CN116595783A - High-speed train dynamic system fault detection method based on interval observer - Google Patents
High-speed train dynamic system fault detection method based on interval observer Download PDFInfo
- Publication number
- CN116595783A CN116595783A CN202310593631.8A CN202310593631A CN116595783A CN 116595783 A CN116595783 A CN 116595783A CN 202310593631 A CN202310593631 A CN 202310593631A CN 116595783 A CN116595783 A CN 116595783A
- Authority
- CN
- China
- Prior art keywords
- speed train
- carriage
- state
- speed
- representing
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000001514 detection method Methods 0.000 title claims abstract description 35
- 239000011159 matrix material Substances 0.000 claims abstract description 62
- 238000000034 method Methods 0.000 claims abstract description 35
- 239000002245 particle Substances 0.000 claims abstract description 29
- 238000005457 optimization Methods 0.000 claims abstract description 7
- 239000000654 additive Substances 0.000 claims description 6
- 230000000996 additive effect Effects 0.000 claims description 6
- 230000009471 action Effects 0.000 claims description 5
- 238000006073 displacement reaction Methods 0.000 claims description 4
- 230000008569 process Effects 0.000 claims description 4
- 230000001133 acceleration Effects 0.000 claims description 3
- 238000005096 rolling process Methods 0.000 claims description 3
- 238000004088 simulation Methods 0.000 description 7
- 230000008859 change Effects 0.000 description 4
- 238000003745 diagnosis Methods 0.000 description 4
- 238000002474 experimental method Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 101100346177 Arabidopsis thaliana MORC5 gene Proteins 0.000 description 1
- 230000002159 abnormal effect Effects 0.000 description 1
- 238000005299 abrasion Methods 0.000 description 1
- 230000032683 aging Effects 0.000 description 1
- 230000003139 buffering effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 239000000306 component Substances 0.000 description 1
- 239000008358 core component Substances 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000007774 longterm Effects 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Data Mining & Analysis (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Algebra (AREA)
- Software Systems (AREA)
- Databases & Information Systems (AREA)
- Operations Research (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- Computing Systems (AREA)
- Train Traffic Observation, Control, And Security (AREA)
Abstract
The invention discloses a high-speed train dynamic system fault detection method based on an interval observer, and belongs to the field of high-speed train fault detection. Firstly, constructing a longitudinal unknown bounded dynamics model of multiple mass points of a high-speed train, and obtaining the traction force output by each carriage in a balanced state; establishing a multi-particle velocity tracking state space model and a system state equation when an actuator fails according to the established dynamics model; constructing a fault detection interval observer and obtaining an observer gain matrix by solving a linear matrix inequality constraint optimization problem; and defining an upper bound and a lower bound of a system state error, constructing a state error dynamics model of the interval observer to obtain estimated values of the upper bound and the lower bound of the state error of the designed interval observer, and judging whether a high-speed train dynamic system fails according to the estimated values. The method can realize fault detection on the multi-particle dynamics characteristic of the high-speed train without obtaining accurate model parameters and workshop forces of the high-speed train in advance.
Description
Technical Field
The invention belongs to the field of high-speed train fault detection, and particularly relates to a high-speed train dynamic system fault detection method based on an interval observer.
Background
Along with the development of rail transit in China, a high-speed train becomes the first choice for people to travel by virtue of the advantages of high speed and large transportation capacity. As a core component of the high-speed train, the traction and braking actuator runs under high load in a complex environment for a long time, and the high-speed train cannot complete a designated running task due to the fact that the high-speed train is inevitably aged and worn to cause faults, so that the running safety of the high-speed train is reduced, even the running safety of the high-speed train is out of control and a safety accident is caused. Therefore, the research of carrying out the traction of the high-speed train and the fault detection of the brake actuator has important theoretical and practical significance. At present, fault diagnosis of a traction system of a high-speed train is mainly focused on fault diagnosis and fault-tolerant control of a traction motor, the overall running condition of the train is not considered, the fault of the traction motor is detected only by a model method or a data driving method, and although the fault detection and diagnosis of the high-speed train can be realized by the method, unnecessary redundant measures are needed to be adopted on the traction motor; the method for diagnosing faults of the train overall system often needs to model workshop forces and input vehicle parameters, but changes of the vehicle parameters are caused by long-term running of the train and abrasion or aging of components; in addition, the shop buffer device is generally difficult to build an accurate model, and is also difficult to measure in the running process, so that a train dynamics model has large uncertainty, and fault detection is difficult to be performed through the accurate model.
For the fault of the actuator, a designed observer method can be adopted to observe the model to realize fault diagnosis, and particularly, the section observer fault detection scheme is not limited by model uncertainty and observer matching conditions aiming at the observation of the model containing unknown but bounded items, so that the adaptability of fault detection of a dynamic system of a high-speed train is improved, and the method has very important theoretical and practical significance. However, since the gain requirements of the section observer are high, it is generally difficult to obtain the gain of the observer which meets the requirements, most of the researches on the section observer are still in the theoretical research stage.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide the fault detection method of the dynamic system of the high-speed train based on the interval observer, which can detect faults of the multi-particle dynamics characteristic of the high-speed train under the condition that accurate model parameters and workshop force of the high-speed train are not required to be obtained in advance, overcomes the defects of the traditional fault detection method and improves the adaptability of the fault detection method of the dynamic system of the high-speed train.
In order to achieve the above object, the solution of the present invention is:
a high-speed train dynamic system fault detection method based on an interval observer comprises the following steps:
firstly, constructing a longitudinal unknown bounded dynamics model of multiple mass points of the high-speed train under the action of mechanical resistance and air resistance, and obtaining the traction force output by each carriage when the high-speed train is in a balanced state;
step two, based on the longitudinal unknown bounded dynamics model of the high-speed train multi-particle and the obtained traction force output by each carriage in the balanced state, constructing a high-speed train multi-particle speed tracking state space model, and establishing a system state equation when the high-speed train has an actuator fault;
step three, constructing a fault detection interval observer based on the high-speed train multi-particle velocity tracking state space model constructed in the step two and a system state equation when an actuator fails, and obtaining a gain matrix of the observer by solving a linear matrix inequality constraint optimization problem;
and step four, based on the interval observer designed in the step three, defining an upper bound and a lower bound of a system state error, constructing a state error dynamics model of the interval observer to obtain estimated values of the upper bound and the lower bound of the state error, judging whether the dynamic system of the high-speed train has faults, and if the estimated values of the upper bound and the lower bound of the state error of the interval observer are more than or equal to 0, no faults exist, otherwise, the dynamic system of the high-speed train has faults.
In the first step, under the action of mechanical resistance and air resistance, a longitudinal unknown bounded dynamics model of a plurality of particles of a high-speed train with n carriages is constructed as follows:
in the above formula, i=2, 3, carrying out n-1; m is m 1 、m i 、m n The mass of the 1 st carriage, the i th carriage and the n th carriage of the high-speed train are respectively shown; v 1 、v i 、v n The speeds of the 1 st carriage, the i th carriage and the n th carriage of the high-speed train are respectively shown; f (F) 1 、F i 、F n Respectively representing resultant forces of traction force and braking force applied to the 1 st carriage, the i th carriage and the n th carriage of the high-speed train;the general resistances of the 1 st, i th and n th carriages of the high-speed train are respectively shown, and the general resistance of the i th carriage is shown as follows by using the Davis equation:
R i ＝a i +b i v i (t)+c i v i 2 (t)
in the above, v i (t) represents the speed of the i-th car of the high-speed train; a, a i Representing the fixed resistance coefficient of the ith carriage of the high-speed train, b i Representing the rolling resistance coefficient of the ith carriage of the high-speed train, c i The air resistance coefficient of the ith carriage of the high-speed train is shown, and the air resistance is considered to only act on the 1 st carriage, so that the resistance coefficient of each carriage of the high-speed train is obtained as follows:
R i ＝a i +b i v i (t)
R n ＝a n +b n v n (t)
in the above formula, i=2, 3, carrying out n-1; r is R 1 、R i 、R n Respectively representing the resistance coefficients of the 1 st carriage, the i th carriage and the n th carriage of the high-speed train;
in the high speed train multi-particle longitudinal dynamics model described above,representing the workshop force between the ith carriage of the high-speed train and the (i-1) th carriage; according to the working characteristics of the car coupler buffer device for connecting the carriages of the high-speed train, the physical characteristics of the car coupler buffer device are regarded as springs, and the car coupler buffer device is obtained:
in the above formula, k represents a spring coefficient, pi represents the position of the ith carriage of the high-speed train; at high speed
The workshop force is unknown but bounded in the train running process, namely, the following conditions are satisfied:thereby obtaining the longitudinal unknown bounded dynamics model of the high-speed train multi-mass points;
in the constructed multi-particle longitudinal unknown bounded dynamics model of the high-speed train, the speed of the high-speed train in the balanced state is assumed to be v r The speed of each carriage is equal to v r Acceleration of 0, i.e. satisfying v 1 ＝v 2 ＝…＝v n ＝v r ，And the relative displacement between the two carriages is 0, so that the traction force output by each carriage when the high-speed train is in a balanced state is obtained:
in the above formula, i=2, 3, carrying out the following steps;the traction forces output by the 1 st carriage and the i th carriage when the high-speed train is in the balanced state are respectively shown.
Further, the specific content of the second step is as follows:
and (3) making:Δv i ＝v i -v r ，/>
in the above formula, i=1, 2,3, carrying out the following steps;the traction force output by the ith carriage when the high-speed train is in a balanced state is shown; />Representing an estimated value of the traction force output by the ith carriage of the high-speed train; v i Representing the speed of an ith carriage of the high-speed train; v r The speed of each carriage when the high-speed train is in a balanced state is shown; deltav i The deviation between the speed of the ith carriage of the high-speed train and the speed of the high-speed train in a balanced state is shown; u (u) i Representing the traction force output by the ith section of the high-speed train; deltau i The deviation of the traction force output by the ith carriage of the high-speed train and the traction force output by the ith carriage of the high-speed train when the high-speed train is in a balanced state is shown;
neglecting the high-order items, and constructing a high-speed train multi-particle speed tracking state space model as follows:
y(t)＝Cx(t)
wherein x (t) ∈R n 、u(t)∈R n 、y(t)∈R n Respectively representing a state vector, an input vector and an output vector of the constructed state space model; w (x, t) ∈R n Representing an unknown but bounded term in the kinetic equation, primarily the force F between the cars in Is the disturbance vector of the constructed state space model; a epsilon R n×n ，B∈R n×n ，C∈R n×n Respectively representing a state matrix, an input matrix and an output matrix of the constructed trace state space model;
x(t)＝[Δv 1 ,Δv 2 ,…,Δv n ] T ，u(t)＝[Δu 1 ,Δu 2 ,…,Δu n ] T ，
C＝I n ，I n is an n-dimensional identity matrix;
aiming at the high-speed train multi-particle speed tracking state space model, when an actuator fault occurs, the input vector is expressed as follows:
u(t)＝B f ·(u o (t)+u f )＝B f u o (t)+B f u f
in the above, B f ∈R n×n Representing a multiplicative fault matrix; u (u) f ∈R n Representing an additive fault factor; u (u) o (t)∈R n Representing a normal input vector; u (t) ∈R n Representing an input vector when an actuator fault occurs;
the system state equation for the failure of the actuator of the high-speed train is established as follows:
further, the specific content of the third step is: first, the following assumptions are made:
suppose 1: a, C are considerable;
suppose 2: the existence of χ (not less than |sup) for the system state vector x (t) t≥0 x (t) |, initial value thereofSystem state matrix A epsilon R n×n And->Interference (I) wherein /> x(0) X (0) represents the upper and lower bounds and the true value of the system state vector at the initial moment respectively; /> AA represents the upper and lower bounds and the true value of the system state matrix respectively; /> w(x, t), w (x, t) represent the upper, lower bounds and true values of the system disturbance vector, respectively;
if the observability of hypothesis 1 and the desirability of hypothesis 2 are established, a Long Beige type interval observer can be constructed as follows:
wherein ,
in the above-mentioned method, the step of, x(t)∈R n respectively represent the upper and lower bounds of the system state vector,/-> B∈R n Respectively representing the upper and lower bounds of the system input matrix,x + (t) represents the lower bound of the system state vectorxA vector obtained after all elements smaller than 0 in (t) are replaced by 0; />Representing the upper bound of the system state vector +.>The vector obtained after all elements larger than 0 are replaced by 0; l epsilon R n×n Is the observer gain matrix;
suppose 3: when L meetsALC is a Hurwitz matrix,in the case of Metzler matrix, forA-LC is a Metzler matrix and a Hurwitz matrix at the same time, and the solution of the established system state equation when the high-speed train has an actuator fault is satisfied>
If the assumption 3 is satisfied, the section observer constructed as described above is a section observer of the system state equation when the established high-speed train fails to perform an actuator.
Further, in the third step, the specific content of obtaining the observer gain matrix by solving the linear matrix inequality constraint optimization problem is:
in the above, 1 n ∈R n A vector representing all elements as 1; 0 n ∈R n A vector representing all elements as 0; 0 n×n ∈R n×n Representing an n-dimensional zero matrix; beta represents a parameter to be optimized; lambda E R n×n 、Z∈R n×n Representing parameters to be solved; the observer gain matrix is obtained by solving the following equation:
L＝diag(λ) -1 Z T 。
further, the specific content of the fourth step is:
defining an upper bound for system state errorsThe method comprises the following steps:
defining a lower bound for system state errorse(t)∈R n The method comprises the following steps:
e(t)＝x(t)-x(t)；
the section observer state error dynamics model is constructed as follows:
the state error dynamic model of the interval observer can obtain the estimated values of the upper and lower boundaries of the state errorAnde(t) and judging whether the dynamic system of the high-speed train is according to the following fault detection schemeFailure occurs:
when the system operates normally, the system state is always within the interval range, and the following conditions should be satisfied: eand (5) not less than 0, otherwise, indicating that the system fails.
Compared with the prior art, the invention has the beneficial effects that:
according to the fault detection method of the high-speed train dynamic system based on the interval observer, which is disclosed by the invention, aiming at the problems that vehicle parameters are inaccurate and workshop force is difficult to measure, a longitudinal unknown bounded dynamics model of multiple particles of the high-speed train is established from the high-speed train dynamics angle, and the fault detection method of the dynamic system by adopting the interval observer is provided.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
the graph in fig. 2 represents the steady-state speed error of the carriage No. 2 of the high-speed train as a function of time when the actuator of the carriage No. 2 fails 1;
the graph in fig. 3 represents the steady state speed error of carriage No. 2 of the high speed train as a function of time when the actuator of carriage No. 2 fails 2;
the graph in fig. 4 represents the steady state speed error of carriage No. 2 of the high speed train as a function of time when the actuator of carriage No. 2 fails 3;
the graph in fig. 5 represents the steady state speed error of carriage No. 2 of the high speed train over time when the actuator of carriage No. 2 fails 4;
the curve in fig. 6 represents the change condition of the observation error output by the high-speed train No. 3 carriage section observer with time when the No. 2 carriage actuator fails 1;
the curve in fig. 7 represents the change condition of the observation error output by the high-speed train No. 3 carriage section observer with time when the No. 2 carriage actuator fails 2;
the curve in fig. 8 represents the change condition of the observation error output by the high-speed train carriage section 4 observer with time when the carriage 2 actuator fails 3;
the curve in fig. 9 represents the change condition of the observation error output by the high-speed train No. 3 carriage section observer with time when the No. 2 carriage actuator fails 4;
Detailed Description
In order to make the technical solution of the present invention better understood by those skilled in the art, the technical solution and the beneficial effects of the present invention will be further described below with reference to the accompanying drawings and specific examples in the embodiments of the present invention.
Referring to fig. 1-9, the invention provides a method for detecting faults of a dynamic system of a high-speed train based on an interval observer, which aims at faults of traction and brake actuators in running of the high-speed train by taking a dynamic system model of the high-speed train as an implementation object. The effectiveness of the method is verified through the fault simulation example, the method can detect faults of the multi-particle dynamics characteristics of the high-speed train under the condition that accurate model parameters and workshop forces of the high-speed train are not required to be obtained in advance, the method is not limited by uncertainty of the high-speed train model and matching conditions of an observer, and adaptability and convenience of fault detection of a dynamic system of the high-speed train are improved.
In the embodiment model, a high-speed train model is set by CRH5 of 4-movement and 4-dragging for simulation experiments, and the train is simplified into 4 high-speed train carriages; the high-speed train carriages are connected by adopting a coupler buffer device, so that the coupler buffer device is used for transmitting and buffering impact force, and the carriages keep a certain distance from each other, and the physical characteristics of the coupler buffer device can be regarded as springs, so that the coupler buffer device is assumed to be a linear spring in a simulation experiment model; the experimental parameters refer to the value ranges in the train traction calculation (3 rd edition) published by China railway Press, rao Zhong and Jiao Fengchuan, and the actual values are shown in the following table 1:
table 1 simulation and actual values
The fault detection method of the invention comprises the following steps:
firstly, constructing a longitudinal unknown bounded dynamics model of multiple particles of the high-speed train under the action of mechanical resistance and air resistance according to Newton's second law, and obtaining traction force output by each carriage when the high-speed train is in a balanced state;
the longitudinal unknown bounded dynamics model of the multi-mass points of the high-speed train with 4 carriages is as follows:
in the above formula, i=2, 3; m is m 1 、m i 、m 4 The mass of the 1 st carriage, the i th carriage and the 4 th carriage of the high-speed train are shown in the table 1; v 1 、v i 、v n The speeds of the 1 st carriage, the i th carriage and the 4 th carriage of the high-speed train are respectively shown; f (F) 1 、F i 、F 4 Respectively representing resultant forces of traction force and braking force applied to the 1 st carriage, the i th carriage and the 4 th carriage of the high-speed train;respectively represent the 1 st carriage, i th carriage and 4 th carriage of the high-speed trainThe general resistance of the ith car is expressed by the davis equation as:
R i ＝a i +b i v i (t)+c i v i 2 (t)
in the above, v i (t) represents the speed of the i-th car of the high-speed train; a, a i Representing the fixed resistance coefficient of the ith carriage of the high-speed train, b i Representing the rolling resistance coefficient of the ith carriage of the high-speed train, c i The air resistance coefficient of the ith carriage of the high-speed train is shown, and the air resistance is considered to only act on the 1 st carriage, so that the resistance coefficient of each carriage of the high-speed train is obtained as follows:
R i ＝a i +b i v i (t)
R 4 ＝a 4 +b 4 v 4 (t)
in the above formula, i=2, 3; r is R 1 、R i 、R 4 Respectively representing the resistance coefficients of the 1 st carriage, the i th carriage and the 4 th carriage of the high-speed train;
in the high speed train multi-particle longitudinal dynamics model described above,representing the shop force between the ith carriage and the (i-1) th carriage of the high-speed train; according to the working characteristics of the car coupler buffer device for connecting the carriages of the high-speed train, the physical characteristics of the car coupler buffer device are regarded as springs, and the car coupler buffer device is obtained:
in the above, k represents a springThe coefficient pi represents the position of the ith carriage of the high-speed train; the workshop force is unknown but bounded in the running process of the high-speed train, namely, the following conditions are satisfied:thereby obtaining the longitudinal unknown bounded dynamics model of the high-speed train multi-mass points;
in the constructed multi-particle longitudinal unknown bounded dynamics model of the high-speed train with 4 carriages in total, if the speed of the high-speed train is in an equilibrium state, the speed is v r =80 m/s, then the speeds of the carriages are equal to v r =80 m/s, acceleration is 0, i.e. v is satisfied 1 ＝v 2 ＝…＝v n ＝v r ，And the relative displacement between the two carriages is 0, so that the traction output when each carriage of the high-speed train is in a balanced state is obtained:
in the above formula, i=2, 3,4;the traction forces output by the 1 st carriage and the i th carriage when the high-speed train is in the balanced state are respectively shown.
Step two, based on the longitudinal unknown bounded dynamics model of the high-speed train multi-particle constructed in the step one and the obtained traction force output when each carriage of the high-speed train is in a balanced state, constructing a high-speed train multi-particle speed tracking state space model, and establishing a system state equation when the high-speed train has an actuator fault;
and (3) making:Δv i ＝v i -v r ，/>
in the above formula, i=1, 2,3,4;the traction force output by the ith carriage when the high-speed train is in a balanced state is shown; />Representing an estimated value of the traction force output by the ith carriage of the high-speed train; v i Representing the speed of an ith carriage of the high-speed train; v r Representing the speeds of carriages of a high-speed train in a balanced state, v r ＝80m/s；Δv i The deviation between the speed of the ith carriage of the high-speed train and the speed of the high-speed train in a balanced state is shown; u (u) i Representing the traction force output by the ith section of the high-speed train; deltau i The deviation between the traction force output by the ith carriage of the high-speed train and the traction force output by the ith carriage when the high-speed train is in a balanced state is shown;
neglecting the high-order items, and constructing a high-speed train multi-particle speed tracking state space model as follows:
y(t)＝Cx(t)
wherein x (t) ∈R 4 、u(t)∈R 4 、y(t)∈R 4 Respectively representing a state vector, an input vector and an output vector of the constructed state space model; w (x, t) ∈R 4 Is a disturbance vector of the constructed state space model; a epsilon R 4×4 ，B∈R 4×4 ，C∈R 4 ×4 Respectively representing a state matrix, an input matrix and an output matrix of the constructed trace state space model;
x(t)＝[Δv 1 ,Δv 2 ,…,Δv 4 ] T ，u(t)＝[Δu 1 ,Δu 2 ,…,Δu 4 ] T ，
C＝I 4 ，I 4 is a 4-dimensional identity matrix;
for disturbance vector w (x, t) ∈R 4 Representing an unknown but bounded term in the kinetic equation, principally the force F between the cars in Let the relative displacement between two carriages be Deltap when the high-speed train is running 1 ,Δp 2 ,Δp 3 ,Δp 4 ；
Under the above parameters, establishing a real experiment model of the high-speed train:
y(t)＝C m z(t)
wherein z (t) = [ Δv ] 1 ,Δv 2 ,Δv 3 ,Δv 4 ,Δp 1 ,Δp 2 ,Δp 3 ,Δp 4 ] T ；
In the above formula, z (t) ∈R 8 、u(t)∈R 4 、y(t)∈R 4 Respectively representing a state vector, an input vector and an output vector of the established real experiment model of the high-speed train; a is that m ∈R 8×8 ，B m ∈R 8×4 ，C m ∈R 4×8 Respectively representing a state matrix, an input matrix and an output matrix of the established real experiment model of the high-speed train;
0 4×4 ∈R 4×4 representing a 4-dimensional zero matrix;
C m ＝[I 4 ,0 4×4 ]；
establishing state feedback control to let u o = -Kz, using LQR control law to find control matrix K, yielding:
aiming at the high-speed train multi-particle speed tracking state space model, when an actuator fault occurs, the input vector is expressed as follows:
u(t)＝B f ·(u o (t)+u f )＝B f u o (t)+B f u f
in the above, B f ∈R 4×4 Representing a multiplicative fault matrix; u (u) f ∈R 4 Representing an additive fault factor; u (u) o (t)∈R 4 Representing a normal input vector; u (t) ∈R 4 Representing an input vector when an actuator fault occurs;
the system state equation when the high-speed train has the actuator fault is established as follows:
step three, constructing a fault detection interval observer based on the high-speed train multi-particle velocity tracking state space model constructed in the step two and a system state equation when an actuator fails, and obtaining a gain matrix of the observer by solving a linear matrix inequality constraint optimization problem;
suppose 1: a, C are considerable;
suppose 2: the existence of χ (not less than |sup) for the system state vector x (t) t≥0 x (t) |, initial value thereofSystem state matrix A epsilon R 4×4 And->Interference (I) wherein /> x(0) X (0) represents the upper and lower bounds and the true value of the system state vector at the initial moment respectively; /> AA represents the upper and lower bounds and the true value of the system state matrix respectively; /> w(x, t), w (x, t) represent the upper, lower bounds and true values of the system disturbance vector, respectively;
if the observability of hypothesis 1 and the desirability of hypothesis 2 are established, a Long Beige type interval observer can be constructed as follows:
wherein ,
in the above-mentioned method, the step of, x(t)∈R 4 respectively represent the upper and lower bounds of the system state vector,/-> B∈R 4 Respectively representing the upper and lower bounds of the system input matrix,x + (t) represents the lower bound of the system state vectorxA vector obtained after all elements smaller than 0 in (t) are replaced by 0; />Representing the upper bound of the system state vector +.>The vector obtained after all elements larger than 0 are replaced by 0; l epsilon R 4×4 Is the observer gain matrix; suppose 3: when L meetsALC is a Hurwitz matrix,in the case of the Metzler matrix, for +.>A-LC is a Metzler matrix and a Hurwitz matrix at the same time, and the solution of the established system state equation of the failure of the actuator of the high-speed train is satisfied +.>/>
If the assumption 3 is satisfied, the section observer constructed as described above is a section observer of the system state equation when the established high-speed train fails to perform an actuator.
Obtaining an observer gain matrix by solving a linear matrix inequality constraint optimization problem:
step four, based on the interval observer designed in the step three, defining an upper bound and a lower bound of a system state error, constructing a state error dynamics model of the interval observer to obtain estimated values of the upper bound and the lower bound of the state error of the designed interval observer, judging whether a high-speed train dynamic system breaks down, if the estimated values of the upper bound and the lower bound of the state error of the interval observer are more than or equal to 0, no fault exists, otherwise, the high-speed train dynamic system breaks down;
defining an upper bound for system state errorsThe method comprises the following steps:
defining a lower bound for system state errorse(t)∈R 4 The method comprises the following steps:
e(t)＝x(t)-x(t)
the section observer state error dynamics model is constructed as follows:
the state error dynamic model of the interval observer can obtain the estimated values of the upper and lower boundaries of the state errorAnde(t) judging whether the dynamic system of the high-speed train fails according to the following failure detection scheme:
when the system operates normally, the system state is always within the interval range, and the following conditions should be satisfied: eand (5) not less than 0, otherwise, indicating that the system fails.
In order to verify the effect of the fault detection method provided by the invention, a simulation environment is built by using a simulink module in Matlab, a fault model of an actuator is simulated, the simulation duration is 20s, the fault occurs in 5s, and the performance of an interval observer is verified under the condition of state feedback and no state feedback respectively;
fault 1: when no state feedback exists, the No. 2 carriage driver has additive fault, u f ＝[0,-611,0,0] T ，B f ＝I n ；
Fault 2: when there is status feedback, there is additive fault in carriage 2 driver, u f ＝[0,-611,0,0] T ，B f ＝I n ；
Fault 3: when there is state feedback, the carriage driver No. 2 has multiplicative fault, u f ＝[0,0,0,0] T ，B f ＝diag([1,0.3,1,1])；
Fault 4: when there is state feedback, the carriage driver No. 2 has additive multiplicative mixed fault, u f ＝[0,0,-674,0] T ，B f ＝diag([1,1,0.5,1])；
The curves in fig. 2,3,4 and 5 represent the steady-state speed error of the high-speed train (only the car No. 2 is taken as an example) with time when the car No. 2 actuator fails to fail 1, fails to fail 2, fails to fail 3 and fails to fail 4 respectively; the curve in fig. 6 represents the observation error output by the cabin section observer of the No. 3 high-speed train when the cabin actuator No. 2 fails 1; the graph in fig. 7 represents the observation error output by the car section observer of the No. 3 of the high-speed train when the car actuator No. 2 fails 2; the graph in fig. 8 represents the observation error output by the cabin section observer of the No. 4 high-speed train when the cabin actuator No. 2 fails 3; the graph in fig. 9 represents the observation error output by the car section observer of the No. 3 of the high-speed train when the car actuator No. 2 fails 4; the detection times of the section observer for the different faults are shown in table 2 below:
TABLE 2 section observer detection failure time/s
| Failure of | Observer detects failure time | Detecting failure time |
| Failure (1) | 7.58 | 2.58 |
| Failure (2) | 7.62 | 2.62 |
| Failure (3) | 11.18 | 6.18 |
| Fault (4) | 8.44 | 3.44 |
As can be seen from simulation results, when the high-speed train actuator fails, the failure detection method based on the interval observer can detect abnormal states, accurate model parameters and workshop force of the high-speed train are not required to be obtained in advance, the constraint of uncertainty of a train model and matching conditions of the observer is avoided, and the adaptability and convenience of failure detection of a dynamic system of the high-speed train are improved. The invention has important applicable reference value for the fault detection of the dynamic system of the high-speed train under the condition that the actuator breaks down.
The above specific embodiments are specific support for the technical idea of the high-speed train dynamic system fault detection method based on the interval observer, and cannot limit the protection scope of the invention, and any modification made on the basis of the technical scheme according to the technical idea of the invention still belongs to the protection scope of the technical scheme of the invention.
Claims (6)
1. A high-speed train dynamic system fault detection method based on an interval observer is characterized by comprising the following steps:
firstly, constructing a longitudinal unknown bounded dynamics model of multiple mass points of the high-speed train under the action of mechanical resistance and air resistance, and obtaining the traction force output by each carriage when the high-speed train is in a balanced state;
step two, based on the longitudinal unknown bounded dynamics model of the high-speed train multi-particle and the obtained traction force output by each carriage in the balanced state, constructing a high-speed train multi-particle speed tracking state space model, and establishing a system state equation when the high-speed train has an actuator fault;
step three, constructing a fault detection interval observer based on the high-speed train multi-particle velocity tracking state space model constructed in the step two and a system state equation when an actuator fails, and obtaining a gain matrix of the observer by solving a linear matrix inequality constraint optimization problem;
and step four, based on the interval observer designed in the step three, defining an upper bound and a lower bound of a system state error, constructing a state error dynamics model of the interval observer to obtain estimated values of the upper bound and the lower bound of the state error, judging whether the dynamic system of the high-speed train has faults, and if the estimated values of the upper bound and the lower bound of the state error of the interval observer are more than or equal to 0, no faults exist, otherwise, the dynamic system of the high-speed train has faults.
2. The method for detecting the faults of the dynamic system of the high-speed train based on the interval observer as claimed in claim 1, wherein the method comprises the following steps of: in the first step, under the action of mechanical resistance and air resistance, a longitudinal unknown bounded dynamics model of a plurality of particles of a high-speed train with n carriages is constructed as follows:
in the above formula, i=2, 3, carrying out n-1; m is m 1 、m i 、m n The mass of the 1 st carriage, the i th carriage and the n th carriage of the high-speed train are respectively shown; v 1 、v i 、v n The speeds of the 1 st carriage, the i th carriage and the n th carriage of the high-speed train are respectively shown; f (F) 1 、F i 、F n Respectively representing resultant forces of traction force and braking force applied to the 1 st carriage, the i th carriage and the n th carriage of the high-speed train;the general resistances of the 1 st, i th and n th carriages of the high-speed train are respectively shown, and the general resistance of the i th carriage is shown as follows by using the Davis equation:
F Ri ＝m i R i
R i ＝a i +b i v i (t)+c i v i 2 (t)
in the above, v i (t) represents the speed of the i-th car of the high-speed train; a, a i Representing the fixed resistance coefficient of the ith carriage of the high-speed train, b i Representing the rolling resistance coefficient of the ith carriage of the high-speed train, c i The air resistance coefficient of the ith carriage of the high-speed train is shown, and the air resistance is considered to only act on the 1 st carriage, so that the resistance coefficient of each carriage of the high-speed train is obtained as follows:
R i ＝a i +b i v i (t)
R n ＝a n +b n v n (t)
in the above formula, i=2, 3, carrying out n-1; r is R 1 、R i 、R n Respectively representing the resistance coefficients of the 1 st carriage, the i th carriage and the n th carriage of the high-speed train;
in the high speed train multi-particle longitudinal dynamics model described above,representing the shop force between the ith carriage and the (i-1) th carriage of the high-speed train; according to the working characteristics of the car coupler buffer device for connecting the carriages of the high-speed train, the physical characteristics of the car coupler buffer device are regarded as springs, and the car coupler buffer device is obtained:
in the above formula, k represents a spring coefficient, pi represents the position of the ith carriage of the high-speed train; the workshop force is unknown but bounded in the running process of the high-speed train, namely, the following conditions are satisfied:thereby obtaining the longitudinal unknown bounded dynamics model of the high-speed train multi-mass points;
in the constructed multi-particle longitudinal unknown bounded dynamics model of the high-speed train, the speed of the high-speed train in the balanced state is assumed to be v r The speed of each carriage is equal to v r Acceleration of 0, i.e. satisfying v 1 ＝v 2 ＝…＝v n ＝v r ，And the relative displacement between the two carriages is 0, so that the traction force output by each carriage when the high-speed train is in a balanced state is obtained:
in the above formula, i=2, 3, carrying out the following steps;the traction forces output by the 1 st carriage and the i th carriage when the high-speed train is in the balanced state are respectively shown.
3. The method for detecting the faults of the dynamic system of the high-speed train based on the interval observer as claimed in claim 1, wherein the method comprises the following steps of: the specific content of the second step is as follows:
and (3) making:Δv i ＝v i -v r ，/>
in the above formula, i=1, 2,3, carrying out the following steps;the traction force output by the ith carriage when the high-speed train is in a balanced state is shown; />Representing an estimated value of the traction force output by the ith carriage of the high-speed train; v i Representing the speed of an ith carriage of the high-speed train; v r The speed of each carriage when the high-speed train is in a balanced state is shown; deltav i Representing the deviation of the speed of the ith carriage of the high-speed train and the speed of the high-speed train in the balanced stateDifference; u (u) i Representing the traction force output by the ith section of the high-speed train; deltau i The deviation of the traction force output by the ith carriage of the high-speed train and the traction force output by the ith carriage of the high-speed train when the high-speed train is in a balanced state is shown;
neglecting the high-order items, and constructing a high-speed train multi-particle speed tracking state space model as follows:
y(t)＝Cx(t)
wherein x (t) ∈R n 、u(t)∈R n 、y(t)∈R n Respectively representing a state vector, an input vector and an output vector of the constructed state space model; w (x, t) ∈R n Representing an unknown but bounded term in the kinetic equation, primarily the force F between the cars in Is the disturbance vector of the constructed state space model; a epsilon R n×n ，B∈R n×n ，C∈R n×n Respectively representing a state matrix, an input matrix and an output matrix of the constructed trace state space model;
x(t)＝[Δv 1 ,Δv 2 ,…,Δv n ] T ，u(t)＝[Δu 1 ,Δu 2 ,…,Δu n ] T ，
C＝I n ，I n is an n-dimensional identity matrix;
aiming at the high-speed train multi-particle speed tracking state space model, when an actuator fault occurs, the input vector is expressed as follows:
u(t)＝B f ·(u o (t)+u f )＝B f u o (t)+B f u f
in the above, B f ∈R n×n Representing a multiplicative fault matrix; u (u) f ∈R n Representing an additive fault factor; u (u) o (t)∈R n Representing a normal input vector; u (t) ∈R n Representing an input vector when an actuator fault occurs;
the system state equation when the high-speed train has the actuator fault is established as follows:
4. the method for detecting the faults of the dynamic system of the high-speed train based on the interval observer as claimed in claim 1, wherein the method comprises the following steps of: the specific content of the third step is as follows: first, the following assumptions are made:
suppose 1: a, C are considerable;
suppose 2: the existence of χ (not less than |sup) for the system state vector x (t) t≥0 x (t) |, initial value thereofSystem state matrix A epsilon R n×n And->Interference-> wherein /> x(0) X (0) represents the upper and lower bounds and the true value of the system state vector at the initial moment respectively; /> AA represents the upper and lower bounds and the true value of the system state matrix respectively; /> w(x, t), w (x, t) represent the upper, lower bounds and true values of the system disturbance vector, respectively;
if the observability of hypothesis 1 and the desirability of hypothesis 2 are established, a Long Beige type interval observer can be constructed as follows:
wherein ,
in the above-mentioned method, the step of, x(t)∈R n respectively represent the upper and lower bounds of the system state vector,/-> B∈R n Respectively representing the upper and lower bounds of the system input matrix,x + (t) represents the lower bound of the system state vectorxA vector obtained after all elements smaller than 0 in (t) are replaced by 0; />Representing the upper bound of the system state vector +.>The vector obtained after all elements larger than 0 are replaced by 0; l epsilon R n×n Is the observer gain matrix;
suppose 3: when L meetsALC isA Hurwitz matrix of the type,in the case of the Metzler matrix, for +.>A-LC is a Metzler matrix and a Hurwitz matrix at the same time, and the solution of the established system state equation when the high-speed train has an actuator fault is satisfied>
If the assumption 3 is satisfied, the section observer constructed as described above is a section observer of the system state equation when the established high-speed train fails to perform an actuator.
5. The method for detecting the faults of the dynamic system of the high-speed train based on the interval observer as claimed in claim 1, wherein the method comprises the following steps of: in the third step, the specific content of the observer gain matrix obtained by solving the linear matrix inequality constraint optimization problem is as follows:
in the above, 1 n ∈R n A vector representing all elements as 1; 0 n ∈R n A vector representing all elements as 0; 0 n×n ∈R n ×n Representing an n-dimensional zero matrix; beta represents a parameter to be optimized; lambda E R n×n 、Z∈R n×n Representing parameters to be solved; the observer gain matrix is obtained by solving the following equation:
L＝diag(λ) -1 Z T 。
6. the method for detecting the faults of the dynamic system of the high-speed train based on the interval observer as claimed in claim 1, wherein the method comprises the following steps of: the specific content of the fourth step is as follows:
defining an upper bound for system state errorsThe method comprises the following steps:
defining a lower bound for system state errorse(t)∈R n The method comprises the following steps:
e(t)＝x(t)-x(t)；
the section observer state error dynamics model is constructed as follows:
the state error dynamic model of the interval observer can obtain the estimated values of the upper and lower boundaries of the state errorAnde(t) judging whether the dynamic system of the high-speed train fails according to the following failure detection scheme:
when the system operates normally, the system state is always within the interval range, and the following conditions should be satisfied: eand (5) not less than 0, otherwise, indicating that the system fails.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310593631.8A CN116595783A (en) | 2023-05-24 | 2023-05-24 | High-speed train dynamic system fault detection method based on interval observer |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310593631.8A CN116595783A (en) | 2023-05-24 | 2023-05-24 | High-speed train dynamic system fault detection method based on interval observer |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116595783A true CN116595783A (en) | 2023-08-15 |
Family
ID=87607790
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310593631.8A Pending CN116595783A (en) | 2023-05-24 | 2023-05-24 | High-speed train dynamic system fault detection method based on interval observer |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116595783A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117389158A (en) * | 2023-12-11 | 2024-01-12 | 华东交通大学 | High-speed train tracking control method and system based on hook buffer constraint condition |
-
2023
- 2023-05-24 CN CN202310593631.8A patent/CN116595783A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117389158A (en) * | 2023-12-11 | 2024-01-12 | 华东交通大学 | High-speed train tracking control method and system based on hook buffer constraint condition |
| CN117389158B (en) * | 2023-12-11 | 2024-03-08 | 华东交通大学 | High-speed train tracking control method and system based on hook buffer constraint condition |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110647031B (en) | Anti-saturation self-adaptive pseudo PID sliding mode fault tolerance control method for high-speed train | |
| Hu et al. | Fault-tolerant traction control of electric vehicles | |
| Isermann | Model-based fault-detection and diagnosis–status and applications | |
| CN116595783A (en) | High-speed train dynamic system fault detection method based on interval observer | |
| CN108628169B (en) | Motor train unit parking consistency control method based on multiple intelligent agents | |
| CN109375510B (en) | Self-adaptive sliding mode fault-tolerant control method for high-speed train | |
| CN110789350A (en) | Fault-tolerant control method for four-wheel drive electric vehicle | |
| CN104155968A (en) | Tiny fault diagnosis method for final controlling element of high-speed train suspension system | |
| CN113110042B (en) | Train fault tolerance control method | |
| Hu et al. | Dual neural networks based active fault-tolerant control for electromechanical systems with actuator and sensor failure | |
| CN114167733B (en) | High-speed train speed control method and system | |
| CN111027235A (en) | Heavy-duty train sliding mode tracking control method with input saturation | |
| CN111891133B (en) | Vehicle mass estimation method and system adaptive to various road conditions | |
| Mal et al. | A new estimation of nonlinear contact forces of railway vehicle | |
| Yin et al. | Dynamic hybrid observer-based early slipping fault detection for high-speed train wheelsets | |
| CN113311810B (en) | Distributed interconnection system fault isolation method based on Kalman decomposition | |
| Angeringer et al. | Drive line control for electrically driven vehicles using generalized second order sliding modes | |
| Abdulkareem et al. | Fault Detection and Fault Tolerant Control for Anti-lock Braking Systems) ABS) Speed Sensors by Using Neural Networks | |
| Oudghiri et al. | Control and sensor fault-tolerance of vehicle lateral dynamics | |
| Unger et al. | Fault tolerant sensors for vehicle dynamics control | |
| Hur et al. | A study on the critical speed of worn wheel profile using a scale model | |
| Liss et al. | Principles of formation of a vehicle’s braking system complex diagnostics | |
| CN113721497B (en) | Heavy-duty train sliding mode consistency tracking control method under safety distance constraint | |
| Kim et al. | Adaptive sliding mode control of adhesion force in railway rolling stocks | |
| Qin et al. | A robust fault estimation scheme for heavy-haul trains equipped with ECP brake systems |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |