A method, medium and device for modeling random evolution of maglev track irregularities

Abstract

The application discloses a maglev track irregularity random evolution modeling method, medium and equipment, and belongs to the field of track engineering and random dynamics modeling. The method comprises the following steps: acquiring maglev track irregularity data collected along the line direction, and acquiring track structure parameters and vehicle load statistical characteristics corresponding to the line; calculating the track irregularity state increment between adjacent sampling points, and constructing a state variable set based on the track irregularity quantity, the track structure parameters and the vehicle load statistical characteristics; dividing the state interval according to the value range of the state variable set, and statistically counting the conditional statistics of the state increment in each interval; and identifying the drift term and the diffusion term function in the random differential equation by using the conditional statistical information, through statistical inversion, machine learning or a fusion mode thereof, and constructing a track irregularity random evolution model. The application can reflect the non-stationary and state-dependent characteristics of the track irregularity under the action of the track structure and the vehicle load, and can be used for track state evaluation, dynamics simulation and maintenance decision.

Description

Technical Field

[0001] This invention relates to the field of track engineering and stochastic dynamics modeling technology, and more specifically, to a method, medium, and device for modeling the stochastic evolution of irregularities in maglev tracks. Background Technology

[0002] Track irregularities are a key factor affecting track structural condition and vehicle operation safety and comfort. Their spatial distribution characteristics directly relate to vehicle-track dynamics response, structural fatigue damage, and track maintenance decisions. Furthermore, the evolution of track irregularities is not only related to their own condition but also influenced by track structural conditions and vehicle loads. Therefore, establishing a mathematical model that reflects the spatial stochastic characteristics of track irregularities and considers the influencing factors of track structure and vehicle loads is of great significance for vehicle dynamics simulation analysis, track condition assessment, and track maintenance management.

[0003] In existing technologies, stochastic modeling methods for track irregularities are mainly based on power spectral density or correlation functions. These methods typically generate track irregularity samples with specified frequency domain statistical characteristics by providing a standard spectrum or measured spectral characteristics. While this approach can reflect the overall frequency domain characteristics of track irregularities, it usually assumes that the irregularity is a stationary stochastic process with its statistical characteristics remaining spatially constant. Modeling methods based on power spectral density or correlation functions rely heavily on global statistical characteristics, failing to adequately utilize information on local state changes and making it difficult to directly model the actual changes between adjacent measurement points. This results in discrepancies between the generated irregularity samples and measured data in terms of local evolution characteristics. Furthermore, existing methods often focus on sample generation while insufficiently characterizing the probability distribution changes of track irregularities as they evolve spatially. In addition, these methods typically model only the track irregularity itself, failing to comprehensively consider the influence of engineering factors such as track structure conditions and vehicle loads on the evolution of track irregularities, making it difficult to reflect the multi-factor coupling effects in actual track systems.

[0004] Analysis reveals a lack of existing technologies that can directly identify and describe the spatial stochastic evolution of track irregularities based on measured track irregularity data, combined with track structure parameters and vehicle load statistical characteristics, starting from the state change information between adjacent measuring points. Consequently, it is difficult to establish a stochastic dynamic model that reflects the stochastic evolution mechanism of track irregularities along the track direction under the combined effects of track structure conditions and vehicle loads. Therefore, there is an urgent need for a modeling method based on measured data, capable of comprehensively utilizing local state change information of track irregularities and related engineering factors, establishing a state-related stochastic evolution model, and achieving unified identification of the stochastic dynamic characteristics of track irregularities. This would improve the model's accuracy, adaptability, and engineering application value. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, medium, and device for modeling orbital irregularities and stochastic evolution.

[0006] According to a first aspect of the present invention, a method for modeling the stochastic evolution of irregularities in magnetic levitation tracks is provided. The method includes the following steps:

[0007] Data characterizing the geometric state of the track are acquired and preprocessed to obtain a random sample sequence of maglev track irregularities distributed along the line mileage direction. At the same time, track structure parameters and vehicle load statistical characteristics corresponding to the line are acquired. The track structure parameters include track stiffness, and the vehicle load statistical characteristics include vehicle axle load statistical characteristics, vehicle passing frequency, and vehicle load variance.

[0008] For the sample sequence, multiple state intervals are obtained by dividing the intervals based on track irregularity, track structure parameters and vehicle load statistical characteristics.

[0009] Within each of the aforementioned state intervals, calculate the conditional statistics of the track irregularity state increment;

[0010] Based on the conditional statistics, the functional relationship between the drift term and the diffusion term in the stochastic differential equation is identified.

[0011] Based on the functional relationship between the drift term and the diffusion term, a stochastic differential equation model is established to describe the state-related stochastic evolution characteristics of track irregularities along the track direction.

[0012] According to a second aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method for modeling the random evolution of magnetic levitation track irregularities.

[0013] According to a third aspect of the present invention, a computer device is provided, including a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method for modeling the random evolution of magnetic levitation track irregularities.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] (1) Based on the statistical information of state increment conditions between adjacent sampling points in the state interval, the present invention identifies the state-dependent functions of the drift term and diffusion term in the stochastic differential equation, so that the drift term and diffusion term are expressed as functions of track irregularity, track structure parameters and vehicle load statistical characteristics, thereby describing the non-stationary and nonlinear stochastic evolution law of track irregularity under track structure conditions and vehicle load with state change, and improving the expressive power and refinement of the model.

[0016] (2) The present invention is based on the statistical information of local state increment between adjacent sampling points. It does not rely on power spectral density, correlation function or stationarity assumptions, which reduces the dependence on long samples and global statistical stability. It is also applicable to short samples, local sections or track data with obvious changes in statistical characteristics along the line, thus improving adaptability and practicality.

[0017] (3) This invention divides samples according to state intervals and ensures that each interval has a sufficient number of samples, making the conditional statistical results more stable; at the same time, it combines statistical inversion methods, machine learning methods or a combination of both, and introduces statistical consistency constraints, probability evolution constraints, stability constraints and physical rationality constraints in the function identification process, so that the established model can simultaneously meet the requirements of data characteristics, stochastic process theory and engineering physics, thereby improving the reliability and interpretability of the model.

[0018] (4) By introducing track structure parameters and vehicle load statistical characteristics in the random evolution modeling process, this invention can reflect the influence of track structure conditions and vehicle load changes on the track irregularity evolution process, thereby more realistically depicting the multi-factor coupling effect in the actual track system and improving the engineering applicability of the model.

[0019] (5) Based on the established state-dependent stochastic differential equation model, this invention can generate random samples of track irregularities with state-dependent fluctuation characteristics, thereby more realistically reflecting the spatial evolution characteristics of track irregularities along the track direction, and is suitable for vehicle-track dynamics simulation and system safety analysis.

[0020] (6) The present invention can analyze the random sample distribution of track irregularities given the current track condition and related engineering conditions, and can assess the probability level of track condition exceeding the limit, providing a quantitative basis for track condition assessment and maintenance decision analysis.

[0021] (7) By analyzing the functional forms of the drift and diffusion terms obtained by the present invention, the evolution characteristics of orbit irregularities with state changes can be identified, providing technical support for the analysis of orbit degradation mechanism and the study of state evolution law.

[0022] Other features and advantages of the invention will become clear from the following detailed description of exemplary embodiments of the invention with reference to the accompanying drawings. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments of the invention and, together with their description, serve to explain the principles of the invention.

[0024] Figure 1This is a flowchart of a method for modeling the stochastic evolution of magnetic levitation track irregularities according to an embodiment of the present invention;

[0025] Figure 2 This is a schematic diagram of a method for modeling the stochastic evolution of magnetic levitation track irregularities according to an embodiment of the present invention;

[0026] Figure 3 This is a schematic diagram illustrating the calculation of the state increment of adjacent sampling points according to an embodiment of the present invention;

[0027] Figure 4 This is a schematic diagram of state interval division and state increment condition statistics according to an embodiment of the present invention. Detailed Implementation

[0028] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0029] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0030] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0031] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0032] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0033] Combination Figure 1 and Figure 2 As shown, the provided method for modeling the stochastic evolution of maglev track irregularities includes the following steps.

[0034] Step S1: Obtain data characterizing the track geometry and preprocess it to obtain a random sample sequence of track irregularities distributed along the track mileage direction, and obtain the track structure parameters and vehicle load statistical characteristics of the corresponding line.

[0035] Measured data on track irregularities (or simply track irregularities) are acquired along the mileage direction of the maglev track. This data includes, but is not limited to, track elevation irregularities, directional irregularities, gauge irregularities, or other quantities characterizing the track's geometric state. Simultaneously, track structure parameters and vehicle load statistical characteristics for the corresponding line are acquired. The track structure parameters include track stiffness, and the vehicle load statistical characteristics include vehicle axle load statistics, vehicle passing frequency, and vehicle load variance. To ensure the effectiveness of subsequent stochastic modeling, the raw measured data is preprocessed. This preprocessing includes, for example, one or more of the following: removing trend terms or long-term drift components from the measurement data; filtering the measured data to eliminate measurement noise or irrelevant frequency components; identifying and removing outliers; and interpolating the data to obtain an evenly spaced spatial sampling sequence.

[0036] After data preprocessing, a random sample sequence of track irregularities distributed along the track mileage direction is obtained. Simultaneously, the orbital structure parameters at the corresponding sampling positions are obtained. and vehicle load statistical characteristics .in For the first The route mileage location of each sampling point For the first The value of track unevenness at each sampling location. The total number of sampling points is and the distance between adjacent sampling points is . .

[0037] Step S2: For the obtained sample sequence, divide it into intervals based on the state variables to obtain multiple state intervals.

[0038] Combination Figure 3 As shown, the state increment between adjacent sampling points is calculated using formula (1). , obtain sample pairs ,in Indicates the first Track irregularity values ​​at each sampling point.

[0039] (1);

[0040] This leads to the formation of a sample set:

[0041] (2);

[0042] in, Indicates the first Track structure parameters at each sampling point Indicates the first Statistical characteristics of vehicle load at each sampling point This represents the track irregularity value at the (i+1)th sampling point. Indicates the first The route mileage location of each sampling point;

[0043] Since the measured track irregularity state is a continuous variable, the number of samples corresponding to a single state point is limited or non-existent. Therefore, by dividing the state variable into intervals, the conditional statistical characteristics of the track irregularity state increment are estimated using neighborhood samples within each interval, so as to improve the stability and reliability of the statistical results.

[0044] Specifically, based on the track irregularity value Track structure parameters and vehicle load statistical characteristics The range of values ​​is used to divide the sample data into... Let there be n state intervals, and let the set of state variables be . The dimensions for dividing the state intervals can be selected or combined based on data characteristics, engineering requirements, or sample size to ensure that each interval has a sufficient number of samples and can reflect the main influencing factors of orbital irregularities.

[0045] For example, different interval partitioning dimensions can be used in the following situations:

[0046] (1) Based solely on track irregularities Perform interval division

[0047] When the track structure conditions and vehicle loads vary little within the study section, or when only the influence of the track irregularity itself on its evolution is considered, the study can be based solely on the amount of track irregularity. The value range is divided into intervals. In this case, the track structure parameters... Vehicle load statistical characteristics It can be retained in the sample data as supplementary information for subsequent analysis or model expansion.

[0048] (2) Based on track irregularity With track structure parameters Or vehicle load statistical characteristics Perform joint interval partitioning

[0049] When there are significant differences in track structure conditions between different sections of the line, such as differences in track stiffness, track structure type, or support conditions, and these differences may affect the evolution characteristics of track irregularities, the amount of track irregularity can be used as a reference. With track structure parameters Joint interval divisions are performed to reflect the irregular evolution patterns under different structural conditions.

[0050] When there are significant differences in vehicle load levels across different sections or time periods—for example, differences in axle load distribution, vehicle frequency, or load variance—and these factors may influence the evolution of track irregularities, the amount of track irregularity can be used as a reference. Vehicle load statistical characteristics Joint interval divisions are performed to reflect the irregular evolution characteristics under vehicle load.

[0051] (3) Based on track irregularity Track structure parameters and vehicle load statistical characteristics Perform joint interval partitioning

[0052] When both track structure conditions and vehicle load conditions have a significant impact on the evolution of track irregularities, and the sample size is sufficient to support multidimensional statistics, it is possible to determine the appropriate approach based on... , and Joint interval division is performed to characterize the stochastic evolution law under the coupling effect of multiple factors.

[0053] In practical applications, the interval dimensions can be adjusted appropriately based on the sample size. For example, when the sample size is limited, a low-dimensional interval partitioning method can be used first to ensure statistical stability; when the sample size is large, a high-dimensional joint interval partitioning method can be used to improve the model's ability to characterize the influence of multiple factors.

[0054] State interval partitioning methods include, for example, equal-width interval partitioning, equal-sample interval partitioning, and adaptive partitioning based on data distribution. State interval partitioning ensures that the number of samples within each interval is not less than a preset threshold to guarantee statistical stability.

[0055] In this embodiment, the conditional statistical moments are for state intervals. The results are obtained from a sample within a given range, therefore the statistical results essentially correspond to an interval. The statistical characteristics. When performing function identification, a representative state value can be selected for each state interval. This serves as an approximate state point for that interval.

[0056] The representative state value can be selected, for example, the interval center value, the sample mean within the interval, or other representative quantities that can reflect the statistical characteristics of the interval.

[0057] When using a set of state variables When performing interval partitioning, the first The representative state value of each interval can be represented as:

[0058] (3);

[0059] in: For interval Representative value of inner track irregularity; For interval Representative values ​​of the internal track structure parameters; This represents the statistical characteristics of vehicle load within the interval.

[0060] When only some state variables are used for interval division, the variables that are not involved in the interval division can take the average value of the samples within the interval or other statistical representative values.

[0061] Step S3: Calculate the conditional statistics of the state increment within each state interval.

[0062] Combination Figure 4 As shown, Figure 4 This shows the results based solely on track irregularities. A schematic diagram illustrating the statistical conditions of state intervals and state increments during interval partitioning, wherein... This represents the minimum value within the range of track irregularities. This represents the minimum value within the range of track irregularities. Within each state interval, calculate the first-order conditional statistical moments of the state increment. and second-order conditional statistical moments :

[0063] (4);

[0064] (5);

[0065] in, , Representing the state intervals respectively The first-order conditional statistical moments and the second-order conditional statistical moments within the context, Represents the mathematical expectation operator. For interval Internal sample size It is a general representation of state increment.

[0066] Step S4: Based on conditional statistics, identify the functional relationship between the drift term and the diffusion term in the stochastic differential equation.

[0067] The functional relationship between drift and diffusion terms can be identified in various ways, such as statistical inversion, machine learning models, or a combination of both. When using statistical inversion, the state-dependent functional relationship between drift and diffusion terms can be directly determined based on the relationship between the first and second-order conditional statistical moments of the state increment and the sampling interval. Alternatively, when using a parameterized model, the function parameters can be estimated through conditional statistical moments. When using machine learning, a function identification model can be constructed to identify the state-dependent functional relationship between drift and diffusion terms, and physical constraints can be introduced during model training or solution to determine the functional relationship. When statistical inversion is combined with machine learning, statistical information can be used to initialize, regularize, and / or constrain the training process of the function identification model.

[0068] In one embodiment, the drift term and diffusion term functions in the stochastic differential equation are identified using a statistical inversion method, specifically including:

[0069] S41. Obtain the drift term estimate at discrete state points. With diffusion term estimate , respectively represented as:

[0070] (6);

[0071] (7);

[0072] in, This indicates the distance between adjacent sampling points in terms of line mileage.

[0073] S42. Select a parameterized function model, such as a linear function, polynomial function, piecewise function, exponential or power function, etc.

[0074] S43. Solve for the function parameters. For example, construct the objective function and solve for the function parameters using the least squares method or weighted least squares method.

[0075] The drift term function is constructed using the statistical inversion method described above. With diffusion term function This method is used to establish stochastic differential equation models for track irregularities. It can directly determine stochastic differential equation models from measured track irregularity data without introducing additional empirical assumptions.

[0076] In another embodiment, instead of pre-setting the functional form, a machine learning method (or machine learning model) is used to learn the functional relationship between the drift term and the diffusion term.

[0077] During model training, physical constraints are set to ensure that the identified drift and diffusion terms satisfy the statistical consistency, probabilistic evolution characteristics, and engineering physical rationality of the stochastic differential equations. Furthermore, during function identification, an objective function or loss function is constructed to constrain the function identification model. For example, physical constraints include, but are not limited to, one or a combination of the following:

[0078] 1) Statistical consistency constraint: Based on the statistical relationship of state increments of stochastic differential equations, the identified drift terms and diffusion terms satisfy the first-order and second-order conditional statistical properties between adjacent sampling points;

[0079] 2) Discrete evolution constraints: State transition relationships are established based on discrete stochastic differential equations, so that the identified drift and diffusion terms can describe the stochastic evolution process between adjacent sampling points;

[0080] 3) Probabilistic evolution constraints: Consistency constraints are established based on the probability density evolution relationship corresponding to the stochastic differential equation or the conditional probability distribution of adjacent sampling points. The state dependency function relationship of the drift term and diffusion term is determined through maximum likelihood estimation or equivalent optimization.

[0081] 4) Stability constraints: Based on the stability conditions of stochastic processes, the identified stochastic differential equations are established to satisfy the mean stability, variance boundedness, or convergence properties.

[0082] 5) Physical rationality constraints: including nonnegativity constraints on diffusion terms and / or continuity, smoothness, or boundedness constraints between drift and diffusion terms.

[0083] In addition, statistical inversion methods can be combined with machine learning methods to obtain the state dependency function relationship of drift and diffusion terms, thereby improving the stability and accuracy of parameter identification for stochastic differential equations.

[0084] For example, the preliminary results of drift and diffusion terms obtained from statistical inversion can be used to initialize the machine learning model; the machine learning model can be used to supplement the modeling of nonlinear features that are difficult to characterize by statistical inversion; and statistical relations obtained from statistical inversion can be introduced as regularization or constraints during the training process of the machine learning model.

[0085] Step S5: Based on the functional relationship between the drift term and the diffusion term, establish a stochastic differential equation model for track irregularities to describe the state-related stochastic evolution characteristics of track irregularities along the track direction.

[0086] Based on the functional relationship between the identified drift and diffusion terms, a stochastic differential equation for orbital irregularity is established as the orbital irregularity model (or orbital irregularity stochastic differential equation model), expressed as:

[0087] (8);

[0088] in, Indicates the location of the line mileage. The track is uneven at this point. Indicates the track structure parameters, This indicates the statistical characteristics of vehicle load. Represents spatial variables along the route. It is the drift term function obtained through identification, used to describe the average evolution trend of track irregularities along the track direction under the combined effects of track irregularity conditions, track structure parameters, and vehicle load conditions. It is the diffusion term function obtained through identification, used to describe the intensity of random fluctuations in track irregularities under the combined effects of track irregularity conditions, track structure parameters, and vehicle load conditions. This is a standard Wiener procedure.

[0089] In some implementations, when track structure parameters are not introduced... Vehicle load statistical characteristics When this happens, the above stochastic differential equation can be degenerated into a model based solely on orbital irregularities:

[0090] (9);

[0091] in, This is a drift term function based solely on orbital irregularities, used to describe the average evolution trend of orbital irregularities. This is a diffusion term function based solely on orbital irregularities, used to describe the intensity of random fluctuations caused by orbital irregularities. This is a standard Wiener process. The model describes the state-dependent stochastic evolution characteristics of track irregularities along the track direction and can be used for track condition assessment and prediction, vehicle-track dynamics analysis, or track maintenance decisions.

[0092] It should be noted that, to ensure the accuracy of the track irregularity model, the functional relationship between the drift and diffusion terms can be adjusted as needed in practical applications. For example, random samples of track irregularities can be generated based on the identified stochastic differential equations, and the statistical characteristics of the generated samples can be calculated. These statistical characteristics can then be compared with the statistical characteristics of the measured data, and the functional relationship between the drift and diffusion terms can be adjusted or iteratively updated based on the comparison results.

[0093] To further verify the effectiveness of the invention, experiments were conducted. Based on the established stochastic differential equations, random samples of track irregularities were generated using numerical methods. The statistical characteristics of the generated samples were calculated, such as mean and variance, conditional statistical moments, and probability distribution characteristics. These statistical results were compared with measured data, and the functional relationships between the drift and diffusion terms were adjusted or iteratively optimized based on the comparison results. When the statistical characteristics met the preset error requirements, the final model was determined. The verification results show that the invention provides an implementation path for constructing stochastic differential equation models based on measured track irregularity data. This path does not rely on empirical settings and can flexibly employ statistical inversion methods, machine learning methods, or a combination of both to identify model parameters, exhibiting good versatility and engineering adaptability.

[0094] In summary, existing stochastic modeling methods for track irregularities mainly rely on global statistical properties such as power spectral density or correlation functions. They typically assume track irregularities to be stationary stochastic processes, failing to adequately utilize local state change information between adjacent sampling points. This makes it difficult to characterize the state-related stochastic evolution of track irregularities under the influence of track structure parameters and vehicle loads. To overcome these shortcomings, this invention designs a novel stochastic evolution modeling method for track irregularities. By statistically analyzing the state increment conditions between adjacent sampling points, and identifying the state dependency relationships of drift and diffusion terms in the stochastic differential equations, a mathematical model is established that describes the state-related stochastic evolution characteristics of track irregularities along the track direction. This model not only reflects the overall statistical characteristics of track irregularities but also characterizes the local evolution features under different state conditions. This invention does not rely on power spectral density or global stationarity assumptions and improves model stability, reliability, and engineering applicability through statistical consistency, probabilistic evolution, and physical constraints.

[0095] This invention can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of the invention.

[0096] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0097] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0098] The computer program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent 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++, Python, etc., and conventional procedural programming languages ​​such as "C" or similar languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions. This electronic circuitry can execute the computer-readable program instructions to implement various aspects of the invention.

[0099] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0100] 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, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions 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 that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0101] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause 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, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0102] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions. It will be known to those skilled in the art that implementation in hardware, implementation in software, and implementation using a combination of software and hardware are equivalent.

[0103] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, and are not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein. The scope of the invention is defined by the appended claims.

Claims

1. A method for modeling the stochastic evolution of maglev track irregularities, characterized in that, Includes the following steps: Data characterizing the geometric state of the track are acquired and preprocessed to obtain a random sample sequence of track irregularities distributed along the track mileage direction. The corresponding maglev track structural parameters and vehicle load statistical characteristics are also obtained. The track structural parameters include track stiffness, and the vehicle load statistical characteristics include vehicle axle load statistical characteristics, vehicle passing frequency, and vehicle load variance. For the sample sequence, multiple state intervals are obtained by dividing it into intervals based on the track irregularity, the track structural parameters, and the vehicle load statistical characteristics. Within each of the aforementioned state intervals, calculate the conditional statistics of the track irregularity state increment; Based on the conditional statistics, the functional relationship between the drift term and the diffusion term in the stochastic differential equation is identified. Based on the functional relationship between the drift term and the diffusion term, a stochastic differential equation model is established to describe the state-related stochastic evolution characteristics of track irregularities along the track direction. The stochastic differential equation model is expressed as follows: in, Indicates the location of the line mileage. The track is uneven at this point. Indicates the track structure parameters, This indicates the statistical characteristics of vehicle load. Represents spatial variables along the route. It is the drift term function obtained through identification, used to describe the average evolution trend of track irregularities along the track direction under the combined effects of track irregularity conditions, track structure parameters, and vehicle load conditions. It is the diffusion term function obtained through identification, used to describe the intensity of random fluctuations in track irregularities under the combined effects of track irregularity conditions, track structure parameters, and vehicle load conditions. This is a standard Wiener procedure.

2. The method according to claim 1, characterized in that, The state interval is obtained according to the following steps: The increment of track irregularity between adjacent sampling points is calculated using the following formula. , obtain sample pairs : Forming a sample set: in, Indicates the first Track unevenness at each sampling point Indicates the first Track structure parameters at each sampling point Indicates the first Statistical characteristics of vehicle load at each sampling point This represents the track irregularity at the (i+1)th sampling point. Indicates the first The route mileage location of each sampling point; According to track irregularity Track structure parameters and vehicle load statistical characteristics The range of values ​​is used to divide the sample data into... Let there be n state intervals, and let the set of state variables be . The dimensions for dividing the state intervals include at least one of the following: based solely on track irregularity. Divide the track into intervals; based on track irregularities. With track structure parameters Or vehicle load statistical characteristics Perform joint interval division; based on track irregularity. Track structure parameters and vehicle load statistical characteristics Perform joint interval partitioning; Among them, the number of samples in each state interval is not less than a preset threshold, the first k Each state interval is represented as , The number of interval divisions, the first The representative state values ​​for each state interval are represented as follows: in, State interval Representative value of inner track irregularity; State interval Representative values ​​of the internal track structure parameters; State interval Representative values ​​of the statistical characteristics of vehicle loads within the vehicle system.

3. The method according to claim 2, characterized in that, The state intervals are divided using equal-width intervals, equal-sample intervals, or adaptive intervals based on data distribution.

4. The method according to claim 2, characterized in that, The conditional statistics include the first-order and second-order conditional statistical moments of the orbital irregularity state increment, respectively expressed as: in, , Representing the state intervals respectively The first-order conditional statistical moments and the second-order conditional statistical moments within the context, Represents the mathematical expectation operator. State interval Number of internal samples.

5. The method according to claim 4, characterized in that, The functional relationship between the drift term and the diffusion term is obtained through statistical inversion, machine learning model, or a combination of statistical inversion and machine learning model.

6. The method according to claim 5, characterized in that, When the functional relationship between the drift term and the diffusion term is obtained through statistical inversion, it includes: Calculate the drift term estimate at discrete state points With diffusion term estimate , respectively represented as: in, Indicates the distance between adjacent sampling points in terms of line mileage; For the drift term estimate With diffusion term estimate Select a parameterized function model; For the parameterized function model, an objective function is constructed, and the parameterized function model is solved through statistical inversion to obtain the drift term function. With diffusion term function Furthermore, the stochastic differential equation model is established.

7. The method according to claim 5, characterized in that, When the functional relationship between the drift term and the diffusion term is obtained by training a machine learning model under set physical constraints, the physical constraints are used to ensure that the identified drift term and diffusion term satisfy the statistical consistency, probabilistic evolution characteristics and engineering physical rationality of the stochastic differential equation model.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

9. A computer device comprising a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

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