A high-speed train basic resistance online estimation method, device, equipment and medium

Abstract

The application discloses a high-speed train basic resistance online estimation method, device, equipment and medium, relates to the field of track traffic control and high-speed train dynamics control, and the method comprises the following steps: constructing a multi-particle longitudinal dynamics equation of a high-speed train based on the internal coupling force of the high-speed train; designing an adaptive observer based on the multi-particle longitudinal dynamics equation; the adaptive observer comprises a state estimation equation, a parameter adaptive law, an auxiliary variable dynamic equation, a gain matrix updating law and a basic resistance equation; and the basic resistance of the high-speed train is estimated online based on the adaptive observer, so that the basic resistance estimation values of each carriage of the high-speed train are obtained. The application can effectively estimate the basic resistance online and asymptotically, significantly reduces the test cost and improves the robust performance, does not need to rely on complex offline tests, and has both high precision and strong robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rail transit control and high-speed train dynamics control, and in particular to a high-speed train basic resistance online estimation method, device, equipment and medium. BACKGROUND

[0002] The basic resistance of a high-speed train during operation is a key factor affecting its dynamic characteristics and control accuracy. The resistance is composed of mechanical resistance (such as wheel-rail rolling resistance and bearing friction resistance, etc.) and aerodynamic resistance, and is usually described by the Davis equation containing the train basic resistance parameter (TBRP). Accurate acquisition of the resistance parameters , and (TBRP or Davis parameter) in the equation is a core prerequisite for realizing precise train traction and braking control, energy optimization and trajectory tracking.

[0003] Existing parameter acquisition methods mainly include real vehicle test, wind tunnel test and numerical simulation. Although real vehicle test can reflect real working conditions, it requires special lines and equipment, has high single cost, is strongly dependent on the environment, has large measurement noise and difficult data processing; the wind tunnel test simulates the aerodynamic characteristics through a scaled model, but the scaled effect is caused by the difference in Reynolds number, which cannot completely reproduce the real flow state, and the mechanical resistance characteristics cannot be effectively simulated, resulting in increased resistance prediction error; numerical simulation relies on offline simulation data and cannot truly reflect the dynamic characteristics of resistance under complex environments (such as crosswind disturbance and component deformation), resulting in systematic deviation between model output and measured value. In addition, the deployment cost of high-precision sensors is high and they are easily affected by mechanical vibration.

[0004] In addition, the above-mentioned traditional offline method adopts the same type of train parameter consistency principle, and it is difficult to update the TBRP of a certain train in a specified time period. In terms of control strategy, the existing adaptive method only realizes speed tracking by indirectly compensating for parameter uncertainty, without explicitly estimating the basic resistance, resulting in the lack of feedforward control.

[0005] With the development of intelligent and unmanned high-speed trains, the high cost and insufficient robustness of traditional offline methods have become a core bottleneck restricting the improvement of train control performance. There is an urgent need for an online asymptotic estimation method that does not rely on complex offline tests and has both precision and strong robustness to break through the limitations of traditional technology and provide key support for intelligent train control. SUMMARY

[0006] The purpose of the present application is to provide a high-speed train basic resistance online estimation method, device, equipment and medium without relying on complex offline tests and with both precision and strong robustness.

[0007] To achieve the above object, the application provides the following scheme.

[0008] In a first aspect, the application provides a high-speed train basic resistance online estimation method, comprising the following steps.

[0009] A multi-particle longitudinal dynamics equation of the high-speed train is constructed based on the internal coupler force of the high-speed train.

[0010] An adaptive observer is designed based on the multi-particle longitudinal dynamics equation; the adaptive observer comprises a state estimation equation, a parameter adaptive law, an auxiliary variable dynamic equation, a gain matrix update law and a basic resistance equation.

[0011] The basic resistance of the high-speed train is online estimated based on the adaptive observer, and the basic resistance estimation value of each car of the high-speed train is obtained.

[0012] In a second aspect, the application provides a high-speed train basic resistance online estimation device, comprising the following modules.

[0013] A multi-particle longitudinal dynamics equation establishment module is configured to construct a multi-particle longitudinal dynamics equation of the high-speed train based on the internal coupler force of the high-speed train.

[0014] An adaptive observer design module is configured to design an adaptive observer based on the multi-particle longitudinal dynamics equation; the adaptive observer comprises a state estimation equation, a parameter adaptive law, an auxiliary variable dynamic equation, a gain matrix update law and a basic resistance equation.

[0015] A basic resistance estimation module is configured to online estimate the basic resistance of the high-speed train based on the adaptive observer, and obtain the basic resistance estimation value of each car of the high-speed train.

[0016] In a third aspect, the application provides a computer device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to realize the high-speed train basic resistance online estimation method.

[0017] In a fourth aspect, the application provides a computer readable storage medium, which stores a computer program, wherein the computer program is executed by a processor to realize the high-speed train basic resistance online estimation method.

[0018] According to the specific embodiments provided in this application, this application discloses the following technical effects: This application provides a method, device, equipment and medium for online estimation of the basic resistance of a high-speed train. An adaptive observer is designed through the multi-particle longitudinal dynamic equation of the high-speed train, and then the basic resistance of the high-speed train is estimated online based on the adaptive observer to obtain the basic resistance estimation value of each carriage of the high-speed train. The adaptive observer includes a state estimation equation, a parameter adaptation law, an auxiliary variable dynamic equation, a gain matrix update law and a basic resistance equation, which effectively realizes the online asymptotic estimation of the basic resistance during train operation. Compared with traditional offline TBRP estimation methods (actual vehicle testing, wind tunnel testing and numerical simulation methods), it significantly reduces testing costs and improves robustness, does not rely on complex offline testing, and has both accuracy and strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0020] Figure 1 This is a diagram of the application environment of an online estimation method for basic resistance of a high-speed train in one embodiment of the present application.

[0021] Figure 2 A flowchart of an online estimation method for the basic resistance of a high-speed train provided in one embodiment of the present application.

[0022] Figure 3 A flowchart of the adaptive observer design and stability analysis provided in one embodiment of the present application.

[0023] Figure 4 This is a force analysis diagram of adjacent carriages of a high-speed train provided in one embodiment of the present application.

[0024] Figure 5 This is a block diagram of the design of basic resistance estimation for high-speed trains provided in one embodiment of the present application.

[0025] Figure 6 The first basic resistance parameter provided in an embodiment of the present application A graph showing changes in estimated values.

[0026] Figure 7 The second basic resistance parameter provided in an embodiment of the present application A graph showing changes in estimated values.

[0027] Figure 8 The third basic resistance parameter provided in an embodiment of the present application is A plot of the variation of the estimated value.

[0028] Figure 9 An estimated error diagram of the train basic resistance parameter provided by an embodiment of the present application.

[0029] Figure 10 A diagram of the actual value and the estimated value of the basic resistance of each car of the high-speed train provided by an embodiment of the present application.

[0030] Figure 11 An estimated error diagram of the basic resistance of each car of the high-speed train provided by an embodiment of the present application.

[0031] Figure 12 A diagram of the expected speed of the basic resistance of each car of the high-speed train provided by an embodiment of the present application.

[0032] Figure 13 A diagram of the speed and position tracking error of each car of the high-speed train provided by an embodiment of the present application.

[0033] Figure 14 A structural diagram of a computer device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those of ordinary skill in the art without any creative work fall within the scope of protection of the present application.

[0035] The above-mentioned purposes, features and advantages of the present application can be more obvious and easy to understand. The present application will be described in further detail below with reference to the drawings and specific embodiments.

[0036] The high-speed train basic resistance online estimation method provided by the embodiments of the present application can be applied to, for example, Figure 1The application environment is shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data required by the server 104 to process. The data storage system can be set up separately, or integrated on the server 104, or placed on the cloud or other servers. The terminal 102 can send a request to be processed to the server 104, and the server 104 receives the request to be processed, constructs a multi-particle longitudinal dynamics equation of the high-speed train based on the internal coupler force of the high-speed train, designs an adaptive observer based on the multi-particle longitudinal dynamics equation, estimates the basic resistance of the high-speed train online based on the adaptive observer, and obtains the basic resistance estimation value of each car of the high-speed train. The server 104 can feed back the basic resistance estimation value of each car of the high-speed train obtained to the terminal 102. In addition, in some embodiments, the high-speed train basic resistance online estimation method can also be realized by the server 104 or the terminal 102 alone, such as directly estimating the basic resistance online for the request to be processed by the terminal 102, or obtaining the request to be processed from the data storage system by the server 104 and estimating the basic resistance online for the request to be processed.

[0037] Among them, the terminal 102 can be, but not limited to, various desktop computers, notebook computers and tablet computers. The server 104 can be realized by an independent server or a server cluster composed of multiple servers, and can also be a cloud server.

[0038] In an exemplary embodiment, as shown in Figure 2 , a high-speed train basic resistance online estimation method is provided, which is executed by a computer device, specifically can be executed by a terminal or a server computer device alone, or can be executed by a terminal and a server together. In the embodiment of the present application, the server 104 in the Figure 1 is taken as an example to illustrate the method, which includes the following steps 201 to 203.

[0039] Step 201, constructing a multi-particle longitudinal dynamics equation of the high-speed train based on the internal coupler force of the high-speed train.

[0040] Step 202, designing an adaptive observer based on the multi-particle longitudinal dynamics equation; the adaptive observer includes a state estimation equation, a parameter adaptive law, an auxiliary variable dynamic equation, a gain matrix update law and a basic resistance equation.

[0041] Step 203, estimating the basic resistance of the high-speed train online based on the adaptive observer, and obtaining the basic resistance estimation value of each car of the high-speed train.

[0042] The steps 201 to 203 are implemented, an adaptive observer is designed through a multi-particle longitudinal dynamics equation of the high-speed train, and then the basic resistance of the high-speed train is estimated online based on the adaptive observer, so that the basic resistance estimation value of each car of the high-speed train is obtained, the adaptive observer includes a state estimation equation, a parameter adaptive law, an auxiliary variable dynamic equation, a gain matrix update law and a basic resistance equation, the online asymptotic estimation of the basic resistance of the train during operation is effectively realized, compared with a traditional offline TBRP estimation method (real vehicle test, wind tunnel test and numerical simulation method), the test cost is significantly reduced and the robustness is improved, the complex offline test is not needed, and the accuracy and strong robustness are combined.

[0043] The application designs an adaptive observer for a high-speed train system with basic resistance, so that the basic resistance of the train can be estimated online, and the basic resistance estimation error asymptotically converges to the origin without disturbance, and the basic resistance estimation error is uniformly ultimately bounded when there is disturbance. Finally, the basic resistance of the high-speed train is estimated online, and the advantages of low cost and strong robustness are realized. First, a multi-particle longitudinal dynamics model of the high-speed train in the equilibrium state is established, which contains the car coupler spring damping characteristics and the aerodynamic resistance concentrated in the head car, and the dynamics equation of each car in the model is expressed in the form of a matrix state space equation. From the above preparation, an adaptive observer is designed, and a Lyapunov function is constructed based on the error system and the sustained excitation condition, so that the basic resistance estimation problem of the high-speed train can be guaranteed.

[0044] As shown in Figure 3 , the adaptive observer design includes the following steps S101-S107.

[0045] S101: Considering the coupling force in the train (i.e. the high-speed train internal car coupler force), a nonlinear multi-particle dynamics model of the train (i.e. a multi-particle longitudinal dynamics equation) is constructed, specifically: based on the coupling displacement, velocity correlation term and unknown disturbance, a multi-particle longitudinal dynamics equation is constructed. The force analysis of adjacent cars of the high-speed train is as shown in Figure 4 .

[0046] S102: The dynamics model (i.e. the multi-particle longitudinal dynamics equation) designed in S101 above is converted into a train state space equation.

[0047] S103: Based on the system model and output error feedback, a state estimation equation is constructed. The system model refers to the multi-particle longitudinal dynamics equation shown in formula (2).

[0048] S104: A parameter estimation update law (i.e. a parameter adaptive law) is designed, and the parameter asymptotic convergence is realized through a dynamic gain matrix and an auxiliary variable.

[0049] S105: Define auxiliary variable dynamic equation, enhance the coupling relationship between state and parameter.

[0050] S106: Design gain matrix update law, meet the asymptotic stability of parameter estimation under continuous excitation condition by dynamically updating gain matrix.

[0051] S107: Substitute the estimated TBRP parameters (train basic resistance parameters) into the basic resistance equation (Davis equation) to calculate the basic resistance estimate value of each car.

[0052] In step 201, the expression of high-speed train coupler force is as follows:

[0053] (1);

[0054] (2);

[0055] (3);

[0056] (4);

[0057] Where, is the coupling force between the kth car and the (k+1)th car of the high-speed train at time t; and and represent the elastic coupling coefficient and the damping coupling coefficient, respectively; is the force caused by spring deformation, is the damping force caused by the motion of the object; is the coupler displacement between the kth car and the (k+1)th car at time t; and and are the speed and position of the kth car at time t; and are the speed and position of the (k+1)th car at time t; is the length of the car; represents the original length of the coupler before deformation; is the fixed length of the car.

[0058] The multi-particle longitudinal dynamics equation of the high-speed train is constructed by formulas (1)-(4), which is shown as follows:

[0059] (5);​​​​​​​​

[0060] in, , and Respectively Timetable high-speed train The position, velocity and acceleration of the carriages, is the total number of carriages of the high-speed train; for About time The first derivative of ; For the The quality of the carriage, ; yes Moment Control input vector of the carriage; and denote the elastic coupling coefficient and the damping coupling coefficient respectively; for Timetable high-speed train The speed of the carriage; the basic resistance parameters of the train include the first basic resistance parameter , the second basic resistance parameter and the third basic resistance parameter ; yes The lumped disturbance at every moment is composed of additional resistance and unknown external disturbance. The additional resistance includes curve resistance, slope resistance and tunnel resistance. It is the middle length of the carriage.

[0061] To get the unknown parameter vector Based on the multi-particle longitudinal dynamic equations of the train, this application designs an adaptive observer in the form of the following equations (7)-(11).

[0062] In another exemplary embodiment of the present application, in the above step 202 , an adaptive observer is designed based on the multi-particle longitudinal dynamics equation, which specifically includes the following steps 301 to 306 .

[0063] Step 301: Convert the multi-particle longitudinal dynamics equation into a train state space equation.

[0064] By converting the multi-particle longitudinal dynamic equations of the above design as shown in formula (5) into the train state space equations as shown in formula (6), the above high-speed train system can be expressed in a more compact matrix form as follows.

[0065] (6);

[0066] in , , and They are the state vector, control input vector, output vector and unknown parameter vector of the high-speed train system model (i.e., the multi-particle longitudinal dynamics equation), and the system order is is known; for The aggregate disturbance of high-speed trains at scheduled times; is a known constant matrix; the function is continuous, controlling the input vector It is bounded.

[0067] Among them, the specific parameter matrix form is as follows:

[0068] ;

[0069] ; ; ;

[0070] ; ; ;

[0071] ; ;

[0072] in, for A zero matrix of size , for The identity matrix of size; is the intermediate matrix; Section 1, Section 2, Section 3, Section, The quality of the carriage, For the The quality of the carriage; is the state-dependent function, Section 1, Section 2, Section 3, The speed of the carriage; is the intermediate amount; is the unknown parameter vector, which is composed of the basic resistance parameters of the train; Section 1, Section 2, Carriage position and speed; is the aggregate disturbance of the high-speed train, Section 1, Section 2, The aggregate disturbance of the carriage.

[0073] Step 302: Construct a state estimation equation; the state estimation equation is expressed as follows:

[0074] (7);

[0075] in, 、 and They are The state vector, control input vector and unknown parameter vector of the high-speed train at this moment, for dimensional real number set; and The state vectors are The estimated value and unknown parameter vector estimated value of; is the estimated value of the state vector About time The first derivative of ; is a known constant matrix, for dimensional real number set; is a state-dependent function; is the error correction term, is the coefficient of the error correction term; is an auxiliary variable; is an estimate of the unknown parameter vector About time The first-order derivative of . This formula is based on the state dynamic equation in the system equation , using the estimated value and Replace the real value and , and add error correction terms make sure Converges to In order to couple the dynamics of parameter estimation to state estimation and enhance the collaborative update of the two, the parameter change rate term is added .

[0076] Step 303: Design a parameter adaptive law, update the basic resistance parameters of the train according to the gain matrix and the auxiliary variables, and obtain an estimated value of the basic resistance parameters of the train.

[0077] The parameter adaptation law is expressed as follows:

[0078] (8);

[0079] in, for Moment gain matrix; represents the transpose. Where the gain matrix The parameter update rate can be adjusted, and the auxiliary variable The state error is mapped to the parameter space to provide direction information for the parameter update.

[0080] Step 304: Define the auxiliary variable dynamic equation to dynamically update the auxiliary variable. The auxiliary variable dynamic equation is represented as follows:

[0081] (9);

[0082] wherein, is the first-order derivative of the auxiliary variable with respect to time . Through the dynamic evolution of the system matrix and the state-related function , the auxiliary variable carries the system state information. By designing the auxiliary variable dynamic equation to satisfy the persistent excitation condition, the unknown parameter variable can be identified.

[0083] Step 305: Design the gain matrix update law to dynamically update the gain matrix. The gain matrix update law is represented as follows:

[0084] (10);

[0085] wherein, is the gain matrix at time ; is the first-order derivative of the gain matrix with respect to time . This formula ensures that the gain matrix is positive definite and bounded, avoiding divergence and ensuring is bounded, thereby guaranteeing the stability of the parameter update. Wherein, is the inverse matrix of .

[0086] The positive definiteness and boundedness of the gain matrix (which is guaranteed by formula (10)) are crucial. Through the gain matrix update law of formula (10), the gain matrix remains positive definite and bounded under the persistent excitation condition, thereby ensuring that the time derivative of the Lyapunov function V̇ is negative, and further guaranteeing the asymptotic convergence of the parameter estimation error.

[0087] The role of the auxiliary variable is to accumulate sufficient information to satisfy the persistent excitation condition. The persistent excitation condition requires that the system input or state contains sufficient information so that the parameter can be uniquely determined. The auxiliary variable The dynamic generation of the adaptive observer can help the system to meet this condition, so that the update of the adaptive observer can effectively adjust the convergence process of the parameter estimation.

[0088] Step 306: input the estimated value of the train basic resistance parameter into the basic resistance equation to calculate the estimated value of the basic resistance of each car of the high-speed train.

[0089] The basic resistance equation is expressed as follows:

[0090] (11);

[0091] The estimated train basic resistance parameters are substituted into the basic resistance equation to obtain the estimated value of the basic resistance of each car. The estimated values of the first basic resistance parameter , the second basic resistance parameter and the third basic resistance parameter of the first car are respectively .

[0092] In the equations (7)-(11), , are the estimates of and in the train state space equation shown in equation (6), respectively, and need to satisfy Hurwitz matrix. Obviously, the adaptive observer is composed of the state estimation equation, the parameter adaptive law, the auxiliary variable dynamic equation, the gain matrix update law and the basic resistance equation. The state estimation equation combines the multi-particle longitudinal dynamics equation, uses the current input and the estimated parameter to predict the state vector, and corrects through the output error (through matrix). At the same time, may introduce the adjustment of the parameter estimation into the state estimation, enhancing the coupling of the two. The parameter adaptive law uses the dynamic gain matrix R and the auxiliary variable to ensure the asymptotic convergence of the estimated parameter, and the adaptive observer can realize the asymptotic convergence of the state and parameter estimation errors under the premise of meeting the persistent excitation condition.

[0093] After the adaptive observer is designed, the stability and convergence of the adaptive observer need to be analyzed and verified, as shown in Figure 3 , the stability analysis includes the following steps S201-S206.

[0094] S201: define the error system and the extended error variable under the undisturbed condition.

[0095] Determine the train system state equation under the undisturbed condition:

[0096] (12).

[0097] For the convenience of stability analysis, define the state error without disturbance , and the TBRP parameter error is In addition, define the extended error variable The extended error formula is constructed as follows:

[0098] (13).

[0099] From equations (7), (8), (9) and (13), we have:

[0100] (14);

[0101] (15);

[0102] where is the first derivative of the variable , and is the first derivative of the TBRP parameter error.

[0103] S202: Construct Lyapunov function based on error system and persistent excitation condition.

[0104] Assume that the persistent excitation condition is satisfied as follows:

[0105] Using the fact that the time-varying gain matrix is bounded and symmetric positive definite, assume that the following persistent excitation condition is satisfied: so that

[0106] (16);

[0107] where is a positive constant, is a positive real set; is an identity matrix; is time; is the initial time.

[0108] Under this assumption, it can be proved that is bounded, that is, a simplified representation of , that is, the inverse matrix of , and satisfies:

[0109] (17).

[0110] Therefore, there are two positive constants such that the following equation is satisfied:

[0111] (18).

[0112] because is Hurwitz, for any positive constant , there exists a symmetric positive definite matrix ,satisfy:

[0113] (19).

[0114] Consider the following Lyapunov function:

[0115] (20);

[0116] in, is the calculation result of the Lyapunov function without disturbance.

[0117] S203: Further derivation and scaling of the Lyapunov function prove that the TBRP error system is asymptotically stable, thereby achieving an asymptotic estimate of the basic resistance encountered by the train during operation.

[0118] Pick About time The derivative of :

[0119] (twenty one);

[0120] in for About time The first derivative of ; is a positive constant, yes Any upper bound of , it is easy to see Always present; = ;choose to satisfy , which means Through The appropriate choice to meet the requirements, as well as the selection of intermediate parameters Make In (21), the following inequality is used:

[0121] (twenty two);

[0122] (twenty three);

[0123] The deduction result of formula (21) is not strictly less than zero, only if and only if and At the same time, the establishment of the time, only to get , so by Lyapunov function can be estimated error system asymptotically stable, that is, asymptotically estimated .

[0124] S204: extended to the error system under disturbance conditions and extended error variables.

[0125] Train system state equation with disturbance as follows:

[0126] (24);

[0127] Definition of state error with disturbance , and define the following extended error formula:

[0128] (25);

[0129] Where, is the extended error variable with disturbance.

[0130] From equation (7), (8), (9) and (25) can be obtained:

[0131] (26);

[0132] (27);

[0133] Where, is the first derivative of .

[0134] S205: under the condition of disturbance, construct Lyapunov function.

[0135] Assume that the disturbance satisfies: , is the set disturbance threshold (i.e. the boundary of external disturbance), and satisfies the same above continuous excitation conditions, it can be proved that the estimated error parameter and the extended error variable with disturbance is uniformly ultimately bounded, and the basic resistance estimation error is uniformly ultimately bounded.

[0136] Proof: since is Hurwitz, for any normal number , there exists a symmetric positive definite matrix , satisfies:

[0137] (28).

[0138] Construct the following Lyapunov function:

[0139] (29);

[0140] in, is the calculation result of the Lyapunov function under disturbance.

[0141] S206: By derivatizing and scaling the Lyapunov function, it is proved that the TBRP error system is uniformly and ultimately stable, which improves the robustness performance.

[0142] Pick About time The derivative of :

[0143] (30);

[0144] in, for About time The first derivative of ; the intermediate matrix , the intermediate matrix , the intermediate matrix , a positive constant ; Corresponding to and Any upper bound of .because It's Hurwitz, easy to see There always exists a symmetric positive definite matrix It is chosen and also exists. It can be written in another form as , and the same can be done for other options. to satisfy , which means Through The appropriate choice to meet the requirements, as well as the selection of intermediate parameters Make In equation (30), we used the following inequality:

[0145] (31);

[0146] (32);

[0147] (33);

[0148] That is, under the relevant conditions, the intermediate matrix M , W Can meet: .

[0149] From formula (30), we can get:

[0150] (34);

[0151] in, , Corresponding to the intermediate matrix M , W The minimum eigenvalue of . From (34) we can get:

[0152] (35);

[0153] or

[0154] (36);

[0155] It can be seen from formula (35) that when When , formula (29) reaches its maximum value, that is:

[0156] (37);

[0157] in, for The maximum eigenvalue of .

[0158] The same logic applies The range is:

[0159] (38);

[0160] in, are symmetric positive definite matrices The maximum and minimum eigenvalues ​​of .

[0161] So we can get:

[0162] (39);

[0163] (40);

[0164] in, are the estimation error of basic resistance, the estimated value of basic resistance and the true value of basic resistance respectively; Respectively The first basic resistance parameter of the carriage , the second basic resistance parameter and the third basic resistance parameter estimated value of; Respectively The first basic resistance parameter of the carriage , the second basic resistance parameter and a third basic resistance parameter .

[0165] It can be seen that the TBRP estimation error is uniformly ultimately bounded, which further indicates that the basic resistance estimation error is also uniformly ultimately bounded, and these bounds are proportional to the bound of the external disturbance.

[0166] Theoretical analysis shows that, under the condition of continuous excitation, the designed adaptive observer can ensure that the TBRP estimation error is uniformly ultimately bounded in the presence of disturbance. The ultimate bound of these errors is in explicit linear proportion to the disturbance amplitude (i.e., the set disturbance threshold) D. Specifically, when the system is subjected to a bounded disturbance, using Lyapunov stability analysis, the convergence bound of this estimation error can be found, which is: where the estimation error convergence coefficient This shows that even in the presence of disturbance or environmental noise, the observer can keep the estimation error within a controllable range, thereby ensuring accurate online estimation of the basic resistance, reflecting the robust performance of the observer.

[0167] Since in actual operation, the train will not only be subjected to the basic resistance, but also to additional resistance and other unknown disturbances, the embodiment can be concentrated into an unknown total disturbance . Therefore, the stability proof is given under both disturbance-free and disturbed conditions. The designed Lyapunov function is as follows:

[0168] (41).

[0169] Where the first term on the right side of the equation reflects the dynamic energy of the state estimation error, i.e., formula (20); the second term represents the energy of the parameter estimation error, i.e., formula (29).

[0170] To verify the effectiveness of the high-speed train basic resistance estimation method based on the adaptive observer proposed in this embodiment, the following establishes a simulation model based on the CRH3 train parameters, performs simulation experiments on the performance of the adaptive observer proposed, and analyzes the results of the simulation experiments.

[0171] The basic parameters of the simulated CRH3 high-speed train are shown in Table 1.

[0172] Table 1 Basic parameters of CRH3 high-speed train

[0173]

[0174] It can be obtained that:

[0175] ;

[0176] ;

[0177] ;

[0178] ;

[0179] The LMI toolbox of MATLAB software can effectively solve the LMI. Once the feasible solutions P and Q are obtained, the observer gain The elements in the observer gain

[0180] ;

[0181] ;

[0182] ;

[0183] ;

[0184] wherein, , , and are the elements in the observer gain

[0185] The variation curves of the estimated values of , and are shown in Figure 6 , Figure 7 and Figure 8 . Figure 9 The estimation errors of the basic resistance parameters of the train , and . It can be seen that the estimated , and stably reach the expected values before 20 s. Figure 10 The basic resistance estimation values and actual values of each car of the high-speed train are shown in the figure, wherein, are the actual values of the basic resistance of the 1st, 2nd, 3rd and 4th cars respectively, are the estimated values of the basic resistance of the 1st, 2nd, 3rd and 4th cars respectively. Figure 11 The basic resistance estimation errors of each car of the high-speed train are shown in are the basic resistance estimation errors of the 1st, 2nd, 3rd and 4th cars respectively, which converge to the vicinity of zero within less than 10 s. Figure 12 The expected speeds of each car of the high-speed train are shown in​​ are the desired speeds of the 1st, 2nd, 3rd, 4th carriages respectively, and Figure 13 The speed and position tracking errors of each carriage of the high-speed train are shown, are the position tracking errors of the 1st, 2nd, 3rd, 4th carriages respectively, are the speed tracking errors of the 1st, 2nd, 3rd, 4th carriages respectively.

[0186] From Figure 10 and Figure 11 It can be seen that, for a given actual basic resistance curve, under the control method proposed in the present application, all carriages of the train can achieve accurate tracking and converge to near zero in a short time.

[0187] Simulation device and platform: the computer CPU is 11th Gen Intel(R) Core(TM) i5-1135G7, 2.42GHz, the operating system is Windows 10 Professional, and the simulation platform is MATLAB R2022a.

[0188] In view of the problems of parameter updating lag and poor environmental adaptability caused by the high-cost offline scheme such as real vehicle test and wind tunnel experiment of the existing resistance parameter measurement method, a multi-particle longitudinal dynamics model containing car coupling force is constructed, and an adaptive observer with a dynamic gain matrix is designed. The adaptive observer includes a state estimation equation, a parameter adaptive law, an auxiliary variable updating mechanism (the auxiliary variable updating mechanism is an auxiliary variable dynamic equation), a gain matrix updating law and a basic resistance equation. By introducing the Lyapunov stability analysis under the condition of continuous excitation, it is proved that the resistance parameter estimation error is asymptotically stable without disturbance, and it is uniformly ultimately bounded when there is disturbance. The scheme proposed in the present application can effectively estimate the basic resistance on line and asymptotically, significantly reducing the test cost and improving the robustness.

[0189] The present application has the following beneficial effects: 1. The adaptive observer is applied to the high-speed train system, a new adaptive observer is designed, and the basic resistance during the running of the train is effectively estimated on line; 2. The traditional offline TBRP estimation method (real vehicle test, wind tunnel test and numerical simulation) has two shortcomings: (1) there is inevitably an estimation error; (2) they need considerable time and capital investment. Unlike the offline TBRP estimation method, the present application proposes an online adaptive observer, which can asymptotically estimate the TBRP and has high robustness; 3. The present application is easy to integrate into the existing high-speed train tracking control method, thereby improving the tracking accuracy of the high-speed train. Specifically, the inverse value of the estimated basic resistance value is added to the control input as a feedforward signal, which effectively offsets and compensates the basic resistance, thereby enhancing the tracking performance of the high-speed train.

[0190] The application also provides an application scenario of the online estimation method of the basic resistance of the high-speed train. Specifically, the online estimation method of the basic resistance of the high-speed train provided in this embodiment can be applied in the estimation scenario of the basic resistance of the high-speed train. The estimation scenario of the basic resistance of the high-speed train includes a request issuing link and an online estimation link of the basic resistance. The request to be processed enters the online estimation link of the basic resistance from the request issuing link, and the estimation value of the basic resistance of each car of the high-speed train is obtained. The online estimation method of the basic resistance of the high-speed train provided in this embodiment belongs to the online estimation link of the basic resistance. Specifically, in the process of the online estimation link of the basic resistance for the request to be processed, the multi-particle longitudinal dynamics equation of the high-speed train can be constructed based on the internal coupler force of the high-speed train, the adaptive observer can be designed based on the multi-particle longitudinal dynamics equation, the basic resistance of the high-speed train can be estimated online based on the adaptive observer, and the estimation value of the basic resistance of each car of the high-speed train is obtained.

[0191] Based on the same inventive concept, the application also provides an online estimation device of the basic resistance of the high-speed train for implementing the online estimation method of the basic resistance of the high-speed train. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme described in the above method, and therefore the specific limitations in one or more online estimation device embodiments of the basic resistance of the high-speed train provided below can be referred to the limitations of the online estimation method of the basic resistance of the high-speed train described above, which will not be described herein again.

[0192] In an exemplary embodiment, an online estimation device of the basic resistance of the high-speed train is provided, which includes the following modules:

[0193] A multi-particle longitudinal dynamics equation establishing module is configured to construct a multi-particle longitudinal dynamics equation of the high-speed train based on the internal coupler force of the high-speed train.

[0194] An adaptive observer designing module is configured to design an adaptive observer based on the multi-particle longitudinal dynamics equation. The adaptive observer includes a state estimation equation, a parameter adaptive law, an auxiliary variable dynamic equation, a gain matrix updating law, and a basic resistance equation.

[0195] A basic resistance estimating module is configured to estimate the basic resistance of the high-speed train online based on the adaptive observer, and obtain the estimation value of the basic resistance of each car of the high-speed train.

[0196] In an exemplary embodiment, a computer device is provided, which can be a server or a terminal, and the internal structure diagram of the computer device can be as shown in Figure 14As shown in the figure. The computer device includes a processor, a memory, an Input / Output (I / O) interface and a communication interface. Among them, the processor, the memory and the input / output interface are connected through the system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capability. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store train basic resistance online estimation data. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through network connection. The computer program is executed by the processor to realize a high-speed train basic resistance online estimation method.

[0197] Those skilled in the art can understand that, Figure 14 The structure shown in the figure is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. The specific computer device can include more or fewer components than those shown in the figure, or combine certain components, or have a different component arrangement.

[0198] In an exemplary embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps in the above method embodiments.

[0199] In an exemplary embodiment, a computer readable storage medium is provided, storing a computer program, and the computer program is executed by the processor to implement the steps in the above method embodiments.

[0200] The technical features of the above embodiments can be combined in any way. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described, but as long as the combination of the technical features does not exist contradictory, it should be considered as the scope of the present application.

[0201] The principles and implementation modes of the present application are described by applying specific examples herein, and the above embodiment descriptions are only used to help understand the method and its core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In view of the above, the content of the present application should not be understood as a limitation.

Claims

1. A method for online estimation of basic resistance of high-speed trains, characterized in that: The high-speed train basic resistance online estimation method comprises: The multi-mass longitudinal dynamic equation of high-speed train is constructed based on the internal coupler force of high-speed train; An adaptive observer is designed based on the multi-particle longitudinal dynamic equation. The adaptive observer includes a state estimation equation, a parameter adaptation law, an auxiliary variable dynamic equation, a gain matrix update law, and a basic resistance equation. The state estimation equation is expressed as follows: ； in, 、 and They are The state vector, control input vector and unknown parameter vector of the high-speed train at this moment, for dimensional real number set; and The state vectors are The estimated value and unknown parameter vector estimated value of; is the estimated value of the state vector About time The first derivative of ; is a known constant matrix, for dimensional real number set; is a state-dependent function; is the error correction term, is the coefficient of the error correction term; is an auxiliary variable; is an estimate of the unknown parameter vector About time The first derivative of ; The basic resistance of the high-speed train is estimated online based on the adaptive observer to obtain an estimated value of the basic resistance of each carriage of the high-speed train.

2. The method for online estimation of basic resistance of high-speed train according to claim 1, characterized in that: Designing an adaptive observer based on the multi-particle longitudinal dynamics equation specifically includes: Converting the multi-particle longitudinal dynamics equation into a train state space equation; Construct state estimation equation; Design parameter adaptive law, update the basic resistance parameters of the train according to the gain matrix and auxiliary variables, and obtain the estimated value of the basic resistance parameters of the train; Define dynamic equations for auxiliary variables and dynamically update the auxiliary variables; Design the gain matrix update law to dynamically update the gain matrix; The estimated values ​​of the basic resistance parameters of the train are input into the basic resistance equation to calculate the estimated basic resistance values ​​of each carriage of the high-speed train.

3. The method for online estimation of basic resistance of high-speed train according to claim 1, characterized in that: The multi-particle longitudinal dynamic equation is expressed as follows: ； in, , and Respectively Timetable high-speed train The position, velocity and acceleration of the carriages, is the total number of carriages of the high-speed train; for About time The first derivative of ; For the The quality of the carriage, ; yes Moment Control input vector of the carriage; and denote the elastic coupling coefficient and the damping coupling coefficient respectively; for Timetable high-speed train The speed of the carriage; the basic resistance parameters of the train include the first basic resistance parameter , the second basic resistance parameter and the third basic resistance parameter ; yes The lumped disturbance at every moment is composed of additional resistance and unknown external disturbance. The additional resistance includes curve resistance, slope resistance and tunnel resistance. It is the middle length of the carriage.

4. The method for online estimation of basic resistance of high-speed train according to claim 1, characterized in that: The parameter adaptation law is expressed as follows: ； in, for Moment gain matrix; Indicates transpose.

5. The method for online estimation of basic resistance of high-speed train according to claim 1, characterized in that: The auxiliary variable dynamic equation is expressed as follows: ； in, Auxiliary variables About time The first derivative of .

6. The method for online estimation of basic resistance of high-speed train according to claim 1, characterized in that: The gain matrix update law is expressed as follows: ； in, for Moment gain matrix; is the gain matrix versus time The first derivative of .

7. An online estimation device for basic resistance of high-speed train, characterized in that: The high-speed train basic resistance online estimation device comprises: A module for establishing multi-mass longitudinal dynamic equations, which is used to construct the multi-mass longitudinal dynamic equations of high-speed trains based on the internal coupler forces of high-speed trains; An adaptive observer design module is used to design an adaptive observer based on the multi-particle longitudinal dynamic equation; the adaptive observer includes a state estimation equation, a parameter adaptation law, an auxiliary variable dynamic equation, a gain matrix update law, and a basic resistance equation; the state estimation equation is expressed as follows: ； in, 、 and They are The state vector, control input vector and unknown parameter vector of the high-speed train at this moment, for dimensional real number set; and The state vectors are The estimated value and unknown parameter vector estimated value of; is the estimated value of the state vector About time The first derivative of ; is a known constant matrix, for dimensional real number set; is a state-dependent function; is the error correction term, is the coefficient of the error correction term; is an auxiliary variable; is an estimate of the unknown parameter vector About time The first derivative of ; The basic resistance estimation module is used to estimate the basic resistance of the high-speed train online based on the adaptive observer to obtain the basic resistance estimation value of each car of the high-speed train.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the online estimation method for the basic resistance of a high-speed train according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for online estimation of basic resistance of a high-speed train according to any one of claims 1 to 6 is implemented.

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