State prediction method and system for high-frequency dynamic response of pantograph

Abstract

The application discloses a state prediction method and system for high-frequency dynamic response of a high-speed pantograph, and relates to the technical field of pantograph state simulation. The method comprises the following steps: obtaining a pantograph sequence to be predicted; inputting the pantograph sequence to be predicted into a prediction model to obtain the displacement, velocity and acceleration of the pantograph in three orthogonal directions at the next moment; and wherein the prediction model is obtained by training samples simulated by a flexible pantograph finite element model, and the training process comprises training a predictor based on a joint loss function, and the joint loss function comprises a data-driven prediction loss and a physical consistency loss. The application reduces the calculation complexity under the premise of ensuring that the prediction result conforms to the physical law, and realizes high-fidelity prediction of high-frequency dynamic response.

Description

Technical Field

[0001] This application relates to the field of pantograph state simulation technology, specifically to a method and system for predicting the state of high-frequency dynamic response of a high-speed pantograph. Background Technology

[0002] During high-speed railway operation, stable sliding contact between the pantograph and the overhead contact line is crucial for reliable power reception. With the continuous increase in train speed, the pantograph-over-the-line system exhibits significant high-frequency dynamic characteristics due to the modal excitation of its flexible structure. Traditional lumped-mass pantograph models cannot accurately represent structural flexibility. To accurately assess the dynamic performance of the pantograph-over-the-line system, a fully flexible finite element model is typically used for dynamic simulation. However, while the fully flexible finite element model offers high accuracy, its large degrees of freedom result in extremely long computation times for large-scale or long-term simulations, making it difficult to meet the needs of real-time analysis or rapid iterative design. Summary of the Invention

[0003] This application provides a method and system for predicting the state of high-frequency dynamic response of a high-speed pantograph, which can improve the physical consistency and accuracy of dynamic response prediction while reducing computational complexity.

[0004] This application provides a method for predicting the state of high-frequency dynamic response of a high-speed pantograph, including:

[0005] Obtain the pantograph sequence to be predicted. The pantograph sequence to be predicted includes the pantograph excitation at the current moment and the historical pantograph state response. The historical pantograph state response includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions within a preset time window before the current moment.

[0006] The pantograph sequence to be predicted is input into the prediction model to obtain the pantograph state response at the next moment output by the prediction model. The pantograph state response at the next moment includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions at the next moment.

[0007] The prediction model is trained using flexible pantograph samples, which are obtained by simulating a fully flexible pantograph finite element model. The training process includes training the predictor based on a joint loss function, which includes data-driven prediction loss and physical consistency loss.

[0008] Optionally, the process of determining the prediction model includes:

[0009] Obtain a training sample set, which includes multiple training sample pairs. Each training sample pair includes the historical pantograph state response and pantograph excitation as training samples, and the pantograph state response at the next moment as training labels.

[0010] The parameters of the predictor in the initial model are frozen, and the encoder and decoder of the initial model are iteratively trained until convergence based on the preset loss function and the training sample set to obtain the first model; the initial model includes an encoder, a predictor and a decoder;

[0011] Freeze the parameters of the encoder and decoder in the first model, and iteratively train the predictor of the first model until convergence based on the joint loss function and the training sample set to obtain the prediction model.

[0012] Optionally, the iterative training of the encoder and decoder of the initial model until convergence includes:

[0013] The encoder maps the pantograph state response and pantograph excitation in the training samples to the dynamic latent space to obtain the dynamic latent state sequence.

[0014] The decoder maps the dynamic hidden state sequence back to the physical space to obtain the reconstructed pantograph state response;

[0015] The parameters of the encoder and the decoder are updated based on the reconstruction error between the reconstructed pantograph state response and the pantograph state response in the training samples.

[0016] Optionally, the iterative training of the predictor for the first model until convergence includes:

[0017] The encoder of the first model maps the pantograph state response and pantograph excitation in the training samples to the dynamic latent space to obtain the dynamic latent state sequence.

[0018] The predictor predicts the next time-step hidden state based on the sequence of hidden dynamic states.

[0019] The decoder of the first model maps the hidden dynamic state of the next moment back to the physical space to obtain the predicted pantograph state response.

[0020] The parameters of the predictor are updated based on the joint loss function.

[0021] Optionally, in the joint loss function: the data-driven prediction loss is constructed based on the deviation between the predicted pantograph state response and the pantograph state response at the next moment in the training labels; the physical consistency loss is constructed based on the kinematic constraint relationship between the pantograph state variables, including displacement, velocity, and acceleration.

[0022] Optionally, the process of constructing the physical consistency loss includes:

[0023] The velocity estimate is obtained by solving the displacement finite difference between adjacent time points. The mean square error between the velocity estimate and the velocity in the predicted pantograph state response is calculated to construct a velocity constraint term.

[0024] Acceleration estimates are obtained by solving the velocity finite difference between adjacent time points. The mean square error between the acceleration estimates and the acceleration in the predicted pantograph state response is calculated, and acceleration constraint terms are constructed.

[0025] The physical consistency loss is obtained by summing the velocity constraint term and the acceleration constraint term.

[0026] Optionally, the update formula for the weight coefficients of the data-driven prediction loss and the physical consistency loss in the joint loss function includes:

[0027] ;

[0028] ;

[0029] in, For the first Training Step 1 The rate of decrease of the loss component, For the first Training Step 1 The value of the loss component, For the first Training Step 1 The value of the loss component, This represents the total number of loss components, which include data-driven prediction loss or physical consistency loss. It is an exponential function. For the first Training Step 1 The weighting coefficients corresponding to the loss components, This represents the weights corresponding to the data-driven prediction loss. This represents the weight corresponding to the physical consistency loss.

[0030] To achieve the above and other related objectives, this application provides a high-speed pantograph high-frequency dynamic response state prediction system, comprising:

[0031] The data acquisition module is used to acquire the pantograph sequence to be predicted. The pantograph sequence to be predicted includes the pantograph excitation at the current moment and the historical pantograph state response. The historical pantograph state response includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions within a preset time window before the current moment.

[0032] The prediction module is used to input the pantograph sequence to be predicted into the prediction model to obtain the pantograph state response at the next moment output by the prediction model. The pantograph state response at the next moment includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions at the next moment.

[0033] The prediction model is trained using flexible pantograph samples, which are obtained by simulating a fully flexible pantograph finite element model. The training process includes training the predictor based on a joint loss function, which includes data-driven prediction loss and physical consistency loss.

[0034] Optionally, the high-speed pantograph high-frequency dynamic response state prediction system further includes a training module, which includes:

[0035] The sample acquisition unit is used to acquire a training sample set, which includes multiple training sample pairs. Each training sample pair includes the historical pantograph state response and pantograph excitation as training samples, and the pantograph state response at the next moment as training labels.

[0036] The first training unit is used to freeze the parameters of the predictor in the initial model, and iteratively train the encoder and decoder of the initial model until convergence based on the preset loss function and the training sample set to obtain the first model; the initial model includes an encoder, a predictor and a decoder;

[0037] The second training unit is used to freeze the parameters of the encoder and decoder in the first model, and iteratively train the predictor of the first model until convergence based on the joint loss function and the training sample set to obtain the prediction model.

[0038] Optionally, the first training unit is further configured to:

[0039] The encoder maps the pantograph state response and pantograph excitation in the training samples to the dynamic latent space to obtain the dynamic latent state sequence.

[0040] The decoder maps the dynamic hidden state sequence back to the physical space to obtain the reconstructed pantograph state response;

[0041] The parameters of the encoder and the decoder are updated based on the reconstruction error between the reconstructed pantograph state response and the pantograph state response in the training samples.

[0042] As described above, the state prediction method and system for high-frequency dynamic response of high-speed pantographs provided in this application have the following beneficial effects:

[0043] This application inputs the sequence of data to be predicted—including the current pantograph excitation and displacement, velocity, and acceleration in three orthogonal directions within a historical preset time window—into a prediction model trained on fully flexible pantograph samples, directly achieving an accurate output of the pantograph's state response at the next moment. By replacing traditional implicit or explicit dynamic iterative solutions with this prediction model, this method effectively avoids the inability of traditional lumped mass models to reflect structural flexibility, while overcoming the bottleneck of the large degrees of freedom and extremely long computation time of fully flexible finite element models. This reduces computational complexity and meets the computational efficiency requirements for pantograph-catenary dynamics simulation or pantograph structural analysis. It can reduce the computational complexity of dynamic simulation while preserving the high-frequency dynamic characteristics of the fully flexible model, solving the problem of excessively long simulation computation time of traditional fully flexible finite element models. Attached Figure Description

[0044] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings:

[0045] Figure 1 This is a flowchart illustrating a state prediction method for high-frequency dynamic response of a high-speed pantograph, as shown in an exemplary embodiment of this application.

[0046] Figure 2 This is a schematic diagram of a key node of the pantograph shown in an exemplary embodiment of this application;

[0047] Figure 3 This is a comparison chart of the predictive model and finite element simulation of the dynamic response of the pantograph head.

[0048] Figure 4 It is a comparison curve of the prediction mean square error under different preset time window lengths;

[0049] Figure 5 This is a comparative graph showing the predicted displacement response of the pantograph head under different models, illustrating an exemplary embodiment of this application.

[0050] Figure 6 This is a comparison curve of the pantograph head displacement response prediction results under different models, as shown in another exemplary embodiment of this application;

[0051] Figure 7 This is a flowchart illustrating a high-speed pantograph high-frequency dynamic response state prediction method in another exemplary embodiment of this application;

[0052] Figure 8This is a schematic diagram illustrating the structure of a high-speed pantograph high-frequency dynamic response state prediction system, as shown in an exemplary embodiment of this application. Detailed Implementation

[0053] To better understand the above-mentioned objectives, features, and advantages of this application, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments and features described in the embodiments of this application can be combined with each other.

[0054] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Therefore, the scope of protection of this application is not limited to the specific embodiments disclosed below.

[0055] Please see Figure 1 This is a flowchart illustrating a state prediction method for the high-frequency dynamic response of a high-speed pantograph, as shown in an exemplary embodiment of this application. (See reference...) Figure 1 It can be seen that the state prediction method for the high-frequency dynamic response of the high-speed pantograph may include steps S110 and S120.

[0056] Step S110: Obtain the pantograph sequence to be predicted.

[0057] The pantograph sequence to be predicted includes the current pantograph excitation and the historical pantograph state response. The historical pantograph state response includes the displacement, velocity, and acceleration of the pantograph in three orthogonal directions within a preset time window before the current moment.

[0058] In one embodiment of this application, the pantograph sequence to be predicted can serve as the complete input context for the prediction model. Pantograph excitation typically manifests as a dynamic load applied to the catenary surface, with spectral characteristics covering a wide frequency range from 0 to 200 Hz to simulate the complex pantograph-catenary contact forces in actual operation. Historical pantograph state responses can provide a digital representation of the pantograph's motion state over a past period.

[0059] For example, to accurately capture high-frequency dynamic characteristics, 46 key nodes on the pantograph surface can be selected as observation points. These key nodes can be distributed across core components such as the pantograph head, upper frame, and lower boom to fully characterize the global dynamic behavior. The three orthogonal directions refer to the X-axis, Y-axis, and Z-axis directions established in the pantograph's body coordinate system, corresponding to the pantograph's state response in the lateral, longitudinal, and vertical directions, respectively. The pantograph state response of each key node can include nine state variables: displacement, velocity, and acceleration in the three orthogonal directions of the X, Y, and Z axes. The length of the preset time window can be set according to the actual dynamic characteristics, for example, set to 10 time steps, to ensure that the historical pantograph state response contains sufficient historical information for trend inference while avoiding redundant calculations due to an excessively long window.

[0060] It should be noted that the input dimension of the prediction model can be 414, that is, the input dimension = number of key nodes × 3 (number of axes) × 3 (number of state variables for each axis, namely displacement, velocity and acceleration).

[0061] Step S120: Input the pantograph sequence to be predicted into the prediction model to obtain the pantograph state response at the next moment output by the prediction model.

[0062] The pantograph state response at the next moment includes the pantograph's displacement, velocity, and acceleration in three orthogonal directions at the next moment.

[0063] In one embodiment of this application, the input of the prediction model can receive the pantograph sequence to be predicted. After internal nonlinear transformation, the output of the prediction model outputs the triaxial displacement, velocity, and acceleration of all observed nodes of the pantograph at the next moment. The prediction model can be trained using flexible pantograph samples, which are obtained by simulating a fully flexible pantograph finite element model. The fully flexible pantograph finite element model can be directly imported into the actual three-dimensional geometric model of the pantograph. It uses a large number of solid elements for fine discretization, which can completely restore the physical structure, key connecting parts, and material distribution of the real pantograph in a 1:1 fidelity manner without any stiffening assumptions or structural simplifications. It is based on this high-fidelity data source that the prediction model can learn the complex flexible deformation and modal coupling characteristics of the real structure under high-frequency excitation, rather than just a simplified rigid body motion trajectory.

[0064] Furthermore, to ensure that the prediction results not only conform to statistical data patterns but also follow the laws of physics and mechanics, the training process includes training the predictor based on a joint loss function, which comprises a data-driven prediction loss and a physical consistency loss. The joint loss function serves as a dual constraint during the training phase. The data-driven prediction loss measures the deviation between the model's predicted values ​​and the true values ​​from the fully flexible finite element simulation, ensuring that the prediction model can accurately fit the nonlinear mapping relationships in the sample data. The physical consistency loss mandates that the displacement, velocity, and acceleration output by the prediction model satisfy kinematic differential constraints. Through the joint loss function, the prediction model is infused with prior physical knowledge while learning data features, effectively suppressing the non-physical drift phenomenon that easily occurs in pure data-driven models under long-term prediction or extrapolation conditions, thus ensuring the reliability and robustness of the prediction results in engineering applications.

[0065] It should be noted that as vehicle speed increases, the frequency of pantograph-catenary interaction also increases. Traditional pantograph models cannot accurately characterize the high-frequency characteristics of the pantograph under these conditions. While fully flexible finite element models can characterize the high-frequency dynamic response of high-speed pantographs, they involve significant computational complexity and are time-consuming. The state prediction method for the high-frequency dynamic response of high-speed pantographs provided in this application reduces computational complexity by using a prediction model that satisfies the physical characteristics of the pantograph during movement, achieving both accuracy and reduced computation time. "High-speed" refers to vehicle speeds greater than or equal to 350 km / h, and "high frequency" refers to the pantograph's vibration frequency at speeds greater than or equal to 350 km / h.

[0066] In one embodiment of this application, the process of determining the prediction model may include: obtaining a training sample set, which includes multiple training sample pairs, each training sample pair including a historical pantograph state response and pantograph excitation as training samples, and a pantograph state response at the next moment as a training label; an initial model including an encoder, a predictor, and a decoder; freezing the parameters of the predictor in the initial model, and iteratively training the encoder and decoder of the initial model to convergence based on a preset loss function and the training sample set to obtain a first model; freezing the parameters of the encoder and decoder in the first model, and iteratively training the predictor of the first model to convergence based on a joint loss function and the training sample set to obtain the prediction model.

[0067] The iterative training process of the encoder and decoder of the initial model until convergence can include: mapping the pantograph state response and pantograph excitation in the training samples to the dynamic latent space through the encoder, obtaining a sequence of dynamic latent states; mapping the sequence of dynamic latent states back to the physical space through the decoder, obtaining the reconstructed pantograph state response; and updating the parameters of the encoder and decoder based on the reconstruction error between the reconstructed pantograph state response and the pantograph state response in the training samples. During this stage, the predictor parameters are completely frozen and do not participate in gradient backpropagation. The encoder can, for example, employ a Long Short-Term Memory (LSTM) network, utilizing its gating mechanism to adaptively adjust the decay rate of historical states to simulate the energy dissipation characteristics of the system and extract minimum sufficient dynamic features; the decoder can, for example, employ a Multilayer Perceptron (MLP) to achieve an efficient inverse mapping from latent states to physical states. The preset loss function is typically a purely data-driven reconstruction loss such as Mean Squared Error (MSE). By minimizing the reconstruction error, the encoder is forced to learn a compact latent state representation containing complete dynamic information, ensuring that the latent space has sufficient physical interpretability and information completeness.

[0068] The process of iteratively training the predictor of the first model until convergence can include: mapping the pantograph state response and pantograph excitation in the training samples to the kinetic latent space through the encoder of the first model, obtaining a sequence of kinetic latent states; predicting the kinetic latent state at the next time step based on the sequence of kinetic latent states through the predictor; mapping the kinetic latent state at the next time step back to the physical space through the decoder of the first model, obtaining the predicted pantograph state response; and updating the parameters of the predictor based on the joint loss function. In this stage, the parameters of the encoder and decoder are frozen, and only the predictor participates in training. Since the first stage has accurately and losslessly compressed the complex fully flexible high-frequency response features into a low-dimensional observation space, the predictor no longer needs to consider the quality of feature extraction and can focus on fitting the state transition function. The joint loss function used at this time simultaneously constrains prediction accuracy and physical consistency, ensuring that the evolutionary trajectory learned by the predictor conforms to both the data distribution and the laws of mechanics.

[0069] For example, using a data generation algorithm, six sets of 0-200Hz wideband random excitation signals with varying amplitudes and frequency distributions can be constructed, with a time step of 0.005s. Forty-six key nodes on the pantograph surface are selected to characterize the global dynamics. The state vector of each node includes displacement, velocity, and acceleration along three orthogonal directions: the X-axis, Y-axis, and Z-axis. The generated six sets of random excitations are cyclically applied to the fully flexible pantograph finite element model, and dynamic response data for 4000 time steps after stable convergence are extracted, ultimately forming state data of [6 sets of excitations × 4000 time steps × 46 nodes × 9 state features]. After concatenating the above data samples with the random excitation data, initialization and normalization are performed, ultimately forming a data set containing the input data. and output data The sample set, in which The pantograph state response is given for all times from tm to t, where m is the length of the time window. Let t be the excitation applied to the pantograph at time t. This represents the pantograph state response at all times t+1. The last 1000 sample steps are divided into a test dataset, and the remaining samples are stored in a dataset buffer for training.

[0070] For example, please refer to Figure 2 This is a schematic diagram of key nodes of a pantograph, illustrating an exemplary embodiment of this application. The diagram shows 46 key nodes marked with solid red icons. The coordinate system is indicated in the lower right corner: green arrows represent the Y-axis, blue arrows the Z-axis, and red arrows the X-axis. Each axis corresponds to the displacement, velocity, and acceleration of each key node. The orange arrows within the red dashed boxes indicate the application location of the pantograph excitation (i.e., dynamic load). Sample collection was conducted in six independent simulation experiments. The application points of the dynamic load were randomly distributed within ±0.3 meters of the skateboard centerline. The influence of pull-out values ​​was considered, and contact point migration was incorporated into the training data. High-frequency dynamic response characteristics of displacement, velocity, and acceleration in three orthogonal directions on the 46 selected key nodes within the 0-200Hz range were captured, generating a test dataset for training the model.

[0071] The encoder can be an LSTM, which can extract minimal, sufficient dynamic features from a finite historical sequence. This process can be described as follows: , This represents the sequence of hidden dynamic states from time tm to time t. For dynamic evolution operators, This represents the mapping relationship between the physical space state (actual dynamic response) and the observation space state (hidden state) of the system. This represents the historical pantograph state response from time tm to time t. Let represent the pantograph excitation at time t; after the encoder maps a finite history window to the kinetic hidden states, the kinetic evolution operator propagates these states to the target time step. Subsequently, the MLP decoder transforms the single-step kinetic hidden states back to physical space, the transformation being formally represented as: , Indicates the inverse mapping. This represents the pantograph state response at time t+1. This represents the hidden dynamic state at time t+1.

[0072] The improved Transformer architecture can be used as a predictor. The Transformer architecture has excellent performance in mining pairwise dependencies in time series data and extracting multi-level feature representations. The complete state evolution process can be represented as follows:

[0073] ;

[0074] in, This represents the hidden dynamic state at time t+1.

[0075] Although this embodiment uses a preferred combination of LSTM as the encoder, MLP as the decoder, and Transformer as the predictor as an example, this is not a limitation on the scope of protection of this application. In other embodiments, the encoder may also be a convolutional neural network (CNN), a gated recurrent unit (GRU), or a feature extractor based on an attention mechanism; the decoder may also be a transposed convolutional network or other upsampling structures; and the predictor may also be a recurrent neural network, a state-space model, or other temporal prediction architecture.

[0076] In one embodiment of this application, the predictor may include: a local temporal feature extraction module, used to perform causal convolution operation on the dynamic latent state sequence to extract local temporal dependency features; a physical prior location encoding module, used to embed the physical attribute data of the pantograph observation node into the local temporal dependency features to obtain physical enhancement features, wherein the physical attribute data includes at least one of spatial coordinates or modal frequencies; a self-attention module, used to perform self-attention calculation based on the physical enhancement features to obtain attention features; and a temporal gating module, used to perform information flow modulation on the attention features to output the dynamic latent state.

[0077] The local temporal feature extraction module employs causal convolution as its core operator. Unlike standard convolution, causal convolution strictly limits the temporal direction of the receptive field through a masking mechanism, ensuring that only historical information up to and including time t is used when extracting features at time t, thus preventing the leakage of future information. This is crucial for ensuring the causal logic of state prediction. Furthermore, the high-frequency vibrations of the pantograph often manifest as short-term transient impacts or rapidly decaying modal responses. Causal convolution, with its local connectivity characteristics, can efficiently capture these subtle temporal texture changes, providing a refined feature base for subsequent global modeling. It should be understood that while this embodiment preferably uses causal convolution, other implementations may employ dilated causal convolution to expand the receptive field, or variations such as gated linear units, as long as the function of unidirectional temporal dependency extraction is satisfied.

[0078] In traditional Transformer architectures, position encoding typically only includes sine and cosine functions or learnable absolute position vectors, lacking awareness of physical entity properties. In this embodiment, however, the module explicitly embeds physical attribute data such as the spatial coordinates and intrinsic modal frequencies of the pantograph observation node into the feature representation. For example, spatial coordinate information enables the model to distinguish the dynamic behavior differences between different components such as the bow head, upper frame, and lower boom; modal frequency information provides the model with a priori spectral reference for structural vibration, helping to maintain the physical plausibility of predictions in data-sparse regions. This construction of physically enhanced features can compensate for the cognitive blind spots of purely data-driven models when sample coverage is incomplete, enabling the neural network to not only fit numerical curves but also understand the physical structure and mechanical behavior of the pantograph.

[0079] The self-attention module is responsible for establishing long-range temporal dependencies based on physically enhanced features. Considering the hysteresis effects of energy transfer and dissipation in the pantograph dynamics system, the current state is often influenced by excitations from more distant historical moments. The self-attention mechanism adaptively aggregates key information across the entire temporal range by calculating the correlation between the query vector, key vector, and value vector. The self-attention module generates query vectors, key vectors, and value vectors based on each embedded feature. Based on extensive hyperparameter tuning experiments, the projection dimension d... k Set as the dimension d of the dynamic feature space l twice as much, satisfying Q, K, and V are the query vector, key vector, and value vector, respectively. The set is the real number set. This setting provides the optimal performance balance between fully capturing the complex high-frequency nonlinear structural deformation characteristics of the pantograph and maintaining model computational efficiency; at the same time, this upper limit of dimensionality effectively limits network complexity, avoiding severe overfitting problems caused by excessive expansion of the observation space dimension. To avoid dot products... Excessively large values ​​can cause gradient explosion. A scaled dot product attention mechanism with optimized numerical stability can be used to make the input to the Softmax function smoother and the gradient distribution more uniform. The calculation formula is as follows:

[0080] ;

[0081] The encoded feature sequence is input into a fully connected feedforward layer with a non-linear activation function to deduce the feature sequence for subsequent time steps. The neurons in this layer are fully trained and can learn the inherent variation patterns of temporal data amplitude and periodicity, thereby outputting feature representations with better predictive performance.

[0082] Finally, the temporal gating module modulates the information flow of the self-attention output features. This module is similar to the gating mechanism in recurrent neural networks, but operates on the attention features. It adaptively determines which historical information should be retained, forgotten, or updated based on the current dynamic context, thereby generating the final dynamic hidden state. This modulation mechanism further enhances the model's adaptability to non-stationary dynamic processes, ensuring the continuity and smoothness of the output state.

[0083] By combining four modules—causal convolution, physical encoding, self-attention, and temporal gating—a predictor architecture is constructed that possesses both powerful temporal modeling capabilities and deep integration of physical prior knowledge. Physical prior location encoding can employ various methods such as additive injection, concatenation fusion, or multiplicative modulation; the temporal gating module can also be replaced by GRU or LSTM units.

[0084] In one embodiment of this application, the joint loss function comprises: a data-driven prediction loss constructed based on the deviation between the predicted pantograph state response and the pantograph state response at the next moment in the training labels; and a physical consistency loss constructed based on the kinematic constraints between the pantograph's state variables, including displacement, velocity, and acceleration. The data-driven prediction loss can be used to measure the statistical distance between the pantograph state response output by the first model and the true value of the fully flexible finite element simulation, for example, by using mean squared error (MSE) or mean absolute error (MAE) as a metric to ensure that the model can accurately fit the nonlinear mapping relationships inherent in the sample data.

[0085] For example, data-driven prediction loss can be expressed as:

[0086] ;

[0087] Where N represents the total state dimension of the pantograph system, N = the number of critical nodes (in this embodiment, the number of critical nodes can be 46), and T represents the total time step. For data-driven prediction loss, This represents the pantograph state response at time t+1. For dynamic neural operators, For dynamic evolution operators, , , This represents the functional relationship between the next state of the dynamic system and the previous state, as well as the external loads. This represents the pantograph state response at time t of the i-th node. This represents the pantograph state response at time t+1 of the i-th node. This indicates the pantograph excitation at time t. This indicates the pantograph excitation at time t+1.

[0088] Relying solely on data-driven loss can lead to predictions that violate physical laws in sparse training data regions or under extrapolated conditions. To address this, physical consistency loss can be employed, transforming the kinematic differential relationships in Newtonian mechanics into differentiable soft constraints. Since the displacement, velocity, and acceleration of the pantograph system have inherent derivative relationships in the time domain, this physical prior knowledge, independent of specific sample labels, provides global regularization guidance for the model, effectively suppressing non-physical drift and enhancing the reliability of predictions under high-frequency dynamic conditions.

[0089] Furthermore, the process of constructing the physical consistency loss may include: obtaining a velocity estimate based on the finite difference solution of displacement at adjacent time points, calculating the mean square error between the velocity estimate and the velocity in the predicted pantograph state response, and constructing a velocity constraint term; obtaining an acceleration estimate based on the finite difference solution of velocity at adjacent time points, calculating the mean square error between the acceleration estimate and the acceleration in the predicted pantograph state response, and constructing an acceleration constraint term; and summing the velocity constraint term and the acceleration constraint term to obtain the physical consistency loss.

[0090] Considering that neural networks process discrete-time series, the finite difference method can be used to discretize the continuous kinematic differential equations. (Velocity constraint term) and acceleration constraint terms The calculation formulas are expressed as follows:

[0091] ;

[0092] ;

[0093] in, , , These represent the displacement, velocity, and acceleration states of the i-th node of the pantograph at time t+1, as predicted by the model. , Let represent the displacement and velocity state of the i-th node at time t. The time step is the interval between two adjacent states, which in this embodiment corresponds to the sampling interval (e.g., 0.005s) in a fully flexible finite element simulation; N is the total state dimension of the pantograph system, and T represents the total time step. Through velocity and acceleration constraints, the model is forced to satisfy the condition that the difference in displacement is approximately equal to the velocity and the difference in velocity is approximately equal to the acceleration.

[0094] The physical consistency loss is used to impose dynamic constraints on displacement, velocity, and acceleration, and its expression is as follows:

[0095] ;

[0096] in, This represents the loss of physical consistency.

[0097] In multi-objective optimization, data-driven prediction loss and physical consistency loss often exhibit differences in magnitude and convergence speed. The weights of the data-driven prediction loss and physical consistency loss in the joint loss function are dynamically adjusted using an adaptive equalization algorithm. This algorithm can include: calculating the decrease rate of each of the data-driven prediction loss and physical consistency loss between the current training step and the previous training step; and updating the weights of the data-driven prediction loss and physical consistency loss in the current training step based on the decrease rate.

[0098] Fixed-weight methods require extensive manual trial-and-error parameter tuning and struggle to adapt to dynamic changes in loss during training. If the physical loss weight is too large, the model may prematurely satisfy physical constraints, neglecting data fitting accuracy and resulting in underfitting; conversely, if the data loss weight is too large, physical constraints may become ineffective, causing predictions to deviate from actual mechanical behavior. The adaptive equalization algorithm used in this embodiment can monitor the optimization status of each loss component in real time, automatically balancing the competitive relationship between different objectives to ensure that the model maintains both data accuracy and physical consistency throughout the entire training cycle.

[0099] The joint loss function can be expressed as:

[0100] ;

[0101] in, This represents the joint loss function.

[0102] In one embodiment of this application, the update formula for the weight coefficients of the data-driven prediction loss and the physical consistency loss in the joint loss function includes:

[0103] ;

[0104] ;

[0105] in, For the first Training Step 1 The rate of decrease of the loss component, For the first Training Step 1 The value of the loss component, For the first Training Step 1 The value of the loss component, The total number of loss components, which may include data-driven prediction loss or physical consistency loss. It is an exponential function. For the first Training Step 1 The weighting coefficients corresponding to the loss components, This represents the weights corresponding to the data-driven prediction loss. This represents the weight corresponding to the physical consistency loss.

[0106] The change in loss can be based on an exponential function. Nonlinear amplification and normalization are performed. When a certain loss component decreases rapidly, its change is positive and large, and a higher value representing the rate of decrease is obtained after exponential calculation. This allows for the allocation of corresponding weights. On one hand, the exponential function can amplify small differences in loss, improving the algorithm's sensitivity to optimization trends. On the other hand, the summation and normalization operation of the denominator eliminates the influence of the absolute dimension of the loss and limits the weights within a reasonable range, avoiding drastic weight oscillations caused by individual loss mutations, thus ensuring the smoothness and robustness of the training process.

[0107] For example, this embodiment, in conjunction with specific application scenarios and experimental data, explains the performance of the prediction model and the selection of the preset time window length involved in the aforementioned embodiments.

[0108] Figure 3 This is a comparison chart of the predicted model and finite element simulation of the dynamic response of the pantograph head. Figure 3 In the diagram, the solid blue line represents the true simulation result of the fully flexible pantograph finite element model, and the dashed red line represents the output result of the prediction model of this application. It can be observed that within the test interval of 0 to 1000 time steps, the two curves show a high degree of overlap in the amplitude variation trend and peak position for both displacement, velocity, and acceleration responses. This indicates that the prediction model, trained based on fully flexible samples and optimized using a joint loss function, successfully learns the nonlinear dynamic characteristics of the complex flexible structure of the pantograph, rather than merely fitting a simplified rigid body motion trajectory.

[0109] exist Figure 3 In the subplots from left to right, the first subplot's x-axis represents the time step and the y-axis represents the displacement; the second subplot's x-axis represents the time step and the y-axis represents the velocity; and the third subplot's x-axis represents the time step and the y-axis represents the acceleration.

[0110] like Figure 4As shown, a comparison curve of the mean squared error (MSE) of prediction under different preset time window lengths is displayed. Five preset time window lengths of 3, 5, 10, 20, and 30 steps were set for testing in the experiment. Figure 4 The data shows that when the preset time window length is 3 steps, the prediction error increases sharply over time, reaching approximately 2.0 × 10⁻⁶ after 400 steps. -3 The high error rate is due to the short historical sequence failing to capture the complete periodic information of the pantograph's high-frequency vibration modes, resulting in insufficient context for the model to infer the system's inertial state and energy transfer trends. While the initial error decreased when the preset time window length was increased to 5 steps, it still exhibited significant fluctuations and an upward trend in the later stages, indicating that it had not fully captured the system's critical dynamic memory length. In contrast, when the preset time window length was set to 10 steps, the prediction error remained consistently low throughout the test period (approximately 0.5 × 10⁻⁶). -3 Up to 0.8×10 -3 The curve is most stable between 10 and 30 steps. However, when the window length is further extended to 20 or 30 steps, the prediction accuracy is not significantly improved. Instead, the increased input dimension leads to increased computational overhead and introduces more distant historical noise that is less correlated with the current state, which may negatively affect the model's generalization ability. Therefore, considering prediction accuracy, computational efficiency, and noise resistance, this embodiment sets the preset time window to 10 steps. It should be noted that this preset time window length is based on the 0.005s sampling step size and specific pantograph structural modal characteristics in this embodiment. In practical applications, this window length can be adaptively adjusted according to the pantograph's natural frequency, damping ratio, and sampling rate. For example, for higher frequency vibration modes or lower sampling rate scenarios, the window length can be appropriately increased to cover the complete dynamic cycle.

[0111] like Figure 5 and Figure 6 As shown, a comparison curve of the predicted displacement response of the pantograph head under different models is presented.

[0112] Figure 5 In the diagram, the horizontal axis represents the time step, and the vertical axis represents the position of the pantograph head node. The sign of the value is determined based on the standard working height of the pantograph (i.e., 1600mm). The black solid line represents the finite element simulation result, the blue dashed line represents TCN, the green dashed line represents LSTM, the purple dotted line represents GRU, the purple dashed line represents the traditional Transformer, and the red solid line with red dots represents the surrogate solution and prediction model (i.e., the prediction model provided in the embodiments of this application).

[0113] Figure 6In the diagram, the horizontal axis represents the time step, and the vertical axis represents the position of the pantograph head node. The black solid line represents the finite element simulation results, the yellow dashed line represents Koopman+ linear (Variant A), the yellow dotted line represents Koopman+TCN (Variant B), the pink dotted line represents Koopman+LSTM (Variant C), the red dotted line represents Koopman+GRU (Variant D), and the red solid line with red dots represents the surrogate solution and prediction model. Figure 6 The blue box in the image shows a magnified view of a portion of the image.

[0114] As can be clearly seen from the magnified area, the prediction curves of traditional TCN, LSTM, GRU, and standard Transformer models deviate from the true finite element values ​​to varying degrees (solid black line), especially at high-frequency transient features such as peaks and troughs. In contrast, the prediction model of this application (red dotted line) demonstrates better tracking capabilities.

[0115] Table 1 lists the average mean square error (MSE) and mean absolute error (MAE) of the displacement, velocity, and acceleration responses of each model in the last 100 prediction steps. DMSE represents the mean square error of displacement, DMAE represents the mean absolute error of displacement, VMSE represents the mean square error of velocity, VMAE represents the mean absolute error of velocity, AMSE represents the mean square error of acceleration, and AMAE represents the mean absolute error of acceleration.

[0116] Table 1. Values ​​of evaluation metrics for each model

[0117] DMSE 0.00465 0.00334 0.00353 0.00187 0.00474 0.00158 0.00123 0.00125 0.000735 DMAE 0.0521 0.0502 0.0487 0.0342 0.0531 0.0318 0.0287 0.0255 0.0187 VMSE 0.00460 0.00366 0.00240 0.00211 0.00488 0.00212 0.00167 0.00128 0.000759 VMAE 0.0573 0.0534 0.0386 0.0361 0.0575 0.0358 0.0320 0.0266 0.0199 AMSE 0.00465 0.00380 0.00346 0.00239 0.00555 0.00269 0.00170 0.00131 0.00104 AMAE 0.0581 0.0540 0.0495 0.0383 0.0590 0.0399 0.0332 0.0254 0.0223

[0118] As shown in the table above, the proposed method achieves the best performance across all evaluation metrics. For example, the displacement mean square error (DMSE) of the proposed method is only 0.000735, which is approximately 40% lower than the well-performing Koopman+LSTM variant and approximately 60% lower than the traditional Transformer. On one hand, batch training of the encoder, decoder, and predictor avoids gradient conflicts between feature extraction and state evolution, enabling the model to establish a more robust dynamic latent space. On the other hand, the deep integration of physical prior position encoding with causal convolution and self-attention mechanisms gives the model the physical cognitive ability lacking in purely data-driven models when dealing with high-frequency nonlinear deformations, thus maintaining high-precision prediction output even under sparse data or extrapolation conditions.

[0119] Finally, regarding computational efficiency, in the test environment of this embodiment, the dynamic response simulation of the fully flexible multi-body pantograph model using ANSYS software for 1000 time steps took more than 16 hours, while the state prediction using the prediction model trained in this application only took about 10.88 seconds. This means that while maintaining prediction accuracy comparable to high-precision finite element simulation, this application has improved the computational speed by more than three orders of magnitude. This leap in efficiency allows refined dynamic analysis, which was originally only applicable to offline design, to be applied to scenarios with extremely high timeliness requirements, such as vehicle-mounted real-time monitoring, online synchronization of digital twins, and rapid iterative verification of active control strategies. This effectively solves the industry pain point of difficulty in balancing accuracy and efficiency in high-frequency dynamic response simulation of high-speed pantographs.

[0120] Please see Figure 7 The flowchart illustrates a state prediction method for the high-frequency dynamic response of a high-speed pantograph, which is another exemplary embodiment of this application. The flowchart includes A. pantograph dynamic response measurement (i.e., sample preparation stage), B. training stage, and C. inference stage.

[0121] Please see Figure 8 This is a schematic diagram illustrating the structure of a high-speed pantograph high-frequency dynamic response state prediction system 800, as shown in an exemplary embodiment of this application. The high-speed pantograph high-frequency dynamic response state prediction system 800 may include:

[0122] The data acquisition module 810 is used to acquire the pantograph sequence to be predicted. The pantograph sequence to be predicted includes the pantograph excitation at the current moment and the historical pantograph state response. The historical pantograph state response includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions within a preset time window before the current moment.

[0123] The data acquisition module acts as the interface between the system and the external physical world or data sources. In actual engineering deployments, the data sources for this module are diverse: in vehicle-mounted real-time monitoring scenarios, it can directly interface with inertial measurement units (IMUs), laser displacement sensors, and force sensors installed on key parts such as the pantograph's sliding plate and frame to collect high-frequency vibration signals and contact force data in real time; in ground simulation or digital twin applications, it can also be configured to read recorded data from historical test databases or directly call the simulation output interface of the fully flexible pantograph finite element model to generate virtual samples. The data acquisition module needs to preprocess the raw signals, organizing them into a time-series tensor format that conforms to the input specifications of the prediction model, which includes the current excitation value and 9-dimensional state variables of 46 key nodes in the three orthogonal directions of X, Y, and Z within a preset time window (e.g., 10 time steps).

[0124] The prediction module 820 is used to input the pantograph sequence to be predicted into the prediction model to obtain the pantograph state response at the next moment output by the prediction model. The pantograph state response at the next moment includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions at the next moment. The prediction model is trained using flexible pantograph samples, which are obtained by simulating the finite element model of the fully flexible pantograph.

[0125] The prediction module encapsulates the prediction model trained using any of the above embodiments and is the core computing unit of the system. This module is configured to perform efficient forward inference operations, mapping the multi-dimensional temporal context provided by the data acquisition module to the full-field dynamic state at the next moment. Thanks to its spatiotemporal decoupling architecture and lightweight network design, the prediction module's computation time for a single state deduction is only in the millisecond range, representing an order-of-magnitude improvement compared to the hours-long solution time of traditional fully flexible finite element simulations. This makes real-time prediction of high-frequency dynamic responses possible. Furthermore, the synchronous three-dimensional prediction results of displacement, velocity, and acceleration output by the prediction module can not only be directly used to visualize the transient vibration morphology of the pantograph but also serve as high-confidence input data for downstream application modules (such as pantograph-catenary contact quality assessment, structural fatigue damage accumulation calculation, or active control command generation). In terms of hardware deployment, the prediction module can be integrated into train-mounted edge computing devices to support localized real-time diagnostics, or deployed on high-performance ground workstations or cloud server clusters to support large-scale offline analysis and model iteration updates. This flexible deployment capability enables the system provided in this application to adapt to the application needs throughout the entire lifecycle, from research and development design to operation and maintenance monitoring.

[0126] In one embodiment of this application, the high-speed pantograph high-frequency dynamic response state prediction system further includes a training module, which includes:

[0127] The sample acquisition unit is used to acquire a training sample set, which includes multiple training sample pairs. Each training sample pair includes the historical pantograph state response and pantograph excitation as training samples, and the next pantograph state response as training labels.

[0128] The first training unit is used to freeze the parameters of the predictor in the initial model, and iteratively train the encoder and decoder of the initial model until convergence based on the preset loss function and training sample set to obtain the first model; the initial model includes an encoder, a predictor and a decoder;

[0129] The second training unit is used to freeze the parameters of the encoder and decoder in the first model, and iteratively train the predictor of the first model until convergence based on the joint loss function and the training sample set to obtain the prediction model.

[0130] In one embodiment of this application, the first training unit is further configured to:

[0131] The encoder maps the pantograph state response and pantograph excitation in the training samples to the dynamic latent space to obtain the dynamic latent state sequence.

[0132] The reconstructed pantograph state response is obtained by mapping the dynamic hidden state sequence back to the physical space through a decoder.

[0133] The parameters of the encoder and decoder are updated based on the reconstruction error between the reconstructed pantograph state response and the pantograph state response in the training samples.

[0134] It should be noted that the high-speed pantograph high-frequency dynamic response state prediction system and the high-speed pantograph high-frequency dynamic response state prediction method provided in the above embodiments belong to the same concept. The specific operation methods of each module and unit have been described in detail in the method embodiments and will not be repeated here. In practical applications, the high-speed pantograph high-frequency dynamic response state prediction system provided in the above embodiments can be assigned to different functional modules as needed, that is, the internal structure of the system can be divided into different functional modules to complete all or part of the functions described above. This is not a limitation here.

[0135] Embodiments of this application also provide an electronic device, including: one or more processors; and a storage device for storing one or more programs, which, when executed by one or more processors, enable the electronic device to implement the state prediction method for high-speed pantograph high-frequency dynamic response provided in the above embodiments.

[0136] Another aspect of this application provides a computer-readable storage medium storing a computer program thereon, which, when executed by a computer's processor, causes the computer to perform the high-speed pantograph high-frequency dynamic response state prediction method provided in the various embodiments above. This computer-readable storage medium may be included in the electronic device described in the above embodiments, or it may exist independently and not assembled into the electronic device.

[0137] Another aspect of this application provides a computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the high-speed pantograph high-frequency dynamic response state prediction method provided in the various embodiments above.

[0138] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0139] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for predicting the state of high-frequency dynamic response of a high-speed pantograph, characterized in that, include: Obtain the pantograph sequence to be predicted. The pantograph sequence to be predicted includes the pantograph excitation at the current moment and the historical pantograph state response. The historical pantograph state response includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions within a preset time window before the current moment. The pantograph sequence to be predicted is input into the prediction model to obtain the pantograph state response at the next moment output by the prediction model. The pantograph state response at the next moment includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions at the next moment. The prediction model is trained using flexible pantograph samples, which are obtained by simulating a fully flexible pantograph finite element model. The training process includes training the predictor based on a joint loss function, which includes data-driven prediction loss and physical consistency loss.

2. The method for predicting the state of high-speed pantograph high-frequency dynamic response according to claim 1, characterized in that, The process of determining the prediction model includes: Obtain a training sample set, which includes multiple training sample pairs. Each training sample pair includes the historical pantograph state response and pantograph excitation as training samples, and the pantograph state response at the next moment as training labels. The parameters of the predictor in the initial model are frozen, and the encoder and decoder of the initial model are iteratively trained until convergence based on the preset loss function and the training sample set to obtain the first model; the initial model includes an encoder, a predictor and a decoder; Freeze the parameters of the encoder and decoder in the first model, and iteratively train the predictor of the first model until convergence based on the joint loss function and the training sample set to obtain the prediction model.

3. The method for predicting the state of high-speed pantograph high-frequency dynamic response according to claim 2, characterized in that, The iterative training of the encoder and decoder of the initial model until convergence includes: The encoder maps the pantograph state response and pantograph excitation in the training samples to the dynamic latent space to obtain the dynamic latent state sequence. The decoder maps the dynamic hidden state sequence back to the physical space to obtain the reconstructed pantograph state response; The parameters of the encoder and the decoder are updated based on the reconstruction error between the reconstructed pantograph state response and the pantograph state response in the training samples.

4. The method for predicting the state of high-speed pantograph high-frequency dynamic response according to claim 2, characterized in that, The iterative training of the predictor of the first model until convergence includes: The encoder of the first model maps the pantograph state response and pantograph excitation in the training samples to the dynamic latent space to obtain the dynamic latent state sequence. The predictor predicts the next time-step hidden state based on the sequence of hidden dynamic states. The decoder of the first model maps the hidden dynamic state of the next moment back to the physical space to obtain the predicted pantograph state response. The parameters of the predictor are updated based on the joint loss function.

5. The method for predicting the state of high-speed pantograph high-frequency dynamic response according to claim 4, characterized in that, In the joint loss function: the data-driven prediction loss is constructed based on the deviation between the predicted pantograph state response and the pantograph state response at the next moment in the training labels; the physical consistency loss is constructed based on the kinematic constraint relationship between the pantograph state variables, including displacement, velocity, and acceleration.

6. The method for predicting the state of high-speed pantograph high-frequency dynamic response according to claim 5, characterized in that, The process of constructing the physical consistency loss includes: The velocity estimate is obtained by solving the displacement finite difference between adjacent time points. The mean square error between the velocity estimate and the velocity in the predicted pantograph state response is calculated to construct a velocity constraint term. Acceleration estimates are obtained by solving the velocity finite difference between adjacent time points. The mean square error between the acceleration estimates and the acceleration in the predicted pantograph state response is calculated, and acceleration constraint terms are constructed. The physical consistency loss is obtained by summing the velocity constraint term and the acceleration constraint term.

7. The method for predicting the state of high-speed pantograph high-frequency dynamic response according to claim 1, characterized in that, The update formulas for the weight coefficients of the data-driven prediction loss and the physical consistency loss in the joint loss function include: ； ； in, For the first Training Step 1 The rate of decrease of the loss component, For the first Training Step 1 The value of the loss component, For the first Training Step 1 The value of the loss component, This represents the total number of loss components, which include data-driven prediction loss or physical consistency loss. It is an exponential function. For the first Training Step 1 The weighting coefficients corresponding to the loss components, This represents the weights corresponding to the data-driven prediction loss. This represents the weight corresponding to the physical consistency loss.

8. A state prediction system for high-speed pantograph high-frequency dynamic response, characterized in that, include: The data acquisition module is used to acquire the pantograph sequence to be predicted. The pantograph sequence to be predicted includes the pantograph excitation at the current moment and the historical pantograph state response. The historical pantograph state response includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions within a preset time window before the current moment. The prediction module is used to input the pantograph sequence to be predicted into the prediction model to obtain the pantograph state response at the next moment output by the prediction model. The pantograph state response at the next moment includes the displacement, velocity and acceleration of the pantograph in three orthogonal directions at the next moment. The prediction model is trained using flexible pantograph samples, which are obtained by simulating a fully flexible pantograph finite element model. The training process includes training the predictor based on a joint loss function, which includes data-driven prediction loss and physical consistency loss.

9. The high-speed pantograph high-frequency dynamic response state prediction system according to claim 8, characterized in that, The high-speed pantograph high-frequency dynamic response state prediction system also includes a training module, which includes: The sample acquisition unit is used to acquire a training sample set, which includes multiple training sample pairs. Each training sample pair includes the historical pantograph state response and pantograph excitation as training samples, and the pantograph state response at the next moment as training labels. The first training unit is used to freeze the parameters of the predictor in the initial model, and iteratively train the encoder and decoder of the initial model until convergence based on the preset loss function and the training sample set to obtain the first model; the initial model includes an encoder, a predictor and a decoder; The second training unit is used to freeze the parameters of the encoder and decoder in the first model, and iteratively train the predictor of the first model until convergence based on the joint loss function and the training sample set to obtain the prediction model.

10. The high-speed pantograph high-frequency dynamic response state prediction system according to claim 8, characterized in that, The first training unit is also used for: The encoder maps the pantograph state response and pantograph excitation in the training samples to the dynamic latent space to obtain the dynamic latent state sequence. The decoder maps the dynamic hidden state sequence back to the physical space to obtain the reconstructed pantograph state response; The parameters of the encoder and the decoder are updated based on the reconstruction error between the reconstructed pantograph state response and the pantograph state response in the training samples.

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