A high-speed train dynamic system fault detection method based on interval observer

Abstract

The application discloses a high-speed train dynamic system fault detection method based on an interval observer, and belongs to the high-speed train fault detection field. First, a high-speed train multi-particle longitudinal unknown bounded dynamic model is constructed, and the tractive force output by each car compartment in a balanced state is obtained; a multi-particle speed tracking state space model and a system state equation when an actuator fault occurs are established according to the constructed dynamic model; a fault detection interval observer is constructed, and an observer gain matrix is obtained by solving a linear matrix inequality constraint optimization problem; the upper bound and the lower bound of the system state error are defined, a state error dynamic model of the interval observer is constructed to obtain the estimated values of the upper bound and the lower bound of the state error of the designed interval observer, and whether the high-speed train dynamic system has a fault is judged according to the estimated values. The method can realize fault detection on the multi-particle dynamic characteristics of the high-speed train without needing to obtain accurate model parameters and car forces of the high-speed train in advance.

Description

Technical Field

[0001] This invention belongs to the field of high-speed train fault detection, specifically relating to a method for detecting faults in the dynamic system of high-speed trains based on a section observer. Background Technology

[0002] With the development of my country's rail transit, high-speed trains have become the preferred mode of transportation due to their high speed and large capacity. As core components of high-speed trains, traction and braking actuators operate under high loads in complex environments for extended periods, inevitably leading to aging and wear, which in turn causes malfunctions, reducing the operational safety of high-speed trains and even causing loss of control and accidents, preventing them from completing their designated operational tasks. Therefore, research on fault detection of high-speed train traction and braking actuators has significant theoretical and practical importance. Currently, fault diagnosis of high-speed train traction systems mainly focuses on fault diagnosis and fault-tolerant control of traction motors, without considering the overall operation of the train. Faults in traction motors are detected only through model-based or data-driven methods. While these methods can achieve fault detection and diagnosis in high-speed trains, they often require unnecessary redundancy measures on the traction motors. Methods that diagnose faults in the overall train system often require modeling of the train forces and inputting vehicle parameters. However, due to long-term operation, component wear or aging causes changes in vehicle parameters. Furthermore, it is often difficult to establish accurate models of train buffer devices, and they are also difficult to measure during operation, resulting in significant uncertainties in the train dynamics model, making fault detection difficult through accurate models.

[0003] For actuator failures, fault diagnosis can typically be achieved by designing an observer to observe the model, especially for models containing unknown but bounded terms. The section observer fault detection scheme is not constrained by model uncertainties or observer matching conditions, improving its adaptability to fault detection in high-speed train dynamic systems and possessing significant theoretical and practical value. However, due to the high gain requirements of section observers, it is often difficult to obtain the required observer gain; therefore, most research on section observers remains in the theoretical research stage. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, the present invention aims to provide a fault detection method for high-speed train dynamic systems based on a section observer. By using a section observer, fault detection of the multi-mass dynamic characteristics of high-speed trains can be performed without prior knowledge of the precise model parameters and work forces of the high-speed train. This overcomes the defects of traditional fault detection methods and improves the adaptability of fault detection methods for high-speed train dynamic systems.

[0005] To achieve the above objectives, the solution of the present invention is:

[0006] A fault detection method for a high-speed train dynamic system based on an interval observer includes the following steps:

[0007] Step 1: Construct a longitudinal unknown bounded dynamic model of a high-speed train with multiple mass points under the action of mechanical resistance and air resistance, and obtain the traction force output by each carriage when the high-speed train is in equilibrium.

[0008] Step 2: Based on the high-speed train multi-mass longitudinal unknown bounded dynamic model constructed in Step 1 and the traction force output by each carriage when in equilibrium, construct the high-speed train multi-mass velocity tracking state space model and establish the system state equation when the high-speed train has actuator failure.

[0009] Step 3: Based on the high-speed train multi-mass speed tracking state space model constructed in Step 2 and the system state equation when there is an actuator failure, construct a fault detection interval observer and obtain the gain matrix of the observer by solving the linear matrix inequality constraint optimization problem.

[0010] Step four: Based on the interval observer designed in step three, define the upper and lower bounds of the system state error, construct the state error dynamic model of the interval observer to obtain the estimated values ​​of the upper and lower bounds of the state error, and determine whether the high-speed train dynamic system has a fault. If the estimated values ​​of the upper and lower bounds of the state error of the interval observer are both greater than or equal to 0, then there is no fault; otherwise, the high-speed train dynamic system has a fault.

[0011] Furthermore, in step one, the longitudinal unknown bounded dynamic model of a high-speed train with n carriages, constructed under the action of mechanical resistance and air resistance, is as follows:

[0012]

[0013]

[0014]

[0015] In the above formula, i = 2, 3, ..., n-1; m1, m i m n These represent the masses of the 1st, i, and nth carriages of the high-speed train, respectively; v1, v i v n These represent the speeds of the 1st, i, and nth carriages of the high-speed train, respectively; F1, F... i F n These represent the resultant forces of traction and braking on the 1st, i, and nth carriages of the high-speed train, respectively. Let represent the general resistance experienced by the 1st, i, and nth carriages of the high-speed train, respectively. The general resistance experienced by the i-th carriage, expressed using the Davis equation, is:

[0016]

[0017] R i =a i +b i v i (t)+c i v i 2 (t)

[0018] In the above formula, v i (t) represents the speed of the i-th carriage of the high-speed train; a i b represents the fixed drag coefficient of the i-th carriage of a high-speed train. i c represents the rolling resistance coefficient experienced by the i-th carriage of a high-speed train. i Let represent the air resistance coefficient of the i-th carriage of the high-speed train. Considering that air resistance only acts on the first carriage, the resistance coefficients of each carriage of the high-speed train are obtained as follows:

[0019]

[0020] R i =a i +b i v i (t)

[0021] R n =a n +b n v n (t)

[0022] In the above formula, i = 2, 3, ..., n-1; R1, R i R n These represent the drag coefficients of the 1st, i, and nth carriages of the high-speed train, respectively.

[0023] In the aforementioned multi-mass longitudinal dynamics model of a high-speed train, This represents the inter-carriage force exerted on the i-th car of a high-speed train between it and the (i-1)-th car; based on the working characteristics of the coupler buffer device connecting the cars of a high-speed train, its physical properties are considered as springs, resulting in:

[0024]

[0025] In the above formula, k represents the spring constant, and pi represents the position of the i-th carriage of the high-speed train; in high-speed

[0026] During train operation, the forces in the workshop are unknown but bounded, i.e., they satisfy: Thus, the above-mentioned high-speed train multi-mass longitudinal unknown bounded dynamic model is obtained;

[0027] In the aforementioned constructed multi-mass longitudinal unknown bounded dynamic model of a high-speed train, it is assumed that the high-speed train is in equilibrium with a velocity of v. r Then the speed of each carriage is equal to v. r The accelerations are all 0, meaning they satisfy v1 = v2 = ... = v n =v r , Furthermore, the relative displacement between the two carriages is 0, thus yielding the traction force output by each carriage when the high-speed train is in equilibrium:

[0028]

[0029]

[0030] In the above formula, i = 2, 3, ..., n; These represent the traction forces output by the first and i-th carriages when the high-speed train is in a balanced state.

[0031] Furthermore, the specific content of step two is as follows:

[0032] make: Δv i =v i -v r ,

[0033] In the above formula, i = 1, 2, 3, ..., n; This represents the traction force output by the i-th carriage when the high-speed train is in equilibrium. This represents the estimated traction force output by the i-th carriage of a high-speed train; v i v represents the speed of the i-th carriage of a high-speed train; r Δv represents the speed of each carriage when the high-speed train is in equilibrium. i This represents the deviation between the speed of the i-th carriage of a high-speed train and the speed of the high-speed train when it is in equilibrium; u i Δu represents the traction force output by the i-th section of the high-speed train. i This represents the deviation between the traction force output by the i-th carriage of the high-speed train and the traction force output by that carriage when the high-speed train is in equilibrium.

[0034] Ignoring higher-order terms, the state-space model for multi-mass velocity tracking of a high-speed train is constructed as follows:

[0035]

[0036] y(t)=Cx(t)

[0037] Where x(t)∈R nu(t)∈R n y(t)∈R n Let w(x,t) represent the state vector, input vector, and output vector of the constructed state-space model, respectively; n This represents the unknown but bounded terms in the dynamic equations, primarily the forces F between the carriages. in , is the perturbation vector of the constructed state-space model; A∈R n×n , B∈R n×n , C∈R n×n These represent the state matrix, input matrix, and output matrix of the constructed trace state-space model, respectively.

[0038] x(t) = [Δv1, Δv2, ..., Δv n ] T u(t)=[Δu1,Δu2,…,Δu n ] T ,

[0039]

[0040] C = I n I n It is an n-dimensional identity matrix;

[0041] For the aforementioned state-space model of multi-mass velocity tracking for high-speed trains, the input vector when an actuator fault occurs is represented as:

[0042] u(t)=B f ·(u o (t)+u f ) = B f u o (t)+B f u f

[0043] In the above formula, B f ∈R n×n Represents the multiplicative fault matrix; u f ∈R n Indicates the additive fault factor; u o (t)∈R n Represents a normal input vector; u(t)∈R n This represents the input vector when an actuator failure occurs;

[0044] The system state equations for a high-speed train experiencing actuator failure are established as follows:

[0045]

[0046] Furthermore, the specific content of step three is as follows: First, make the following assumptions:

[0047] Assumption 1: A and C are observable;

[0048] Assumption 2: For the system state vector x(t), there exists χ≥|sup t≥0 x(t)|, its initial value System state matrix A∈R n×n ,and interference in x x(0) and x(0) represent the upper and lower bounds and the true value of the system state vector at the initial moment, respectively; A A and B represent the upper and lower bounds and the true value of the system state matrix, respectively; w w(x,t) and w(x,t) represent the upper and lower bounds and the true value of the system disturbance vector, respectively.

[0049] If the observability of assumption 1 and the boundedness of assumption 2 hold, then a Romberg-type interval observer can be constructed as follows:

[0050]

[0051]

[0052] in,

[0053] In the above formula, x (t)∈R n These represent the upper and lower bounds of the system state vector, respectively. B ∈R n These represent the upper and lower bounds of the system input matrix, respectively. x + (t) represents the lower bound of the system state vector. x The vector obtained by replacing all elements less than 0 in (t) with 0; This represents the upper bound of the system state vector. The vector obtained by replacing all elements greater than 0 with 0; L∈R n×n It is the observer gain matrix;

[0054] Assumption 3: When L satisfies A -LC is the Hurwitz matrix. When it is a Metzler matrix, for A-LC is both a Metzler matrix and a Hurwitz matrix. The solution to the system state equation for a high-speed train experiencing actuator failure satisfies...

[0055] If the above assumption 3 holds true, then the constructed interval observer is the interval observer of the system state equation when the high-speed train experiences actuator failure.

[0056] Furthermore, in step three, the specific content of the observer gain matrix obtained by solving the linear matrix inequality constraint optimization problem is as follows:

[0057]

[0058] In the above formula, 1 n ∈R n A vector whose all elements are 1; 0 n ∈R n A vector whose all elements are 0; 0 n×n ∈R n×n Let λ represent an n-dimensional zero matrix; β represent the parameters to be optimized; λ∈R n×n Z∈R n×n The parameters to be solved are represented; the observer gain matrix is ​​obtained by solving the following equation:

[0059] L = diag(λ) -1 Z T .

[0060] Furthermore, the specific content of step four is as follows:

[0061] Define the upper bound of the system state error for:

[0062]

[0063] Define the lower bound of the system state error e (t)∈R n for:

[0064] e (t)=x(t)- x (t);

[0065] The dynamic model of the state error of the interval observer is constructed as follows:

[0066]

[0067] The estimated values ​​of the upper and lower bounds of the state error can be obtained from the above dynamic model of the interval observer state error. and e (t), and determine whether a fault has occurred in the high-speed train dynamic system according to the following fault detection scheme:

[0068] When the system is running normally, the system state always stays within the specified range and should satisfy the following: e≥0, otherwise it indicates that the system has malfunctioned.

[0069] Compared with the prior art, the beneficial effects of the present invention are:

[0070] This invention discloses a fault detection method for high-speed train dynamic systems based on interval observers. Addressing the problems of inaccurate vehicle parameters and difficulty in measuring inter-vehicle forces, this method establishes a longitudinally unknown bounded dynamic model of a high-speed train with multiple mass points from the perspective of high-speed train dynamics. It proposes a method for fault detection of the dynamic system using interval observers. This method can detect faults in the dynamic characteristics of high-speed trains with multiple mass points without prior knowledge of the precise model parameters and inter-vehicle forces. It is not constrained by the uncertainties of the high-speed train model or the matching conditions of the observer, thus improving the adaptability and convenience of fault detection for high-speed train dynamic systems and possessing significant practical reference value. Attached Figure Description

[0071] Figure 1 This is a flowchart of the method of the present invention;

[0072] Figure 2 The curve in the figure represents the change of steady-state speed error of carriage 2 of the high-speed train over time when the actuator of carriage 2 malfunctions.

[0073] Figure 3 The curve in the figure represents the change of steady-state speed error of carriage 2 of the high-speed train over time when the actuator of carriage 2 fails.

[0074] Figure 4 The curve in the figure represents the change of steady-state speed error of carriage 2 of the high-speed train over time when the actuator of carriage 2 fails.

[0075] Figure 5 The curve in the figure represents the change of steady-state speed error of carriage 2 of the high-speed train over time when the actuator of carriage 2 malfunctions by 4.

[0076] Figure 6 The curve in the figure represents the change of the observation error output by the section observer of carriage 3 of the high-speed train over time when the actuator of carriage 2 malfunctions.

[0077] Figure 7 The curve in the figure represents the change of the observation error output by the section observer of carriage 3 of the high-speed train over time when the actuator of carriage 2 malfunctions.

[0078] Figure 8 The curve in the figure represents the change of observation error output by the section observer of carriage 4 of the high-speed train over time when the actuator of carriage 2 malfunctions.

[0079] Figure 9 The curve in the figure represents the change of the observation error output by the section observer of carriage 3 of the high-speed train over time when the actuator of carriage 2 malfunctions. Detailed Implementation

[0080] To enable those skilled in the art to better understand the present invention, the technical solution and beneficial effects of the present invention will be further explained below with reference to the accompanying drawings and specific examples in the embodiments of the present invention.

[0081] See Figures 1-9 This invention focuses on the dynamic system model of a high-speed train. Addressing traction and braking actuator failures during high-speed train operation, it proposes a fault detection method for the dynamic system of a high-speed train based on an interval observer. This method establishes a longitudinally unknown bounded dynamic model of a multi-mass point high-speed train and uses an interval observer to detect faults in the dynamic system. The effectiveness of the proposed method is verified through fault simulation examples. This method can detect faults in the multi-mass dynamic characteristics of a high-speed train without prior knowledge of the precise model parameters and inter-vehicle forces, and is not constrained by the uncertainties of the high-speed train model or the matching conditions of the observer, thus improving the adaptability and convenience of fault detection in the dynamic system of high-speed trains.

[0082] This invention uses a CRH5 high-speed train model with 4 powered and 4 unpowered carriages for simulation experiments. The train is simplified to 4 high-speed train carriages. The carriages are connected by a coupler buffer device to transmit and mitigate impact forces and maintain a certain distance between them. Its physical characteristics can be regarded as springs. Therefore, the coupler buffer device is assumed to be a linear spring in the simulation experiment model. The experimental parameters refer to the value range in "Train Traction Calculation (3rd Edition)" by Rao Zhong and Jiao Fengchuan, published by China Railway Publishing House, and the actual values ​​are shown in Table 1 below.

[0083] Table 1 Simulation value range and actual value

[0084]

[0085] The fault detection method of the present invention includes the following steps:

[0086] Step 1: Based on Newton's second law, construct a longitudinal unknown bounded dynamic model of a high-speed train with multiple mass points under the action of mechanical resistance and air resistance, and obtain the traction force output by each carriage when the high-speed train is in equilibrium.

[0087] The multi-mass longitudinal unknown bounded dynamic model of a high-speed train with four carriages is as follows:

[0088]

[0089]

[0090]

[0091] In the above formula, i = 2, 3; m1, m i m1 and m4 represent the masses of the 1st, i, and 4th carriages of the high-speed train, respectively, as shown in Table 1 above; v1 and v2 represent the masses of the 1st, i, and 4th carriages of the high-speed train, respectively. i v n These represent the speeds of the 1st, i, and 4th carriages of the high-speed train, respectively; F1, F... i F4 represents the resultant force of traction and braking on the 1st, ith, and 4th carriages of the high-speed train, respectively. Let represent the general resistance experienced by carriages 1, i, and 4 of the high-speed train, respectively. The general resistance experienced by carriage i can be expressed using the Davis equation as:

[0092]

[0093] R i =a i +b i v i (t)+c i v i 2 (t)

[0094] In the above formula, v i (t) represents the speed of the i-th carriage of the high-speed train; a i b represents the fixed drag coefficient of the i-th carriage of a high-speed train. i c represents the rolling resistance coefficient experienced by the i-th carriage of a high-speed train. i Let represent the air resistance coefficient of the i-th carriage of the high-speed train. Considering that air resistance only acts on the first carriage, the resistance coefficients of each carriage of the high-speed train are obtained as follows:

[0095]

[0096] R i =a i +b i v i (t)

[0097] R4 = a4 + b4v4(t)

[0098] In the above formula, i = 2, 3; R1, R i R1 and R2 represent the drag coefficients of the 1st, i, and 4th carriages of the high-speed train, respectively.

[0099] In the aforementioned multi-mass longitudinal dynamics model of a high-speed train, Let represent the inter-carriage force exerted on the i-th car of the high-speed train between it and the (i-1)-th car; based on the working characteristics of the coupler buffer device connecting the cars of the high-speed train, its physical properties are considered as springs, resulting in:

[0100]

[0101] In the above formula, k represents the spring constant, and pi represents the position of the i-th carriage of the high-speed train; during the operation of the high-speed train, the inter-vehicle force is unknown but bounded, that is, it satisfies: Thus, the above-mentioned high-speed train multi-mass longitudinal unknown bounded dynamic model is obtained;

[0102] In the aforementioned constructed multi-mass longitudinal unknown bounded dynamic model of a high-speed train with four carriages, if the speed of the high-speed train in equilibrium is v r =80m / s, then the speed of each carriage at this time is equal to v. r =80m / s², acceleration is 0, that is, it satisfies v1=v2=…=v n =v r , Furthermore, the relative displacement between the two carriages is 0, thus yielding the traction force output by each carriage of the high-speed train when they are in equilibrium:

[0103]

[0104]

[0105] In the above formula, i = 2, 3, 4; These represent the traction forces output by the first and i-th carriages when the high-speed train is in a balanced state.

[0106] Step 2: Based on the high-speed train multi-mass longitudinal unknown bounded dynamic model constructed in Step 1 and the traction force output by each carriage of the high-speed train when it is in equilibrium, construct the high-speed train multi-mass velocity tracking state space model and establish the system state equation when the high-speed train has actuator failure.

[0107] make: Δv i =v i -v r ,

[0108] In the above formula, i = 1, 2, 3, 4; This represents the traction force output by the i-th carriage when the high-speed train is in equilibrium. This represents the estimated traction force output by the i-th carriage of a high-speed train; v i v represents the speed of the i-th carriage of a high-speed train; rv represents the speed of each carriage when the high-speed train is in equilibrium. r =80m / s; Δv i This represents the deviation between the speed of the i-th carriage of a high-speed train and the speed of the high-speed train when it is in equilibrium; u i Δu represents the traction force output by the i-th section of the high-speed train. i This represents the deviation between the traction force output by the i-th carriage of the high-speed train and the traction force output by that carriage when the high-speed train is in equilibrium.

[0109] Ignoring higher-order terms, the state-space model for multi-mass velocity tracking of a high-speed train is constructed as follows:

[0110]

[0111] y(t)=Cx(t)

[0112] Where x(t)∈R 4 u(t)∈R 4 y(t)∈R 4 Let w(x,t) represent the state vector, input vector, and output vector of the constructed state-space model, respectively; 4 It is the perturbation vector of the constructed state-space model; A∈R 4×4 , B∈R 4×4 , C∈R 4 ×4 These represent the state matrix, input matrix, and output matrix of the constructed trace state-space model, respectively.

[0113] x(t)=[Δv1,Δv2,…,Δv4] T ,u(t)=[Δu1,Δu2,…,Δu4] T ,

[0114]

[0115] C = I4, where I4 is a 4-dimensional identity matrix;

[0116] For the perturbation vector w(x,t)∈R 4 , represents the unknown but bounded terms in the dynamic equations, mainly the forces F between the carriages. in Assume that the relative displacements between the two carriages of the high-speed train are Δp1, Δp2, Δp3, and Δp4 respectively when the train is running.

[0117] Under the above parameters, a real experimental model of a high-speed train is established:

[0118]

[0119] y(t)=Cm z(t)

[0120] Among them, z(t)=[Δv1,Δv2,Δv3,Δv4,Δp1,Δp2,Δp3,Δp4] T ;

[0121] In the above formula, z(t)∈R 8 u(t)∈R 4 y(t)∈R 4 Let A represent the state vector, input vector, and output vector of the established high-speed train real experimental model, respectively; m ∈R 8×8 B m ∈R 8×4 C m ∈R 4×8 These represent the state matrix, input matrix, and output matrix of the established high-speed train real experimental model, respectively.

[0122]

[0123] 0 4×4 ∈R 4×4 Represents a 4-dimensional zero matrix;

[0124]

[0125] C m =[I4,0 4×4 ];

[0126] Establish state feedback control, let u o =-Kz, using the LQR control law to obtain the control matrix K, we get:

[0127]

[0128] For the aforementioned state-space model of multi-mass velocity tracking for high-speed trains, the input vector when an actuator fault occurs is represented as:

[0129] u(t)=B f ·(u o (t)+u f ) = B f u o (t)+B f u f

[0130] In the above formula, B f ∈R 4×4 Represents the multiplicative fault matrix; u f ∈R 4 Indicates the additive fault factor; u o (t)∈R4 Represents a normal input vector; u(t)∈R 4 This represents the input vector when an actuator failure occurs;

[0131] The system state equations for a high-speed train experiencing actuator failure are established as follows:

[0132]

[0133] Step 3: Based on the high-speed train multi-mass speed tracking state space model constructed in Step 2 and the system state equation when there is an actuator failure, construct a fault detection interval observer and obtain the gain matrix of the observer by solving the linear matrix inequality constraint optimization problem.

[0134] Assumption 1: A and C are observable;

[0135] Assumption 2: For the system state vector x(t), there exists χ≥|sup t≥0 x(t)|, its initial value System state matrix A∈R 4×4 ,and interference in x x(0) and x(0) represent the upper and lower bounds and the true value of the system state vector at the initial moment, respectively; A A and B represent the upper and lower bounds and the true value of the system state matrix, respectively; w w(x,t) and w(x,t) represent the upper and lower bounds and the true value of the system disturbance vector, respectively.

[0136] If the observability of assumption 1 and the boundedness of assumption 2 hold, then a Romberg-type interval observer can be constructed as follows:

[0137]

[0138]

[0139] in,

[0140] In the above formula, x (t)∈R 4 These represent the upper and lower bounds of the system state vector, respectively. B ∈R 4 These represent the upper and lower bounds of the system input matrix, respectively. x + (t) represents the lower bound of the system state vector. xThe vector obtained by replacing all elements less than 0 in (t) with 0; This represents the upper bound of the system state vector. The vector obtained by replacing all elements greater than 0 with 0; L∈R 4×4 It is the observer gain matrix; Assumption 3: When L satisfies A -LC is the Hurwitz matrix. When it is a Metzler matrix, for A-LC is both a Metzler matrix and a Hurwitz matrix. The solution to the system state equation for a high-speed train experiencing actuator failure satisfies...

[0141] If the above assumption 3 holds true, then the constructed interval observer is the interval observer of the system state equation when the high-speed train experiences actuator failure.

[0142] The observer gain matrix is ​​obtained by solving the linear matrix inequality constraint optimization problem:

[0143]

[0144] Step 4: Based on the section observer designed in Step 3, define the upper and lower bounds of the system state error, and construct the state error dynamic model of the section observer to obtain the estimated values ​​of the upper and lower bounds of the designed section observer state error. Determine whether the high-speed train dynamic system has a fault. If the estimated values ​​of the upper and lower bounds of the section observer state error are both greater than or equal to 0, then there is no fault; otherwise, the high-speed train dynamic system has a fault.

[0145] Define the upper bound of the system state error for:

[0146]

[0147] Define the lower bound of the system state error e (t)∈R 4 for:

[0148] e (t)=x(t)- x (t)

[0149] The dynamic model of the state error of the interval observer is constructed as follows:

[0150]

[0151] The estimated values ​​of the upper and lower bounds of the state error can be obtained from the above dynamic model of the interval observer state error. and e(t), and determine whether a fault has occurred in the high-speed train dynamic system according to the following fault detection scheme:

[0152] When the system is running normally, the system state always stays within the specified range and should satisfy the following: e ≥0, otherwise it indicates that the system has malfunctioned.

[0153] To verify the effectiveness of the fault detection method proposed in this invention, a simulation environment was built using the Simulink module in Matlab. The following fault model of the actuator was simulated. The simulation time was 20 seconds, and the fault occurred at 5 seconds. The performance of the interval observer was verified under the conditions of state feedback and without state feedback.

[0154] Fault 1: When there is no status feedback, the drive unit of car 2 has an additive fault. f =[0,-611,0,0] T B f =I n ;

[0155] Fault 2: When status feedback is available, the drive unit of car number 2 has an additive fault. f =[0,-611,0,0] T B f =I n ;

[0156] Fault 3: When status feedback is available, the drive unit of car number 2 has a multiplicative fault. f =[0,0,0,0] T B f =diag([1,0.3,1,1]);

[0157] Fault 4: When status feedback is available, the drive unit of car number 2 exhibits a mixed additive and multiplicative fault. f =[0,0,-674,0] T B f =diag([1,1,0.5,1]);

[0158] Figure 2 , Figure 3 , Figure 4 , Figure 5 The curves in the figure represent the changes in the steady-state speed error of the high-speed train (taking carriage 2 as an example) over time when the actuator of carriage 2 experiences faults 1, 2, 3, and 4, respectively. Figure 6 The curve in the figure represents the observation error output by the section observer of carriage 3 of the high-speed train when the actuator of carriage 2 malfunctions. Figure 7The curve in the figure represents the observation error output by the section observer of carriage 3 of the high-speed train when the actuator of carriage 2 malfunctions. Figure 8 The curve in the figure represents the observation error output by the section observer of carriage 4 of the high-speed train when the actuator of carriage 2 malfunctions. Figure 9 The curve in the figure represents the observation error output by the section observer in carriage 3 of the high-speed train when the actuator in carriage 2 malfunctions (fault 4). The detection time of the section observer for different faults is shown in Table 2 below:

[0159] Table 2. Fault detection time of the interval observer (s)

[0160] Fault The observer detected the fault time. Fault detection time Fault (1) 7.58 2.58 Fault (2) 7.62 2.62 Fault (3) 11.18 6.18 Fault (4) 8.44 3.44

[0161] Simulation results show that when a high-speed train actuator malfunctions, the fault detection method based on the section observer designed in this invention can detect abnormal states without prior knowledge of the high-speed train's precise model parameters and inter-vehicle forces. It is unaffected by train model uncertainties and observer matching conditions, thus improving the adaptability and convenience of fault detection for high-speed train dynamic systems. This invention has significant practical reference value for fault detection in high-speed train dynamic systems under actuator failure conditions.

[0162] The above specific embodiments are specific support for the technical concept of the high-speed train dynamic system fault detection method based on the section observer proposed in this invention, and should not be used to limit the scope of protection of this invention. Any modifications made based on the technical concept proposed in this invention shall still fall within the scope of protection of this invention.

Claims

1. A fault detection method for a high-speed train dynamic system based on an interval observer, characterized in that... Includes the following steps: Step 1: Construct a longitudinal unknown bounded dynamic model of a high-speed train with multiple mass points under the action of mechanical resistance and air resistance, and obtain the traction force output by each carriage when the high-speed train is in equilibrium. Step 2: Based on the high-speed train multi-mass longitudinal unknown bounded dynamic model constructed in Step 1 and the traction force output by each carriage when in equilibrium, construct the high-speed train multi-mass velocity tracking state space model and establish the system state equation when the high-speed train has actuator failure. The specific content of step two is as follows: make: , , , In the above formula, ; This represents the traction force output by the i-th carriage when the high-speed train is in equilibrium. This represents the estimated traction force output by the i-th carriage of a high-speed train; This represents the speed of the i-th carriage of the high-speed train; This indicates the speed of each carriage when the high-speed train is in a balanced state. This represents the deviation between the speed of the i-th carriage of the high-speed train and the speed of the high-speed train when it is in equilibrium. This represents the traction force output by the i-th section of the high-speed train; This represents the deviation between the traction force output by the i-th carriage of the high-speed train and the traction force output by that carriage when the high-speed train is in equilibrium. Ignoring higher-order terms, the state-space model for multi-mass velocity tracking of a high-speed train is constructed as follows: in, , , These represent the state vector, input vector, and output vector of the constructed state-space model, respectively. This represents the unknown but bounded terms in the dynamic equations, mainly the forces between the carriages. , is the perturbation vector of the constructed state-space model; , , These represent the state matrix, input matrix, and output matrix of the constructed trace state-space model, respectively. ， ， ， , , It is an n-dimensional identity matrix; For the aforementioned state-space model of multi-mass velocity tracking for high-speed trains, the input vector when an actuator fault occurs is represented as: In the above formula, Represents the multiplicative fault matrix; u f ∈R n Represents the additive fault factor; u0(t)∈R n This represents a normal input vector; This represents the input vector when an actuator failure occurs; The system state equations for a high-speed train experiencing actuator failure are established as follows: ； Step 3: Based on the high-speed train multi-mass speed tracking state space model constructed in Step 2 and the system state equation when there is an actuator failure, construct a fault detection interval observer and obtain the gain matrix of the observer by solving the linear matrix inequality constraint optimization problem. The specific content of step three is as follows: First, make the following assumptions: Assumption 1: A, It is considerable; Assumption 2: For the system state vector x(t), there exists Its initial value System state matrix ,and ,interference ,in , , These represent the upper and lower bounds and the true value of the system state vector at the initial moment, respectively; , , These represent the upper and lower bounds and the true value of the system state matrix, respectively. , , These represent the upper and lower bounds and the true value of the system disturbance vector, respectively; If the observability of assumption 1 and the boundedness of assumption 2 hold, then a Romberg-type interval observer can be constructed as follows: in, , In the above formula, , These represent the upper and lower bounds of the system state vector, respectively. , These represent the upper and lower bounds of the system input matrix, respectively. This represents the lower bound of the system state vector. The vector obtained by replacing all elements less than 0 with 0; This represents the upper bound of the system state vector. The vector obtained by replacing all elements greater than 0 with 0; It is the observer gain matrix; Assumption 3: When satisfy For Hurwitz matrices, When it is a Metzler matrix, for , The solution to the system state equation for a high-speed train experiencing actuator failure, which is simultaneously a Metzler matrix and a Hurwitz matrix, satisfies... ; If the above assumption 3 holds true, then the constructed interval observer is the interval observer of the system state equation when the high-speed train experiences actuator failure. Step four: Based on the interval observer designed in step three, define the upper and lower bounds of the system state error, construct the state error dynamic model of the interval observer to obtain the estimated values ​​of the upper and lower bounds of the state error, and determine whether the high-speed train dynamic system has a fault. If the estimated values ​​of the upper and lower bounds of the state error of the interval observer are both greater than or equal to 0, then there is no fault; otherwise, the high-speed train dynamic system has a fault.

2. The fault detection method for a high-speed train dynamic system based on an interval observer according to claim 1, characterized in that: In step one, the longitudinal unknown bounded dynamic model of a high-speed train with n carriages, constructed under the action of mechanical resistance and air resistance, is as follows: In the above formula, m1, m i m n These represent the masses of the 1st, i, and nth carriages of the high-speed train, respectively; v1, v i v n These represent the speeds of the 1st, i, and nth carriages of the high-speed train, respectively; F1, F... i F n These represent the resultant forces of traction and braking on the 1st, i, and nth carriages of the high-speed train, respectively. , , Let represent the general resistance experienced by the 1st, i, and nth carriages of the high-speed train, respectively. The general resistance experienced by the i-th carriage, expressed using the Davis equation, is: In the above formula, a represents the speed of the i-th carriage of a high-speed train; i b represents the fixed drag coefficient of the i-th carriage of a high-speed train. i c represents the rolling resistance coefficient experienced by the i-th carriage of a high-speed train. i Let represent the air resistance coefficient of the i-th carriage of the high-speed train. Considering that air resistance only acts on the first carriage, the resistance coefficients of each carriage of the high-speed train are obtained as follows: In the above formula, ; , , These represent the drag coefficients of the 1st, i, and nth carriages of the high-speed train, respectively. In the aforementioned multi-mass longitudinal dynamics model of a high-speed train, Let represent the inter-carriage force exerted on the i-th car of the high-speed train between it and the (i-1)-th car; based on the working characteristics of the coupler buffer device connecting the cars of the high-speed train, its physical properties are considered as springs, resulting in: In the above formula, k represents the spring constant, and pi represents the position of the i-th carriage of the high-speed train; On the highway During train operation, the forces in the workshop are unknown but bounded, i.e., they satisfy: Thus, the above-mentioned high-speed train multi-mass longitudinal unknown bounded dynamic model is obtained; In the aforementioned constructed multi-mass longitudinal unknown bounded dynamic model of a high-speed train, it is assumed that the speed of the high-speed train in equilibrium is... Then the speed of each carriage is equal to The acceleration is 0, which satisfies the condition. , Furthermore, the relative displacement between the two carriages is 0, thus yielding the traction force output by each carriage when the high-speed train is in equilibrium: In the above formula, ; , These represent the traction forces output by the first and i-th carriages when the high-speed train is in a balanced state.

3. The high-speed train dynamic system fault detection method based on an interval observer according to claim 1, characterized in that: In step three, the specific content of the observer gain matrix obtained by solving the linear matrix inequality constraint optimization problem is as follows: ， In the above formula, Represents a vector in which all elements are 1; Represents a vector in which all elements are 0; Represents an n-dimensional zero matrix; Indicates the parameters to be optimized; , The parameters to be solved are represented; the observer gain matrix is ​​obtained by solving the following equation: 。 4. The high-speed train dynamic system fault detection method based on an interval observer according to claim 1, characterized in that: The specific content of step four is as follows: Define the upper bound of the system state error for: ； Define the lower bound of the system state error for: ； The dynamic model of the state error of the interval observer is constructed as follows: ， The estimated values ​​of the upper and lower bounds of the state error can be obtained from the above dynamic model of the interval observer state error. and The following fault detection scheme is used to determine whether a fault has occurred in the dynamic system of the high-speed train: When the system is running normally, the system state always stays within the specified range and should satisfy the following: , Otherwise, it indicates a system malfunction.

Images