Stable condition determination method and device for superconducting electric aerotrain

Abstract

The invention relates to a stable condition determination method and device for a superconducting electric aerotrain, and the method comprises the steps: determining the corresponding longitudinal speed and running conditions of the train in the running process of the train, and determining a plurality of initial motion conditions based on the longitudinal speed and running conditions of the train, and determining a motion state corresponding to each initial motion condition according to a preset motion state judgment algorithm, wherein the motion state comprises a stable state and an unstable state. And determining a corresponding stable condition curve according to the initial motion condition corresponding to each stable state. Simulation is carried out through the initial motion condition in the train running process and the preset simulation algorithm, the initial motion condition of the train in the stable state is judged, and the corresponding stability curve is drawn to further improve the stability and safety in the train running process based on the stability curve.

Description

Technical Field

[0001] The present disclosure relates to the field of transportation, and in particular, to a method and device for determining the stability conditions of a superconducting maglev train. Background Art

[0002] In recent years, maglev rail transit has gradually come into people's view and become a research hotspot in the field of rail transit. Superconducting maglev trains have good application prospects in the field of high-speed and ultra-high-speed maglev rail transit due to their advantages such as self-stabilization of suspension and guidance, large suspension gap, and high floating resistance ratio. The vertical and lateral suspension and guidance system of a superconducting maglev train is a self-stabilizing system, which is also an important advantage compared with other types of maglev trains. However, in fact, this self-stabilizing system is not globally asymptotically stable and there is still a stability boundary, and there is currently no relevant research on the quantitative analysis of the stability of the suspension and guidance system of superconducting maglev trains. Summary of the Invention

[0003] In view of this, the present disclosure provides a method and device for determining the stability conditions of a superconducting maglev train, aiming to improve the stability of the superconducting maglev train.

[0004] According to a first aspect of the present disclosure, there is provided a method for determining the stability conditions of a superconducting maglev train, the method comprising:

[0005] Determining the corresponding longitudinal speed and driving conditions of the train during driving;

[0006] Determining a plurality of initial motion conditions based on the longitudinal speed of the train and the driving conditions;

[0007] Determining the motion state corresponding to each of the initial motion conditions according to a preset motion state judgment algorithm, the motion state including a stable state and an unstable state;

[0008] Determining a corresponding stability condition curve according to the initial motion conditions corresponding to each stable state.

[0009] In a possible implementation manner, the driving conditions include displacement conditions or speed conditions, the displacement conditions include a car body displacement range and a bogie displacement range, the car body displacement range includes a car body vertical displacement range or a car body lateral displacement range, the bogie displacement range includes a bogie vertical displacement range or a bogie lateral displacement range, the speed conditions include a car body speed range and a bogie speed range, the car body speed range includes a car body vertical speed range or a car body lateral speed range, and the bogie speed range includes a bogie lateral speed range or a bogie vertical speed range.

[0010] In a possible implementation, determining a plurality of initial motion conditions based on the longitudinal speed of the train and the driving conditions includes:

[0011] Dividing the carbody displacement range and the bogie displacement range respectively according to corresponding value intervals to obtain a plurality of carbody displacements and bogie displacements;

[0012] Determining corresponding initial motion conditions according to the longitudinal speed of the train, the carbody displacement, and the bogie displacement.

[0013] In a possible implementation, determining a plurality of initial motion conditions based on the longitudinal speed of the train and the driving conditions includes:

[0014] Dividing the carbody speed range and the bogie speed range respectively according to corresponding value intervals to obtain a plurality of carbody speeds and bogie speeds;

[0015] Determining corresponding initial motion conditions according to the longitudinal speed of the train, the carbody speed, and the bogie speed.

[0016] In a possible implementation, determining the motion state corresponding to each of the initial motion conditions according to a preset motion state judgment algorithm includes:

[0017] Taking the initial motion conditions as inputs, simulating the driving process of the train with a preset simulation time and simulation step length to obtain corresponding final carbody displacement, final carbody speed, final bogie displacement, and final bogie speed;

[0018] In response to the initial motion conditions including carbody displacement and bogie displacement, determining a motion result according to the final carbody displacement and the final bogie displacement;

[0019] In response to the initial motion conditions including carbody speed and bogie speed, determining a motion result according to the final carbody speed and the final bogie speed;

[0020] Determining the motion state corresponding to the motion result according to the motion result, the final carbody speed, and the final bogie speed.

[0021] In a possible implementation, determining the motion state corresponding to the motion result according to the motion result, the final carbody speed, and the final bogie speed includes:

[0022] Judging whether the motion result satisfies the equilibrium condition of the non-longitudinal dynamics model equation;

[0023] Calculating the train system energy according to the final carbody speed and the final bogie speed

[0024] In response to the energy of the train system being 0 and the motion result satisfying the equilibrium condition of the non-longitudinal dynamics model equation, determine that the motion state is a stable state.

[0025] In a possible implementation manner, the determining the motion state corresponding to each initial motion condition according to a preset motion state determination algorithm includes:

[0026] Taking each initial motion condition as the initial input of the non-linear system dynamics equation, and obtaining a target vector group after performing a preset number of iterations;

[0027] Calculating the Lyapunov exponent according to the target vector group;

[0028] In response to the corresponding Lyapunov exponent being less than 0, determine that the motion state is a stable state.

[0029] According to a second aspect of the present disclosure, there is provided a device for determining the stable condition of a superconducting maglev train, the device includes:

[0030] A condition determination module, configured to determine the corresponding longitudinal speed and driving conditions of the train during driving;

[0031] An initial condition determination module, configured to determine a plurality of initial motion conditions based on the longitudinal speed of the train and the driving conditions;

[0032] A motion state determination module, configured to determine the motion state corresponding to each initial motion condition according to a preset motion state determination algorithm, where the motion state includes a stable state and an unstable state;

[0033] A curve determination module, configured to determine a corresponding stable condition curve according to the initial motion conditions corresponding to each stable state.

[0034] In a possible implementation manner, the driving conditions include displacement conditions or speed conditions, the displacement conditions include a car body displacement range and a bogie displacement range, the car body displacement range includes a car body vertical displacement range or a car body lateral displacement range, the bogie displacement range includes a bogie vertical displacement range or a bogie lateral displacement range, the speed conditions include a car body speed range and a bogie speed range, the car body speed range includes a car body vertical speed range or a car body lateral speed range, and the bogie speed range includes a bogie lateral speed range or a bogie vertical speed range.

[0035] In a possible implementation manner, the initial condition determination module is further configured to:

[0036] Divide the body displacement range and the bogie displacement range respectively according to the corresponding value intervals to obtain a plurality of body displacements and bogie displacements;

[0037] Determine the corresponding initial motion conditions according to the longitudinal speed of the train, the body displacement and the bogie displacement.

[0038] In a possible implementation manner, the initial condition determination module is further configured to:

[0039] Divide the body speed range and the bogie speed range respectively according to the corresponding value intervals to obtain a plurality of body speeds and bogie speeds;

[0040] Determine the corresponding initial motion conditions according to the longitudinal speed of the train, the body speed and the bogie speed.

[0041] In a possible implementation manner, the motion state determination module is further configured to:

[0042] Use the initial motion conditions as inputs, and simulate the driving process of the train with a preset simulation time and simulation step size to obtain the corresponding final body displacement, final body speed, final bogie displacement and final bogie speed;

[0043] In response to the initial motion conditions including the body displacement and the bogie displacement, determine the motion result according to the final body displacement and the final bogie displacement;

[0044] In response to the initial motion conditions including the body speed and the bogie speed, determine the motion result according to the final body speed and the final bogie speed;

[0045] Determine the motion state corresponding to the motion result according to the motion result, the final body speed and the final bogie speed.

[0046] In a possible implementation manner, the motion state determination module is further configured to:

[0047] Judge whether the motion result satisfies the equilibrium condition of the non-longitudinal dynamics model equation;

[0048] Calculate the train system energy according to the final body speed and the final bogie speed;

[0049] In response to the train system energy being 0 and the motion result satisfying the equilibrium condition of the non-longitudinal dynamics model equation, determine that the motion state is a stable state.

[0050] In a possible implementation manner, the motion state determination module is further configured to:

[0051] Using each of the initial motion conditions as the initial input of the non - linear system dynamics equation, after performing a preset number of iterations, a target vector group is obtained;

[0052] Calculate the Lyapunov exponent according to the target vector group;

[0053] In response to the corresponding Lyapunov exponent being less than 0, determine that the motion state is a stable state.

[0054] According to the third aspect of the present disclosure, an electronic device is provided, including: a processor; a memory for storing processor - executable instructions; wherein, the processor is configured to implement the above - mentioned method when executing the instructions stored in the memory.

[0055] According to the fourth aspect of the present disclosure, a non - volatile computer - readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions implement the above - mentioned method when executed by a processor.

[0056] According to the fifth aspect of the present disclosure, a computer program product is provided, including computer - readable code, or a non - volatile computer - readable storage medium carrying the computer - readable code, when the computer - readable code runs in the processor of an electronic device, the processor in the electronic device executes the above - mentioned method.

[0057] In the embodiments of the present disclosure, the corresponding longitudinal speed and driving conditions of the train during driving are determined, a plurality of initial motion conditions are determined based on the longitudinal speed and driving conditions of the train, and the motion state corresponding to each initial motion condition is determined according to a preset motion state judgment algorithm, where the motion state includes a stable state and an unstable state. The corresponding stable condition curve is determined according to the initial motion conditions corresponding to each stable state. The present disclosure performs simulation through the initial motion conditions during the train driving process and a preset simulation algorithm, judges the initial motion conditions in the stable state of the train, and draws the corresponding stable curve to further improve the stability and safety during the train motion process based on the stable curve.

[0058] According to the following detailed description of the exemplary embodiments with reference to the accompanying drawings, other features and aspects of the present disclosure will become clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The drawings included in the specification and constituting a part of the specification, together with the specification, illustrate the exemplary embodiments, features and aspects of the present disclosure, and are used to explain the principles of the present disclosure.

[0060] Figure 1 A flowchart showing a method for determining the stable conditions of a superconducting maglev train according to an embodiment of the present disclosure;

[0061] Figure 2 A schematic diagram showing the determination of a steady state according to an embodiment of the present disclosure;

[0062] Figure 3 A schematic diagram showing a range of stability conditions according to an embodiment of the present disclosure;

[0063] Figure 4 A schematic diagram showing a device for determining the stability conditions of a superconducting maglev train according to an embodiment of the present disclosure;

[0064] Figure 5 A schematic diagram showing an electronic device according to an embodiment of the present disclosure. Detailed implementation manners

[0065] Various exemplary embodiments, features, and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. Like reference numerals in the drawings denote elements having the same or similar functions. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0066] The term "exemplary" used herein means "serving as an example, embodiment, or illustration". Any embodiment described herein as "exemplary" is not necessarily to be construed as superior or better than other embodiments.

[0067] In addition, for a better description of the present disclosure, numerous specific details are given in the following detailed implementation manners. Those skilled in the art should understand that the present disclosure can be implemented without some specific details. In some instances, methods, means, elements, and circuits well known to those skilled in the art are not described in detail so as to highlight the gist of the present disclosure.

[0068] The method for determining the stability conditions of a superconducting maglev train according to an embodiment of the present disclosure can be executed by an electronic device such as a terminal device or a server. Among them, the terminal device can be any fixed or mobile terminal such as a user equipment (UE), a mobile device, a user terminal, a terminal, a cellular phone, a cordless phone, a personal digital assistant (PDA), a handheld device, a computing device, a vehicle-mounted device, a wearable device, etc. The server can be a single server or a server cluster composed of multiple servers. Any electronic device can implement the method for determining the stability conditions of a superconducting maglev train according to an embodiment of the present disclosure by a processor calling computer-readable instructions stored in a memory.

[0069] Figure 1 A flowchart showing a method for determining the stability conditions of a superconducting maglev train according to an embodiment of the present disclosure. As Figure 1As shown, the method for determining the stability condition of the superconducting maglev train according to the embodiments of the present disclosure may include the following steps S10-S40.

[0070] Step S10, determining the longitudinal speed of the train and the driving conditions corresponding during the train driving process.

[0071] In a possible implementation manner, the longitudinal speed of the train and the driving conditions during the train driving process may be pre-determined by an electronic device, so as to further simulate the train driving process through the longitudinal speed of the train and the driving conditions. Among them, the longitudinal speed of the train is the train driving speed parallel to the track direction. The driving conditions include displacement conditions or speed conditions. The displacement conditions include the car body displacement range and the bogie displacement range. The car body displacement range includes the car body vertical displacement range or the car body lateral displacement range. The bogie displacement range includes the bogie vertical displacement range or the bogie lateral displacement range. The speed conditions include the car body speed range and the bogie speed range. The car body speed range includes the car body vertical speed range or the car body lateral speed range. The bogie speed range includes the bogie lateral speed range or the bogie vertical speed range. Optionally, the vertical direction is the direction perpendicular to the track direction, and the vertical direction is generally perpendicular to the ground. The lateral direction is the direction parallel to the ground and perpendicular to the longitudinal direction of the car body, that is, the vertical, lateral, and longitudinal directions are perpendicular to each other in space.

[0072] Further, embodiments of the present disclosure can preset the vertical displacement range of the vehicle body, the lateral displacement range of the vehicle body, the vertical displacement range of the bogie, the lateral displacement range of the bogie, the vertical speed range of the vehicle body, the lateral speed range of the vehicle body, the lateral speed range of the bogie, and the vertical speed range of the bogie, and select the direction according to the type of the stability condition curve to be determined and the vehicle body speed / displacement range and bogie speed / displacement range of the same type to determine the driving conditions. Among them, the stability condition curves to be determined may include a lateral displacement range curve, a vertical displacement range curve, a lateral speed range curve, and a vertical speed range curve. That is, when the type of the stability condition curve to be determined is a vertical displacement range curve, the driving conditions include displacement conditions, the vehicle body displacement range includes the vertical displacement range of the vehicle body, and the bogie displacement range includes the vertical displacement range of the bogie. When the type of the stability condition curve to be determined is a lateral displacement range curve, the driving conditions include displacement conditions, the vehicle body displacement range includes the lateral displacement range of the vehicle body, and the bogie displacement range includes the lateral displacement range of the bogie. When the type of the stability condition curve to be determined is a vertical speed range curve, the driving conditions include speed conditions, the vehicle body speed range includes the vertical speed range of the vehicle body, and the bogie speed range includes the vertical speed range of the bogie. When the type of the stability condition curve to be determined is a lateral speed range curve, the driving conditions include speed conditions, the vehicle body speed range includes the lateral speed range of the vehicle body, and the bogie displacement range includes the lateral speed range of the bogie.

[0073] Further, after determining the longitudinal speed and driving conditions of the train, the electronic device can determine a two-dimensional phase space composed of a train motion state based on the directions respectively corresponding to the driving conditions. The two-dimensional phase space can be regarded as a two-dimensional coordinate system representing the relationship between two train driving conditions. There are four types of two-dimensional phase spaces, namely the vertical displacement of the vehicle body and the vertical displacement of the bogie, the lateral displacement of the vehicle body and the lateral displacement of the bogie, the vertical speed of the vehicle body and the vertical speed of the bogie, and the lateral speed of the vehicle body and the lateral speed of the bogie. Simulation analysis can be carried out based on the two-dimensional phase space and the energy characteristics during the train motion process to judge the stable state of the train.

[0074] Step S20: Determine a plurality of initial motion conditions based on the longitudinal speed of the train and the driving conditions.

[0075] In a possible implementation, after determining the longitudinal speed and driving conditions of the train during the train's travel, the electronic device may determine multiple initial motion conditions based on the longitudinal speed and driving conditions of the train. Among them, the information included in the initial motion conditions can be determined according to the application scenario, that is, it can be determined based on the type of the stable condition curve to be determined. Exemplarily, since a superconducting maglev train includes two parts, a car body and a bogie, when the type of the stable condition curve to be determined is a lateral displacement range curve, the initial motion conditions may include the longitudinal speed of the train, the lateral displacement range of the car body, and the lateral displacement range of the bogie. When the type of the stable condition curve to be determined is a vertical displacement range curve, the initial motion conditions may include the longitudinal speed of the train, the vertical displacement range of the car body, and the vertical displacement range of the bogie. When the type of the stable condition curve to be determined is a lateral speed range curve, the initial motion conditions may include the longitudinal speed of the train, the lateral speed range of the car body, and the lateral speed range of the bogie. When the type of the stable condition curve to be determined is a vertical speed range curve, the initial motion conditions may include the longitudinal speed of the train, the vertical speed range of the car body, and the vertical speed range of the bogie.

[0076] Optionally, when the type of the stable condition curve to be determined is a lateral displacement range curve or a vertical displacement range curve, the electronic device may directly divide the car body displacement range and the bogie displacement range according to the preset value intervals respectively to obtain multiple car body displacements and bogie displacements, and then determine the corresponding initial motion conditions according to the longitudinal speed of the train, one car body displacement, and one bogie displacement. Among them, the same initial motion conditions are not included, that is, at least one of the car body displacement or the bogie displacement included in each initial motion condition is different. For example, it may be that the car body displacement is the same while the bogie displacement is different, or the bogie displacement is the same while the car body displacement is different, or both the car body displacement and the bogie displacement are different. Exemplarily, when the longitudinal speed of the train is the longitudinal speed v x = 150 m / s, and the displacement condition is that the vertical displacement range of the bogie is (-0.5:0.1:0.2) m and the vertical displacement range of the car body is (-0.7:0.1:0.3) m, the electronic device may first divide the vertical displacement range of the bogie (-0.5:0.2) and the vertical displacement range of the car body (-0.7:0.3) according to the preset value interval of 0.1 to obtain multiple corresponding bogie displacements -0.5, -0.4, -0.3, …, 0.1, 0.2, and car body displacements -0.7, -0.6, -0.5, …, 0.3, and then determine an initial motion condition according to the longitudinal speed of the train and the randomly selected bogie displacement and car body displacement. Optionally, when the longitudinal speed of the train also includes at least one, the longitudinal speed of the train, the bogie displacement, and the car body displacement may be randomly selected to determine an initial motion condition.

[0077] Similarly, when the type of the stable condition curve to be determined is a lateral speed range curve or a vertical speed range curve, the electronic device can directly divide the vehicle body speed range and the bogie speed range according to a preset value interval respectively, obtain multiple vehicle body speeds and bogie speeds, and then determine the corresponding initial motion conditions according to the longitudinal speed of the train, a vehicle body speed, and a bogie speed. Among them, the same initial motion conditions are not included, that is, at least one of the vehicle body speed or the bogie speed included in each initial motion condition is different. Exemplarily, when the longitudinal speed of the train is the longitudinal speed v of the train x = 150 m / s, the speed condition is that the vertical speed range of the bogie is (-15:0.25:10) m / s, and the vertical speed range of the vehicle body is (-6:0.25:4) m / s, the electronic device can first divide the vertical speed range of the bogie (-15:10) and the vertical speed range of the vehicle body (-6:4) according to the preset value interval of 0.25 to obtain multiple corresponding bogie speeds -15, -14.75, …, 9.75, 10, and vehicle body speeds -6, -5.75, …, 4, and then determine an initial motion condition according to the longitudinal speed of the train and the randomly selected bogie speed and vehicle body speed. Optionally, when the longitudinal speed of the train also includes at least one, the longitudinal speed of the train, the bogie speed, and the vehicle body speed can be randomly selected to determine an initial motion condition.

[0078] Step S30: Determine the motion state corresponding to each of the initial motion conditions according to a preset motion state judgment algorithm.

[0079] In a possible implementation manner, the electronic device pre-sets at least one motion state judgment algorithm to judge whether the motion state corresponding to the initial motion condition is a stable state according to the preset state judgment algorithm after determining each initial motion condition, that is, the motion state of the train includes two states: a stable state and an unstable state. Among them, at least one of the preset motion state judgment algorithms can be to judge the motion state by means of simulation, and another state judgment algorithm can be to judge the motion state by calculating the Lyapunov exponent.

[0080] Optionally, in the case of judging the motion state by means of simulation, the electronic device can use the initial motion conditions as input, simulate the driving process of the train with a preset simulation time and simulation step length, and obtain the corresponding final carbody displacement, final carbody speed, final bogie displacement, and final bogie speed. When the initial motion conditions include the carbody displacement and the bogie displacement, the motion result is determined according to the final carbody displacement and the final bogie displacement. When the initial motion conditions include the carbody speed and the bogie speed, the motion result is determined according to the final carbody speed and the final bogie speed. Then, according to the motion result, the final carbody speed, and the final bogie speed, the motion state corresponding to the motion result is determined.

[0081] Furthermore, the motion state can be jointly judged by the equilibrium condition of the preset non-longitudinal dynamics model equation of the superconducting maglev train and the train system energy, that is, the electronic device can first judge whether the motion result meets the equilibrium condition of the non-longitudinal dynamics model equation, and then calculate the train system energy according to the final carbody speed and the final bogie speed. When the train system energy is 0 and the motion result meets the equilibrium condition of the non-longitudinal dynamics model equation, it is determined that the motion state of the train is a stable state. When the train system energy is not 0, or the motion result does not meet the equilibrium condition of the non-longitudinal dynamics model equation, it is determined that the motion state of the train is an unstable state. Among them, the non-longitudinal dynamics model equation and its corresponding equilibrium condition can refer to the content of the journal literature "L. Liu, H. Ye, W. Dong and J. Cui, Comprehensive Model Construction and Simulation for Superconducting Electrodynamic Suspension Train, Complex System Modeling and Simulation, vol. 3, no. 3, pp. 220 - 235, September 2023", which will not be elaborated here. When the type of the stable condition curve to be determined is a lateral displacement range curve or a lateral speed range curve, the final carbody speed includes the final carbody lateral speed, and the final bogie speed can include the final bogie lateral speed. The electronic device can obtain the lateral energy as the train system energy by calculating half of the sum of the squares of the two speeds. When the type of the stable condition curve to be determined is a vertical displacement range curve or a vertical speed range curve, the final carbody speed includes the final carbody vertical speed, and the final bogie speed can include the final bogie vertical speed. The electronic device can obtain the vertical energy as the train system energy by calculating half of the sum of the squares of the two speeds.

[0082] Figure 2A schematic diagram showing the determination of a steady state according to an embodiment of the present disclosure. As Figure 2 shown, when the type of the steady-state condition curve to be determined is the vertical displacement range curve, multiple initial motion conditions of the electronic device are carried out and model simulation is performed. The green dots in the figure are the initial states of the train, and the red dots are the end states of the train. Each curve represents the motion process corresponding to an initial motion condition. During the simulation process, after the vertical displacements of the train carbody and the bogie have fluctuated to a certain extent, they quickly reach the equilibrium state of the system and reach a non-equilibrium state (the judgment basis is that the equilibrium state cannot be reached after a certain simulation time). The former is the steady state, and the latter is the non-steady state. For the two states, the vertical and lateral motion states of the train carbody and the bogie can reach the equilibrium state by relying on the self-stability of the train suspension and guidance system from the steady state, while the non-steady state cannot reach the equilibrium state and may eventually be in a divergent or oscillating state.

[0083] Optionally, the algorithm code for determining the steady state by means of simulation can be:

[0084]

[0085]

[0086] In a possible implementation manner, the motion state can also be judged by calculating the Lyapunov exponent. The Lyapunov Exponent is an important concept and index for characterizing the stability of a dynamic system, which can describe the average exponential rate of the convergence or divergence of the state space orbit of the system after being perturbed, and is suitable for the motion stability analysis of complex nonlinear systems. If a system has a negative Lyapunov exponent and the sum of all Lyapunov exponents is less than zero, then the system is a stable dissipative system. For a dissipative system with a steady state and a stable region, starting from any initial condition in the stable region corresponding to the same steady state, its Lyapunov exponent has the same value. That is, when the Lyapunov exponent calculated based on the initial motion condition is less than 0, the motion state is determined to be the steady state, and when the Lyapunov exponent calculated based on the initial motion condition is not less than 0, the motion state is determined to be the non-steady state.

[0087] Optionally, embodiments of the present disclosure may solve the Lyapunov exponents of the suspension and guidance system of a superconducting maglev train based on the orthogonalization method of the kinetic equation to determine the motion state of each initial motion condition. Among them, the electronic device may first determine the non-linear system kinetic equation, and then use each initial motion condition as the initial input of the non-linear system kinetic equation, and obtain the target vector group after performing a preset number of iterations. Calculate the Lyapunov exponent according to the target vector group. When the corresponding Lyapunov exponent is less than 0, determine that the motion state is a stable state. When the corresponding Lyapunov exponent is not less than 0, determine that the motion state is an unstable state.

[0088] Specifically, the non-linear system kinetic equation is where \(f(x)\) is an \(n\)-dimensional non-linear vector function and \(x\) is an \(n\)-dimensional state vector. To monitor the evolution of the main axis of the system, perform the transformation as shown in the formula to obtain the equation \(\psi\) t is the state transition matrix of the linearized system \(\delta x(t)=\psi\) t \(\delta x(0)\), and \(F(t)\) is the \(n\)-dimensional Jacobian matrix of the system. An initial state transition matrix can be preset The initial main axes are selected as orthogonal vectors of \(e_1(0)=(1,0,\cdots,0)\), \(e_2(0)=(0,1,\cdots,0)\), \(\cdots\), \(e\) n (0)=(0,0,\cdots,1). Then, determine the vector \(x_0\) according to each parameter in the initial motion condition, and according to the set solution step \(dt\), substitute into the transformed equation to calculate the next set of vectors \(V\), that is, \(v_1(dt)\), \(v_2(dt)\), \(\cdots\), \(v\) n (dt), perform GSR orthogonalization processing on \(V\), update the main axis based on the following formula, and substitute it back into the transformed equation for iterative calculation for a preset number of times.

[0089]

[0090] After iterative calculation for a preset number of times, store the denominators of \(e_1(dt)\), \(e_2(dt)\), \(\cdots\), \(e\) n (dt) as \(p_1(1)\), \(p_2(2)\), \(\cdots\), \(p\) n (1), and calculate the Lyapunov exponent based on the formula where \(M\) is the number of iterations.

[0091] Optionally, the algorithm code for determining the stable state by calculating the Lyapunov exponent may be:

[0092]

[0093]

[0094] Step S40: Determine the corresponding stable condition curve according to the initial motion conditions corresponding to each stable state.

[0095] In a possible implementation manner, after the electronic device determines the motion state corresponding to each initial motion condition, it determines the corresponding stable condition curve according to the initial motion conditions corresponding to each stable state, so as to adjust the driving conditions of the superconducting maglev train according to the stable condition curve to ensure the safety performance during the train driving process. The stable condition curve is a curve in the two-dimensional phase space composed of the types of driving conditions included in the initial motion conditions. The drawing method of this curve can be to use two driving conditions included in the initial motion conditions as the x-axis and y-axis to determine the two-dimensional phase space, and then use the values of the two driving conditions in the initial motion conditions whose corresponding motion state is a stable state as the abscissa value and the ordinate value respectively to determine their positions in the two-dimensional phase space. Further, according to the positions of the initial motion conditions whose each motion state is a stable state in the two-dimensional phase space, fitting is performed to draw the stable condition curve.

[0096] Figure 3 A schematic diagram showing a stable condition range according to an embodiment of the present disclosure is shown. As Figure 3 shown, since each initial motion condition includes the driving states of the car body and the bogie in the lateral or vertical directions, the electronic device can determine the two-dimensional phase space based on the two driving states, and draw the stable condition curve according to the values corresponding to the two driving states in multiple initial motion conditions whose motion state is a stable state, so as to obtain the corresponding stable region (i.e., the region surrounded by the stable condition curve). Optionally, based on different types of stable condition curves, the three-dimensional stable region formed by corresponding the two-dimensional stable region to each different state can be sequentially defined as the vertical displacement protection curve, the vertical velocity protection curve, the lateral displacement protection curve, and the lateral velocity protection curve. Among them, the three-dimensional stable region adds the dimension of the curve type relative to the two-dimensional stable region. These four groups of curves together can form the vertical and lateral protection curves of the superconducting maglev train for ensuring the safety performance during the train driving process.

[0097] Take Figure 3Taking the upper left figure as an example, the type of the determined stable condition curve of this figure is the vertical displacement range curve, and the numerical points in the figure are the initial operating conditions corresponding to the stable state, where the initial motion conditions include the vertical displacement of the car body and the vertical displacement of the bogie. That is, taking the vertical displacement of the bogie as the abscissa and the vertical displacement of the car body as the ordinate to construct a two-dimensional phase space, and based on the values of the vertical displacement of the bogie and the vertical displacement of the car body in the initial motion conditions where each motion state is a stable state, as its abscissa value and ordinate value in the two-dimensional phase space to determine the coordinate position. Further, according to the coordinate positions of the initial motion conditions where each motion state is a stable state in the two-dimensional phase space, a curve is drawn (for example, the points in the coordinate system are curve-fitted to obtain a curve), and a vertical displacement protection curve is obtained. Similarly, stable condition curves of four different types, namely the vertical displacement protection curve, the vertical velocity protection curve, the lateral displacement protection curve, and the lateral velocity protection curve, can be drawn respectively, and they are jointly used as the vertical and lateral protection curve of the train. The protection curve can be used as a reference condition or a constraint condition during the train operation process to ensure that the displacement and velocity of the train in the lateral and vertical directions are within the safe range.

[0098] Based on the above technical features, the embodiments of the present disclosure can perform simulations through the initial motion conditions during the train operation process and a preset motion state judgment algorithm, judge the initial motion conditions in the stable state of the train, and draw corresponding stable curves to further improve the stability and safety during the train motion process based on the stable curves. This method can draw stable curves from four dimensions of lateral displacement, vertical displacement, lateral velocity, and vertical velocity respectively to jointly ensure the stability of the train operation process from four dimensions and improve the overall safety performance.

[0099] Figure 4 The figure shows a schematic diagram of a device for determining the stable conditions of a superconducting maglev train according to an embodiment of the present disclosure. As Figure 4 shown, the device for determining the stable conditions of the superconducting maglev train according to the embodiments of the present disclosure may include:

[0100] A condition determination module 40, configured to determine the corresponding longitudinal speed and driving conditions of the train during the train operation process;

[0101] An initial condition determination module 41, configured to determine a plurality of initial motion conditions based on the longitudinal speed of the train and the driving conditions;

[0102] A motion state determination module 42, configured to determine the motion state corresponding to each of the initial motion conditions according to a preset motion state judgment algorithm, where the motion state includes a stable state and an unstable state;

[0103] A curve determination module 43, configured to determine a corresponding stable condition curve according to the initial motion conditions corresponding to each stable state.

[0104] In a possible implementation, the driving conditions include displacement conditions or speed conditions. The displacement conditions include a carbody displacement range and a bogie displacement range. The carbody displacement range includes a carbody vertical displacement range or a carbody lateral displacement range. The bogie displacement range includes a bogie vertical displacement range or a bogie lateral displacement range. The speed conditions include a carbody speed range and a bogie speed range. The carbody speed range includes a carbody vertical speed range or a carbody lateral speed range. The bogie speed range includes a bogie lateral speed range or a bogie vertical speed range.

[0105] In a possible implementation, the initial condition determination module 41 is further configured to:

[0106] Divide the carbody displacement range and the bogie displacement range respectively according to corresponding value intervals to obtain a plurality of carbody displacements and bogie displacements;

[0107] Determine corresponding initial motion conditions according to the longitudinal speed of the train, the carbody displacement, and the bogie displacement.

[0108] In a possible implementation, the initial condition determination module 41 is further configured to:

[0109] Divide the carbody speed range and the bogie speed range respectively according to corresponding value intervals to obtain a plurality of carbody speeds and bogie speeds;

[0110] Determine corresponding initial motion conditions according to the longitudinal speed of the train, the carbody speed, and the bogie speed.

[0111] In a possible implementation, the motion state determination module 42 is further configured to:

[0112] Use the initial motion conditions as inputs, and simulate the driving process of the train with a preset simulation time and simulation step length to obtain corresponding final carbody displacement, final carbody speed, final bogie displacement, and final bogie speed;

[0113] In response to the initial motion conditions including carbody displacement and bogie displacement, determine a motion result according to the final carbody displacement and the final bogie displacement;

[0114] In response to the initial motion conditions including carbody speed and bogie speed, determine a motion result according to the final carbody speed and the final bogie speed;

[0115] Determine the motion state corresponding to the motion result according to the motion result, the final carbody speed, and the final bogie speed.

[0116] In a possible implementation, the motion state determination module 42 is further configured to:

[0117] Determine whether the motion result satisfies the equilibrium condition of the non-longitudinal dynamics model equation;

[0118] Calculate the train system energy based on the termination car body speed and the termination bogie speed;

[0119] In response to the train system energy being 0 and the motion result satisfying the equilibrium condition of the non-longitudinal dynamics model equation, determine that the motion state is a stable state.

[0120] In a possible implementation, the motion state determination module 42 is further configured to:

[0121] Use each of the initial motion conditions as the initial input of the non-linear system dynamics equation, and obtain a target vector group after performing a preset number of iterations;

[0122] Calculate the Lyapunov exponent based on the target vector group;

[0123] In response to the corresponding Lyapunov exponent being less than 0, determine that the motion state is a stable state.

[0124] In some embodiments, the functions or modules included in the device provided by the embodiments of the present disclosure can be used to execute the methods described in the above method embodiments. The specific implementation can refer to the description of the above method embodiments. For the sake of brevity, it will not be repeated here.

[0125] The embodiments of the present disclosure also propose a computer-readable storage medium, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the above methods are implemented. The computer-readable storage medium can be a volatile or non-volatile computer-readable storage medium.

[0126] The embodiments of the present disclosure also propose an electronic device, including: a processor; a memory for storing processor-executable instructions; wherein, the processor is configured to implement the above methods when executing the instructions stored in the memory.

[0127] The embodiments of the present disclosure also provide a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying the computer-readable code. When the computer-readable code runs in the processor of the electronic device, the processor in the electronic device executes the above methods.

[0128] Figure 5A schematic diagram of an electronic device 1900 according to an embodiment of the present disclosure is shown. For example, the electronic device 1900 may be provided as a server or a terminal device. Referring to Figure 5 , the electronic device 1900 includes a processing component 1922, which further includes one or more processors, and memory resources represented by a memory 1932 for storing instructions executable by the processing component 1922, such as application programs. The application programs stored in the memory 1932 may include one or more modules each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute instructions to perform the above method.

[0129] The electronic device 1900 may further include a power supply component 1926 configured to perform power management of the electronic device 1900, a wired or wireless network interface 1950 configured to connect the electronic device 1900 to a network, and an input / output interface 1958 (I / O interface). The electronic device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server TM , Mac OS X TM , Unix TM , Linux TM , FreeBSD TM or the like.

[0130] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as the memory 1932 including computer program instructions, and the above computer program instructions can be executed by the processing component 1922 of the electronic device 1900 to complete the above method.

[0131] The present disclosure may be a system, a method, and / or a computer program product. The computer program product may include a computer-readable storage medium having thereon computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0132] A computer-readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. A computer-readable storage medium may be, for example—but not limited to—an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), a memory stick, a floppy disk, a mechanically encoded device, such as a punched card or raised structures in grooves having instructions stored thereon, and any suitable combination of the foregoing. The computer-readable storage medium as used herein is not construed as being a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagated through a waveguide or other transmission medium (e.g., an optical pulse through an optical fiber cable), or an electrical signal transmitted through a wire.

[0133] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to respective computing / processing devices, or can be downloaded to an external computer or an external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network may include a copper transmission cable, an optical fiber transmission, a wireless transmission, a router, a firewall, a switch, a gateway computer, and / or an edge server. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in a computer-readable storage medium in each computing / processing device.

[0134] The computer program instructions for performing the operations of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine - related instructions, microcode, firmware instructions, state - setting data, or source code or object code written in any combination of one or more programming languages, including object - oriented programming languages such as Smalltalk, C++, etc., and conventional procedural programming languages such as the "C" language or similar programming languages. The computer - readable program instructions may be executed entirely on the user's computer, partially on the user's computer, executed as a stand - alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or, alternatively, may be connected to an external computer (e.g., through the Internet using an Internet service provider). In some embodiments, by using the state information of the computer - readable program instructions to customize an electronic circuit, such as a programmable logic circuit, a field - programmable gate array (FPGA), or a programmable logic array (PLA), the electronic circuit can execute the computer - readable program instructions to implement various aspects of the present disclosure.

[0135] Aspects of the present disclosure are described herein with reference to the flowchart and / or block diagram of methods, apparatus (systems), and computer program products according to embodiments of the present disclosure. It should be understood that each block of the flowchart and / or block diagram, and the combinations of blocks in the flowchart and / or block diagram, can be implemented by computer - readable program instructions.

[0136] These computer - readable program instructions can be provided to a processor of a general - purpose computer, a special - purpose computer, or other programmable data - processing apparatus to produce a machine such that the instructions, when executed by the processor of the computer or other programmable data - processing apparatus, create a means for implementing the functions / acts specified in one or more blocks of the flowchart and / or block diagram. These computer - readable program instructions can also be stored in a computer - readable storage medium, which causes a computer, a programmable data - processing apparatus, and / or other devices to operate in a particular manner, so that the computer - readable medium storing the instructions includes a manufacture, which includes instructions for implementing various aspects of the functions / acts specified in one or more blocks of the flowchart and / or block diagram.

[0137] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device, causing a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process such that the instructions executed on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in one or more boxes of the flowchart and / or block diagram.

[0138] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagram may represent a module, a segment of code, or a portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two consecutive blocks may in fact be executed substantially in parallel, or they may sometimes be executed in the reverse order, depending upon the functionality involved. It should also be noted that each block of the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented by a dedicated hardware-based system that performs the specified function or act, or by a combination of dedicated hardware and computer instructions.

[0139] The embodiments of the present disclosure have been described above. The above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The choice of terms used herein is intended to best explain the principles of the embodiments, the practical application, or improvements made to the technology in the marketplace, or to enable other ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A method for determining the stability conditions of a superconducting maglev train, characterized in that, The method includes: Determining the corresponding longitudinal train speed and driving conditions during the train's operation; Determining a plurality of initial motion conditions based on the longitudinal train speed and the driving conditions; Determining the motion state corresponding to each of the initial motion conditions according to a preset motion state judgment algorithm, where the motion state includes a stable state and an unstable state; Determining the corresponding stable condition curve according to the initial motion conditions corresponding to each stable state.

2. The method according to claim 1, characterized in that, The driving conditions include displacement conditions or speed conditions. The displacement conditions include a carbody displacement range and a bogie displacement range. The carbody displacement range includes a carbody vertical displacement range or a carbody lateral displacement range. The bogie displacement range includes a bogie vertical displacement range or a bogie lateral displacement range. The speed conditions include a carbody speed range and a bogie speed range. The carbody speed range includes a carbody vertical speed range or a carbody lateral speed range. The bogie speed range includes a bogie lateral speed range or a bogie vertical speed range.

3. The method according to claim 2, characterized in that, The determining of a plurality of initial motion conditions based on the longitudinal train speed and the driving conditions includes: Dividing the carbody displacement range and the bogie displacement range respectively according to corresponding value intervals to obtain a plurality of carbody displacements and bogie displacements; Determining the corresponding initial motion conditions according to the longitudinal train speed, the carbody displacement, and the bogie displacement.

4. The method according to claim 2, characterized in that, The determining of a plurality of initial motion conditions based on the longitudinal train speed and the driving conditions includes: Dividing the carbody speed range and the bogie speed range respectively according to corresponding value intervals to obtain a plurality of carbody speeds and bogie speeds; Determining the corresponding initial motion conditions according to the longitudinal train speed, the carbody speed, and the bogie speed.

5. The method according to any one of claims 1 - 4, characterized in that, The determining of the motion state corresponding to each of the initial motion conditions according to a preset motion state judgment algorithm includes: Taking the initial motion conditions as input, simulating the train's operation process with a preset simulation time and simulation step length to obtain the corresponding final carbody displacement, final carbody speed, final bogie displacement, and final bogie speed; In response to the initial motion conditions including carbody displacement and bogie displacement, determining a motion result according to the final carbody displacement and the final bogie displacement; In response to the initial motion conditions including carbody speed and bogie speed, determining a motion result according to the final carbody speed and the final bogie speed; Determining the motion state corresponding to the motion result according to the motion result, the final carbody speed, and the final bogie speed.

6. The method according to claim 5, characterized in that, The determining of the motion state corresponding to the motion result according to the motion result, the final carbody speed, and the final bogie speed includes: Judging whether the motion result satisfies the equilibrium condition of the non-longitudinal dynamics model equation; Calculating the train system energy according to the final carbody speed and the final bogie speed; In response to the train system energy being 0 and the motion result satisfying the equilibrium condition of the non-longitudinal dynamics model equation, determining the motion state as the stable state.

7. The method according to any one of claims 1 - 4, characterized in that, Determining the motion state corresponding to each of the initial motion conditions according to a preset motion state determination algorithm includes: Taking each of the initial motion conditions as the initial input of the non-linear system dynamics equation, and obtaining a target vector group after performing a preset number of iterations; Calculating the Lyapunov exponent according to the target vector group; In response to the corresponding Lyapunov exponent being less than 0, determining that the motion state is a stable state.

8. A device for determining the stability conditions of a superconducting maglev train, characterized in that, The device includes: A condition determination module, configured to determine the corresponding longitudinal speed and driving conditions of the train during the driving process; An initial condition determination module, configured to determine a plurality of initial motion conditions based on the longitudinal speed of the train and the driving conditions; A motion state determination module, configured to determine the motion state corresponding to each of the initial motion conditions according to a preset motion state determination algorithm, where the motion state includes a stable state and an unstable state; A curve determination module, configured to determine a corresponding stable condition curve according to the initial motion conditions corresponding to each stable state.

9. An electronic device, characterized in that,including: A processor; A memory for storing instructions executable by the processor; Wherein, the processor is configured to implement the method according to any one of claims 1 to 7 when executing the instructions stored in the memory.

10. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that, The computer program instructions, when executed by the processor, implement the method according to any one of claims 1 to 7.

Images