fault detection). As can be seen from fig. 2, both the existing method and the method proposed by the present invention can implement fault detection after the mixed noise motor system fails, and the present invention detects that the motor system fails at the time when k is 102, and then is always in a fault state; the existing method detects that the motor system is in failure at the moment k-103, and the failure signal becomes 0 at the moment k-124, which means that the existing method does not detect the motor system failure at the moment k-124, and missed diagnosis occurs, because the existing method adopts the method of selecting the same weight to process random noise and collective noise, and does not use a sliding window, and only uses the estimated data at one sampling moment to detect the failure, resulting in the missed diagnosis. The simulation result shown in fig. 2 shows that the method provided by the invention can detect the occurrence of the fault more quickly, and has no condition of missed diagnosis, and the fault detection accuracy is higher.
Fig. 3 is a process of effectively identifying a fault type according to a fault estimation interval after a fault is detected by using the method of the present invention. In the figure, gray boxes represent the projection of a fault estimation interval on an X-Y plane, a plus sign represents the projection of a fault value of a fault type 1 on the X-Y plane, and a minus sign represents the projection of a fault value of a fault type 2 on the X-Y plane. It can be seen that when the motor has no fault, the fault estimation section wraps the "+" type mark located at the origin; after the fault occurs, the fault estimation interval is gradually wrapped by the '+' type mark which is positioned at the coordinate (-0.4, 0) and positioned at the coordinate (-1, 0) and represents the fault value projection of the fault type 1. In the fault identification process, the fault estimation section is not wrapped with the "·" type mark representing the fault value projection of the fault type 2, which shows that the method provided by the invention can effectively identify the fault type.
Fig. 4 is a process of effectively identifying a fault type according to a fault estimation interval after a fault is detected by using the method of the present invention. In the figure, gray boxes represent the projection of a fault estimation interval on an X-Z plane, a plus sign represents the projection of a fault value of a fault type 1 on the X-Z plane, and a minus sign represents the projection of a fault value of a fault type 3 on the X-Z plane. It can be seen that when the motor has no fault, the fault estimation section wraps the "+" type mark located at the origin; after the fault occurs, the fault estimation interval is gradually wrapped by the '+' type mark which is positioned at the coordinate (-0.4, 0) and positioned at the coordinate (-1, 0) and represents the fault value projection of the fault type 1. In the fault identification process, the fault estimation section is not wrapped with the "·" type mark representing the fault value projection of the fault type 3, which shows that the method provided by the invention can effectively identify the fault type.
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 diagnosis method based on mixed noise double filtering is characterized by comprising the following steps:
the method comprises the following steps: establishing an unknown discrete motor model mixed with bounded noise and Gaussian noise;
step two: designing a dynamic state interval observer, and acquiring a state estimation interval of the motor system at the moment k;
step three: acquiring a measurement residual interval at the moment k according to an output vector obtained under the actual operation condition of the motor at the moment k; the output vector is a vector formed by the angular position of the motor, the rotating speed of the motor and the armature current obtained by measurement;
step four: acquiring upper and lower boundaries of a fault detection factor at the k moment according to the measurement residual interval at the k moment;
step five: detecting whether the motor system has a fault according to the upper and lower bounds of the fault detection factor;
the discrete motor model of the unknown but bounded noise mixed with Gaussian noise established in the first step is as follows:
Figure FDA0003072439890000011
wherein the content of the first and second substances,
Figure FDA0003072439890000012
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 FDA0003072439890000013
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 FDA0003072439890000014
the output vector of the motor at the k time is respectively represented byA vector consisting of a motor angular position, a motor rotating speed and an armature current which are actually measured by a speed sensor, a position sensor and a current sensor;
a denotes a state space matrix, B denotes an input matrix, C denotes an output matrix, F denotes a malfunction matrix, wk∈<0,W>Representing an unknown but bounded process noise vector, v, of the motor system at time kk∈<0,V>Representing an unknown but bounded measurement noise vector, d, of the motor system at time kkN (0, R) represents the process noise vector of the motor system at the time k, which is subject to a Gaussian distribution, ekN (0, Q) represents the Gaussian-distributed measurement noise vector of the motor system at time k,
Figure FDA0003072439890000015
indicating an additive fault;
the second step is as follows: designing a dynamic state interval observer, and acquiring a state estimation interval of the motor system at the moment k comprises the following steps:
2.1 constructing a dynamic state interval observer:
Figure FDA0003072439890000016
wherein the content of the first and second substances,
Figure FDA0003072439890000017
indicating the observed state at time k, GkAn observer gain representing time k;
determining the state error at the time k +1 according to equations (3) and (4):
Figure FDA0003072439890000018
wherein z isk+1Representing the state error of an unknown but bounded portion of time k +1, from a fully symmetric multicellular body < 0, Hk+1Is expressed, a matrix H is generatedk+1Comprises the following steps:
Hk+1＝[(A-GkC)HkW-GkV] (6)
z0representing state errors of unknown but bounded parts at an initial instant, from a fully symmetric multicellular body < 0, H0H denotes0A generator matrix representing a fully symmetric multicellular body;
gk+1indicating that the time k +1 obeys the Gaussian distribution N (0, P)k+1) Partial state error, covariance matrix Pk+1Comprises the following steps:
Figure FDA0003072439890000021
g0indicating that the initial time obeys a Gaussian distribution N (0, P)0) Partial state error, P0Representing a covariance matrix;
obtaining an optimum criterion J according to (6) and (7)kComprises the following steps:
Figure FDA0003072439890000022
wherein eta iskAn optimal weight coefficient representing the k time;
unknown but bounded noise wkAnd vkIs a bounded signal with average power equal to the sum of the squares of the respective signals, using a fully symmetric multi-cell volume < 0, WWT〉、〈0,VVTIs indicated by (9); gaussian noise dkAnd ekThe average power of (a) is the respective covariance matrix;
the state error of the unknown but bounded portion is at time k ═ 1:
z1＝Az0+w0 (9)
wherein, w0Representing an unknown but bounded process noise vector of the motor system at the initial moment, the state error mean power of the unknown but bounded part being Pz1∈<0,Z1>Generating a matrix of
Figure FDA0003072439890000023
The state error of the gaussian uncertainty part is:
g1＝Ag0+d0 (10)
wherein d is0Representing the process noise vector of the motor system at the initial moment and obeying Gaussian distribution, and the state error average power of the Gaussian uncertain part is equal to the covariance matrix P of the state error average powerG1＝AP0AT+R；
The optimal weight coefficient at the moment when k is 1 is:
Figure FDA0003072439890000024
according to equation (6) and equation (7), the optimal weight coefficient at the time when k >1 is:
Figure FDA0003072439890000025
solving (8) to obtain observer gain Gk：
Figure FDA0003072439890000031
Wherein the content of the first and second substances,
Figure FDA0003072439890000032
Qηk＝(1-ηk)VVT+ηkQ；
2.2 determining the observer State estimation interval at the time k according to equations (4) and (5)
Figure FDA0003072439890000033
The upper and lower bounds of (A) are:
Figure FDA0003072439890000034
wherein the content of the first and second substances,
Figure FDA0003072439890000035
andz krespectively representing the upper and lower bounds of an unknown but bounded state error interval,
Figure FDA0003072439890000036
andg krepresenting the upper and lower bounds of the gaussian state error confidence interval, respectively.
2. The method of claim 1, further comprising: and when the motor system is detected to be in fault, calculating a fault estimation interval at the moment k and judging the fault type of the motor system in fault.
3. The method of claim 1, wherein the step three: obtaining a measurement residual interval at the moment k according to a state vector obtained under the actual operation condition of the motor at the moment k, wherein the measurement residual interval comprises the following steps:
determining a measurement residual interval at time k:
[rk]＝yk-C[xk] (15)
wherein [ r ]k]Denotes the measurement residual interval at time k, ykAnd the state vector obtained under the actual operation condition of the motor at the moment k is shown.
4. The method of claim 3, wherein the fourth step: acquiring the upper and lower bounds of the fault detection factor at the k moment according to the measurement residual interval at the k moment, wherein the method comprises the following steps:
defining the fault detection factor at the moment k as:
Figure FDA0003072439890000037
wherein, p (r)k|fk) Indicating the occurrence of a faultP (r) is a probability density function ofk|fk0) represents the probability density function without failure;
from equations (3) and (5), the measurement residual at time k is expressed as:
Figure FDA0003072439890000038
wherein the content of the first and second substances,
Figure FDA0003072439890000041
central value, Γ, representing the measurement residual at time kk＝(A-Gk-1C)Γk-1+F，
Figure FDA0003072439890000042
Representing the unknown but bounded portion of the measurement residual at time k,
Figure FDA0003072439890000043
representing the Gaussian distribution obeying to the measured residual at the k time
Figure FDA0003072439890000044
Part of, covariance matrix
Figure FDA0003072439890000045
The measurement residuals at time k follow a gaussian distribution:
Figure FDA0003072439890000046
the upper bound of the fault detection factor is obtained from equations (14) and (15):
Figure FDA0003072439890000047
the lower bound is:
Figure FDA0003072439890000048
wherein the content of the first and second substances,
Figure FDA0003072439890000049
represents the upper bound of the measurement residual interval at time k,r krepresents the lower bound of the measurement residual interval at time k,
Figure FDA00030724398900000410
represents the upper bound of the fault estimation interval at time k,f krepresenting the lower bound of the fault estimation interval at the moment k;
solving an optimization problem:
Figure FDA0003072439890000051
obtaining an optimal solution of an upper boundary and a lower boundary of a fault estimation interval:
Figure FDA0003072439890000052
wherein the content of the first and second substances,
Figure FDA0003072439890000053
Figure FDA0003072439890000054
Figure FDA0003072439890000055
obtaining upper and lower bounds of the fault detection factor at the time k according to the formula (19), the formula (20) and the formula (22):
Figure FDA0003072439890000056
5. the method of claim 4, wherein step five: whether the motor system breaks down or not is detected according to the upper and lower bounds of the fault detection factor, and the method comprises the following steps:
calculating the midpoint of the fault detection factor interval
Figure FDA0003072439890000057
When the middle point of the fault detection factor interval at continuous Q moments meets
Figure FDA0003072439890000058
When the motor system is always in the right state, the motor system is judged to have a fault from the k-Q moment to the k moment, wherein lambdathrIs given a threshold value.
6. The method according to claim 5, wherein when the motor system is detected to have a fault, calculating a fault estimation interval at the time k and determining the fault type of the fault of the motor system comprises:
obtaining a fault interval of the motor system at the moment k according to the formula (22), wherein k < l, and l is the length of a given sliding window;
when k is larger than l, the fault interval of the motor system obtained by adopting a sliding window filtering method is as follows:
Figure FDA0003072439890000059
and searching for the type of the fault value within the fault estimation interval in the known fault types, and determining the fault type of the motor system.
7. A fault diagnosis system, characterized in that it performs fault diagnosis using the fault diagnosis method of any one of claims 1 to 6.
8. The fault diagnosis system according to claim 7, characterized in that the fault diagnosis system is provided with a speed sensor, a position sensor and a current sensor to measure the motor angular position, the motor rotational speed, the armature current.
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