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

Abstract

The invention discloses a high-speed train basic resistance online estimation method and device, equipment and a medium, and relates to the field of rail traffic control and high-speed train dynamics control, and the method comprises the steps: constructing a multi-mass-point longitudinal kinetic equation of a high-speed train based on the acting force of a coupler in the high-speed train; designing a self-adaptive observer based on the multi-mass-point longitudinal kinetic 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; the basic resistance of the high-speed train is estimated on line based on the self-adaptive observer, and the basic resistance estimated value of each compartment of the high-speed train is obtained. According to the method, the basic resistance can be effectively and asymptotically estimated on line, the test cost is remarkably reduced, the robustness performance is improved, dependence on complex off-line tests is not needed, and precision and high robustness are achieved.

Description

Technical Field

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

[0002] The basic resistance of a high-speed train during operation is a key factor affecting its dynamic characteristics and control accuracy. This resistance is composed of mechanical resistance (such as wheel-rail rolling resistance and bearing friction resistance) and aerodynamic resistance. The Davis equation ( ) to describe it. Accurately obtain the resistance parameters in the equation 、 and (TBRP or Davis parameter) is the core prerequisite for achieving precise train traction and braking control, energy consumption optimization and trajectory tracking.

[0003] The main existing parameter acquisition methods include: vehicle testing, wind tunnel testing, and numerical simulation. Although vehicle testing can reflect real-world operating conditions, it requires dedicated lines and equipment, resulting in high single-time costs, strong environmental dependence, and significant measurement noise and data processing difficulties. Wind tunnel testing simulates aerodynamic characteristics using scaled models, but due to the scale effect caused by differences in Reynolds numbers, it cannot fully reproduce the actual flow state and cannot effectively simulate mechanical resistance characteristics, resulting in increased resistance prediction errors. Numerical simulation relies on offline simulation data and cannot truly reflect the dynamic characteristics of resistance in complex environments (such as crosswind disturbances and component deformation), resulting in systematic deviations between model output and measured values. In addition, the deployment of high-precision sensors is expensive and susceptible to mechanical vibration.

[0004] Furthermore, these traditional offline methods rely on consistent parameters for all trains of the same model, making it difficult to timely update the TBRP of a specific train online within a specified time period. At the control strategy level, existing adaptive methods only achieve speed tracking by indirectly compensating for parameter uncertainty, without explicitly estimating the base resistance, resulting in a lack of feedforward control.

[0005] As high-speed trains evolve toward intelligent and unmanned operation, the high cost and insufficient robustness of traditional offline methods have become a core bottleneck hindering improvements in train control performance. An online asymptotic estimation method that combines accuracy and robustness without relying on complex offline testing is urgently needed to overcome the limitations of traditional technologies and provide key support for intelligent train control. Summary of the Invention

[0006] The purpose of this application is to provide a method, device, equipment and medium for online estimation of the basic resistance of a high-speed train, which does not rely on complex offline tests and has both accuracy and strong robustness.

[0007] To achieve the above objectives, this application provides the following solutions.

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

[0009] The multi-mass longitudinal dynamic equation of high-speed train is constructed based on the internal coupler force of high-speed train.

[0010] 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.

[0011] 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.

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

[0013] The multi-mass longitudinal dynamic equation establishment module is used to construct the multi-mass longitudinal dynamic equation of the high-speed train based on the internal coupler force of the high-speed train.

[0014] 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.

[0015] 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.

[0016] In a third aspect, the present 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 implement the above-mentioned online estimation method for the basic resistance of a high-speed train.

[0017] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned online estimation method for the basic resistance of a high-speed train.

[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 graph showing changes in estimated values.

[0028] Figure 9 A schematic diagram of the estimation error of the basic resistance parameters of a train provided in one embodiment of the present application.

[0029] Figure 10 A schematic diagram of the actual and estimated values of the basic resistance of each carriage of a high-speed train provided in one embodiment of the present application.

[0030] Figure 11 A schematic diagram of the estimated error of the basic resistance of each carriage of a high-speed train provided in one embodiment of the present application.

[0031] Figure 12 A schematic diagram of the expected speed of the basic resistance of each carriage of a high-speed train provided in one embodiment of the present application.

[0032] Figure 13 A schematic diagram of the speed and position tracking error of each carriage of a high-speed train provided in one embodiment of the present application.

[0033] Figure 14 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0034] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0035] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0036] The online estimation method of the basic resistance of a high-speed train provided in the embodiment of the present application can be applied to Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store data that server 104 needs to process. The data storage system can be provided separately, integrated with server 104, or located in the cloud or on another server. Terminal 102 can send a request to be processed to server 104. After receiving the request, server 104 constructs a multi-particle longitudinal dynamic equation for the high-speed train based on the internal coupler forces of the high-speed train, designs an adaptive observer based on the multi-particle longitudinal dynamic equation, and online estimates the basic resistance of the high-speed train based on the adaptive observer to obtain an estimated basic resistance value for each car of the high-speed train. Server 104 can feed back the obtained estimated basic resistance value for each car of the high-speed train to terminal 102. In some embodiments, the online estimation method for the basic resistance of a high-speed train can also be implemented independently by server 104 or terminal 102. For example, terminal 102 can directly perform online basic resistance estimation for the request to be processed, or server 104 can obtain the request to be processed from the data storage system and perform online basic resistance estimation for the request to be processed.

[0037] The terminal 102 may be, but is not limited to, various desktop computers, laptop computers, and tablet computers. The server 104 may be implemented as an independent server or a server cluster consisting of multiple servers, or may be a cloud server.

[0038] In an exemplary embodiment, Figure 2 As shown, a method for online estimation of basic resistance of high-speed train is provided. The method is executed by a computer device, specifically a computer device such as a terminal or a server, or a terminal and a server. In the embodiment of the present application, the method is applied to Figure 1 The server 104 in the example is used for explanation, including the following steps 201 to 203.

[0039] Step 201: construct a multi-mass longitudinal dynamic equation of the high-speed train based on the internal coupler force of the high-speed train.

[0040] Step 202 : 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.

[0041] Step 203 : estimating the basic resistance of the high-speed train online based on the adaptive observer to obtain an estimated value of the basic resistance of each carriage of the high-speed train.

[0042] By implementing the above steps 201 to 203, an adaptive observer is designed based on the multi-particle longitudinal dynamic equations of the high-speed train. Then, based on the adaptive observer, the basic resistance of the high-speed train is estimated online to obtain the estimated basic resistance of each car 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. It effectively realizes the online asymptotic estimation of the basic resistance of the train during 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.

[0043] This application designs an adaptive observer for a high-speed train system subject to basic resistance, so that the basic resistance of the train can be estimated online, and as the running time goes by, the basic resistance estimation error converges asymptotically to the origin when there is no disturbance, and the basic resistance estimation error is uniformly bounded in the presence of disturbance. Ultimately, the online estimation of the basic resistance of the high-speed train is achieved, while having the advantages of low cost and strong robustness. First, a multi-particle longitudinal dynamic model of the high-speed train in equilibrium is established, which contains the damping characteristics of the coupler spring and the aerodynamic resistance concentrated in the head car. Secondly, the dynamic equations of each car in the model are expressed as state-space equations in matrix form. Based on the above preparatory work, an adaptive observer is designed, and then a Lyapunov function is constructed based on the error system and the continuous excitation condition, so that the problem of estimating the basic resistance of the high-speed train can be guaranteed.

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

[0045] S101: Considering the coupling forces within the train (i.e., the forces acting on the couplers within the high-speed train), a nonlinear multi-mass dynamic model of the train (i.e., the multi-mass longitudinal dynamic equation) is constructed. Specifically: Based on the forces acting on the couplers within the train and the basic resistance characteristics, a multi-mass longitudinal dynamic equation including coupling displacement, velocity-related terms, and unknown disturbances is constructed. Force analysis of adjacent carriages of a high-speed train is as follows: Figure 4 shown.

[0046] S102: Convert the dynamic model designed in S101 (i.e., the multi-particle longitudinal dynamic equation) into a train state space equation.

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

[0048] S104: Design a parameter estimation update law (i.e., a parameter adaptation law) to achieve asymptotic convergence of parameters through a dynamic gain matrix and auxiliary variables.

[0049] S105: Define auxiliary variable dynamic equations to enhance the coupling relationship between state and parameters.

[0050] S106: Design a gain matrix update law to dynamically update the gain matrix to ensure the asymptotic stability of parameter estimation under continuous excitation conditions.

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

[0052] In step 201, the expression of the high-speed train coupler force is as follows: (1); (2); (3); (4); in, yes Timetable for high-speed trains Carriage and Coupling forces between carriages; and denote the elastic coupling coefficient and the damping coupling coefficient respectively; is the force caused by the deformation of the spring, Damping forces caused by the motion of an object; for Moment Carriage and Coupler displacement between carriages; and yes Moment The speed and position of the carriages; and yes Moment The speed and position of the carriages; It is the middle length of the carriage; represents the original length of the coupler before deformation; is the fixed length of the carriage.

[0053] The multi-mass longitudinal dynamic equations of high-speed trains are constructed from formulas (1)-(4) and are expressed as follows: (5); 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.

[0054] In order to obtain 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).

[0055] 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 .

[0056] Step 301: Convert the multi-particle longitudinal dynamics equation into a train state space equation.

[0057] 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.

[0058] (6); 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.

[0059] Among them, the specific parameter matrix form is as follows: ; ; ; ; ; ; ; ; ; 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 lumped disturbance of the high-speed train, Section 1, Section 2, The aggregate disturbance of the carriage.

[0060] Step 302: Construct a state estimation equation; the state estimation equation is expressed as follows: (7); 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 .

[0061] 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.

[0062] The parameter adaptation law is expressed as follows: (8); in, for Moment gain matrix; represents the transpose. Where the gain matrix Parameter update rate can be adjusted, auxiliary variables The state error Mapped to the parameter space, it provides direction information for parameter updates.

[0063] Step 304: Define the auxiliary variable dynamic equation and dynamically update the auxiliary variable. The auxiliary variable dynamic equation is expressed as follows: (9); in, Auxiliary variables About time The first derivative of . Through the system matrix and state-related functions Dynamic evolution of auxiliary variables Carry system status information. By design The auxiliary variable dynamic equation ensures that the continuous excitation condition is satisfied so that the unknown parameter variable Recognizable.

[0064] Step 305: Design a gain matrix update law to dynamically update the gain matrix. The gain matrix update law is expressed as follows: (10); in, for Moment gain matrix; is the gain matrix versus time The first-order derivative of . This formula ensures that the gain matrix Positive and bounded, avoid divergence, ensure is bounded, thus ensuring the stability of parameter updates. for The inverse matrix of .

[0065] Gain Matrix The positivity and boundedness of (guaranteed by formula (10)) are key. By the gain matrix update law of formula (10), the gain matrix It remains positive and bounded under continuous excitation conditions, thus ensuring that the time derivative V̇ of the Lyapunov function is negative definite, thereby guaranteeing the asymptotic convergence of the parameter estimation error.

[0066] Auxiliary variables The role of is to accumulate enough information to meet the continuous excitation condition. The continuous excitation condition requires that the system input or state contains enough information so that the parameters can be uniquely determined. The dynamic generation of can help the system meet this condition, so that The update of can effectively regulate the convergence process of parameter estimation.

[0067] Step 306: Input the estimated values of the basic resistance parameters of the train into the basic resistance equation to calculate the estimated basic resistance values of each carriage of the high-speed train.

[0068] The basic resistance equation is expressed as follows: (11); The estimated basic train resistance parameters Substituting into the basic resistance equation, we can obtain the estimated basic resistance of each car. Respectively The first basic resistance parameter of the carriage , the second basic resistance parameter and the third basic resistance parameter estimated value.

[0069] In formulas (7)-(11) , They are respectively the train state space equations shown in Equation (6) and Estimates, It must satisfy the Hurwitz matrix. Obviously, the adaptive observer consists of the state estimation equation, parameter adaptation law, auxiliary variable dynamic equation, gain matrix update law and basic resistance equation. The state estimation equation is combined with the multi-particle longitudinal dynamic equation, using the current input and estimated parameters to predict the state vector, and outputs the error (through Matrix) for correction. At the same time, It is possible to introduce the adjustment of parameter estimation into state estimation to enhance the coupling between the two. The parameter adaptation law uses the dynamic gain matrix R and auxiliary variables To ensure the asymptotic convergence of the estimated parameters, the adaptive observer can achieve asymptotic convergence of the state and parameter estimation errors under the premise of satisfying the continuous excitation conditions.

[0070] After the adaptive observer is designed, it is necessary to analyze and verify the stability and convergence of the adaptive observer, such as Figure 3 As shown, the stability analysis includes the following steps S201 to S206.

[0071] S201: Define the error system and extended error variables under undisturbed conditions.

[0072] Determine the train system state equation under no disturbance: (12).

[0073] In order to facilitate stability analysis, the state error under no disturbance is defined as , the TBRP parameter error is In addition, define the expansion error variable Construct the expansion error formula: (13).

[0074] From equations (7), (8), (9) and (13), we can get: (14); (15); in, For variables The first derivative of is the first derivative of the TBRP parameter error.

[0075] S202: Construct Lyapunov function based on error system and continuous excitation condition.

[0076] Assume that the following conditions for continued incentives are met: Using the time-varying gain matrix is bounded symmetric positive definite, assuming the following continuous excitation conditions hold: , making (16); in, is a positive constant, is the set of positive real numbers; is the identity matrix; For time; is the initial moment.

[0077] Under this assumption, it can be proved that It is bounded. Right now The simplified representation of The inverse matrix of . And satisfy: (17).

[0078] Therefore, there are two positive constants , so that the following equation holds: (18).

[0079] because is Hurwitz, for any positive constant , there exists a symmetric positive definite matrix ,satisfy: (19).

[0080] Consider the following Lyapunov function: (20); in, is the calculation result of the Lyapunov function without disturbance.

[0081] 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.

[0082] Pick About time The derivative of : (twenty one); 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: (twenty two); (twenty three); The deduction result of formula (21) is not strictly less than zero, only if and only if and When both are established, , so the estimation error system can be obtained from the Lyapunov function to be asymptotically stable, that is, it can be estimated asymptotically .

[0083] S204: Extending the error system and extended error variables under disturbance conditions.

[0084] The state equation of the train system in the presence of disturbance is as follows: (twenty four); Define the state error in the presence of disturbances , and define the following expansion error formula: (25); in, is the expanded error variable in the presence of disturbance.

[0085] From equations (7), (8), (9) and (25), we can obtain: (26); (27); in, for The first derivative of .

[0086] S205: Construct Lyapunov function under perturbation conditions.

[0087] Assume perturbation satisfy: , To set the disturbance threshold (i.e., the limit of external disturbance), and satisfy the same continuous excitation conditions, it can be proved that the estimated error parameter and the expanded error variable with disturbances is uniformly eventually bounded, and the basic resistance estimation error is uniformly eventually bounded.

[0088] Proof: Due to is Hurwitz, for any positive constant , there exists a symmetric positive definite matrix ,satisfy: (28).

[0089] Construct the following Lyapunov function: (29); in, is the calculation result of the Lyapunov function under disturbance.

[0090] 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.

[0091] Pick About time The derivative of : (30); 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: (31); (32); (33); That is, under the relevant conditions, the intermediate matrix M , W Can meet: .

[0092] From formula (30), we can get: (34); in, , Corresponding to the intermediate matrix M , W The minimum eigenvalue of . From (34) we can get: (35); or (36); It can be seen from formula (35) that when When , formula (29) reaches its maximum value, that is: (37); in, for The maximum eigenvalue of .

[0093] The same logic applies The range is: (38); in, are symmetric positive definite matrices The maximum and minimum eigenvalues of .

[0094] So we can get: (39); (40); 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 the third basic resistance parameter .

[0095] It can be seen that the TBRP estimation error is uniformly bounded, which shows that the error in the basic resistance estimate is also uniformly bounded, and these bounds are consistent with the bounds of the external disturbance. Directly proportional.

[0096] Theoretical analysis shows that under the condition of continuous excitation, the designed adaptive observer can ensure that the TBRP estimation error is is uniformly and ultimately bounded. The ultimate bounds of these errors are explicitly linearly proportional to the perturbation amplitude (i.e., the set perturbation threshold) D. Specifically, when the system is subjected to bounded perturbations, using Lyapunov stability analysis, we can find the convergence bound of this estimation error, which is: , where the estimated error convergence coefficient is This shows that even in the presence of interference or environmental noise, the observer can keep the estimation error within a controllable range, thus ensuring the effect of accurate online estimation of the basic resistance and reflecting the robust performance of the observer.

[0097] Since in actual operation, the train will be subject to not only basic resistance, but also additional resistance and other unknown disturbances, this embodiment can be concentrated into an unknown total disturbance Therefore, the stability proof is given in both the case of no disturbance and the case of disturbance. The designed Lyapunov function is as follows: (41).

[0098] The first term on the right side of the equation reflects the dynamic energy of the state estimation error, that is, formula (20); the second term represents the energy of the parameter estimation error, that is, formula (29).

[0099] In order to verify the effectiveness of the high-speed train basic resistance estimation method based on the adaptive observer proposed in this embodiment, a simulation model is established using CRH3 train parameters, and simulation experiments are conducted on the performance of the proposed adaptive observer and the results of the simulation experiments are analyzed.

[0100] The basic parameters of the simulated CRH3 high-speed train are shown in Table 1.

[0101] Table 1 Basic parameters of CRH3 high-speed train

[0102] You can get: ; ; ; ; The LMI toolbox in MATLAB can be used to solve LMI effectively. Once the feasible solutions P and Q are obtained, the observer gain The observer gain can be obtained as follows Elements in: ; ; ; ; in, 、 、 and is the observer gain Elements in .

[0103] Obtained through simulation , and The estimated value of the curve is as follows Figure 6 、 Figure 7 and Figure 8 shown. Figure 9 is the basic resistance parameter of the train ( , and ). It can be seen that the estimated , and Stable reach to the desired value before 20 s. Figure 10 The estimated and actual values of basic resistance of each carriage of high-speed train are shown in the figure. are the actual values of the basic resistance of the 1st, 2nd, 3rd and 4th carriages respectively, These are the estimated values of the basic resistance of carriages 1, 2, 3, and 4, respectively. Figure 11 The basic drag estimation error of each carriage of the high-speed train is shown. These are the basic resistance estimation errors of the 1st, 2nd, 3rd and 4th carriages, respectively. The errors converge to near zero in less than 10 seconds. Figure 12 Shows the expected speed of each car of the high-speed train ( are the expected speeds of the 1st, 2nd, 3rd and 4th carriages respectively), and Figure 13The 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 and 4th carriages respectively, are the speed tracking errors of the 1st, 2nd, 3rd and 4th carriages respectively.

[0104] from Figure 10 and Figure 11 It can be seen that for a given actual basic resistance curve, under the control method proposed in this application, all carriages of the train can achieve accurate tracking and converge to near zero in a relatively short time.

[0105] Simulation equipment and platform: The computer CPU is 11th Gen Intel(R) Core(TM) i5-1135G7, 2.42GHz, Windows 10 Professional operating system, and the simulation platform is MATLAB R2022a.

[0106] To address the problems of parameter update lag and poor environmental adaptability caused by existing drag parameter measurement methods relying on high-cost offline solutions such as actual vehicle testing and wind tunnel experiments, this application designs an adaptive observer with a dynamic gain matrix by constructing a multi-particle longitudinal dynamic model that includes coupler coupling forces. The adaptive observer includes a state estimation equation, a parameter adaptation law, an auxiliary variable update mechanism (the auxiliary variable update mechanism is the auxiliary variable dynamic equation), a gain matrix update law, and a basic drag equation. By introducing Lyapunov stability analysis under continuous excitation conditions, it is proved that the drag parameter estimation error is asymptotically stable in the absence of interference and is uniformly and ultimately bounded in the presence of disturbances. The scheme proposed in this application can effectively estimate the basic drag asymptotically online, significantly reducing testing costs and improving robust performance.

[0107] The present application has the following beneficial effects: 1. The present application applies an adaptive observer to a high-speed train system and designs a new adaptive observer, which effectively realizes the online asymptotic estimation of the basic resistance of the train during operation; 2. Traditional offline TBRP estimation methods (real vehicle testing, wind tunnel testing and numerical simulation) have two disadvantages: (1) estimation errors are inevitable; (2) they require considerable time and financial investment. Unlike offline TBRP estimation methods, the present application proposes an online adaptive observer that enables asymptotic estimation of TBRP with high robustness; 3. The present application is easy to integrate into existing high-speed train tracking control methods, thereby improving the tracking accuracy of high-speed trains. Specifically, the opposite value of the estimated basic resistance value is added as a feedforward signal to the control input, effectively offsetting and compensating the basic resistance, thereby enhancing the tracking performance of high-speed trains.

[0108] The present application also provides an application scenario, which applies the above-mentioned method for online estimation of basic resistance of high-speed trains. Specifically: the method for online estimation of basic resistance of high-speed trains provided in this embodiment can be applied in the scenario of basic resistance estimation of high-speed trains. The scenario of basic resistance estimation of high-speed trains includes a request sending link and a basic resistance online estimation link; the request to be processed enters the basic resistance online estimation link from the request sending link to obtain the basic resistance estimation value of each car of the high-speed train. The method for online estimation of basic resistance of high-speed trains provided in this embodiment belongs to the basic resistance online estimation link. Specifically, in the process of online estimation of basic resistance for requests 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 basic resistance estimation value of each car of the high-speed train can be obtained.

[0109] Based on the same inventive concept, embodiments of the present application also provide a high-speed train basic resistance online estimation device for implementing the above-mentioned high-speed train basic resistance online estimation method. The solution provided by this device is similar to the solution described in the above-mentioned method. Therefore, the specific limitations of one or more embodiments of the high-speed train basic resistance online estimation device provided below can be found in the above-mentioned limitations of the high-speed train basic resistance online estimation method and will not be repeated here.

[0110] In an exemplary embodiment, a high-speed train basic resistance online estimation device is provided, comprising the following modules: 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 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.

[0111] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 14As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, memory and input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. 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 computer program in the non-volatile storage medium. The database of the computer device is used to store online estimation data of the basic resistance of the train. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for online estimation of the basic resistance of a high-speed train is implemented.

[0112] Those skilled in the art will understand that Figure 14 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0113] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0114] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0115] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

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; Designing 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 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 2, characterized in that: 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 .

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

6. The method for online estimation of basic resistance of high-speed train according to claim 4, characterized in that: The auxiliary variable dynamic equation is expressed as follows: ； in, Auxiliary variables About time The first derivative of .

7. The method for online estimation of basic resistance of high-speed train according to claim 4, 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 .

8. 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 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.

9. 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 method for online estimation of basic resistance of a high-speed train according to any one of claims 1 to 7.

10. 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 estimating the basic resistance of a high-speed train according to any one of claims 1 to 7 is implemented.

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