High-efficiency computing method, system and device for vehicle-track coupled dynamics based on physical-data hybrid driving and medium

Abstract

This invention discloses a method, system, device, and medium for efficient calculation of vehicle-track coupled dynamics based on a physics-data hybrid-driven approach. The method includes: uniformly generating a representative set of sample points for operating conditions to obtain rail spatiotemporal displacement field response data; extracting the optimal low-dimensional basis function matrix from the rail spatiotemporal displacement field response data using an intrinsic orthogonal decomposition method; constructing a physics-data hybrid-driven model framework with Fourier neural operators as its core, where the physics-driven module directly predicts and outputs the train spatiotemporal dynamic response, and the data-driven module predicts and outputs the rail time coefficient matrix, which is then combined with the optimal low-dimensional basis function matrix to reconstruct the rail spatiotemporal displacement field; incorporating data constraints, physical constraints, and derivative constraints into the loss function; training the physics-data hybrid-driven model; and using the physics-data hybrid-driven model to perform vehicle-track coupled dynamics calculations. This invention enables accurate and efficient solutions for large-scale vehicle-track coupled dynamic responses.

Description

Technical Field

[0001] This invention relates to the field of rail transit engineering, and in particular to a method, system, device and medium for efficient calculation of vehicle-track coupling dynamics based on physical-data hybrid driving. Background Technology

[0002] With the continuous expansion of high-speed railway networks and the steady increase in operating speed, the dynamic coupling of train-track systems has become increasingly complex, posing a core technological bottleneck affecting the service safety, operational performance, and structural durability of high-speed railways. During train operation, factors such as track irregularities, fluctuations in vehicle structural parameters, and speed variations collectively trigger complex dynamic responses in both the track and the vehicle body. These responses not only directly threaten operational stability and safety, leading to abnormal wheel-rail wear, fatigue damage to vehicle components, and roadbed settlement, but also affect passenger comfort, generating additional vibrations and noise. Simultaneously, they increase the maintenance costs of the track system and shorten the service life of key track and vehicle components. However, current vehicle-track coupling dynamic analysis primarily relies on dynamic simulation. Existing methods are inefficient when dealing with multiple random factors and various operating conditions, making large-scale simulation calculations difficult and failing to meet the needs of efficient evaluation and batch analysis in engineering projects.

[0003] In recent years, thanks to the significant improvement in computer hardware performance, deep learning methods have entered a stage of rapid development. To improve the computational efficiency of structural dynamic response analysis, deep learning methods, with their powerful modeling capabilities and efficient data processing advantages, have been highly favored by scholars. These methods are mainly divided into two categories: purely data-driven methods and data-physics-driven methods. Purely data-driven methods are essentially black-box models, heavily reliant on large datasets, and their generalization ability is easily limited, sometimes even producing results that contradict physical laws. The core of data-physics-driven methods lies in embedding physical information into the loss function, using this constraint to optimize the neural network training process, thus constructing models that combine physical consistency and strong generalization ability. However, these classic neural networks essentially learn a mapping from finite-dimensional inputs to finite-dimensional outputs, which is easily limited by the choice of discretization method, restricting the efficiency and globality of train-track coupled dynamic prediction. Summary of the Invention

[0004] To address the problems of inefficiency of traditional numerical methods under multiple operating conditions and the difficulty of classical neural networks in characterizing the global coupling of a system, this invention provides a method, system, device, and medium for efficient calculation of vehicle-track coupling dynamics based on a physics-data hybrid driving approach, which can achieve accurate and efficient solutions for large-scale vehicle-track coupling dynamic responses.

[0005] Firstly, a highly efficient calculation method for vehicle-track coupled dynamics based on a physics-data hybrid approach is provided, comprising the following steps: S1: A representative working condition sample point set of the train-track spatial coupling system is uniformly generated using the Latin hypercube sampling strategy. The rail deterministic analysis is performed using the representative working condition sample point set to obtain the rail spatiotemporal displacement field response data. S2: Extract the optimal low-dimensional basis function matrix from the spatiotemporal displacement field response data of rails using the intrinsic orthogonal decomposition method; S3: Construct a physics-data hybrid driven model framework with Fourier neural operators as the core backbone. The combined data of train speed, train physical parameters and track irregularity excitation are simultaneously input into the following two modules: the physics-driven module directly predicts and outputs the train spatiotemporal dynamic response; the data-driven module predicts and outputs the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method, and reconstructs the rail spatiotemporal displacement field by combining the optimal low-dimensional basis function matrix. S4: Construct a loss function for the physics-driven module, incorporating corresponding data constraints, physical constraints, and derivative constraints into the loss function; for the data-driven module, incorporate the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method into the data constraints of the loss function; then train the physics-data hybrid driven model based on the constructed sample dataset. S5: Perform vehicle-track coupled dynamics calculations using a trained physics-data hybrid driving model.

[0006] Further, step S1 includes: A dynamic model of the train-track spatial coupling system is constructed to generate samples of the train-track coupled dynamic response. A Latin hypercube sampling strategy was used to obtain a representative set of sample points for the train-track spatial coupling system under various operating conditions. Deterministic analysis of rails is performed using a representative set of working condition sample points to obtain rail spatiotemporal displacement field response data, which is a matrix arranged by node × time.

[0007] Furthermore, in step S2, the order of the intrinsic orthogonal decomposition basis functions is determined by truncating the first 99.9% of the total energy percentage, thus obtaining the optimal low-dimensional basis function matrix.

[0008] Furthermore, in step S3, both the physics-driven module and the data-driven module include an input fully connected layer, a Fourier neural operator, and an output fully connected layer connected in sequence. The input fully connected layer elevates the model input to a high-dimensional space, and after iterative updates by the Fourier convolutional layer in the Fourier neural operator, it is output to the target dimension through the output fully connected layer.

[0009] Furthermore, in step S3, the rail time coefficient matrix output by the data-driven module is multiplied by the optimal low-dimensional basis function matrix to obtain an approximate fluctuating displacement field, as shown below: ; in, This represents the approximate fluctuating displacement field after dimensionality reduction; row vectors It is the orthogonal feature pattern extracted by singular value decomposition of the pulsation snapshot matrix, corresponding to the i-th row vector of the optimal low-dimensional basis function matrix; column vector It is the orthogonal time mode extracted by singular value decomposition, corresponding to the i-th column vector of the rail time coefficient matrix; k is the order of the basis functions in the optimal low-dimensional basis function matrix; Mean snapshot matrix obtained by combining the intrinsic orthogonal decomposition method This allows for the reconstruction of the complete spatiotemporal displacement field of the rail, which takes the following form: ; In the formula, The reconstructed spacetime displacement field of the rail.

[0010] Furthermore, in step S3, the train's physical parameters include the train's mass, moment of inertia, stiffness, and damping.

[0011] Furthermore, in step S4, the loss function is expressed as follows: ; In the formula, For the total loss, , and Data loss , For the residual loss of the train dynamics control equations, For derivative loss, and Let be the solution functions in the solution space for the train and the rail, respectively. and These are the physical drive module and the data drive module, respectively. This is the set of control equations for train dynamics. For time, For model inputs sampled from the distribution of solution functions corresponding to the train Take the expected value. To represent the model input sampled from the distribution of solution functions corresponding to the rails. Take the expected value. The total number of samples, Let be the solution domain of the problem.

[0012] Secondly, a high-efficiency calculation system for vehicle-track coupled dynamics based on a physics-data hybrid driving approach is provided, including: The rail spatiotemporal displacement field response data acquisition module is used to uniformly generate a representative working condition sample point set of the train-track spatial coupling system using a Latin hypercube sampling strategy, and to perform deterministic analysis of the rail through the representative working condition sample point set to obtain the rail spatiotemporal displacement field response data. The optimal low-dimensional basis function acquisition module is used to extract the optimal low-dimensional basis function matrix from the rail spatiotemporal displacement field response data using the intrinsic orthogonal decomposition method. The model framework construction module is used to build a physics-data hybrid driven model framework with Fourier neural operators as the core backbone. The combined data of train speed, train physical parameters and track irregularity excitation are simultaneously input into the following two modules: the physics-driven module directly predicts and outputs the train spatiotemporal dynamic response; the data-driven module predicts and outputs the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method, and reconstructs the rail spatiotemporal displacement field by combining the optimal low-dimensional basis function matrix. The damage function construction and training module is used to construct the loss function. For the physics-driven module, the corresponding data constraints, physical constraints, and derivative constraints are incorporated into the loss function. For the data-driven module, the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method is incorporated into the data constraints of the loss function. Then, the physics-data hybrid driven model is trained based on the constructed sample dataset. The dynamics calculation module is used to perform vehicle-track coupled dynamics calculations using a trained physics-data hybrid driving model.

[0013] Thirdly, an electronic device is provided, comprising: one or more processors and a memory; the memory is coupled to the one or more processors, the memory being used to store a computer program, and the one or more processors calling the computer program to cause the electronic device to execute the previously described efficient calculation method for vehicle-track coupling dynamics based on physics-data hybrid drive.

[0014] Fourthly, a computer-readable storage medium is provided, which stores a computer program that, when run on an electronic device, causes the electronic device to perform the previously described efficient calculation method for vehicle-track coupling dynamics based on a physics-data hybrid drive.

[0015] This invention proposes an efficient calculation method, system, device, and medium for vehicle-track coupling dynamics based on a physics-data hybrid driving approach, which has the following beneficial effects:

[0016] (1) This invention is the first to integrate physical information, FNO (Fourier neural operator) and POD (intrinsic orthogonal decomposition) to construct a physical-data hybrid driven model, which breaks through the limitations of the imbalance between accuracy and efficiency of pure physical modeling and the lack of physical consistency of pure data driven model, and fills the application gap of neural operators that integrate physical information in the field of global response solution.

[0017] (2) The present invention establishes an efficient solution mechanism. Comparison with probability density evolution (PDEM) shows that the prediction results of the present invention have high consistency. At the same time, it achieves a thousand-fold improvement in computational efficiency, significantly improving the shortcomings of traditional numerical methods that consume a lot of time, and providing efficient technical support for large-scale working condition simulation.

[0018] (3) Based on actual measurement data and noise test verification, the present invention has both excellent engineering generalization and noise resistance robustness, and can stably adapt to actual application scenarios, thereby improving the engineering adaptability of this type of method. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of the efficient calculation method for vehicle-track coupling dynamics based on physics-data hybrid driving provided in this embodiment of the invention; Figure 2 Modal cumulative energy percentage diagram provided in embodiments of the present invention; Figure 3 A flowchart of the physical-data hybrid driven model framework provided in this embodiment of the invention; Figure 4 The vehicle body vertical random acceleration response diagram provided in the embodiment of the present invention is shown in which (a) is the probability density function evolution surface, (b) is the contour line, (c) is the mean, and (d) is the standard deviation. Figure 5 The image shows the vertical random displacement response of the rail provided in this embodiment of the invention, where (a) is the probability density function evolution surface, (b) is the contour line, (c) is the mean, and (d) is the standard deviation. Figure 6 The following is a comparison diagram of train acceleration response time history based on measured track irregularity data provided in an embodiment of the present invention, wherein (a) is the lateral acceleration of the car body, (b) is the vertical acceleration of the car body, (c) is the lateral acceleration of the bogie, (d) is the vertical acceleration of the bogie, (e) is the lateral acceleration of the wheelset, and (f) is the vertical acceleration of the wheelset. Figure 7 The image shows a comparison of rail displacement fields based on measured track irregularity data provided in this embodiment of the invention, where (a) is the actual displacement field, (b) is the predicted displacement field, and (c) is the displacement field error. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0022] like Figure 1 As shown, this embodiment of the invention provides an efficient calculation method for vehicle-track coupling dynamics based on a physics-data hybrid driving approach, comprising the following steps: S1: A representative working condition sample point set of the train-track spatial coupling system is uniformly generated using the Latin hypercube sampling strategy. The rail deterministic analysis is then performed using the representative working condition sample point set to obtain the rail spatiotemporal displacement field response data.

[0023] Specifically, a dynamic model of the train-track spatial coupling system is first constructed. For example, in this embodiment, the spatial train model is considered a multi-rigid-body system, including a car body, two bogies, and four wheelsets. Each rigid body has five degrees of freedom: lateral, vertical, roll, yaw, and pitch. Therefore, the train subsystem contains a total of 35 degrees of freedom. The train subsystem and the track subsystem are coupled through wheel-rail spatial interaction. The wheel-rail geometry is determined using the "track method," the Hertz nonlinear contact theory is used for the wheel-rail normal, and the modified saturated nonlinear creep theory is used for the tangential direction. Therefore, based on the vehicle-track coupled dynamics theory and the finite element matrix coupling method, the dynamic equations of the train-track spatial coupling system can be obtained as follows: ; in, , and These represent the mass matrix, damping matrix, and stiffness matrix, respectively. , , and These represent displacement, velocity, acceleration, and force vectors, respectively; subscripts , , and These represent the train, rail, sleeper, and ballast, respectively; in the subscripts, vv indicates the coupling between trains, and vr indicates the coupling between the train and the rail. This represents the coupling stiffness matrix between the train and the rails; the others follow the same principle and will not be explained in detail here.

[0024] In MATLAB software, an explicit-implicit hybrid integration method is used to jointly solve the system dynamic equations to obtain vehicle-track coupled dynamic response samples. A Latin hypercube sampling strategy is employed to obtain a representative set of 500 working conditions of the train-track spatial coupling system from the vehicle-track coupled dynamic response samples. Deterministic analysis of the rail is then performed using this representative working condition sample set to obtain the rail spatiotemporal displacement field response data, which is a matrix arranged by node × time (the time responses corresponding to the 500 working conditions are arranged sequentially).

[0025] S2: Extract the optimal low-dimensional basis function matrix from the spatiotemporal displacement field response data of rails using the intrinsic orthogonal decomposition (POD) method.

[0026] In this embodiment, the order of the intrinsic orthogonal decomposition basis functions is determined by extracting the first 99.9% of the total energy, thus obtaining the optimal low-dimensional basis function matrix. The corresponding modal cumulative energy percentage in this embodiment is as follows: Figure 2 As shown, from Figure 2 It can be observed that the first 93 fundamental modes contain 99.9% of the energy, and the root mean square error between the rail displacement field reconstructed by POD and the actual rail displacement field is 0.0057. This indicates that POD can effectively reduce the data dimensionality, and by extracting the features of 93 modes, it can capture the information of the original dataset quite well. In other embodiments, if further dimensionality reduction is needed, it can be achieved by reducing the proportion of total energy (such as the first 99.5%, 99.7%, etc.). The rail displacement field sample data can be decomposed using the optimal low-dimensional basis function matrix, thereby obtaining the fundamental mode time coefficient samples required by this invention.

[0027] When calculating the percentage of total energy, the former Percentage of total energy of POD basis functions It can be represented as: ; in, The elements of the main diagonal of the singular value matrix satisfy the following conditions: Due to singular values It exhibits rapid decay characteristics, and efficient order reduction and reconstruction of the displacement field can be achieved by truncating higher-order, low-energy modes. This represents the total number of singular values ​​in the POD decomposition.

[0028] S3: Construct a physical-data hybrid driven model framework with Fourier neural operators as the core backbone, such as... Figure 3As shown, the combined data of train speed, train physical parameters, and track irregularity excitation are simultaneously input into the following two modules: the physics-driven module directly predicts and outputs the train's spatiotemporal dynamic response; the data-driven module predicts and outputs the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method, and reconstructs the rail spatiotemporal displacement field by combining it with the optimal low-dimensional basis function matrix.

[0029] In this embodiment, both the physics-driven module and the data-driven module include an input fully connected layer, a Fourier neural operator, and an output fully connected layer connected in sequence. The input fully connected layer elevates the model input to a high-dimensional space. After iterative feature updates via the Fourier convolutional layer in the Fourier neural operator, the output is then sent to the target dimension via the output fully connected layer. ; in, For the first Layer feature representation, For feature representation dimension, It is a local linear transformation matrix. It is a non-linear activation function. and These are the Fourier transform and its inverse transform, respectively. The Fourier transform of the kernel function These represent the coordinates in physical space and the solution domain, respectively.

[0030] The physics-driven module directly predicts the train's spatiotemporal dynamic response solution function in the form of displacement. If the train's speed and acceleration responses are required, they must be obtained through finite difference methods. The data-driven module reconstructs the rail's spatiotemporal displacement field as follows: The rail time coefficient matrix output by the data-driven module is multiplied by the optimal low-dimensional basis function matrix to obtain an approximate fluctuating displacement field, as shown below: ;

[0031] in, This represents the approximate fluctuating displacement field after dimensionality reduction; row vectors It is the orthogonal feature pattern extracted by singular value decomposition of the pulsation snapshot matrix, corresponding to the i-th row vector of the optimal low-dimensional basis function matrix; column vector It is the orthogonal time mode extracted by singular value decomposition, corresponding to the i-th column vector of the rail time coefficient matrix; k is the order of the basis functions in the optimal low-dimensional basis function matrix; Mean snapshot matrix obtained by combining the intrinsic orthogonal decomposition method (By averaging all snapshots row by row to obtain the mean snapshot matrix), the complete spatiotemporal displacement field of the rail can be reconstructed, which takes the form of: ; In the formula, The reconstructed spacetime displacement field of the rail.

[0032] S4: Construct a loss function for the physics-driven module, incorporating corresponding data constraints, physical constraints, and derivative constraints into the loss function; for the data-driven module, incorporate the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method into the data constraints of the loss function; then train the physics-data hybrid driven model based on the constructed sample dataset.

[0033] For the physics-driven module of the train subsystem, the train dynamics control equation constraints, data constraints, and derivative constraints are simultaneously incorporated into the loss function to ensure that the prediction results satisfy physical laws. For the data-driven module of the rail subsystem, the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method is incorporated into the data constraints of the loss function to achieve model training under a physics-data hybrid driving approach.

[0034] The loss function is expressed as follows: ; In the formula, For the total loss, , and Data loss , For the residual loss of the train dynamics control equations, For derivative loss, and Let be the solution functions in the solution space for the train and the rail, respectively. and These are the physical drive module and the data drive module, respectively. This is the set of control equations for train dynamics. For time, For model inputs sampled from the distribution of solution functions corresponding to the train Take the expected value. To represent the model input sampled from the distribution of solution functions corresponding to the rails. Take the expected value. The total number of samples, This represents the solution domain of the problem. In this embodiment... .

[0035] The sample dataset can be constructed based on the aforementioned train-track spatial coupling system dynamics model. A large amount of combined data on train speed, train physical parameters, and track irregularity excitations is generated as input samples for the model. Train physical parameters include the train's mass, moment of inertia, stiffness, and damping. When constructing the samples, the parameters of the CRH380A train are used as a benchmark, and 80%–120% of these benchmark parameters are selected as input parameters. Both track elevation and directional irregularities are comprehensively considered, and a German "low-interference" sample spectrum is generated based on a frequency domain power spectrum equivalence algorithm. It should be noted that since the train-track spatial coupling system dynamics model outputs the train's spatiotemporal dynamic response and the rail's spatiotemporal displacement field, but the data-driven module outputs the rail time coefficient matrix, it is necessary to first deduce the rail time coefficient matrix given the known rail spatiotemporal displacement field and the optimal low-dimensional basis function matrix. This allows for the construction of labels including both the train's spatiotemporal dynamic response and the rail time coefficient matrix. In this embodiment, 10,000 and 2,000 sets of data are randomly selected as training and testing sets, respectively, and normalization technology is introduced to reduce the differences in the dimensions and values ​​of different degrees of freedom, so as to improve the training efficiency and performance of the model.

[0036] To improve the performance of the physics-data hybrid driven model and optimize the network architecture design, a Bayesian optimization strategy was introduced to automatically adjust key hyperparameters. A tree-structured Parzen estimator was used to search and optimize the hyperparameter space. Fifty rounds of sampling and evaluation were conducted, and the optimal hyperparameter combination was determined within the search space for final model training. Table 1 shows the search range and optimal configuration results of the key hyperparameters. Other model parameters were configured as follows: batch size was set to 32; the optimizer was Adam, with an initial learning rate of 0.001 and a learning rate decay strategy set to decay by a factor of 0.75 every 50 iterations; to achieve a balance between preserving effective frequency information and ensuring computational efficiency, the maximum truncation mode of the Fourier convolutional layer was set to 300; the activation function was the exponential linear unit (ELU). The model trained in this embodiment and subsequent MATLAB numerical simulations were built on a computer equipped with a 13th generation Intel Core i5-13600KF CPU, 16.0 GB of memory, and an NVIDIA GeForce RTX 4060 GPU (with 8.0 GB of dedicated GPU memory).

[0037] Table 1 Optimization results of key hyperparameters of the model

[0038]

[0039] To quantitatively compare and analyze the prediction accuracy of different benchmark methods, a relative L2 loss is introduced ( ) and coefficient of determination ( Two indicators are used to comprehensively evaluate the prediction results. The formula for the evaluation indicators can be written in the following form: ; ; in, The total number of test samples, For the first Each model predicts a value. For the first A baseline true value, This is the average value. When The smaller the value or The larger the value, the higher the prediction accuracy of the model. When the model's prediction accuracy is high, It tends to 1.

[0040] S5: Perform vehicle-track coupled dynamics calculations using a trained physics-data hybrid driving model.

[0041] After model training is complete, the trained physics-data hybrid driven model can be directly used for vehicle-track coupled dynamics calculations. The combined data of train speed, physical parameters, and track irregularity excitations are normalized and used as model input, which is then fed into the physics-data hybrid driven model. The physics-data hybrid driven model's physics-driven module for the train subsystem directly outputs the train's spatiotemporal dynamic response, while the data-driven module for the rail subsystem outputs the corresponding rail time coefficient matrix. time coefficient With the optimal low-dimensional basis function matrix By multiplying these components, the complete spatiotemporal displacement field response of the rail can be reconstructed, enabling efficient prediction of the response of the vehicle-rail coupled system.

[0042] Next, this invention incorporates train parameters and track irregularities into random factors for dynamic response analysis, selecting 4... The spatial frequency and phase angle parameters are used to generate a series of random orbital irregularities. The lower and upper limits of the spatial frequency parameter are set to 0.05. and 3 and take The train employs 22 random parameters, totaling 422-dimensional random variables. Simultaneously, 1000 representative points are generated using the GF-biased point selection method as random samples for probability density evolution (PDEM). It should be noted that among the train random parameters, the coefficients of variation for the mass of the car body, bogie, and wheelsets are 1%, while the coefficients of variation for stiffness and damping are both 10%. Since the trained physical-data hybrid driven model (FNO-PD) can achieve rapid prediction of a large number of train-track coupled operating condition samples, Monte Carlo simulation was directly used to predict 50,000 operating condition samples based on this invention. Taking the stochastic dynamic response at a train speed of 300 km / h as an example, the accuracy and efficiency of this invention and PDEM are compared and analyzed.

[0043] The time histories of the vehicle body's vertical random acceleration and the rail's vertical random displacement response based on this invention and PDEM are as follows: Figure 4 and Figure 5 As shown, the mean response of the FNO-PD method and PDEM in this invention exhibits good consistency. The slight deviation is due to the small sample size of PDEM, which fails to fully cover the high-dimensional sample space. This fully verifies the high accuracy of this invention in predicting the coupled random response of vehicle and track. Furthermore, under the premise of comparable prediction accuracy, the prediction time for 50,000 working condition samples based on the FNO-PD method is approximately 5 minutes, while the prediction time for 1,000 representative point samples based on PDEM is approximately 6,002 minutes. The computational efficiency of this invention is approximately 1200 times higher than that of PDEM.

[0044] To explore the generalization performance of this invention in practical engineering, actual track irregularity data measured by a track inspection vehicle on a certain section of the line were input into the trained model. The time history response of the vehicle-track coupled dynamics obtained based on the FNO-PD framework and simulation was compared and analyzed. It should be noted that, taking the standard parameters of the CRH380A train as an example, the train speed was set to 350 km / h. Figure 6 This section presents a comparison of train acceleration response time histories based on measured track irregularity data. Figure 6 It can be observed that the acceleration responses of the car body, bogie, and wheelsets predicted by this invention perfectly match the acceleration responses obtained from simulation. Specifically, the rLSE of the train acceleration response is 4.59%. The result of 0.9988 indicates that the present invention can still accurately predict the acceleration response of the train subsystem under measured track irregularity data, demonstrating outstanding generalization performance.

[0045] Figure 7 The results show a comparison of rail displacement fields based on measured track irregularity data. From Figure 7As can be seen from (a) and (b), the spatiotemporal variation trend and amplitude range of the rail displacement field predicted by this invention are almost identical to those of the actual displacement field, and the rLSE of the corresponding displacement field is only 3.29%. Up to 0.9989. Furthermore, Figure 7 (c) shows that the displacement error field is in the low range of 0 to 0.028 and there is no concentrated large error area, which fully demonstrates the high prediction accuracy and excellent generalization performance of the present invention under measured track irregularity data.

[0046] This invention also provides a high-efficiency calculation system for vehicle-track coupling dynamics based on a physics-data hybrid driving approach, comprising: The rail spatiotemporal displacement field response data acquisition module is used to uniformly generate a representative working condition sample point set of the train-track spatial coupling system using a Latin hypercube sampling strategy, and to perform deterministic analysis of the rail through the representative working condition sample point set to obtain the rail spatiotemporal displacement field response data. The optimal low-dimensional basis function acquisition module is used to extract the optimal low-dimensional basis function matrix from the rail spatiotemporal displacement field response data using the intrinsic orthogonal decomposition method. The model framework construction module is used to build a physics-data hybrid driven model framework with Fourier neural operators as the core backbone. The combined data of train speed, train physical parameters and track irregularity excitation are simultaneously input into the following two modules: the physics-driven module directly predicts and outputs the train spatiotemporal dynamic response; the data-driven module predicts and outputs the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method, and reconstructs the rail spatiotemporal displacement field by combining the optimal low-dimensional basis function matrix. The damage function construction and training module is used to construct the loss function. For the physics-driven module, the corresponding data constraints, physical constraints, and derivative constraints are incorporated into the loss function. For the data-driven module, the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method is incorporated into the data constraints of the loss function. Then, the physics-data hybrid driven model is trained based on the constructed sample dataset. The dynamics calculation module is used to perform vehicle-track coupled dynamics calculations using a trained physics-data hybrid driving model.

[0047] It should be understood that the functional unit modules in the various embodiments of the present invention can be concentrated in one processing unit, or each unit module can exist physically separately, or two or more unit modules can be integrated into one unit module, and can be implemented in hardware or software.

[0048] This invention also provides an electronic device, which includes one or more processors and a memory; the memory is coupled to the one or more processors, and the memory is used to store a computer program. The one or more processors call the computer program to cause the electronic device to execute the efficient calculation method for vehicle-track coupling dynamics based on physics-data hybrid drive as described above.

[0049] This invention also provides a computer-readable storage medium storing a computer program that, when run on an electronic device, causes the electronic device to execute the previously described efficient calculation method for vehicle-track coupling dynamics based on a physics-data hybrid drive.

[0050] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0051] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0052] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will 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 program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0053] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0054] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0055] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A highly efficient calculation method for vehicle-track coupled dynamics based on a physics-data hybrid driving approach, characterized in that, Includes the following steps: S1: A representative working condition sample point set of the train-track spatial coupling system is uniformly generated using the Latin hypercube sampling strategy. The rail deterministic analysis is performed using the representative working condition sample point set to obtain the rail spatiotemporal displacement field response data. S2: Extract the optimal low-dimensional basis function matrix from the spatiotemporal displacement field response data of rails using the intrinsic orthogonal decomposition method; S3: Construct a physics-data hybrid driven model framework with Fourier neural operators as the core backbone. The combined data of train speed, train physical parameters and track irregularity excitation are simultaneously input into the following two modules: the physics-driven module directly predicts and outputs the train spatiotemporal dynamic response; the data-driven module predicts and outputs the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method, and reconstructs the rail spatiotemporal displacement field by combining the optimal low-dimensional basis function matrix. S4: Construct a loss function for the physics-driven module, incorporating corresponding data constraints, physical constraints, and derivative constraints into the loss function; for the data-driven module, incorporate the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method into the data constraints of the loss function; then train the physics-data hybrid driven model based on the constructed sample dataset. S5: Perform vehicle-track coupled dynamics calculations using a trained physics-data hybrid driving model.

2. The efficient calculation method for vehicle-track coupled dynamics based on physics-data hybrid driving as described in claim 1, characterized in that, Step S1 includes: A dynamic model of the train-track spatial coupling system is constructed to generate samples of the train-track coupled dynamic response. A Latin hypercube sampling strategy was used to obtain a representative set of sample points for the train-track spatial coupling system under various operating conditions. Deterministic analysis of rails is performed using a representative set of working condition sample points to obtain the spatiotemporal displacement field response data of the rails.

3. The efficient calculation method for vehicle-track coupled dynamics based on physics-data hybrid driving as described in claim 1, characterized in that, In step S2, the order of the intrinsic orthogonal decomposition basis functions is determined by extracting the first 99.9% of the total energy percentage, thus obtaining the optimal low-dimensional basis function matrix.

4. The efficient calculation method for vehicle-track coupled dynamics based on physics-data hybrid driving as described in claim 1, characterized in that, In step S3, both the physics-driven module and the data-driven module include an input fully connected layer, a Fourier neural operator, and an output fully connected layer connected in sequence. The input fully connected layer elevates the model input to a high-dimensional space, and after iterative updates by the Fourier convolutional layer in the Fourier neural operator, it is output to the target dimension through the output fully connected layer.

5. The efficient calculation method for vehicle-track coupled dynamics based on physics-data hybrid driving as described in claim 1, characterized in that, In step S3, the rail time coefficient matrix output by the data-driven module is multiplied by the optimal low-dimensional basis function matrix to obtain the approximate fluctuating displacement field, as shown below: ； in, This represents the approximate fluctuating displacement field after dimensionality reduction; row vectors It is the orthogonal feature pattern extracted by singular value decomposition of the pulsation snapshot matrix, corresponding to the i-th row vector of the optimal low-dimensional basis function matrix; column vector It is the orthogonal time mode extracted by singular value decomposition, corresponding to the i-th column vector of the rail time coefficient matrix; k is the order of the basis functions in the optimal low-dimensional basis function matrix; Mean snapshot matrix obtained by combining the intrinsic orthogonal decomposition method This allows for the reconstruction of the complete spatiotemporal displacement field of the rail, which takes the following form: ； In the formula, The reconstructed spacetime displacement field of the rail.

6. The efficient calculation method for vehicle-track coupled dynamics based on physics-data hybrid driving as described in claim 1, characterized in that, In step S3, the train's physical parameters include its mass, moment of inertia, stiffness, and damping.

7. The efficient calculation method for vehicle-track coupled dynamics based on physical-data hybrid driving according to any one of claims 1 to 6, characterized in that, In step S4, the loss function is expressed as follows: ； In the formula, For the total loss, , and Data loss , For the residual loss of the train dynamics control equations, For derivative loss, and Let be the solution functions in the solution space for the train and the rail, respectively. and These are the physical drive module and the data drive module, respectively. This is the set of control equations for train dynamics. For time, For model inputs sampled from the distribution of the corresponding solution functions of the train Take the expected value. To represent the model input sampled from the distribution of the corresponding solution functions of the rail. Take the expected value. The total number of samples, Let be the solution domain of the problem.

8. A high-efficiency calculation system for vehicle-track coupled dynamics based on physics-data hybrid driving, characterized in that, include: The rail spatiotemporal displacement field response data acquisition module is used to uniformly generate a representative working condition sample point set of the train-track spatial coupling system using a Latin hypercube sampling strategy, and to perform deterministic analysis of the rail through the representative working condition sample point set to obtain the rail spatiotemporal displacement field response data. The optimal low-dimensional basis function acquisition module is used to extract the optimal low-dimensional basis function matrix from the rail spatiotemporal displacement field response data using the intrinsic orthogonal decomposition method. The model framework construction module is used to build a physics-data hybrid driven model framework with Fourier neural operators as the core backbone. The combined data of train speed, train physical parameters and track irregularity excitation are simultaneously input into the following two modules: the physics-driven module directly predicts and outputs the train spatiotemporal dynamic response; the data-driven module predicts and outputs the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method, and reconstructs the rail spatiotemporal displacement field by combining the optimal low-dimensional basis function matrix. The damage function construction and training module is used to construct the loss function. For the physics-driven module, the corresponding data constraints, physical constraints, and derivative constraints are incorporated into the loss function. For the data-driven module, the rail time coefficient matrix corresponding to the intrinsic orthogonal decomposition method is incorporated into the data constraints of the loss function. Then, the physics-data hybrid driven model is trained based on the constructed sample dataset. The dynamics calculation module is used to perform vehicle-track coupled dynamics calculations using a trained physics-data hybrid driving model.

9. An electronic device, characterized in that, The electronic device includes: one or more processors and a memory; the memory is coupled to the one or more processors, the memory is used to store a computer program, and the one or more processors call the computer program to cause the electronic device to execute the efficient calculation method for vehicle-track coupling dynamics based on physical-data hybrid drive as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when run on an electronic device, causes the electronic device to perform the efficient calculation method for vehicle-track coupling dynamics based on physical-data hybrid drive as described in any one of claims 1-7.

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