CN115032894A - High-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR - Google Patents

High-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR Download PDF

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CN115032894A
CN115032894A CN202210528413.1A CN202210528413A CN115032894A CN 115032894 A CN115032894 A CN 115032894A CN 202210528413 A CN202210528413 A CN 202210528413A CN 115032894 A CN115032894 A CN 115032894A
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fault
data
tomfir
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吴云凯
苏宇
周扬
朱志宇
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Jiangsu University of Science and Technology
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses a high-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR, which comprises the following steps: carrying out T-S fuzzy modeling on a train suspension system and a regular system, and carrying out data modeling on the obtained T-S fuzzy models of the real system and the regular system to obtain data models of the real system and the regular system; acquiring real system and regular system outputs when the train suspension system operates by using an instrument, and constructing input and output data matrixes of the real system and the regular system; designing a fault information full-scale residual error based on data driving by using an identification technology; constructing an evaluation function, and alarming when the detection index is larger than a threshold value; designing a suspension system sensor fault isolation algorithm to isolate sensor faults; and designing a fault isolation algorithm of the actuator of the suspension system to isolate the fault of the actuator. The method can effectively detect and isolate the faults when the suspension system has faults, even slowly-varying or intermittent micro faults.

Description

High-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR
Technical Field
The invention belongs to the technical field of high-speed train suspension system fault diagnosis, and relates to a high-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR.
Background
The high-speed train suspension system plays a role in supporting a train body and a bogie, simultaneously isolates wheel-rail acting force caused by track irregularity, and ensures the stability and safety of a train in high-speed operation, so that the high-speed train suspension system has high reliability requirements. Since the opening of a CRH (China Railway High-speed) motor train unit train with a speed of more than 200 kilometers per hour on a main trunk line in 2008, China has built a highway network with the largest scale and the fastest operation speed all over the world through the development of more than 10 years. The method has important significance for improving the safety of high-speed rail operation in China and aiming at the research of detecting the tiny faults of the suspension system.
The high-speed train suspension system comprises an active suspension and a semi-active suspension and adopts a closed-loop control structure. The suspension system adopts a primary suspension device which is arranged between the axle box and the bogie frame, and a secondary suspension device which is arranged between the bogie frame and the vehicle body. Contains a large number of components including coil springs, lateral/vertical dampers, air springs, active actuators and sensors. The active actuator is used as an important actuator part and is important for the safe running and riding comfort of a high-speed train; active actuators calculate the active control force required by the active suspension system from the vehicle output signal measured by the sensor, and therefore the sensor is also of high importance.
Suspension system failures can be classified as actuator failures, sensor failures, and mechanical component failures. As the on-track running time of a train increases, some parts in the suspension system, such as a coil spring, a shock absorber, an air spring, an active/semi-active actuator and a sensor, all generate a certain degree of performance degradation, and induce minor faults, such as fine cracking of the coil spring, slight oil leakage/leakage of the shock absorber, slight air leakage of the air spring, small-amplitude loss of the actuation performance of the actuator, deviation drift of the sensor and the like, so as to bring potential danger to the driving safety of the train.
The method for diagnosing the faults of the suspension system of the high-speed train in the prior art mainly aims at permanent faults, namely the faults cannot disappear automatically after occurring. Because the occurrence time of the intermittent fault is unknown, the amplitude of the fault is random, and the fault disappears automatically after the occurrence of the fault. The traditional detection method aiming at the permanent fault is difficult to be directly applied to intermittent fault diagnosis. In addition, most high-speed train suspension system fault diagnosis methods ignore nonlinearity in the suspension system, and can affect the accuracy of fault diagnosis.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a high-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR. The method aims at a nonlinear suspension system of a high-speed train with a closed-loop control structure, takes an active actuator and a sensor as fault diagnosis objects, and can detect the fault in real time and accurately isolate the fault when the suspension system has a fault, even an early tiny fault with gradual or intermittent characteristics.
In order to solve the technical problems, the invention adopts the following technical scheme.
A high-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR takes an active actuator and a sensor as fault diagnosis objects and comprises the following steps:
step 1, performing T-S fuzzy modeling on a high-speed train suspension system and a regular system thereof, and performing data modeling on the obtained real system T-S fuzzy model and the regular system T-S fuzzy model to obtain an input and output data model of the real system and an input and output data model of the regular system;
step 2, utilizing a displacement sensor and a gyroscope to obtain a vertical displacement of the mass center of the carriage of the train, an angular velocity signal and a vertical displacement signal of the mass center of the bogie frame when the high-speed train runs, wherein the signals of the sensor and the gyroscope are output by a real system; the input and output signals of the real system are used for constructing an input and output data matrix of the real system, and the input and output signals of the regular system are used for constructing an input and output data matrix of the regular system;
step 3, performing matrix identification and designing a fault information full-scale residual error based on data driving by using the input and output data matrix of the real system and the input and output data matrix of the regular system obtained in the step 2;
step 4, constructing an evaluation function J by using the data-driven-based fault information full-scale residual error designed in the step 3, and alarming when the detection index reaches an alarm threshold value by combining a fault detection alarm threshold value;
step 5, utilizing the fault information full-scale residual error based on data driving designed in the step 3, designing a suspension system sensor fault isolation algorithm to isolate the sensor fault;
step 6, utilizing the fault information full-scale residual error based on data driving designed in the step 3, designing a fault isolation algorithm of a suspension system actuator to isolate actuator faults;
the specific process of the step 1 comprises the following steps:
step 1.1, discrete nonlinear real system G and regular system G of high-speed train suspension system 0 Can be respectively expressed as:
Figure BDA0003645247790000021
Figure BDA0003645247790000022
wherein, A, B, C, E d ,E f ,F f A coefficient matrix corresponding to the space state equation; x (k), g (·), u (k), d (k), y (k) are state variables, nonlinear functions, control input variables, orbit disturbance excitation and output variables of a real system respectively; (k) characterizing all possible faults;
Figure BDA0003645247790000023
ξ (k) are process noise and measurement noise, respectively; x is the number of 0 (k),y 0 (k),u 0 (k) Respectively a state variable, an output variable and a control input variable of the regular system;
step 1.2, a discrete nonlinear real system G and a regular system G of the suspension system in the step 1.1 are adopted 0 The method comprises the following steps:
Plant rule
Figure BDA0003645247790000024
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000025
Figure BDA0003645247790000026
wherein θ (k) ═ θ 1 (k) … θ p (k)]Representing measurable precondition variables;
Figure BDA00036452477900000312
expressing the ith fuzzy inference rule; n is a radical of j,i (j ═ 1,2, …, p) represents a fuzzy set; v represents the number of inference rules;
by standard fuzzy inference methods, the output of the fuzzy system can be inferred:
Figure BDA0003645247790000031
Figure BDA0003645247790000032
wherein mu i (theta (k)) represents a fuzzy membership function satisfying mu i (θ (k)). gtoreq.0 and
Figure BDA0003645247790000033
step 1.3. the T-S fuzzy system (3) of the real system of the suspension system in the step 1.2 comprises the following steps:
Plant rule
Figure BDA0003645247790000034
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000035
wherein y is l (k),u l (k),d l (k),f l (k),
Figure BDA0003645247790000036
ξ l (k) Being a stacked matrix, Γ i,l ,H i,u,l ,H i,d,l ,H i,f,l ,
Figure BDA0003645247790000037
The specific form of the corresponding coefficient matrix is as follows:
Figure BDA0003645247790000038
Figure BDA0003645247790000039
Figure BDA00036452477900000310
Figure BDA00036452477900000311
step 1.4. the expression (7) obtained in step 1.3 contains a state variable x (k), and in order to eliminate the state variable x (k), the expression can be obtained by the T-S fuzzy system (3) of the real system of the suspension system in step 1.2:
Figure BDA0003645247790000041
wherein the content of the first and second substances,
Figure BDA0003645247790000042
step 1.5. substituting the expression (10) obtained in step 1.4 into the expression (7) obtained in step 1.3, having
Plant rule
Figure BDA0003645247790000043
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000044
Wherein
H i,u,p,l ＝[Γ i,l Q i,u H i,u,l ],
Figure BDA0003645247790000045
H i,d,p,l ＝[Γ i,l Q i,d H i,d,l ],
Figure BDA0003645247790000046
H i,f,p,l ＝[Γ i,l Q i,f H i,f,l ],
Figure BDA0003645247790000047
Figure BDA0003645247790000048
Step 1.6. similarly, the T-S fuzzy system (4) of the suspension system regular system in the step 1.2 comprises:
Plant rule
Figure BDA0003645247790000049
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA00036452477900000410
wherein the content of the first and second substances,
Figure BDA00036452477900000411
specifically, the process of designing the data-driven-based fault information full-metric residual error in step 3 includes:
step 3.1. defining output residual r y (k) Output difference for characterizing real and canonical systems
Figure BDA00036452477900000412
Step 3.2. defining controller residual error r u (k) For characterizing the output difference of controllers in real and regular systems
Figure BDA0003645247790000051
Step 3.3, defining fault information full-scale residual error under closed-loop control structure
Figure BDA0003645247790000052
Wherein
Figure BDA0003645247790000053
Representing system output of the regular system under the drive of a real-time input signal;
step 3.4. taking into account the time interval N, from expression (11) obtained in step 1.5, one can obtain:
Y k,l ＝H i,u,p,l U k,p,l +H i,d,p,l D k,p,l +H i,f,p,l F k,p,l +H i,e,p,l E k,p,l (17)
and 3.5, performing LQ decomposition on the process data:
Figure BDA0003645247790000054
can obtain
Figure BDA0003645247790000055
Step 3.6. matrix H based on step 3.5 identification i,u,p,l The fuzzy data driven ToMFIR can be written as:
Plant rule
Figure BDA0003645247790000056
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000057
wherein
Figure BDA0003645247790000058
Then, the global data driven ToFMIR may be written as:
Figure BDA0003645247790000059
wherein
Figure BDA00036452477900000510
Specifically, in the step 4, the detection of the micro fault of the suspension system is performed by using the fault information full-scale residual error based on data driving, and the process includes:
step 4.1. residual signal ToMFIR (k) E R m Writable as ToMFIR (k) ═ τ 1 ,…,τ m ] T (ii) a Assume that ToMFIR (k) obeys orApproximately obey a Gaussian distribution having
Figure BDA00036452477900000511
Wherein
Figure BDA00036452477900000512
Step 4.2. introduce the residual error signal of the trouble
Figure BDA0003645247790000061
ToMFIR rf (k) For a fault-free time, ToMFIR (k), according to step 4.1, there is the same principle
Figure BDA0003645247790000062
Wherein
Figure BDA0003645247790000063
Figure BDA0003645247790000064
Step 4.3 based on Jensen-Shannon divergence, the following evaluation function can be defined:
Figure BDA0003645247790000065
and 4.4, aiming at the tiny fault of the suspension system of the high-speed train, utilizing the designed fault information full-scale residual error based on data driving and an evaluation function, wherein the fault detection mechanism is
Figure BDA0003645247790000066
Specifically, in the step 5, isolation of a minor fault of a suspension system sensor is performed by using a fault information full-metric residual error based on data driving, and the process includes:
step 5.1. output residual r y,l (k)＝[r y (k),…,r y (k+l f )] T Obey or approximately obey Gaussian scoresCloth is provided with
Figure BDA0003645247790000067
Wherein
Figure BDA0003645247790000068
Step 5.2, when the fault is detected, collecting fault operation data, and then establishing a dynamic fault model for outputting residual errors as follows:
Figure BDA0003645247790000069
wherein
Figure BDA00036452477900000610
The presence of the data is represented by the presence data,
Figure BDA00036452477900000611
to represent
Figure BDA00036452477900000612
The reconstructed non-faulty portion is then reconstructed,
Figure BDA00036452477900000613
express identity matrix
Figure BDA00036452477900000614
Xi and xi s Kronecker product of (a), wherein
Figure BDA00036452477900000615
A fault distribution matrix representing the output residuals, where n represents the number of fault variables, g i ∈{1,2,…,k y Represents the position of the ith fault variable,
Figure BDA00036452477900000616
is a unit matrix
Figure BDA00036452477900000617
The ith column;
the probability density function of the sample vector is:
Figure BDA0003645247790000071
wherein
Figure BDA0003645247790000072
To estimate the size of the fault, generalized least squares are established as follows
Figure BDA0003645247790000073
f s,l (k) Is estimated as
Figure BDA0003645247790000074
The reconstructed output residual can be written as
Figure BDA0003645247790000075
The reconstructed global data-driven ToFMIR may be written as
Figure BDA0003645247790000076
The evaluation function after reconstruction is
J(ToMFIR * (k))＝JS(ToMFIR * (k)‖ToMFIR rf (k)) (29)
Step 5.3, initialization: order to
Figure BDA0003645247790000077
n-0 denotes xi s Distributing the number of vectors;
step 5.4.for i ═ 1: k y -n, structure
Figure BDA0003645247790000078
Wherein
Figure BDA0003645247790000079
Is an identity matrix
Figure BDA00036452477900000710
The ith column;
step 5.5. according to the expressions (26) - (29) in the step 5.2, calculating and
Figure BDA00036452477900000711
relevant reconstruction statistics
Figure BDA00036452477900000712
Step 5.6. will
Figure BDA00036452477900000713
Insertion into xi s In (1), let n be n + 1;
step 5.7, calculating xi s Relevant reconstruction statistics
Figure BDA00036452477900000714
If it is
Figure BDA00036452477900000715
Returning to the step 5.4;
step 5.8. based on the result obtained in step 5.7
Figure BDA00036452477900000716
Isolating fault variables
Figure BDA00036452477900000717
Specifically, in step 6, the isolation of the minor fault of the actuator of the suspension system is performed by using the fault information full-metric residual error based on data driving, and the process includes:
step 6.1. same as the output residual error, the controller residual error follows Gaussian distribution
Figure BDA0003645247790000081
Wherein
Figure BDA0003645247790000082
Step 6.2, when the fault is detected, collecting fault operation data, and then establishing a dynamic fault model of the residual error of the controller as follows:
Figure BDA0003645247790000083
wherein
Figure BDA0003645247790000084
The presence of the data is represented by the presence data,
Figure BDA0003645247790000085
to represent
Figure BDA0003645247790000086
The reconstructed non-faulty part is then reconstructed,
Figure BDA0003645247790000087
express identity matrix
Figure BDA0003645247790000088
Xi and xi a Kronecker product of (a); wherein
Figure BDA0003645247790000089
A fault distribution matrix representing the controller residual, n representing the number of fault variables, g i ∈{1,2,…,k y Represents the position of the ith fault variable,
Figure BDA00036452477900000810
is an identity matrix
Figure BDA00036452477900000811
The ith column;
the probability density function of the sample vector is:
Figure BDA00036452477900000812
wherein
Figure BDA00036452477900000813
To estimate the size of the fault, a generalized least squares fit is made as follows
Figure BDA00036452477900000814
f a,p,l (k) Is estimated as
Figure BDA00036452477900000815
The reconstructed controller residual can be written as
Figure BDA0003645247790000091
When the actuator fails, the output will also contain failure information; reconstructed controller residuals may be used
Figure BDA0003645247790000092
And the matrix determined in step 3.5 represents the output residuals corresponding to the post-reconstruction controller residuals; according to expression (11) in step 1.5 and expression (13) in step 1.6, there are:
Plant rule
Figure BDA0003645247790000093
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000094
reconstructed blurred data driven ToFMIR may be written as
Plant rule
Figure BDA0003645247790000095
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000096
The reconstructed global data driven ToFMIR can be written as
Figure BDA0003645247790000097
The evaluation function after reconstruction is
J(ToMFIR * (k))＝JS(ToMFIR * (k)‖ToMFIR rf (k)) (38)
Step 6.3, initialization: order to
Figure BDA0003645247790000098
n-0 denotes xi a Distributing the number of vectors;
step 6.4.for i ═ 1: k u -n, structure
Figure BDA0003645247790000099
Wherein
Figure BDA00036452477900000910
Is an identity matrix
Figure BDA00036452477900000911
The ith column;
step 6.5, according to the expressions (33) - (38) in the step 6.2, calculating and
Figure BDA00036452477900000912
related reconstruction statistics
Figure BDA00036452477900000913
Step 6.6. will
Figure BDA00036452477900000914
Inserted into xi a In (1), let n be n + 1;
step 6.7, calculate xi a Relevant reconstruction statistics
Figure BDA00036452477900000915
If it is
Figure BDA00036452477900000916
Returning to the step 6.4;
step 6.8. based on the result obtained in step 6.7
Figure BDA00036452477900000917
Isolating fault controller variables
Figure BDA00036452477900000918
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the method aims at the suspension system of the closed-loop control structure of the high-speed train, takes the active actuator and the sensor as fault diagnosis objects, and can detect and accurately isolate the faults in real time when the suspension system has faults, even early tiny faults such as gradual change, intermittence and the like.
2. The fault diagnosis method only depends on input and output data of a real system and a regular system of the train suspension system, does not need to know an accurate system model, and is a fault diagnosis method based on data driving.
3. The fault diagnosis method can collect more comprehensive fault information, makes the fault information more sensitive to micro faults of actuators and sensors of a suspension system of the high-speed railway, and can effectively and timely detect early micro faults such as slow change, intermittence and the like.
4. The fault diagnosis method can effectively isolate the micro faults of the actuator and the sensor of the suspension system of the high-speed railway.
5. The fault diagnosis method has higher sensitivity to the faults and even the tiny faults of the suspension system of the high-speed train, effectively solves the problems of diagnosis and engineering practicability of the tiny faults of the suspension system of the high-speed train under a closed-loop control structure, and has important significance for tiny early warning and real-time monitoring of the suspension faults of the high-speed train.
Drawings
Fig. 1 is a structural schematic diagram of a high-speed train suspension system fault diagnosis system according to an embodiment of the invention.
Fig. 2 is a schematic diagram of installation positions of sensors and gyroscopes in a high-speed train suspension system according to an embodiment of the present invention.
Fig. 3 is a flow chart of a fault diagnosis method of an embodiment of the invention.
FIG. 4 is a graph of suspension sensor glitch detection simulation for an embodiment of the present invention.
FIG. 5 is a graph of a suspension sensor micro fault isolation simulation of an embodiment of the present invention.
Fig. 6 is a simulation graph of a suspension actuator creep minor fault detection according to an embodiment of the present invention.
FIG. 7 is a graph of a suspension actuator creep minor fault isolation simulation in accordance with an embodiment of the present invention.
Fig. 8 is a graph of suspension actuator intermittent glitch detection simulation for an embodiment of the present invention.
FIG. 9 is a graph of a suspension actuator intermittent micro-fault isolation simulation in accordance with an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
fig. 1 is a structural schematic diagram of a high-speed train suspension system fault diagnosis system according to an embodiment of the invention. As shown in fig. 1, the fault diagnosis system includes: the sensor is used for acquiring the vertical displacement and the pitch angle of the gravity center of the train and the vertical displacement of the gravity center of the bogie frame; the acquisition system acquires and processes the measurement data of the sensor and then sends the measurement data to the fault diagnosis host; and the fault diagnosis host machine judges whether the high-speed train suspension system has a fault or not according to the acquired information and estimates the fault amplitude. The installation positions of the sensors and the gyroscopes in each carriage are shown in figure 2.
As shown in fig. 3, the method for diagnosing suspension fault of high-speed train based on T-S fuzzy data-driven ToMFIR according to an embodiment of the present invention uses active actuators and sensors as fault diagnosis targets, and includes the following steps:
step 1, performing T-S fuzzy modeling on a high-speed train suspension system and a regular system thereof, and performing data modeling on an obtained real system T-S fuzzy model and the regular system T-S fuzzy model to obtain an input and output data model of the real system and an input and output data model of the regular system;
step 2, utilizing a displacement sensor and a gyroscope to obtain a vertical displacement signal of the mass center of the carriage of the train and an angular velocity signal and a vertical displacement signal of the mass center of the bogie frame when the high-speed train runs, wherein the signals of the sensor and the gyroscope are output by a real system; the input and output signals of the real system are used for constructing an input and output data matrix of the real system, and the input and output signals of the regular system are used for constructing an input and output data matrix of the regular system;
step 3, performing matrix identification and designing a fault information full-scale residual error based on data driving by using the input and output data matrix of the real system and the input and output data matrix of the regular system obtained in the step 2;
step 4, constructing an evaluation function J by using the data-driven-based fault information full-scale residual error designed in the step 3, and alarming when the detection index reaches an alarm threshold value by combining a fault detection alarm threshold value;
step 5, utilizing the fault information full-scale residual error based on data driving designed in the step 3, designing a suspension system sensor fault isolation algorithm to isolate the sensor fault;
and 6, designing a suspension system actuator fault isolation algorithm to isolate actuator faults by using the data drive-based fault information full-scale residual error designed in the step 3.
In the step 1, the concrete process of performing T-S fuzzy modeling on the high-speed train suspension system and the regular system thereof, and then performing data modeling on the real system T-S fuzzy model and the regular system T-S fuzzy model obtained by fuzzy modeling comprises the following steps:
step 1.1. discrete nonlinear real system G and regular system G of the vertical suspension system according to the diagram in FIG. 2 0 Can be expressed as:
Figure BDA0003645247790000111
Figure BDA0003645247790000112
wherein, A, B, C, E d ,E f ,F f A coefficient matrix corresponding to the space state equation; x (k), g (·), u (k), d (k), and y (k) are respectively a state variable, a nonlinear function, a control input variable, a track disturbance excitation and an output variable of a real system; f (k) characterizing all possible faults;
Figure BDA0003645247790000118
ξ (k) are the process noise and the measurement noise, respectively. x is the number of 0 (k),y 0 (k),u 0 (k) Respectively, a state variable, an output variable and a control input variable of the canonical system.
Step 1.2, a discrete nonlinear real system G and a regular system G of the suspension system in the step 1.1 are adopted 0 The method comprises the following steps:
Plant rule
Figure BDA0003645247790000113
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000114
Figure BDA0003645247790000115
wherein θ (k) ═ θ 1 (k) … θ p (k)]Representing measurable precondition variables;
Figure BDA0003645247790000116
expressing the ith fuzzy inference rule; n is a radical of j,i (j ═ 1,2, …, p) denotes a fuzzy set. ν denotes the number of inference rules.
By standard fuzzy inference methods, the output of the fuzzy system can be inferred as follows:
Figure BDA0003645247790000117
Figure BDA0003645247790000121
wherein mu i (θ (k)) represents a fuzzy membership function satisfying μ i (theta (k)) > 0 or more and
Figure BDA0003645247790000122
step 1.3. the T-S fuzzy system (3) of the real system of the suspension system in the step 1.2 comprises the following steps:
Plant rule
Figure BDA0003645247790000123
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000124
wherein y is l (k),u l (k),d l (k),f l (k),
Figure BDA0003645247790000125
ξ l (k) Being a stacked matrix, Γ i,l ,H i,u,l ,H i,d,l ,H i,f,l ,
Figure BDA0003645247790000126
Is a corresponding coefficient matrix, and is specifically formed as follows
Figure BDA0003645247790000127
Figure BDA0003645247790000128
Figure BDA0003645247790000129
Figure BDA00036452477900001210
Step 1.4. the expression (7) obtained in step 1.3 contains a state variable x (k), and in order to eliminate the state variable x (k), the T-S fuzzy system (3) of the real system of the suspension system in step 1.2 can obtain
Figure BDA00036452477900001211
Wherein
Figure BDA0003645247790000131
Step 1.5. substituting the expression (10) obtained in step 1.4 into the expression (7) obtained in step 1.3, having
Plant rule
Figure BDA0003645247790000132
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000133
Wherein
H i,u,p,l ＝[Γ i,l Q i,u H i,u,l ],
Figure BDA0003645247790000134
H i,d,p,l ＝[Γ i,l Q i,d H i,d,l ],
Figure BDA0003645247790000135
H i,f,p,l ＝[Γ i,l Q i,f H i,f,l ],
Figure BDA0003645247790000136
Figure BDA0003645247790000137
Step 1.6. similarly, the T-S fuzzy system (4) of the suspension system regular system in the step 1.2 comprises:
Plant rule
Figure BDA0003645247790000138
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000139
wherein the content of the first and second substances,
Figure BDA00036452477900001310
in step 3, a specific process for designing a data-driven fault information full-scale residual error includes:
step 3.1. defining output residual r y (k) Output difference for characterizing real and canonical systems
Figure BDA00036452477900001311
Step 3.2. defining controller residual error r u (k) For characterizing the output difference of controllers in real and regular systems
Figure BDA00036452477900001312
Step 3.3, defining fault information full-scale residual error under closed-loop control structure
Figure BDA0003645247790000141
Wherein
Figure BDA0003645247790000142
And characterizing the system output of the regular system under the drive of the real-time input signal.
Step 3.4. taking into account the time interval N, from expression (11) obtained in step 1.5, one can obtain:
Y k,l ＝H i,u,p,l U k,p,l +H i,d,p,l D k,p,l +H i,f,p,l F k,p,l +H i,e,p,l E k,p,l (17)
and 3.5, performing LQ decomposition on the process data:
Figure BDA0003645247790000143
can obtain the product
Figure BDA0003645247790000144
Step 3.6. matrix H based on step 3.5 identification i,u,p,l Fuzzy data-driven ToMFIR can be written as:
Plant rule
Figure BDA0003645247790000145
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000146
wherein
Figure BDA0003645247790000147
Then, the global data driven ToFMIR may be written as:
Figure BDA0003645247790000148
wherein
Figure BDA0003645247790000149
In step 4, the detection of the micro-fault of the suspension system is performed by using the fault information full-scale residual error based on the data driving. The method comprises the following specific steps:
step 4.1. residual signal ToMFIR (k) E R m Writable as ToMFIR (k) ═ τ 1 ,…,τ m ] T . Assuming that ToMFIR (k) follows or approximates a Gaussian distribution, there
Figure BDA00036452477900001410
Wherein
Figure BDA00036452477900001411
Step 4.2. introduce the residual error signal without fault
Figure BDA00036452477900001412
ToMFIR rf (k) For a fault-free time, ToMFIR (k), according to step 4.1, there is the same principle
Figure BDA00036452477900001413
Wherein
Figure BDA00036452477900001414
Figure BDA0003645247790000151
Step 4.3 based on Jensen-Shannon divergence, the following evaluation function can be defined:
Figure BDA0003645247790000152
and 4.4, aiming at the tiny fault of the suspension system of the high-speed train, utilizing the designed fault information full-scale residual error based on data driving and an evaluation function, wherein the fault detection mechanism is
Figure BDA0003645247790000153
In step 5, isolation of a minor fault of the suspension system sensor is performed by using a fault information full-scale residual error based on data driving. The method comprises the following specific steps:
step 5.1. output residual r y,l (k)＝[r y (k),…,r y (k+l f )] T Obey or approximately obey a Gaussian distribution having
Figure BDA0003645247790000154
Wherein
Figure BDA0003645247790000155
Step 5.2, when the fault is detected, collecting fault operation data, and then establishing a dynamic fault model for outputting residual errors as follows:
Figure BDA0003645247790000156
wherein
Figure BDA0003645247790000157
The presence of the data is represented by the presence data,
Figure BDA0003645247790000158
to represent
Figure BDA0003645247790000159
The reconstructed non-faulty part is then reconstructed,
Figure BDA00036452477900001510
express identity matrix
Figure BDA00036452477900001511
Xi and xi s The Kronecker product of (a), wherein
Figure BDA00036452477900001512
A fault distribution matrix representing the output residuals, where n represents the number of fault variables, g i ∈{1,2,…,k y Denotes the position of the ith fault variable,
Figure BDA00036452477900001513
is an identity matrix
Figure BDA00036452477900001514
Column i.
The probability density function of the sample vector is:
Figure BDA00036452477900001515
wherein
Figure BDA0003645247790000161
To estimate the size of the fault, generalized least squares are established as follows
Figure BDA0003645247790000162
f s,l (k) Is estimated as
Figure BDA0003645247790000163
The reconstructed output residual can be written as
Figure BDA0003645247790000164
The reconstructed global data driven ToFMIR can be written as
Figure BDA0003645247790000165
The evaluation function after reconstruction is
J(ToMFIR * (k))＝JS(ToMFIR * (k)‖ToMFIR rf (k)) (29)
Step 5.3, initialization: order to
Figure BDA0003645247790000166
n-0 denotes xi s The number of vectors distributed in the vector.
Step 5.4.for i ═ 1: k y -n, structure
Figure BDA0003645247790000167
Wherein
Figure BDA0003645247790000168
Is an identity matrix
Figure BDA0003645247790000169
Column i.
Step 5.5, according to the expressions (26) to (29) in the step 5.2, calculating and
Figure BDA00036452477900001610
relevant reconstruction statistics
Figure BDA00036452477900001611
Step 5.6. will
Figure BDA00036452477900001612
Insertion into xi s In (1), let n be n + 1;
step 5.7, calculating xi s Relevant reconstruction statistics
Figure BDA00036452477900001613
If it is
Figure BDA00036452477900001614
And returning to the step 5.4.
Step 5.8. based on the result obtained in step 5.7
Figure BDA00036452477900001615
Isolating fault variables
Figure BDA00036452477900001616
In step 6, isolation of a minor fault of the suspension actuator is performed using the fault information full-scale residual error based on the data driving. The method comprises the following specific steps:
step 6.1. the controller residual obeys Gaussian distribution as the output residual
Figure BDA00036452477900001617
Wherein
Figure BDA00036452477900001618
Step 6.2, when the fault is detected, collecting fault operation data, and then establishing a dynamic fault model of the residual error of the controller as follows:
Figure BDA0003645247790000171
wherein
Figure BDA0003645247790000172
The presence of the data is represented by the presence data,
Figure BDA0003645247790000173
to represent
Figure BDA0003645247790000174
The reconstructed non-faulty part is then reconstructed,
Figure BDA0003645247790000175
express identity matrix
Figure BDA0003645247790000176
Xi and xi a The Kronecker product of (a), wherein
Figure BDA0003645247790000177
A fault distribution matrix representing controller residuals, where n represents the number of fault variables, g i ∈{1,2,…,k y Represents the position of the ith fault variable,
Figure BDA0003645247790000178
is an identity matrix
Figure BDA0003645247790000179
Column i.
The probability density function of the sample vector is:
Figure BDA00036452477900001710
wherein
Figure BDA00036452477900001711
To estimate the size of the fault, generalized least squares are established as follows
Figure BDA00036452477900001712
f a,p,l (k) Is estimated as
Figure BDA00036452477900001713
The reconstructed controller residual can be written as
Figure BDA00036452477900001714
When the actuator fails, the output will also contain failure information. Reconstructed controller residuals may be used
Figure BDA00036452477900001715
And the matrix determined in step 3.5 to represent the output residuals corresponding to the post reconstruction controller residuals. According to expression (11) in step 1.5 and expression (13) in step 1.6, there are:
Plant rule
Figure BDA0003645247790000181
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000182
reconstructed blurred data driven ToFMIR may be written as
Plant rule
Figure BDA0003645247790000183
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure BDA0003645247790000184
The reconstructed global data driven ToFMIR can be written as
Figure BDA0003645247790000185
The evaluation function after reconstruction is
J(ToMFIR * (k))＝JS(ToMFIR * (k)‖ToMFIR rf (k)) (38)
Step 6.3, initialization: order to
Figure BDA0003645247790000186
n-0 denotes xi a The number of vectors distributed in the vector.
Step 6.4.for i ═ 1: k u -n, structure
Figure BDA0003645247790000187
Wherein
Figure BDA0003645247790000188
Is an identity matrix
Figure BDA0003645247790000189
Column i.
Step 6.5. according to the expressions (33) - (38) in the step 6.2, calculating and
Figure BDA00036452477900001810
relevant reconstruction statistics
Figure BDA00036452477900001811
Step 6.6. will
Figure BDA00036452477900001812
Insertion into xi a In (1), let n be n + 1;
step 6.7, calculate xi a Relevant reconstruction statistics
Figure BDA00036452477900001813
If it is
Figure BDA00036452477900001814
And returning to the step 6.4.
Step 6.8. based on the result obtained in step 6.7
Figure BDA00036452477900001815
Isolating fault controller variables
Figure BDA00036452477900001816
The following simulation verification of the method of the present invention,
step 1, setting characteristic information of sensor drift faults, comprising the following steps: the method comprises the following steps that (1) a small gradual drift fault occurs in a car sensor, the drift amount is theta (t) 0.01 x (0.25+0.02sin (t) +0.01sin (0.2t)), the fault starting time is 60 seconds, the fault ending time is simulation ending time, and the fault is injected through software by a fault injection module to establish a fault model;
step 2, setting characteristic information of the actuator slowly-varying fault, comprising the following steps: the method comprises the following steps that a front bogie actuator slowly changes to lose 10%, the fault starting time is 60 seconds, the fault ending time is simulation ending time, software injection is carried out on a fault through a fault injection module, and a fault model is established;
and 3, setting characteristic information of the intermittent fault of the actuator, comprising the following steps: the front bogie actuator fails by 10%, the fault time is from 20 th to 30 th seconds and from 60 th to 80 th seconds, and the fault is injected by software through a fault injection module to establish a fault model;
and 4, adopting SIMPACK and Matlab/Simulink for combined simulation, importing the track-train coupled model established in the SIMPACK into the Matlab/Simulink, and establishing a train vertical suspension system control simulation model in the Simulink. The running speed of the vehicle is set to 250Km/h, and the simulation is often 100 seconds.
As shown in FIG. 4, when a creep minor fault occurs in a sensor of a suspension system of a high-speed train, the method provided by the invention can well detect the occurrence of the minor fault of the sensor of the suspension system of the train.
As shown in FIG. 5, when a creep minor fault occurs in a sensor of a suspension system of a high-speed train, the method provided by the invention can well isolate the minor fault of the sensor of the suspension system of the train.
As shown in FIG. 6, when a creep micro-fault occurs in a high-speed train suspension system actuator, the method provided by the invention can well detect the occurrence of the creep micro-fault in the train suspension system actuator.
As shown in FIG. 7, when a creep minor fault occurs in a high-speed train suspension system actuator, the method provided by the invention can well isolate the creep minor fault of the train suspension system actuator.
As shown in FIG. 8, when an intermittent micro-fault occurs in a high-speed train suspension system actuator, the method provided by the invention can well detect the occurrence of the intermittent micro-fault in the train suspension system actuator.
As shown in FIG. 9, when the actuator of the suspension system of the high-speed train has intermittent micro-faults, the method provided by the invention can well isolate the intermittent micro-faults of the actuator of the suspension system of the train.
The fault detection method has higher sensitivity to the tiny faults of the suspension system of the high-speed train, can effectively realize the detection and isolation of the tiny faults of the suspension system of the high-speed train, such as slow change, intermittence and the like, effectively solves the detection of the tiny faults under a closed-loop control structure and the practical engineering problems thereof, and has important significance for tiny early warning and real-time monitoring of the suspension faults of the high-speed train.

Claims (6)

1. A high-speed train suspension fault diagnosis method based on T-S fuzzy data driving ToMFIR is characterized in that an active actuator and a sensor are taken as fault diagnosis objects, and the method comprises the following steps:
step 1, performing T-S fuzzy modeling on a high-speed train suspension system and a regular system thereof, and performing data modeling on an obtained real system T-S fuzzy model and the regular system T-S fuzzy model to obtain an input and output data model of the real system and an input and output data model of the regular system;
step 2, utilizing a displacement sensor and a gyroscope to obtain a vertical displacement of the mass center of the carriage of the train, an angular velocity signal and a vertical displacement signal of the mass center of the bogie frame when the high-speed train runs, wherein the signals of the sensor and the gyroscope are output by a real system; the input and output signals of the real system are used for constructing an input and output data matrix of the real system, and the input and output signals of the regular system are used for constructing an input and output data matrix of the regular system;
step 3, performing matrix identification and designing a fault information full-scale residual error based on data driving by using the input and output data matrix of the real system and the input and output data matrix of the regular system obtained in the step 2;
step 4, constructing an evaluation function J by using the data-driven-based fault information full-scale residual error designed in the step 3, and alarming when the detection index reaches an alarm threshold value by combining a fault detection alarm threshold value;
step 5, utilizing the fault information full-scale residual error based on data driving designed in the step 3, designing a suspension system sensor fault isolation algorithm to isolate the sensor fault;
and 6, designing a suspension system actuator fault isolation algorithm to isolate actuator faults by using the data drive-based fault information full-scale residual error designed in the step 3.
2. The method for diagnosing the suspension fault of the high-speed train based on the T-S fuzzy data driven ToMFIR as claimed in claim 1, wherein the specific process of the step 1 comprises:
step 1.1, discrete nonlinear real system G and regular system G of high-speed train suspension system 0 Can be represented as:
Figure FDA0003645247780000011
Figure FDA0003645247780000012
wherein, A, B, C, E d ,E f ,F f A coefficient matrix corresponding to the space state equation; x (k), g (·), u (k), d (k), y (k) are state variables, nonlinear functions, control input variables, orbit disturbance excitation and output variables of a real system respectively; (k) characterizing all possible faults;
Figure FDA0003645247780000013
process noise and measurement noise, respectively; x is the number of 0 (k),y 0 (k),u 0 (k) Respectively a state variable, an output variable and a control input variable of the regular system;
step 1.2, a discrete nonlinear real system G and a regular system G of the suspension system in the step 1.1 are adopted 0 The method comprises the following steps:
Figure FDA0003645247780000014
IF θ 1 (k) is N 1,i and θ 2 (k)is N 2,i and … and θ p (k) is N p,i ,THEN
Figure FDA0003645247780000015
Figure FDA0003645247780000021
wherein θ (k) ═ θ 1 (k) … θ p (k)]Representing measurable precondition variables;
Figure FDA0003645247780000022
expressing the ith fuzzy inference rule; n is a radical of j,i (j ═ 1,2, …, p) represents a fuzzy set; ν denotes the number of inference rules;
by standard fuzzy inference methods, the output of the fuzzy system can be inferred:
Figure FDA0003645247780000023
Figure FDA0003645247780000024
wherein mu i (θ (k)) represents a fuzzy membership function satisfying μ i (θ (k)). gtoreq.0 and
Figure FDA0003645247780000025
step 1.3. the T-S fuzzy system (3) of the real system of the suspension system in the step 1.2 comprises the following components:
Figure FDA0003645247780000026
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure FDA0003645247780000027
wherein y is l (k),u l (k),d l (k),f l (k),
Figure FDA00036452477800000212
ξ l (k) Being a stacked matrix, Γ i,l ,H i,u,l ,H i,d,l ,H i,f,l ,
Figure FDA0003645247780000028
The specific form of the corresponding coefficient matrix is as follows:
Figure FDA0003645247780000029
Figure FDA00036452477800000210
Figure FDA00036452477800000211
Figure FDA0003645247780000031
step 1.4. the expression (7) obtained in step 1.3 contains a state variable x (k), and in order to eliminate the state variable x (k), the expression can be obtained by the T-S fuzzy system (3) of the real system of the suspension system in step 1.2:
Figure FDA0003645247780000032
wherein the content of the first and second substances,
Figure FDA0003645247780000033
step 1.5. substituting the expression (10) obtained in step 1.4 into the expression (7) obtained in step 1.3, having
Figure FDA0003645247780000034
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure FDA0003645247780000035
Wherein
Figure FDA0003645247780000036
Figure FDA0003645247780000037
Figure FDA0003645247780000038
Figure FDA0003645247780000039
Step 1.6. similarly, the T-S fuzzy system (4) of the suspension system regular system in the step 1.2 comprises:
Figure FDA00036452477800000310
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure FDA00036452477800000311
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00036452477800000312
3. the method for diagnosing the suspension fault of the high-speed train based on the T-S fuzzy data-driven ToMFIR as claimed in claim 1, wherein in the step 3, the specific process of designing the data-driven based fault information full-scale residual error comprises:
step 3.1. defining output residual r y (k) Output difference for characterizing real and canonical systems
Figure FDA0003645247780000041
Step 3.2. defining controller residual r u (k) Output difference of controller for characterizing real system and regular system
Figure FDA0003645247780000042
Step 3.3, defining fault information full-scale residual error under closed-loop control structure
Figure FDA0003645247780000043
Wherein
Figure FDA0003645247780000044
Representing system output of the regular system under the drive of a real-time input signal;
step 3.4. considering the time interval N, from expression (11) obtained in step 1.5, we can obtain:
Y k,l ＝H i,u,p,l U k,p,l +H i,d,p,l D k,p,l +H i,f,p,l F k,p,l +H i,e,p,l E k,p,l (17)
step 3.5, performing LQ decomposition on the process data:
Figure FDA0003645247780000045
can obtain the product
Figure FDA0003645247780000046
Step 3.6. matrix H based on step 3.5 identification i,u,p,l Fuzzy data-driven ToMFIR can be written as:
Figure FDA0003645247780000047
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure FDA0003645247780000048
wherein
Figure FDA0003645247780000049
Then, the global data driven ToFMIR may be written as:
Figure FDA00036452477800000410
wherein
Figure FDA00036452477800000411
4. The method for diagnosing the suspension fault of the high-speed train based on the T-S fuzzy data-driven ToMFIR as claimed in claim 1, wherein in the step 4, the detection of the micro fault of the suspension system is performed by using the full-scale residual error of the fault information based on the data drive, and the specific steps thereof include:
step 4.1. residual signal ToMFIR (k) E R m Which may be written as tomfir (k) ═ τ 1 ,…,τ m ] T (ii) a Assuming that ToMFIR (k) follows or approximates a Gaussian distribution, there
Figure FDA0003645247780000051
Wherein
Figure FDA0003645247780000052
Step 4.2. introduce the residual error signal of the trouble
Figure FDA0003645247780000053
ToMFIR rf (k) For a fault-free time, ToMFIR (k), according to step 4.1, there are
Figure FDA0003645247780000054
Wherein
Figure FDA0003645247780000055
Figure FDA0003645247780000056
Step 4.3 based on Jensen-Shannon divergence, the following evaluation function can be defined:
Figure FDA0003645247780000057
and 4.4, aiming at the tiny fault of the high-speed train suspension system, utilizing the designed fault information full-scale residual error and the evaluation function based on data driving, wherein the fault detection mechanism is that
Figure FDA0003645247780000058
5. The method for diagnosing the suspension fault of the high-speed train based on the T-S fuzzy data-driven ToMFIR as claimed in claim 1, wherein in the step 5, the isolation of the minor fault of the sensor of the suspension system is performed by using the fault information full-scale residual error based on the data drive, and the specific steps thereof include:
step 5.1. output residual r y,l (k)＝[r y (k),…,r y (k+l f )] T Obey or approximately obey a Gaussian distribution having
Figure FDA0003645247780000059
Wherein
Figure FDA00036452477800000510
Step 5.2, when the fault is detected, collecting fault operation data, and then establishing a dynamic fault model for outputting residual errors as follows:
Figure FDA00036452477800000511
wherein
Figure FDA00036452477800000512
The presence of the data is represented by the presence data,
Figure FDA00036452477800000513
to represent
Figure FDA00036452477800000514
The reconstructed non-faulty part is then reconstructed,
Figure FDA00036452477800000515
express identity matrix
Figure FDA0003645247780000061
Xi and xi s The Kronecker product of (a), wherein
Figure FDA0003645247780000062
A fault distribution matrix representing the output residuals, where n represents the number of fault variables, g i ∈{1,2,…,k y Denotes the position of the ith fault variable,
Figure FDA0003645247780000063
is a unit matrix
Figure FDA0003645247780000064
The ith column;
the probability density function of the sample vector is:
Figure FDA0003645247780000065
wherein
Figure FDA0003645247780000066
To estimate the size of the fault, generalized least squares are established as follows
Figure FDA0003645247780000067
f s,l (k) Is estimated as
Figure FDA0003645247780000068
The reconstructed output residual can be written as
Figure FDA0003645247780000069
The reconstructed global data-driven ToFMIR may be written as
Figure FDA00036452477800000610
The evaluation function after reconstruction is
J(ToMFIR * (k))＝JS(ToMFIR * (k)‖ToMFIR rf (k)) (29)
Step 5.3, initialization: order to
Figure FDA00036452477800000611
n-0 denotes xi s Distributing the number of vectors;
step 5.4.for i ═ 1: k y -n, structure
Figure FDA00036452477800000612
Wherein
Figure FDA00036452477800000613
Is an identity matrix
Figure FDA00036452477800000614
The ith column;
step 5.5 calculating xi and xi according to the expressions (26) - (29) in step 5.2 hi Related reconstruction statistics
Figure FDA00036452477800000615
Step 5.6. will
Figure FDA00036452477800000616
Insertion into xi s In (1), let n be n + 1;
step 5.7, calculate xi s Relevant reconstruction statistics
Figure FDA00036452477800000617
If it is
Figure FDA00036452477800000618
Returning to the step 5.4;
step 5.8. based on the result obtained in step 5.7
Figure FDA0003645247780000071
Isolating fault variables
Figure FDA00036452477800000715
6. The method for diagnosing the suspension fault of the high-speed train based on the T-S fuzzy data-driven ToMFIR as claimed in claim 1, wherein in the step 6, the isolation of the minor fault of the actuator of the suspension system is performed by using the fault information full-scale residual error based on the data drive, and the specific steps thereof include:
step 6.1. same as the output residual error, the controller residual error follows Gaussian distribution
Figure FDA0003645247780000072
Wherein
Figure FDA0003645247780000073
Step 6.2, when the fault is detected, collecting fault operation data, and then establishing a dynamic fault model of the residual error of the controller as follows:
Figure FDA0003645247780000074
wherein
Figure FDA0003645247780000075
The presence of the data is represented by the presence data,
Figure FDA0003645247780000076
to represent
Figure FDA0003645247780000077
The reconstructed non-faulty portion is then reconstructed,
Figure FDA0003645247780000078
express identity matrix
Figure FDA0003645247780000079
Xi and xi a Kronecker product of; wherein
Figure FDA00036452477800000710
A fault distribution matrix representing the controller residual, n representing the number of fault variables, g i ∈{1,2,…,k y Denotes the position of the ith fault variable,
Figure FDA00036452477800000714
is a unit matrix
Figure FDA00036452477800000711
The ith column;
the probability density function of the sample vector is:
Figure FDA00036452477800000712
wherein
Figure FDA00036452477800000713
To estimate the size of the fault, generalized least squares are established as follows
Figure FDA0003645247780000081
f a,p,l (k) Is estimated as
Figure FDA0003645247780000082
The reconstructed controller residual can be written as
Figure FDA0003645247780000083
When the actuator fails, the output will also contain failure information; reconstructed controller residuals may be used
Figure FDA0003645247780000084
And identifying the obtained matrix
Figure FDA0003645247780000085
And
Figure FDA0003645247780000086
to represent an output residual corresponding to the post-reconstruction controller residual; according to expression (11) in step 1.5 and expression (13) in step 1.6, there are:
Figure FDA0003645247780000087
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure FDA0003645247780000088
reconstructed blurred data driven ToFMIR may be written as
Figure FDA0003645247780000089
IF θ 1 (k) is N 1,i and θ 2 (k) is N 2,i and … and θ p (k) is N p,i ,THEN
Figure FDA00036452477800000810
The reconstructed global data driven ToFMIR can be written as
Figure FDA00036452477800000811
The evaluation function after reconstruction is
J(ToMFIR * (k))＝JS(ToMFIR * (k)‖ToMFIR rf (k)) (38)
Step 6.3, initialization: order to
Figure FDA00036452477800000812
n-0 denotes xi a Distributing the number of vectors;
step 6.4.for i ═ 1: k u -n, structure
Figure FDA00036452477800000813
Wherein
Figure FDA00036452477800000814
Is an identity matrix
Figure FDA00036452477800000815
The ith column;
step 6.5, according to the expressions (33) - (38) in the step 6.2, calculating and
Figure FDA00036452477800000816
relevant reconstruction statistics
Figure FDA00036452477800000817
Step 6.6. will
Figure FDA00036452477800000818
Insertion into xi a In (1), let n be n + 1;
step 6.7, calculate xi a Related reconstructionStatistics
Figure FDA0003645247780000091
If it is
Figure FDA0003645247780000092
Returning to the step 6.4;
step 6.8. based on the result obtained in step 6.7
Figure FDA0003645247780000093
Isolating fault controller variables
Figure FDA0003645247780000094
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CN113110042A (en) * 2021-03-22 2021-07-13 青岛科技大学 Train fault tolerance control method
CN113110042B (en) * 2021-03-22 2022-11-22 青岛科技大学 Train fault tolerance control method

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