A pantograph parameter identification method fusing dispersive physical coding and hypergraph network

Abstract

The present application relates to the technical field of rail transit equipment state monitoring, and discloses a pantograph parameter identification method fusing frequency dispersion physical coding and supergraph network, comprising: obtaining pantograph head acceleration response under the running state of the pantograph; performing front-end coding on the pantograph head acceleration response to obtain potential beam response state and potential propagation trend state; constructing a tension beam physical coding operator according to the modal dispersion relationship of the contact line tension Euler-Bernoulli beam, and performing frequency domain propagation modulation on the potential beam response state and the potential propagation trend state by using the tension beam physical coding operator to obtain structure constraint time sequence characteristics; and obtaining the structure state parameters of the pantograph based on the structure constraint time sequence characteristics. The present application embeds the dispersion propagation physics prior of the contact line tension beam into the feature extraction process in a hard coding manner, and can realize accurate identification of the structure state parameters of the pantograph from the pantograph head acceleration response which is easy to collect.

Description

Technical Field

[0001] This invention relates to the field of rail transit equipment condition monitoring technology, and more specifically, to a pantograph parameter identification method that integrates dispersive physical coding and hypergraph networks. Background Technology

[0002] The pantograph is a key component of high-speed railway trains that harvests electrical energy from the overhead contact line. It can typically be represented as a three-mass spring-damped system consisting of the pantograph head, upper frame, and lower frame. The equivalent mass, equivalent damping, and equivalent stiffness of the pantograph head, upper frame, and lower frame, respectively, directly reflect the inertial characteristics, energy dissipation characteristics, and elastic recovery characteristics of the pantograph structure, and are important physical parameters characterizing its structural condition. During long-term service, factors such as carbon plate wear, degradation of connecting components, material fatigue, and high-frequency alternating load impacts can cause time-varying shifts in these equivalent parameters, leading to decreased current collection performance and increased operational risks. The pantograph head acceleration signal is relatively easy to obtain in actual operation. If the structural state parameters of the pantograph can be obtained by inverting the pantograph head acceleration response, it can provide a direct parameterized basis for pantograph structural condition assessment, degradation fault characterization, and predictive maintenance.

[0003] However, inverting the pantograph's structural state parameters from the bow acceleration response is essentially a complex inverse problem: the pantograph's structural state parameters are physical quantities within the system that cannot be directly measured. Under measurement uncertainties such as speed fluctuations, sensor noise, and line condition disturbances, different parameter combinations may produce similar external acceleration responses, leading to non-unique inversion results that are susceptible to interference. Existing methods struggle to address these issues. Traditional multibody dynamics models are computationally expensive and difficult to deploy online; purely data-driven models easily degenerate into black-box mappings, lacking robustness in velocity extrapolation and noise resistance; Physical Information Neural Networks (PINNs) primarily apply soft constraints at the loss function level, failing to embed the physical propagation of the structure into the feature extraction process; and conventional graph structures rely on paired edges to describe parameter relationships, making it difficult to characterize higher-order couplings between mass, damping, and stiffness. Therefore, it is necessary to investigate an intelligent identification technology capable of robustly and physically consistent inverting the pantograph's structural state parameters from the bow acceleration response under measurement uncertainties.

[0004] Therefore, how to provide a pantograph parameter identification method that integrates dispersive physical coding and hypergraph networks is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention proposes a pantograph parameter identification method that integrates dispersive physical coding and hypergraph network. By using tension beam physical coding and adaptive soft hypergraph, the pantograph structural state parameters are robustly inverted from the pantograph head acceleration.

[0006] This invention proposes a pantograph parameter identification method that integrates dispersive physical coding and hypergraph networks. The method is executed through a pre-trained parameter identification model and includes: Obtain the pantograph head acceleration response when the pantograph is in operation; The bow head acceleration response is front-end encoded to obtain the potential beam response state and potential propagation trend state; Based on the modal dispersion relation of the contact line tension Euler-Bernoulli beam, a tension beam physical coding operator is constructed, and the tension beam physical coding operator is used to perform frequency domain propagation modulation on the potential beam response state as the initial state and the potential propagation trend state as the initial rate of change to obtain the structural constraint time series characteristics. The structural constraint temporal features are mapped to multiple parameter vertex features; The multiple parameter vertex features are input into an adaptive soft hypergraph network, and bidirectional message passing between parameter vertices and soft hyperedges is performed through the adaptive soft hypergraph network to obtain enhanced parameter vertex features. Based on the enhanced parameter vertex features, the structural state parameters of the pantograph are obtained.

[0007] Furthermore, when performing front-end encoding on the bow head acceleration response to obtain the potential beam response state and potential propagation trend state, it includes: The potential beam response state is obtained by encoding the bow head acceleration response through the first mapping branch; The potential propagation trend state is obtained by encoding the bow acceleration response through the second mapping branch; The first mapping branch and the second mapping branch are respectively implemented by a one-dimensional convolutional layer in the parameter recognition model, and the learnable parameters of the first mapping branch and the second mapping branch are not shared. The potential beam response state is used as the initial state of the tension beam frequency domain propagation modulation, and the potential propagation trend state is used as the initial rate of change of the tension beam frequency domain propagation modulation.

[0008] Furthermore, when constructing the physical coding operator for the tension beam based on the modal dispersion relation of the contact line tension Euler-Bernoulli beam, it includes: In the modal dispersion relation of the contact wire tension Euler-Bernoulli beam, the contact wire is equivalent to an Euler-Bernoulli beam subjected to axial tension, and the equivalent propagation frequency corresponding to the time-domain frequency variable is determined based on the bending stiffness, axial tension, mass per unit length, and running speed parameters of the contact wire.

[0009] Furthermore, the equivalent propagation frequency is determined by the following relationship: ; in, For time-domain angular frequency variables, The operating speed parameter, For numerically stable terms, Let be the bending stiffness of the contact wire. The axial tension of the contact wire. The mass per unit length of the contact wire is given.

[0010] Furthermore, when using the tension beam physical coding operator to perform frequency domain propagation modulation on the potential beam response state and the potential propagation trend state, it includes: performing a fast Fourier transform on the potential beam response state and the potential propagation trend state along the time dimension to obtain the corresponding frequency domain representation; Damped oscillation propagation is calculated based on the equivalent propagation frequency, the preset equivalent damping ratio, and the preset virtual propagation depth to obtain the frequency domain characteristics after propagation. Perform an inverse fast Fourier transform on the propagated frequency domain features to obtain the structural constraint time-series features.

[0011] Furthermore, the damped oscillation propagation calculation is determined by the following formula: ; in, This is the current response status. Frequency domain representation after performing a fast Fourier transform along the time dimension; For the trend of propagation and evolution Frequency domain representation after performing a fast Fourier transform along the time dimension; The equivalent propagation frequency, The equivalent damping ratio is given. For virtual communication depth, For the damped propagation frequency, It is a numerically stable term.

[0012] Furthermore, when the multiple parameter vertex features are input into an adaptive soft hypergraph network, and bidirectional message passing between parameter vertices and soft hyperedges is performed through the adaptive soft hypergraph network, the process includes: The adaptive soft hypergraph network generates soft hyperedges and a soft participation matrix based on the features of the multiple parameter vertices. The elements in the soft participation matrix represent the degree to which the parameter vertices participate in the soft hyperedge. The parameter vertex features are aggregated into soft hyperedge features by transposing the soft participation matrix, and then the soft hyperedge features are propagated back to the parameter vertices by the soft participation matrix. The propagation results are then residually connected and normalized with the original parameter vertex features to obtain enhanced parameter vertex features.

[0013] Furthermore, when generating soft hyperedges and soft participation matrices using the adaptive soft hypergraph network based on the multiple parameter vertex features, the process includes: A globally learnable soft hyperedge prototype is set up to provide a basic hyperedge representation. Generate global context features based on the vertex features of the multiple parameters; Based on the global context features, the globally learnable soft hyperedge prototype is adaptively corrected to obtain the sample-adaptive soft hyperedge prototype. The similarity between the parameter vertex features and the sample adaptive soft hyperedge prototype is calculated and normalized to obtain the soft participation matrix, where the elements of the soft participation matrix represent the degree to which the parameter vertex participates in the soft hyperedge.

[0014] Furthermore, bidirectional message passing between parameter vertices and soft hyperedges includes: Based on the soft participation matrix, the parameter vertex features are aggregated into soft hyperedge features; The soft hyperedge features are propagated back to the parameter vertices using the soft participation matrix, and the propagation results are residually connected and normalized with the original parameter vertex features to obtain the enhanced parameter vertex features.

[0015] Furthermore, when the method is executed using a pre-trained parameter recognition model, it includes: The parameter identification model is trained using a joint loss function, which includes data loss and physical loss. The data loss is used to constrain the error between the predicted structural state parameters and the actual structural state parameters, and the physical loss is used to constrain the predicted structural state parameters to satisfy the dynamic equations of the pantograph's three mass blocks. The physical loss is obtained by substituting the predicted structural state parameters into the dynamic equation of the three mass blocks of the pantograph to obtain the dynamic residual, and the physical loss is constructed based on the dynamic residual.

[0016] Compared with existing technologies, the advantages of this invention are as follows: This invention only needs to obtain the acceleration response of the pantograph head under high-speed operation to identify the equivalent mass, equivalent damping, and equivalent stiffness of the pantograph head, upper frame, and lower frame, respectively. The pantograph head acceleration signal is relatively easy to obtain in actual operation, without disassembling the pantograph, without installing additional contact force sensors between the pantograph and the catenary, and without conducting complex off-line control bench tests, thus reducing monitoring costs and implementation difficulty.

[0017] This invention constructs a physical coding operator based on the modal dispersion relation of the Euler-Bernoulli beam for contact wire tension. During the feature extraction stage, a physical modulation determined by bending stiffness, axial tension, mass per unit length, and operating speed is applied to each frequency component of the acceleration signal. This hard-coding method makes the physical prior of the contact wire's structural propagation an indispensable element in the model's forward propagation, thereby physically separating the velocity-related and structural-related components of the acceleration signal at the source. This suppresses the influence of measurement uncertainties such as operating speed fluctuations, sensor noise, and line condition disturbances on the inversion results.

[0018] This invention does not extract a single potential state, but constructs a potential beam response state (initial state term) and a potential propagation trend state (initial trend term) through two independent mapping branches. This is based on the fact that the modal propagation of a contact line tension beam is essentially a second-order dynamic process concerning a virtual propagation depth, and a single initial state cannot uniquely determine the propagation evolution outcome. The two independent states serve the cosine and sine terms in the closed-form solution of the propagation equation, respectively. The former characterizes the current response form, and the latter characterizes the propagation direction and phase evolution trend. Together, they constitute the complete initial conditions for the damped oscillation propagation of the tension beam. This avoids the loss of physical information and pathological inversion problems caused by mixing amplitude and trend information in the same feature, ensuring the physical consistency and interpretability of the parameter inversion from the underlying mathematical structure. Attached Figure Description

[0019] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A flowchart illustrating a pantograph parameter identification method that integrates dispersive physical coding and hypergraph networks, provided in an embodiment of the present invention; Figure 2 This is a comparison diagram of the time and frequency domain of the contact force obtained by back-calculation based on the predicted pantograph dynamic parameters in a pantograph parameter identification method that integrates dispersive physical coding and hypergraph networks, provided in an embodiment of the present invention. Figure 3 This is a comparison of experimental results of the ablation of the tension beam physical coding operator in a pantograph parameter discrimination method that integrates dispersion physical coding and hypergraph networks, provided in an embodiment of the present invention. Figure 4 This is a comparison of experimental results of adaptive soft hypergraph network ablation in a pantograph parameter discrimination method that integrates dispersive physical coding and hypergraph network provided in an embodiment of the present invention; Figure 5This is a comparison of the time and frequency domains of the back-calculated contact force under different noise interference conditions in a pantograph parameter identification method that integrates dispersive physical coding and hypergraph networks, provided in an embodiment of the present invention. Detailed Implementation

[0020] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] See Figure 1 and Figure 2 ,in, Figure 2 This is a comparison of the time and frequency domains of the contact force calculated based on the predicted pantograph dynamic parameters. Figure 2 The left column shows the time-domain response of the contact force under operating conditions of V=200km / h, V=300km / h, and V=450km / h, and the right column shows the corresponding frequency-domain amplitude distribution. In some embodiments of this application, this embodiment provides a pantograph parameter identification method that integrates dispersive physical coding and hypergraph networks, including: S1: Obtain the pantograph head acceleration response when the pantograph is in operation.

[0022] Bow acceleration response Accelerometer readings can be obtained from an acceleration sensor mounted on the pantograph head or a rigidly connected component of the pantograph head, or from image measurement, inertial measurement units, or other measurement methods capable of obtaining the pantograph head acceleration.

[0023] In one implementation, the raw acceleration response can be detrended, normalized, resampled, outlier removed, or windowed to improve model stability and noise resistance. Let the sampling time be... ; in, This represents the nth discrete-time sampling point, where n is the index of the discrete sampling point and is a non-negative integer. This indicates a short sampling time (the time interval between two adjacent sampling points), and each sample has a length of [length missing]. The time series data is required. Additionally, the running speed parameters corresponding to the bow head acceleration response also need to be obtained. This information can be obtained from the train operation control system or speed sensors.

[0024] S2: Perform front-end encoding on the bow head acceleration response to obtain the potential beam response state and potential propagation trend state.

[0025] The purpose of front-end encoding is to map the raw acceleration timing signal into a feature space representation suitable for subsequent physical encoding operator processing. Specifically, this embodiment uses a first mapping branch. Encode the bow head acceleration response to obtain the potential beam response state. Through the second mapping branch Encode the bow head acceleration response to obtain the potential propagation trend state. .

[0026] In one implementation, and Each is implemented by a one-dimensional convolutional layer, and the output can be represented as Where C represents the number of latent feature channels, the two mapping branches are set to be independent and do not share learnable parameters, enabling the network to learn features with two different physical meanings: "current response state" and "propagation trend." From a physical perspective, It characterizes the amplitude, phase, local vibration modes, and time-frequency energy distribution of the acceleration signal related to the contact wire structure response, reflecting the current response state. It characterizes the variation trend, phase drift, and velocity-related modulation information of different frequency components in the dispersion propagation process of tension beam, reflecting the propagation evolution trend.

[0027] The physical basis for setting two independent states instead of a single state is that the modal propagation of a tensioned Euler-Bernoulli beam has second-order dynamic characteristics. Giving only one initial state can only describe the current response pattern and cannot determine the propagation direction, velocity, and phase evolution trend. The two independent states serve as the initial state term and initial trend term in the closed-form solution of the propagation equation, respectively, and together they constitute the complete initial conditions for the propagation of damped oscillations in the tensioned beam.

[0028] S3: Construct a tension beam physical coding operator based on the modal dispersion relation of the contact line tension Euler-Bernoulli beam, and use the tension beam physical coding operator to perform frequency domain propagation modulation on the potential beam response state and potential propagation trend state to obtain the structural constraint time sequence characteristics.

[0029] The contact line can be approximated as an Euler-Bernoulli beam subjected to axial tension, whose lateral displacement... Satisfying the forced vibration equation ; in, Mass per unit length For bending stiffness, For axial tension, For the contact force between the bow and the fire net, For running speed, This represents the second partial derivative of the lateral displacement with respect to time, i.e., the vertical acceleration at each point on the contact line. This is the equivalent structural damping coefficient of the contact wire. This is the first partial derivative of the lateral displacement with respect to time, i.e., the vertical velocity at each point on the contact line. Let be the fourth-order partial derivative of the lateral displacement with respect to space, describing the rate of change of the curvature of the beam's bending deformation. Let be the second-order partial derivative of the lateral displacement with respect to space, describing the bending curvature of the beam.

[0030] This equation contains both fourth-order bending terms and second-order tension terms, exhibiting significant dispersion characteristics. For space wavenumbers... The dispersion relation of the tension beam is: .

[0031] When the pantograph is at speed As the object moves along the contact line, there is an approximate relationship between the space wavenumber and the observation time frequency. ; in For time-domain angular frequency variables, This is a numerically stable term. Therefore, the equivalent propagation frequency in the time-series frequency domain is obtained: ; The equivalent propagation frequency indicates that it is subject to bending stiffness. axial tension Mass per unit length and running speed The concept of joint regulation has a clear physical meaning regarding the bow-catenary structure.

[0032] The specific process of frequency domain propagation modulation using the tension beam physical coding operator is as follows. First, for... and Performing a Fast Fourier Transform along the time dimension yields the corresponding frequency domain representation. Subsequently, virtual propagation depth was introduced. and equivalent damping ratio The propagation equation of the tension beam damping is constructed in the time-series frequency domain. and As virtual communication depth The two initial conditions at the location, namely Solving the second-order propagation equation under underdamped conditions yields a closed-form solution. Finally, an inverse fast Fourier transform is performed on the propagated frequency domain characteristics, with the discrete implementation as follows: , in, This is the current response status. Frequency domain representation after performing a fast Fourier transform along the time dimension; For the trend of propagation and evolution Frequency domain representation after performing a fast Fourier transform along the time dimension; The equivalent propagation frequency, The equivalent damping ratio is given. For virtual communication depth, For the damped propagation frequency, It is a numerically stable term.

[0033] This process is equivalent to applying a physical propagation filter controlled by the tension beam dispersion relation to the acceleration characteristics in the frequency domain. The low-frequency components characterize the overall gradual change trend of the system, while the high-frequency components retain the details of local impacts and structural vibrations.

[0034] S4: Map the structural constraint temporal features into multiple parameter vertex features; S5: Input the multiple parameter vertex features into the adaptive soft hypergraph network, and perform bidirectional message passing between parameter vertices and soft hyperedges through the adaptive soft hypergraph network to obtain enhanced parameter vertex features; S6: Based on the enhanced parameter vertex features, obtain the structural state parameters of the pantograph.

[0035] The structural constraint temporal characteristics obtained after modulation by the tension beam physical coding operator The pantograph's structural state parameter vector is obtained by mapping the parameters to multiple parameter vertex features using a parameter mapping function and then pooling these features. In one implementation, a fully connected layer can be used to... Convert to parametric vertex features ,in For batch size, The number of parameters to be identified The feature dimension. In the three-mass pantograph model, there are a total of 9 structural state parameters to be identified, namely... =9, and then perform global average pooling along the feature channel dimension to obtain the final structure state parameter vector: in, These are the predicted values ​​for the equivalent mass, equivalent damping, and equivalent stiffness corresponding to the bow head, respectively. These are the predicted values ​​for the equivalent mass, equivalent damping, and equivalent stiffness of the upper frame, respectively. These are the predicted values ​​of the equivalent mass, equivalent damping, and equivalent stiffness corresponding to the lower frame. This parameter vector represents the pantograph structural state parameters obtained from the pantograph head acceleration response in this embodiment, and can serve as a parameterized basis for pantograph structural state assessment, degradation fault characterization, and predictive maintenance. Figure 2When the structural parameters predicted by the model are substituted into the pantograph dynamic equation, the back-calculated contact force is highly consistent with the actual contact force, proving that the predicted parameters are not only accurate in numerical terms, but also self-consistent in terms of physical dynamics. This proves that the structural state parameters output by the model are reliable and can make the output (contact force) of the entire pantograph dynamic model match the actual situation.

[0036] Understandably, by using the easily acquired pantograph acceleration response during operation as the sole input, there is no need to disassemble the pantograph or install additional contact force sensors, thus reducing monitoring costs and implementation difficulty, making long-term online structural condition monitoring engineering feasible. Two independent mapping branches without shared parameters are used to construct the potential beam response state and the potential propagation trend state, respectively. This allows the network to learn the characteristics of two different physical meanings: "current response state" and "propagation change trend." Together, these constitute the complete initial conditions for the propagation equation of the tension beam damped oscillation, enabling a unique solution for the second-order propagation system. This avoids the ill-conditioned inversion problem caused by a single initial state and reduces the identification uncertainty caused by missing physical information. A physical encoding operator is constructed based on the dispersion relationship of the Euler-Bernoulli beam of the contact wire tension. Bending stiffness, axial tension, mass per unit length, and running speed are embedded into the frequency domain propagation modulation process with deterministic functional relationships. This allows the equivalent propagation frequency to apply differentiated physical modulation to different frequency components of the acceleration characteristics. This hard-coding method ensures that the physical priors of the contact wire structure propagation cannot be bypassed during network forward propagation. Unlike the PINN approach, which only applies soft constraints at the loss function level, this reduces the model's dependence on massive training samples covering all working conditions and improves robustness under velocity extrapolation and contact wire parameter variations. A second-order damped propagation equation regarding the virtual propagation depth is constructed in the frequency domain and efficiently calculated using a closed-form solution. This ensures that high-frequency components decay faster due to the larger equivalent propagation frequency, while low-frequency components decay slower, consistent with the physical law that high-frequency vibration energy dissipates faster along the propagation direction in the contact wire structure. Simultaneously, cosine and sine terms synergistically control the frequency-related oscillation propagation, ensuring that the output features simultaneously contain the temporal information of the original acceleration and the structural constraint information of the contact wire dispersion propagation, providing higher-fidelity feature inputs for subsequent parameter identification. The final output of nine-dimensional structural state parameters corresponds to the equivalent mass, damping, and stiffness of the pantograph head, upper frame, and lower frame, respectively. These parameters can quantitatively reflect the inertial characteristics, energy dissipation characteristics, and elastic recovery capabilities of each key component of the pantograph, providing a directly interpretable quantitative parameterization basis for structural state assessment, degradation fault characterization, and predictive maintenance.

[0037] In some embodiments of this application, when front-end encoding the bow head acceleration response to obtain the potential beam response state and potential propagation trend state, the following steps are included: The bow head acceleration response is encoded by the first mapping branch to obtain the potential beam response state.

[0038] The purpose of front-end encoding is to map the raw acceleration time-series signal into a feature space representation suitable for subsequent processing by the tension beam physical encoding operator. Since the modal propagation of the contact wire tension beam is essentially about the virtual propagation depth... The second-order dynamic process, its propagation equation Two initial conditions are required to uniquely determine the propagation evolution outcome. Therefore, this embodiment constructs these two initial conditions through two independent mapping branches.

[0039] The potential propagation trend state is obtained by encoding the bow acceleration response through the second mapping branch.

[0040] Specifically, through the first mapping branch response to bow acceleration Encode the potential beam response state. via the second mapping branch Encoding the acceleration response of the same bow head yields the potential propagation trend state. .in, Indicates the potential beam response state. Representing the potential propagation trend state, the first and second mapping branches are implemented by a learnable encoder with a one-dimensional convolutional layer.

[0041] The first and second mapping branches are set up to be independent and do not share learnable parameters. This setup allows the network to learn features with different physical meanings: "current response state" and "propagation trend," preventing them from being forcibly compressed into the same feature representation and losing physical distinguishability. From a physical perspective, the latent beam response state, as the initial state term of the tension beam's frequency domain propagation modulation, characterizes the amplitude, phase, local vibration modes, and time-frequency energy distribution in the acceleration signal related to the contact wire structure response, reflecting "the current state of the response," i.e., the virtual propagation depth. Initial modal response characteristics at time 1 Potential spread trend status As the initial trend term of the frequency domain propagation modulation of the tension beam, it characterizes the changing trends, phase drift, and velocity-related modulation information of different frequency components during the dispersion propagation process of the tension beam, reflecting "how this state will continue to propagate or evolve," that is, the initial rate of change of the potential beam response state along the virtual propagation depth direction. .in, For U to virtual propagation depth The first partial derivative of represents the rate of change of the potential beam response state along the virtual propagation direction. For again The value is taken at the initial value when the virtual propagation depth is zero.

[0042] The potential beam response state is used as the initial state term for the frequency domain propagation modulation of the tension beam, and the potential propagation trend state is used as the initial trend term for the frequency domain propagation modulation of the tension beam.

[0043] The mathematical division of labor between the two is clear in subsequent frequency domain propagation modulation: in the closed-form solution of the propagation equation middle, The main term is cosine, which characterizes the preservation and decay of the initial response amplitude and phase. The main component is the sine term, which characterizes the evolution of the initial propagation trend and the direction of phase change. Here, U represents the frequency domain characteristic after propagation, indicating the result of the potential beam response state after virtual propagation in the frequency domain. The angular frequency variable is obtained by performing a Fast Fourier Transform (FFT) on the time-series characteristics and is an independent variable in the frequency domain. In frequency Location, depth of virtual transmission The frequency domain eigenvalues ​​after that, This is an exponential decay term that controls the energy dissipation of different frequency components along the virtual propagation direction.

[0044] Together, these two states constitute the complete initial conditions for the propagation of tension beam damped oscillations, giving the physical encoding operator mathematical completeness. Using only a single potential state is equivalent to providing only the initial displacement without initial velocity, making it impossible to uniquely determine the subsequent evolution of the second-order system and leading to a more ill-conditioned inversion problem. This embodiment, through the aforementioned dual-state design, ensures the physical consistency and interpretability of the parameter inversion from the underlying mathematical structure.

[0045] Understandably, by constructing the potential beam response state and the potential propagation trend state through two independent mapping branches that do not share parameters, the network can learn features with two different physical meanings: "current response state" and "propagation trend." This avoids forcibly compressing the two into the same feature representation, thus preventing the loss of physical distinguishability and improving the ability of subsequent frequency domain modulation to express the dynamic characteristics of the contact line. These two states serve as two independent initial conditions for the propagation equation of the tension beam damped oscillation. The potential beam response state characterizes the initial modal response at the moment when the virtual propagation depth is zero, while the potential propagation trend state characterizes the initial rate of change of this state along the virtual propagation direction. Together, they constitute the complete initial conditions of the second-order propagation system, enabling the second-order partial differential equation to be uniquely solved. This avoids the ill-conditioned inversion problem caused by a single initial state and reduces the identification uncertainty caused by the lack of physical information. In the closed-form solution of the propagation equation, the potential beam response state mainly enters the cosine term to characterize the preservation and decay of the initial response amplitude and phase, while the potential propagation trend state mainly enters the sine term to characterize the evolution of the initial propagation trend and the direction of phase change. The division of labor between the two in the mathematical structure is clear and complementary, which makes the physical coding operator mathematically complete. It ensures the physical consistency and interpretability of parameter inversion from the bottom up, and reduces the risk of physical inaccuracies in the pure data-driven model under measurement uncertainties such as velocity extrapolation and noise interference.

[0046] In some embodiments of this application, when constructing the physical coding operator for the tension beam based on the modal dispersion relation of the contact line tension Euler-Bernoulli beam, the following steps are included: The contact wire is equivalent to an Euler-Bernoulli beam subjected to axial tension, and the equivalent propagation frequency corresponding to the time-domain frequency variable is determined based on the contact wire's bending stiffness, axial tension, mass per unit length, and running speed parameters.

[0047] In actual operation, the contact wire can be equivalent to an Euler-Bernoulli beam subjected to axial tension, and its lateral displacement... Forced vibration equation: ; in, Mass per unit length of the contact wire This is the equivalent structural damping coefficient. Let T be the bending stiffness and T be the axial tension. For the contact force between the bow and the fire net, The operating speed is given. As can be seen from the above, this equation also contains fourth-order bending terms. and second-order tension term It exhibits obvious dispersion characteristics, with different spatial wavenumbers corresponding to different propagation frequencies.

[0048] To transform the aforementioned modal dispersion relationship into a form that can be embedded in a neural network, orthogonal modal expansion is first employed in the spatial direction. Let the equivalent span of the contact line be L, and sinusoidal modes under simply supported boundary conditions are used as the equivalent basis functions. ,in, Let be the mode shape function of the nth mode, representing the spatial shape distribution of the contact line under the nth natural vibration mode, and be a function of the spatial position x.

[0049] Expand the lateral displacement as ,in, This indicates the lateral displacement (vertical vibration displacement) of the contact wire. Represents spatial coordinates, the position along the longitudinal direction (track direction) of the contact line. Represents the time coordinate. Represents the modal coordinates of the nth mode. The mode shape function representing the nth mode is substituted into the vibration equation, and by utilizing the modal orthogonality, the natural frequency corresponding to the nth mode is obtained: The definitions of the above letters are detailed above and will not be repeated here.

[0050] As can be seen from the above equation, the lower-order modes are mainly affected by the tension term. In terms of control, higher-order modes are more significantly affected by the bending stiffness term. The influence of this means that the tensioned beam structure can simultaneously describe the low-frequency global trend and the high-frequency local vibration details.

[0051] For continuous space wavenumber The dispersion relation of a tension beam can be written as: .

[0052] It should be noted that the definitions of the above letters are detailed above and will not be repeated here.

[0053] When the pantograph is at speed When moving along the contact wire, the acceleration timing response observed at the pantograph can be approximated as a moving sample of the spatial disturbance of the contact wire. Based on this, an approximate relationship can be established between the spatial wavenumber and the observation time frequency. ,in For time-domain angular frequency variables, >0 indicates a numerically stable term.

[0054] This yields the equivalent propagation frequency in the time-series frequency domain: ; in, For time-domain angular frequency variables, For operating speed parameters, For numerically stable terms, For the bending stiffness of the contact wire, The axial tension of the contact wire. This refers to the mass per unit length of the contact wire.

[0055] The construction of this equivalent propagation frequency essentially maps the wave characteristics of the contact line as a continuum to the time-series frequency domain. In the formula, The synergistic effect of the contact line and T reflects the core characteristic that distinguishes the contact line as a beam structure from an ideal chord, and the fourth-order bending term. The high-frequency band gradually becomes dominant, giving high-frequency waves a stronger dispersion effect. Second-order tension term. Dominance in the low-frequency range reflects the string vibration dynamics of the tensioned beam. Both factors together determine the modal propagation framework of the contact wire.

[0056] The speed of movement in the denominator It serves as a bridge connecting spatial structures and temporal observations. The bow-head accelerometer moves along the track, collecting signals that are time-domain samples of the spatially distributed contact wire vibrations. This determines the observation frequency corresponding to the same spatial wavenumber, thus affecting the frequency mapping relationship of frequency domain modulation. This design enables the model to adaptively adjust the frequency domain modulation scale according to the current operating speed, obtaining a physically consistent frequency domain representation at different speeds.

[0057] equivalent propagation frequency This is the core physical quantity of the tension beam physical coding operator. In subsequent frequency domain propagation modulation, this physical quantity replaces the constants or learnable frequency parameters in ordinary networks, applying differentiated modulation to different frequency components of the acceleration characteristics, determined by bending stiffness, axial tension, mass per unit length, and running speed. Specifically, different running speeds at the same time-series frequency will produce different equivalent propagation frequencies, thereby changing the attenuation rate and oscillation phase of that frequency component during propagation. Similarly, changes in the bending stiffness, axial tension, and mass per unit length of the contact wire will also affect the feature propagation behavior. Thus, the tension beam physical coding operator can explicitly embed the physical factors of bow-catenary structure propagation into the feature calculation process of the network.

[0058] The role of the equivalent propagation frequency in the entire method is reflected in: when the input velocity changes, Follow Adaptive adjustment changes the frequency response of subsequent frequency domain modulation, thereby eliminating the influence of velocity differences on the acceleration characteristic distribution. When the physical parameters of the contact wire (bending stiffness, tension, linear density) change, Similarly, this response enables the model to perceive differences in line conditions. By embedding these physical parameters into the network with deterministic relationships, the feature extraction process no longer relies on pure data fitting to implicitly learn these physical laws. Each frequency component in the frequency domain is governed by a deterministic function composed of the pantograph-catenary physical parameters. The modulation of this scheme is the essential difference between this scheme and the PINN-style "soft constraint".

[0059] Understandably, by equating the contact line to an Euler-Bernoulli beam subjected to axial tension and establishing a complete modal dispersion relationship based on its forced vibration equation, the physical encoding operator can simultaneously characterize the synergistic influence of the fourth-order bending term and the second-order tension term on the contact line's wave behavior. The increasing dominance of bending stiffness in the high-frequency band preserves the dispersion effect, while the dominance of the tension term in the low-frequency band reflects the string vibration dynamics. Together, they constitute the complete physical framework of the contact line's modal propagation, improving the fidelity of frequency domain modulation in representing the contact line as a continuous wave characteristic. The derivation of modal natural frequencies using orthogonal modal expansion reveals the dispersion nature of low-order modes being controlled by the tension term and high-order modes by the bending stiffness term. This enables the feature extraction process to adaptively distinguish between global trends and local vibration details based on frequency, improving the model's ability to differentiate the contact line's response characteristics across different frequency bands. By establishing an explicit relationship between spatial wavenumber and observation time frequency through the moving observation approximation, the operating speed is incorporated into the frequency mapping process as a bridge connecting the spatial structure and time observation. The model can adaptively adjust the frequency domain modulation scale according to the current speed, obtaining a physically consistent frequency domain representation under different operating conditions and reducing the interference of speed differences on feature distribution. This equivalent propagation frequency, as a function determined by the pantograph-catenary physical parameters, replaces the constant or learnable frequency parameters that need to be obtained through data fitting in ordinary networks. Changes in bending stiffness, axial tension, mass per unit length, and operating speed all directly affect the frequency response of frequency domain modulation through this function. This makes the feature extraction process explicitly rather than implicitly include the physical factors of pantograph-catenary structure propagation, reducing the model's dependence on massive training samples covering all operating conditions and improving physical consistency and generalization ability under scenarios such as changes in contact wire parameters and speed extrapolation.

[0060] Meanwhile, by simultaneously incorporating bending stiffness into the dispersion relation... The fourth-order term and axial tension The second-order term ensures that the equivalent propagation frequency accurately reflects the core physical characteristic of the contact wire as a tensioned beam, distinguishing it from an ideal string. In the low-frequency range, the tension term dominates, reflecting the string vibration dynamics, while in the high-frequency range, the bending stiffness term dominates, reflecting the dispersion effect. Together, they constitute the complete physical framework of the contact wire modal propagation, avoiding the problem of insufficient characterization of high-frequency dispersion characteristics using a single wave equation or pure data fitting. Operating speed parameters. As a bridge connecting spatial structure and temporal observation, it is explicitly incorporated into the frequency mapping relationship, enabling the model to adaptively adjust the frequency domain modulation scale according to the current speed. This achieves physically consistent frequency domain representation under different operating speeds, eliminating the interference of speed differences on acceleration feature distribution and reducing feature distribution shifts caused by speed changes. Physical parameters such as contact wire bending stiffness, axial tension, mass per unit length, and operating speed are embedded into the feature extraction process with deterministic functional relationships, ensuring that each frequency component in the frequency domain is subject to a deterministic function composed of pantograph-catenary physical parameters. Unlike the PINN approach, which only applies soft constraints to physical residuals at the loss function level, this scheme uses hard coding to embed physical priors into the forward propagation process of the network without bypassing them. This makes feature extraction no longer dependent on pure data fitting to implicitly learn these physical laws. This essential difference reduces the model's dependence on massive training samples covering all working conditions, enhances its adaptability to scenarios with different line conditions such as changes in contact wire parameters, and improves the model's robustness and generalization ability under speed extrapolation and parameter drift conditions.

[0061] In some embodiments of this application, when using the tension beam physical coding operator to perform frequency domain propagation modulation on the potential beam response state and the potential propagation trend state, the method includes: performing a fast Fourier transform on the potential beam response state and the potential propagation trend state along the time dimension to obtain the corresponding frequency domain representation.

[0062] First, the potential beam response state obtained in the aforementioned steps... and potential spread trend status Performing a Fast Fourier Transform (FFT) along the time dimension transforms it from the time domain to the frequency domain, yielding the corresponding frequency domain representation. ,in, For a one-dimensional Fast Fourier Transform operator with time dimension delay, for The frequency domain representation obtained after Fourier transform, for The frequency domain representation obtained after Fourier transform.

[0063] Fourier transform is a fundamental transformation technique in signal processing. For discrete-time signals, the Fast Fourier Transform (FFT) algorithm can be used for efficient computation. The purpose of transforming the features from the time domain to the frequency domain is that the dispersion relation of the contact wire tension beam is naturally defined in the frequency-wavenumber domain. Different frequency components have different propagation speeds and attenuation characteristics. Only in the frequency domain can physical modulation be applied independently to each frequency component, which is the basis for subsequent calculations of damped oscillation propagation.

[0064] Damped oscillation propagation is calculated based on equivalent propagation frequency, equivalent damping ratio, and virtual propagation depth to obtain the frequency domain characteristics after propagation.

[0065] Subsequently, based on the equivalent propagation frequency Equivalent damping ratio and virtual communication depth Damped oscillation propagation calculations were performed to obtain the frequency domain characteristics after propagation. The theoretical basis for this calculation stems from the dynamic equations of a second-order damped vibration system. Specifically, a virtual propagation depth was introduced. As independent variables, construct about The second-order propagation equation of damping in a tensioned beam: ,in, Indicates frequency Virtual communication depth The frequency domain characteristics at that point, and the definitions of the remaining letters mentioned above, are detailed above and will not be repeated here. This equation is formally consistent with the governing equations of a classical second-order vibration system. Its physical meaning is that when the characteristic component propagates along the virtual propagation direction, both amplitude attenuation (damping term) and phase evolution (stiffness term) occur. and As virtual communication depth The initial condition at =0, i.e. , Solving this second-order propagation equation requires exactly two initial conditions to uniquely determine the solution, which is precisely what was achieved by setting up two independent mapping branches in the aforementioned steps. and The fundamental reason. Under underdamped conditions, the solution to the equation is: ,in, For the damped propagation frequency, For the numerically stable term, the definitions of the other letters mentioned above are detailed in the foregoing and will not be repeated here. As can be seen from this solution, the exponential term... Controlling frequency-dependent amplitude attenuation, high-frequency components due to Larger frequencies decay faster, while lower frequencies decay more slowly, which aligns with the physical law that high-frequency vibration energy dissipates faster along the propagation direction in contact wire structures. Cosine and sine terms jointly control the propagation of frequency-dependent oscillations, causing different frequency components to undergo frequency-dependent phase evolution during propagation. Discretization calculations are performed based on the above closed-form solution. Let... For discrete frequency sampling points, for each frequency point Calculate the corresponding Substituting into the closed-form solution above, we obtain the frequency domain characteristics at the corresponding frequency points after propagation. In practical implementation, a small constant is added to the division operation to ensure numerical stability. and to The range of values ​​is constrained to ensure that it is in an underdamped state.

[0066] Perform an inverse fast Fourier transform on the propagated frequency domain features to obtain the structurally constrained temporal features.

[0067] Finally, the frequency domain characteristics after propagation Performing an inverse fast Fourier transform (IFFT) along the time dimension yields the structurally constrained temporal features: Its discrete implementation is as follows: ,in, For element-wise multiplication, the definitions of the remaining letters mentioned above are detailed above and will not be repeated here. It should be noted that the virtual propagation depth... The physical meaning of this parameter lies in providing an equivalent propagation scale. It does not correspond to a specific spatial location on the contact line, but rather is an artificial parameter in the network used to control the degree of modulation of features during propagation. Physically, it can be understood as the equivalent normalized distance of feature propagation along the contact line under the influence of the beam structure's dispersion relation. In actual training, It can be used as a fixed hyperparameter or a learnable parameter in end-to-end optimization, and the network automatically adjusts itself during training. The value is used to match the dynamic characteristics of different pantograph-catenary systems.

[0068] The above frequency domain propagation modulation process is equivalent to applying a physical propagation filter controlled by a tensioned Euler-Bernoulli beam dispersion relation to the acceleration characteristics in the frequency domain. The final output... This refers to the temporal characteristics of the contact line structure propagation physical constraints, which can be directly used for subsequent structural state parameter identification.

[0069] The formula contains three core modulation terms, each with a clear physical meaning and mathematical function. The exponential decay term... Controlling the energy dissipation of different frequency components along the virtual propagation direction, the high-frequency components due to Larger frequencies decay faster, while lower frequencies decay more slowly. This is consistent with the physical law that high-frequency vibration energy decays faster along the propagation direction in contact wire structures. Cosine propagation term Make the initial state term Each frequency component and its relation to The associated frequency oscillation propagation characterizes the maintenance and oscillation of the initial response amplitude and phase during propagation. Sine propagation term. Initial trend item Coupling with damping term After merging, the propagation is carried out through a sine term, which characterizes the evolution of the initial propagation trend and the direction of phase change.

[0070] It should be particularly pointed out that, and The mathematical roles in this formula are different. Mainly entering the cosine term, The main input is the sine term, and the two together determine the post-propagation characteristics. The form of this mathematical division corresponds to the physical basis for setting up two independent mapping branches as mentioned above: if there is only one initial state, the above second-order propagation equation cannot be uniquely solved, and the inversion problem will become ill-conditioned.

[0071] The above calculation essentially applies a physical propagation filter controlled by the contact wire tension beam dispersion relationship to different frequency components of the feature in the frequency domain. The frequency response is jointly determined by the contact wire's bending stiffness, axial tension, mass per unit length, and operating speed. This process differs from purely data-driven methods that use fixed convolution kernels or learnable filters; the core difference lies in: It is a frequency response function deterministically determined by the physical parameters of the bow-catenary system, rather than learned by the network. During training, the network does not learn the frequency response characteristics of this filter, but rather learns how to use this physical filter to extract structural constraint features for subsequent parameter identification. Through this hard-coding method, the physical prior of the contact wire's structural propagation is inescapably embedded in the feature extraction process, making the final obtained... It also includes the temporal information of the original acceleration and the structural constraint information of the contact line dispersion propagation, i.e., see [reference]. Figure 3 After adding a CNN encoder, the model can extract local temporal features, but there are still deviations in characterizing the local fluctuations of contact force and the main peak in the frequency domain. Further adding ordinary damped wave propagation results in a contact force curve that is closer to the true value than that of the CNN encoder, indicating that propagation modeling helps enhance the expression of dynamic response features. However, since ordinary damped wave propagation does not explicitly consider the bending stiffness, axial tension, and velocity modulation in the tension beam, it still has certain errors in amplitude response and frequency domain details. In contrast, adding TBPE (Thickened Wire Protector) shows better consistency between the inverse contact force and the true contact force in terms of time-domain waveform, peak position, and the amplitude of the main peak in the frequency domain. Comparative experiments demonstrate the necessity of embedding physical parameters such as contact wire bending stiffness, axial tension, and running speed into the feature extraction process using a "hard-coded" method, verifying the advantages of this invention in terms of physical consistency and identification accuracy.

[0072] Understandably, by transforming the latent features from the time domain to the frequency domain using the Fast Fourier Transform, subsequent physical modulation can act independently on each frequency component in the frequency-wavenumber domain, where the dispersion relation is naturally defined, laying the foundation for differentiated physical modulation. A second-order tensioned beam damped propagation equation for the virtual propagation depth is constructed in the frequency domain, and a closed-form solution is performed using two independent initial conditions: the latent beam response state and the latent propagation trend state. This uniquely determines the evolution process of the second-order system, avoiding ill-conditioned inversion problems caused by a single initial state. The exponential term of this propagation equation causes high-frequency components to decay faster along the virtual propagation direction due to their larger equivalent propagation frequency, while low-frequency components decay more slowly. This is strictly consistent with the physical law that high-frequency vibration energy dissipates faster in contact wire structures, improving the fidelity of the feature representation of the contact wire's dispersion propagation characteristics. The cosine and sine terms synergistically control the frequency-related oscillation propagation, causing different frequency components to undergo frequency-related phase evolution during propagation, thus preserving the complete wave behavior of the contact wire as a dispersion waveguide at the feature level. The essence of this physical propagation filter, which differs from purely data-driven methods, lies in the fact that the equivalent propagation frequency is a deterministic function of physical parameters such as contact wire bending stiffness, axial tension, mass per unit length, and operating speed, rather than something learned through network training. The network only learns how to use this physical filter to extract the most effective structural constraint features. Physical priors are embedded in the feature extraction process through hard-coded methods that cannot be bypassed in forward propagation. The virtual propagation depth participates in end-to-end optimization as a learnable parameter, enabling the model to adaptively adjust the propagation scale to match the dynamic characteristics of different pantograph-catenary systems, thus enhancing the model's adaptability to changes in operating conditions. The final output structural constraint temporal features simultaneously contain the temporal information of the original acceleration and the physical constraint information of contact wire dispersion propagation, providing more physically consistent and better adaptable feature inputs for subsequent structural state parameter identification. This reduces the risk of feature distortion in pure data-driven methods under velocity extrapolation and noise interference scenarios.

[0073] In some embodiments of this application, see Figure 3 As shown, where, Figure 3 This is a comparison of the time and frequency domains of the back-calculated contact force from different modules in the TBPE ablation experiment. The left side shows the time-domain response of the contact force, and the right side shows the corresponding frequency domain amplitude distribution: different curves represent the actual contact force, the back-calculated results after adding a CNN encoder, adding ordinary damped wave propagation, and adding TBPE, respectively, and the damped oscillation propagation is calculated.

[0074] In some embodiments of this application, obtaining the structural state parameters of the pantograph includes: mapping the structural constraint temporal features to multiple parameter vertex features.

[0075] First, the structural constraint time-series features obtained after modulation by the tension beam physical coding operator are... Through the parameter vertex mapping function Mapped to multiple parameter vertex features Where B is the batch size, P is the number of parameters to be identified, and C is the feature dimension of each parameter vertex. In the three-mass pantograph model, there are a total of 9 structural state parameters to be identified, namely the equivalent mass, equivalent damping, and equivalent stiffness corresponding to the pantograph head, upper frame, and lower frame, respectively, so P=9. Each parameter vertex feature Each parameter corresponds one-to-one with a specific structural state parameter. The purpose of this mapping is to decouple the temporal features with physical constraints of contact line structure propagation into independent feature representations corresponding to each physical parameter, providing a foundation for subsequent modeling of higher-order relationships between parameters.

[0076] Multiple parameter vertex features are input into an adaptive soft hypergraph network. The network dynamically generates soft hyperedges and soft participation matrices and performs bidirectional message passing between parameter vertices and soft hyperedges to obtain enhanced parameter vertex features.

[0077] Subsequently, the vertex features of multiple parameters are input into an adaptive soft hypergraph network. The design of this network stems from the physical understanding that the mass, damping, and stiffness parameters of the pantograph are not independent but rather jointly determine the dynamic response of the pantograph-catenary system through inertial effects, elastic coupling, and damping dissipation. For example, the position of the resonance peak is determined by the ratio of mass *m* to stiffness *k*, and the attenuation characteristics are determined by the ratio of damping *c* to *k*. The ratios of these parameters collectively determine the response of a single parameter, which is transmitted to the responses of other parameters through the dynamic equations. Modeling each parameter independently or using paired edges in a typical graph neural network to describe the relationships is insufficient to characterize the high-order couplings formed by the simultaneous interaction of three or more parameters. Hypergraphs, capable of connecting multiple vertices simultaneously through a single hyperedge, are naturally well-suited for describing such multi-parameter collaborative relationships.

[0078] For the b-th sample, its vertex features are... As the set of vertices of a hypergraph, the core logic of the adaptive soft hypergraph network for dynamically generating soft hyperedges and soft participation matrices is as follows: First, a globally learnable soft hyperedge prototype is set. ,in The preset number of soft hyperedges is used. Average pooling and max pooling are performed on the parameter vertex features to obtain global context features. , where b represents the sample index. This indicates that the average value of the vertex feature matrix along the vertex dimension is taken. This represents taking the maximum value along the vertex dimension of the parameter vertex feature matrix. This is achieved through a context-aware mapping function. Generate soft hyperedge prototype correction amount Where p represents the number of parameter vertices, C represents the feature dimension of each parameter vertex, and M represents the preset number of supersoft edges. This represents the correction amount for the ultra-soft edge prototype, resulting in a sample-adaptive ultra-soft edge prototype. , This represents a globally learnable ultrasoft edge prototype. The physical motivation for this design is that the dominant coupling relationship between mass, damping, and stiffness changes under different operating conditions. Stiffness coupling is more significant at high speeds, while the impact of damping dissipation may be more pronounced under specific frequency excitations. Therefore, the higher-order relationship mode represented by the hyperedge should be dynamically adjusted with the input response, rather than remaining fixed. After obtaining the sample adaptive soft hyperedge prototype, the soft participation matrix between the parameter vertices and the soft hyperedge is calculated. Linear preprojection is then performed on the parameter vertex features. , This represents a learnable linear projection matrix. Let H represent the pre-projected parametric vertex features. The parametric vertex features and the soft hyperedge prototypes are divided into H feature heads for multi-head attention computation. The similarity matrix of the h-th feature head is... ,in, This represents the parameter vertex feature in the h-th head. This represents the dimension of each feature head. This represents the adaptive soft hyperedge prototype of the sample in the h-th head. This represents the similarity matrix of the h-th head. The fusion association score matrix is ​​obtained by averaging the results of each head. Subsequently, each soft hyperedge is Softmax normalized across all parameter vertex dimensions to obtain the soft participation matrix. Its elements Indicates the first The parameter vertex participates in the first The degree of soft edge extension: Compared with traditional super Figure 2 Unlike the value-based correlation matrix, this soft-participation matrix describes the correlation strength between parameters and higher-order relational patterns with continuous weights, enabling the model to adaptively adjust the coupling strength between parameters based on the input response. This Softmax normalization is performed along the parameter vertex dimension, ensuring that each soft hyperedge aggregates information from all parameters. The contribution of different parameters to the same higher-order relational pattern is determined by... It is determined dynamically.

[0079] After obtaining the soft participation matrix, bidirectional message passing between parameter vertices and soft hyperedges is performed. First, parameter vertices are aggregated into soft hyperedge features through the transpose of the soft participation matrix, converging information from each parameter at the hyperedge level, enabling each hyperedge to capture high-order cooperative patterns among multiple parameters. Subsequently, the soft hyperedge features are sequentially processed through the hyperedge feature transformation matrix and nonlinear activation, then propagated back to the parameter vertices through the soft participation matrix. After passing through the parameter vertex feature transformation matrix and nonlinear activation, updated parameter vertex features are obtained. Finally, the propagation result is residually connected to the original parameter vertex features and layer normalized to obtain enhanced parameter vertex features. The residual connection preserves the original parameter vertex features, preventing information loss due to excessive network depth. Layer normalization stabilizes the training process. The physical meaning of this bidirectional propagation is that the hyperedge integrates high-order information from multiple parameters and propagates it back to each parameter vertex, allowing the representation of each parameter to obtain globally coupled information from other related parameters, such as bow mass. When updating, the features not only contain their own information, but also receive information from the stiffness of the same hyperedge. Damping Across mass blocks The higher-order information after the parameters are integrated by the hyperedge.

[0080] Based on the enhanced parameter vertex features, the structural state parameter vector of the pantograph is obtained.

[0081] Based on the enhanced parameter vertex features, global average pooling is performed on each parameter vertex along the feature channel dimension to obtain the final structure state parameter vector: This parameter vector is the pantograph structural state parameter obtained from the pantograph head acceleration response in this embodiment, and can be used as a parameterized basis for pantograph structural state assessment, degradation fault characterization and predictive maintenance.

[0082] Understandably, decoupling the temporal features with physical constraints propagating from the contact line structure into independent feature representations corresponding one-to-one with each physical parameter through a parameter vertex mapping function allows subsequent modeling to be refined using parameters as basic units, improving the fidelity of features to parameter semantics and reducing identification interference caused by aliasing between features of different parameters. Utilizing an adaptive soft hypergraph network to model higher-order relationships between parameter vertices overcomes the limitation of ordinary graph neural networks, which can only characterize pairwise relationships. This allows for the full expression of multi-parameter cooperative coupling modes between mass, damping, and stiffness. For example, resonance peaks are jointly determined by the ratio of mass to stiffness, and attenuation characteristics are jointly determined by the ratio of damping to the square root of the mass-stiffness product. Connecting multiple parameter vertices simultaneously through a hyperedge gives the model a natural ability to capture such higher-order physical cooperative relationships. The sample-adaptive soft hyperedge generation mechanism allows the higher-order relationship modes represented by the hyperedge to be dynamically adjusted according to the current operating conditions, avoiding the mismatch problem of relationship expression under different speed or track conditions with a fixed hypergraph structure, thus improving the model's adaptability and generalization ability. The soft participation matrix replaces traditional binary hard connections with continuously differentiable weights, allowing the correlation strength between parameters and higher-order relational patterns to be finely adjusted with the input response, enhancing the flexibility and accuracy of coupling relationship modeling. A bidirectional message passing mechanism, through information exchange in both aggregation and propagation directions, ensures that each hyperedge integrates higher-order collaborative information from multiple parameters and feeds it back to each parameter vertex, guaranteeing that each parameter's representation receives global coupling information from other related parameters. This avoids information loss issues in independent modeling and reduces the risk of error accumulation in the coupled system. Residual connections preserve the original parameter characteristics, and layer normalization stabilizes the feature distribution, jointly ensuring smooth information flow and convergence stability during deep network training. The final output of nine-dimensional structural state parameters directly corresponds to the physical quantities of each component of the pantograph in three directions, providing directly interpretable quantitative evidence for structural state assessment, degradation fault characterization, and predictive maintenance.

[0083] In some embodiments of this application, the dynamic generation of soft hyperedges and soft participation matrices via an adaptive soft hypergraph network includes: Global context features are generated based on vertex features with multiple parameters.

[0084] Multiple parameter vertex features are ,in P represents the number of parameter vertices (P=9 in this example), and C represents the feature dimension. To capture the overall parameter distribution characteristics of the current sample, the parameter vertex features are first subjected to average pooling and max pooling, and then concatenated along the feature dimension to obtain the global context features. ,in, Indicates average pooling. This indicates max pooling. Average pooling reflects the overall average level of parameter features, while max pooling captures the most significant feature responses. Combining the two can more comprehensively characterize the parameter distribution of the current sample.

[0085] Based on global context features, the globally learnable soft hyperedge prototype is adaptively corrected using samples to obtain the sample-adaptive soft hyperedge prototype.

[0086] Subsequently, the globally learnable soft hyperedge prototype is adaptively corrected based on this global contextual feature. (Globally Learnable Soft Hyperedge Prototype) It is a basic hyperedge representation learned through a data-driven approach during training, independent of specific samples, and its dimension includes... The preset number of soft hyperedges represents the number of pre-defined high-order parameter relationship patterns in the model. A context-aware mapping function maps global context features to soft hyperedge prototype correction values, resulting in a sample-adaptive soft hyperedge prototype. This adaptive correction mechanism allows the soft hyperedge prototype to dynamically adjust based on the current sample's pantograph-catenary dynamic response characteristics. The underlying motivation is that the dominant coupling relationships between mass, damping, and stiffness change under different operating conditions. For example, stiffness coupling is more significant at high speeds, while the impact of damping dissipation may be more pronounced under specific frequency excitation. Therefore, the high-order relationship patterns represented by the hyperedges should be dynamically adjusted with the input response, rather than remaining fixed.

[0087] The similarity between the parameter vertex features and the sample adaptive soft hyperedge prototype is calculated and normalized to obtain the soft participation matrix.

[0088] After obtaining the sample adaptive soft hyperedge prototype, the similarity between the parametric vertex features and the soft hyperedge prototype is calculated. First, a linear preprojection is performed on the parametric vertex features. Then, a multi-head mechanism is used to calculate the similarity: the parametric vertex features and the soft hyperedge prototype are divided into H feature heads, and the scaled dot product similarity is calculated in the h-th feature head. The fusion correlation score matrix is ​​obtained by averaging the results of each feature head. ,in, Let represent the similarity matrix between the b-th sample and the h-th attention head. Let represent the vertex feature of the b-th sample and the h-th head weight. This represents the adaptive soft hyperedge prototype for the b-th sample and the h-th head weight. Indicates the scaling factor. This represents the fusion association score matrix of the b-th sample. This represents the element-wise summation of the similarity matrices of H heads. The multi-head mechanism enables the model to capture different association patterns between parameters and hyperedges from multiple subspaces, enhancing the expressive power of relation modeling.

[0089] The elements in the soft participation matrix represent the degree to which the parameter vertex participates in the soft hyperedge.

[0090] Finally, the association score matrix is ​​normalized to obtain the soft participation matrix. Unlike the conventional Softmax normalization along the hyperedge dimension, this embodiment performs Softmax normalization on each soft hyperedge across all parameter vertex dimensions, thereby obtaining the soft participation matrix, whose elements... This represents the degree to which the i-th parameter vertex participates in the m-th soft hyperedge, satisfying a value of 1 for each soft hyperedge. The physical meaning of this normalization direction is that each soft hyperedge represents a potential high-order parameter relationship pattern. By normalizing all parameter vertices, each hyperedge can adaptively aggregate information from all parameters; a higher value indicates a greater contribution of that parameter to this relationship pattern. Compared to traditional hyperedges… Figure 2 Unlike the value correlation matrix (which has only 0 or 1 elements), this soft participation matrix describes the correlation strength between parameters and higher-order relational patterns with continuous weights, enabling the model to adaptively adjust the coupling strength between parameters according to the input response, and more finely characterize the nonlinear coupling relationship between pantograph mass, damping and stiffness.

[0091] Understandably, generating global context features by combining average pooling and max pooling preserves the overall average level of parameter vertex features while capturing the most significant feature responses. This makes the global information upon which subsequent hyperedge adaptive correction is based more comprehensive, reducing correction biases that may result from insufficient representation of parameter distribution states. Based on these global context features, the globally learnable soft hyperedge prototype is subjected to sample adaptive correction. This allows the soft hyperedge prototype to introduce personalized offsets based on the current sample's dynamic bow-net response, building upon a globally stable base. This "global base plus individual offset" design makes the representation of high-order relational patterns both universal and adaptive, avoiding the problem that fixed hypergraph structures cannot adapt to dynamic changes in parameter coupling relationships under different operating conditions. It also reduces the risk of overfitting due to complete reliance on sample adaptation. Employing a multi-head mechanism to calculate the similarity between parameter vertex features and the soft hyperedge prototype enables the model to capture different association patterns between parameters and hyperedges from multiple subspaces, enhancing the expressive power of relational modeling and reducing the risk of a single head missing key coupling information. For each soft hyperedge, Softmax normalization is performed along the parameter vertex dimension. This allows each hyperedge to adaptively aggregate information from all parameter vertices. A higher value indicates a greater contribution of that parameter to the relational pattern. This normalization direction is fundamentally different from traditional normalization along the hyperedge dimension: normalization along the hyperedge dimension leads to competition among hyperedges for the same parameter, while normalization along the vertex dimension leads to competition among parameters for the same hyperedge. The latter is more in line with the physical intuition that "each hyperedge selects its most relevant subset of parameters." Compared to traditional hyperedge normalization... Figure 2Compared with the correlation matrix, this scheme uses continuously differentiable soft weights to describe the correlation strength between parameters and higher-order relational patterns, enabling the model to finely adjust the coupling strength between parameters according to the input response. This improves the accuracy and flexibility of modeling the nonlinear coupling relationship between pantograph mass, damping, and stiffness, and reduces the inaccuracy of relational expression caused by hard connections or fixed weights.

[0092] In some embodiments of this application, see Figure 4 As shown, where, Figure 4 To illustrate the experimental results of adaptive soft hypergraph neural network ablation based on parameter relationships, the bidirectional message passing between parameter vertices and soft hyperedges includes: The parameter vertex features are aggregated into soft hyperedge features by transposing the soft participation matrix. The soft hyperedge features are then propagated back to the parameter vertices using the soft participation matrix. The propagation results are then residually connected and normalized with the original parameter vertex features to obtain enhanced parameter vertex features.

[0093] After obtaining the soft participation matrix, bidirectional message passing between parameter vertices and soft hyperedges is performed. The core design logic of this process is as follows: first, information from each parameter vertex is aggregated to the hyperedge level through "aggregation," enabling each hyperedge to integrate high-order cooperative patterns among multiple parameters. Then, the high-order coupling information integrated by the hyperedges is propagated back to each parameter vertex through "propagation," ensuring that the representation of each parameter receives global information from other related parameters. This bidirectional mechanism of "aggregation first, then propagation" achieves full information interaction between parameter vertices and hyperedges. Specifically, the parameter vertex features are first aggregated into soft hyperedge features through the transpose of the soft participation matrix: The m-th soft hyperedge feature is the feature obtained by aggregating all parameter vertices, specifically the result of a weighted sum of the features of each parameter vertex according to its participation weight. Since each soft hyperedge may connect multiple parameter vertices simultaneously, this aggregation process allows the hyperedge to naturally capture higher-order collaborative relationships between multiple parameters, rather than being limited to pairwise interactions. Subsequently, the aggregated soft hyperedge features are sequentially passed through the hyperedge feature transformation matrix and a nonlinear activation function, and then propagated back to the parameter vertices through the soft participation matrix. The updated parameter vertex features are then obtained through the parameter vertex feature transformation matrix and a nonlinear activation function. During the backpropagation process, the information received by the i-th parameter vertex is the result of a weighted sum of all soft hyperedge features according to their participation weights, that is, a summary of the higher-order relational pattern information associated with that parameter vertex.

[0094] Finally, the propagation results are combined with the original parameter vertex features through residual connections and layer normalization to obtain enhanced parameter vertex features. Residual connections preserve the original parameter vertex features, avoiding the loss of original feature information due to multi-layer message passing and mitigating the gradient vanishing problem in deep network training. Layer normalization normalizes the features after residual connections, stabilizing the training process. Each parameter vertex feature in the enhanced parameter vertex features has incorporated higher-order coupling information from other parameters propagated through hyperedges, and can be directly used for subsequent structural state parameter prediction. To verify the role of ASHG in pantograph dynamic parameter identification, this paper conducts ablation experiments on its key components, with results as follows: Figure 4 As shown in the figure, the experiment removed the complete adaptive soft hypergraph module, the adaptive soft hyperedge generation mechanism, the sparse soft hyperedge selection mechanism, and the load balancing regularization term, and used average RMSE and average As an evaluation metric, the complete ASHG achieved the best results, with an average RMSE of 0.0075. The average RMSE was 0.9991. Removing the complete ASHG resulted in the most significant performance degradation, with the average RMSE increasing to 0.0228. The RSE decreased to 0.9846, indicating a significant high-order coupling relationship between the pantograph's mass, damping, and stiffness parameters, making accurate identification difficult to achieve solely based on time-series features. Furthermore, after removing the adaptive soft hyperedge generation mechanism, the model's average RMSE was 0.0185. The average RMSE is 0.9862, indicating that the fixed hypergraph structure is difficult to adapt to changes in parameter relationships under different operating conditions. After removing the sparse soft hyperedge selection mechanism, the average RMSE is 0.0169. The average RMSE is 0.9874, indicating that redundant soft hyperedges introduce invalid relationship propagation, weakening the expressive power of key parameter coupling features. After removing the load balancing regularization term, the average RMSE is 0.0157. The value of 0.9885 indicates that the load balancing constraint helps to avoid the overactivation of a few soft hyperedges and improves the diversity of the expression of parameter relationships of different soft hyperedges. This indicates that there is a significant high-order coupling relationship between the pantograph mass, damping and stiffness parameters, which is difficult to fully identify by relying solely on time-series characteristics.

[0095] Understandably, by transposing the soft participation matrix, parameter vertex features are aggregated into soft hyperedge features. This allows each soft hyperedge to simultaneously integrate high-order collaborative information from multiple parameter vertices, overcoming the limitation of ordinary graph neural networks that can only model pairwise relationships. This enhances the model's ability to express complex coupling relationships between mass, damping, and stiffness, and reduces inversion bias caused by ignoring the simultaneous interaction of multiple parameters. The transformed soft hyperedge features are then propagated back to each parameter vertex via the soft participation matrix, ensuring that the representation of each parameter incorporates global coupling information from other related parameters within the same hyperedge. This avoids the problem of information silos when each parameter is modeled independently, significantly enhancing the semantic integrity of parameter features in the coupled system. The division of labor between the hyperedge feature transformation matrix and the parameter vertex feature transformation matrix allows information to undergo appropriate transformations at both the hyperedge and vertex levels, improving the efficiency and fidelity of message passing. Residual connections preserve the original parameter vertex features, avoiding the loss of original feature information caused by multi-layer message passing, while also mitigating the gradient vanishing problem during training, thus improving the stability and convergence efficiency of deep network training. Layer normalization further stabilizes the feature distribution and reduces training fluctuations. In the final enhanced parameter vertex features, each parameter vertex incorporates high-order coupling information, making the prediction of subsequent structural state parameters more accurate and robust. This reduces the risk of misjudgment due to insufficient characterization of coupling relationships between parameters and improves the reliability and physical consistency of the pantograph structural state parameter identification results.

[0096] In some embodiments of this application, see Figure 5 As shown, where, Figure 5 This is a comparison of the time-domain and frequency-domain contact force calculated based on the predicted pantograph dynamic parameters under different noise interference conditions. The left column shows the time-domain response of the contact force under noise conditions of -1dB, -3dB, and -5dB, and the right column shows the corresponding frequency-domain amplitude distribution. The method is implemented through a pre-trained parameter recognition model.

[0097] The parameter identification model is trained using a joint loss function, which includes data loss and physical loss.

[0098] Data loss is used to constrain the error between the predicted structural state parameters and the actual structural state parameters, while physical loss is used to constrain the predicted structural state parameters to satisfy the dynamic equations of the pantograph's three mass blocks.

[0099] The physical loss is obtained by substituting the predicted structural state parameters into the dynamic equations of the three mass blocks of the pantograph to obtain the dynamic residuals, and then constructing a model based on the dynamic residuals.

[0100] Specifically, the pantograph is equivalent to a three-mass spring-damped system consisting of a pantograph head, an upper frame, and a lower frame. Within a preset physical range, pantograph parameters and operating speed are sampled, such as the mass of the pantograph head. Sampling was conducted within the range of 1.0~20.0 kg, focusing on the damping of the bow head-upper frame. Sampling was performed within the range of 1.0 to 500.0 N·s / m, and the stiffness of the bow head-upper frame was measured. Sampling was performed within the range of 0.0 to 50000.0 N / m, and the operating speed V was sampled within the range of 200.0 to 450.0 km / h. Simultaneously, contact network structural parameters (including span, dropper arrangement, contact wire tension, and catenary tension) were sampled. The sampled parameters were input into the pantograph-contact network coupled dynamic model for numerical solution. The pantograph adopted a three-mass spring-damped model, with the matrix form as follows: ,in, This refers to the vertical displacement of the bow head, upper frame, and lower frame. , , These are the mass matrix, damping matrix, and stiffness matrix, respectively. This represents the contact force between the bow and the catenary, and is an external force vector. This indicates the static lifting force of the pantograph. This is a function that exceeds the order limit; 0 indicates that there is no direct external force input to the upper frame. The catenary uses a high-fidelity model based on finite element analysis. The contact wire and catenary are equivalent to Euler-Bernoulli beam / cable elements subjected to axial tension, while the hangers, positioning devices, and support structures are equivalent to discrete spring-damped connections. The pantograph-catenary contact uses a penalty function model. ( Calculate the contact force when the value is greater than 0, where, For the contact force between the bow and the fire net, Indicates contact stiffness, Indicates contact damping, This indicates the compression ratio between the bow head and the contact line. This represents the contact deformation rate. The coupled dynamic equations can be solved using the implicit Newmark-β numerical integration method, performing prediction-correction iterations at each time step until convergence. After the solution is obtained, the bow head acceleration is used as the expression. As model input, the sampled As a supervisory label, it is also saved. and its velocity, acceleration and These auxiliary quantities are used to calculate the physical residuals during the training phase. They are only used for calculating the training loss and are not used as input during the model inference phase. The bow acceleration is windowed, resampled, and normalized to construct training samples with a fixed time window. Measurement noise and line disturbances can be added to the training samples to enhance the model's adaptability to uncertainties in actual measurements.

[0101] The parameter identification model is trained using a joint loss function, which includes data loss and physical loss.

[0102] Data loss The error between the predicted structural state parameters and the actual structural state parameters is used to constrain the mean square error. , where B is the batch size.

[0103] Physical loss The structural state parameters used for constraint prediction satisfy the dynamic equations of the pantograph's three mass blocks. The calculation method is as follows: The predicted structural state parameters... Substituting the dynamic equations of the three mass blocks of the pantograph, the dynamic residuals are obtained, and the physical loss is constructed based on these residuals. Specifically, for each training sample, the predicted parameters are compared with the displacements saved from the simulation. ,speed acceleration and contact force Substitute them into the dynamic equations of the three mass blocks and calculate the discrete residuals of the three mass blocks.

[0104] set up , Then the three discrete residuals are: ; ; ; Let be the vertical displacement of the pantograph head at the nth discrete time sampling point. Let the velocity of the pantograph head be the velocity at the nth discrete time sampling point. Let be the vertical acceleration of the pantograph head at the nth discrete-time sampling point. Indicates that the first mass block is in The residual value, This represents the nth discrete-time sampling point. This represents the equivalent mass of the first mass block predicted by the model. This represents the equivalent damping of the first mass block predicted by the model. This represents the equivalent stiffness of the first mass block predicted by the model.

[0105] It should be noted that the displacement, velocity, and acceleration used in the residual calculations described above all originate from the simulation data saved during the training data generation phase, i.e., the actual structural response, rather than being generated backwards from model prediction parameters. The advantage of this approach is that while the structural parameters are identified by the bow head acceleration, and the responses of the upper and lower frames are not used as model inputs, the displacement, velocity, and acceleration of the upper and lower frames can be directly output from the coupled dynamics model during the simulation training phase, serving as auxiliary supervisory information for calculating physical losses. Therefore, the problem of "training samples only containing bow head acceleration and thus being unable to calculate the three-mass block residuals" does not exist.

[0106] The three residuals are summed into a scalar physical loss. In this embodiment, normalized weighted mean squared residuals are used to average the three residuals over the time and mass block dimensions. ,in, For batch size, For time steps, , , The residual weights for the three equations can be set to the default values: ; , , For normalization, the scale can be taken as the root mean square scale corresponding to the external force or the training set residuals, to avoid different dimensions and magnitudes causing a single equation to dominate the training. If all variables have already been dimensionless, the following can also be used: This discretization form approximates the continuous-time integral as a time average, ensuring that the loss value does not change significantly with the number of time steps. Let be the residual value of the dynamic equation for the b-th training sample at the n-th time step and the 1st mass block (bow head). Let be the residual value of the b-th sample, the n-th time step, and the second quality block (upper frame). This is the residual value of the b-th training sample at the n-th time step and the 3rd quality block (lower frame).

[0107] The total loss function is In this embodiment and Using fixed weights, the optimizer learning rate changes dynamically, while the weight coefficients in the loss function remain fixed. A specific implementation can be set as follows: Therefore, the total loss is During training, the AdamW optimizer is used to update network parameters, and a cosine annealing strategy is used to dynamically adjust the learning rate. Training termination can be achieved by reaching the maximum number of training epochs. Early stopping is performed when the total loss on the validation set does not decrease for 30 consecutive iterations; early stopping is performed when the relative decrease in the validation set loss is less than a certain value for 20 consecutive iterations. If the training loss continues to decrease while the validation loss continues to increase, training is stopped and rolled back to the model parameters with the lowest validation set loss. Finally, the model parameters with the lowest validation set loss are saved as the trained parameters to identify the model.

[0108] In practical applications or online inference, the model only needs to input the bow head acceleration to output the desired result. Training loss is no longer calculated, and upper and lower frame responses are not required. Figure 5 The results of the contact force calculated from the predicted pantograph dynamic parameters under different noise intensities are presented. It can be seen that under noise interference of -1dB, -3dB, and -5dB, the calculated contact force maintains good consistency with the actual results in both the time and frequency domains. The curves under different noise conditions do not change significantly, and no obvious response drift or misjudgment of the frequency domain peak is observed. This indicates that when the input acceleration signal is interfered with by noise, the pantograph dynamic parameters predicted by TASH still have good stability and can maintain a reliable dynamic response reconstruction capability.

[0109] Understandably, by employing a joint training strategy combining data loss and physical loss, the model can not only accurately fit the structural state parameters using the bow head acceleration as input, but also construct physical residuals by substituting the predicted parameters into the three-mass block dynamic equations, forcing the prediction results to satisfy the dynamic equilibrium relationship of the pantograph. This significantly improves the physical consistency and reliability of the inversion results, reducing the risk that the parameter combinations in a purely data-driven model may fit the labels but be physically distorted. During the training phase, high-fidelity data generated by coupled dynamic simulations is used to completely preserve the displacement, velocity, and acceleration responses of the bow head, upper frame, and lower frame as auxiliary supervision information. This allows the model to complete parameter identification using only the bow head acceleration during inference, greatly reducing the dependence on actual measurement data of the upper and lower frames and overcoming the difficulty of deploying multiple sensors in actual engineering. Simultaneously, by introducing measurement noise and line disturbances into the simulation samples, the model's adaptability to measurement uncertainties such as velocity fluctuations, sensor noise, and line state changes is enhanced, improving its generalization performance under velocity extrapolation conditions and reducing the degradation of identification accuracy caused by distribution offset. The calculation of physical residuals is based on the actual dynamic response rather than the autoregressive generation of predicted parameters, avoiding the accumulation and amplification of errors during propagation and ensuring the reliability of the physical constraint supervision signal. The inference phase eliminates the need for iterative solution of the dynamic equations; a single forward propagation outputs complete nine-dimensional structural state parameters, significantly reducing computational latency in online applications. Furthermore, the equivalent mass, damping, and stiffness parameters output by the model quantitatively reflect the inertial characteristics, energy dissipation characteristics, and elastic recovery capability of the pantograph structure, providing direct parameterization for structural state assessment and degradation trend analysis, avoiding the uncertainties arising from indirect state inference based solely on response signals. This scheme improves inversion accuracy, physical consistency, and operational adaptability while reducing the need for additional sensors, dependence on the training condition range, and computational burden of online deployment, demonstrating significant engineering practical value.

[0110] In summary, the beneficial effects of this invention are as follows: This invention only requires acquiring the acceleration response of the pantograph head under high-speed operating conditions to identify the equivalent mass, equivalent damping, and equivalent stiffness of the pantograph head, upper frame, and lower frame, respectively. The pantograph head acceleration signal is relatively easy to obtain in actual operation, eliminating the need to disassemble the pantograph, install additional contact force sensors between the pantograph and the catenary, or conduct complex off-line control bench tests, thus reducing monitoring costs and implementation difficulty.

[0111] This invention constructs a physical coding operator based on the modal dispersion relation of the Euler-Bernoulli beam for contact wire tension. During the feature extraction stage, a physical modulation determined by bending stiffness, axial tension, mass per unit length, and operating speed is applied to each frequency component of the acceleration signal. This hard-coding method makes the physical prior of the contact wire's structural propagation an indispensable element in the model's forward propagation, thereby physically separating the velocity-related and structural-related components of the acceleration signal at the source. This suppresses the influence of measurement uncertainties such as operating speed fluctuations, sensor noise, and line condition disturbances on the inversion results.

[0112] This invention does not extract a single potential state, but constructs a potential beam response state (initial state term) and a potential propagation trend state (initial trend term) through two independent mapping branches. This is based on the fact that the modal propagation of a contact line tension beam is essentially a second-order dynamic process concerning a virtual propagation depth, and a single initial state cannot uniquely determine the propagation evolution outcome. The two independent states serve the cosine and sine terms in the closed-form solution of the propagation equation, respectively. The former characterizes the current response form, and the latter characterizes the propagation direction and phase evolution trend. Together, they constitute the complete initial conditions for the damped oscillation propagation of the tension beam. This avoids the loss of physical information and pathological inversion problems caused by mixing amplitude and trend information in the same feature, ensuring the physical consistency and interpretability of the parameter inversion from the underlying mathematical structure.

[0113] This invention compares the upstream transmitting capacity and downstream receiving capacity of each connection edge, marking connections with a transmitting capacity greater than their receiving capacity as unbalanced edges. It then combines consecutively adjacent unbalanced edges along the passenger flow direction into an unbalanced chain. This unbalanced chain determines the congestion initiation cell, the congestion critical cell, and the propagation link, enabling quantitative reasoning about the location of the congestion source, the propagation direction, and the scope of its impact. Furthermore, based on the above information and the predicted cell states for future time periods, it generates scheduling results including target cells, triggering time periods, instruction types, execution objects, and control variables. This allows scheduling strategies to be precisely mapped to specific facilities, equipment, and execution time nodes, significantly improving the precision and executability of passenger flow scheduling.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for pantograph parameter identification that integrates dispersive physical coding and hypergraph networks, characterized in that, The method is executed through a pre-trained parameter recognition model, including: Obtain the pantograph head acceleration response when the pantograph is in operation; The bow head acceleration response is front-end encoded to obtain the potential beam response state and potential propagation trend state; Based on the modal dispersion relation of the contact line tension Euler-Bernoulli beam, a tension beam physical coding operator is constructed, and the tension beam physical coding operator is used to perform frequency domain propagation modulation on the potential beam response state as the initial state and the potential propagation trend state as the initial rate of change to obtain the structural constraint time series characteristics. The structural constraint temporal features are mapped to multiple parameter vertex features; The multiple parameter vertex features are input into an adaptive soft hypergraph network, and bidirectional message passing between parameter vertices and soft hyperedges is performed through the adaptive soft hypergraph network to obtain enhanced parameter vertex features. Based on the enhanced parameter vertex features, the structural state parameters of the pantograph are obtained.

2. The pantograph parameter identification method integrating dispersive physical coding and hypergraph networks according to claim 1, characterized in that, When performing front-end encoding on the bow head acceleration response to obtain the potential beam response state and potential propagation trend state, the following steps are included: The potential beam response state is obtained by encoding the bow head acceleration response through the first mapping branch; The potential propagation trend state is obtained by encoding the bow acceleration response through the second mapping branch; The first mapping branch and the second mapping branch are respectively implemented by a one-dimensional convolutional layer in the parameter recognition model, and the learnable parameters of the first mapping branch and the second mapping branch are not shared. The potential beam response state is used as the initial state of the tension beam frequency domain propagation modulation, and the potential propagation trend state is used as the initial rate of change of the tension beam frequency domain propagation modulation.

3. The pantograph parameter identification method integrating dispersive physical coding and hypergraph networks according to claim 1, characterized in that, When constructing the physical coding operator for a tension beam based on the modal dispersion relation of the contact wire tension Euler-Bernoulli beam, the following are included: In the modal dispersion relation of the contact wire tension Euler-Bernoulli beam, the contact wire is equivalent to an Euler-Bernoulli beam subjected to axial tension, and the equivalent propagation frequency corresponding to the time-domain frequency variable is determined based on the bending stiffness, axial tension, mass per unit length, and running speed parameters of the contact wire.

4. The pantograph parameter identification method integrating dispersive physical coding and hypergraph networks according to claim 3, characterized in that, The equivalent propagation frequency is determined by the following relationship: ; in, For time-domain angular frequency variables, The operating speed parameter, For numerically stable terms, Let be the bending stiffness of the contact wire. The axial tension of the contact wire. The mass per unit length of the contact wire is given.

5. The pantograph parameter identification method according to claim 4, characterized in that, The step of using the tension beam physical coding operator to perform frequency domain propagation modulation on the potential beam response state as the initial state and the potential propagation trend state as the initial rate of change includes: The potential beam response state and the potential propagation trend state are subjected to a fast Fourier transform along the time dimension to obtain the corresponding frequency domain representation; Damped oscillation propagation is calculated based on the equivalent propagation frequency, the preset equivalent damping ratio, and the preset virtual propagation depth to obtain the frequency domain characteristics after propagation. Perform an inverse fast Fourier transform on the propagated frequency domain features to obtain the structural constraint time-series features.

6. The pantograph parameter identification method integrating dispersive physical coding and hypergraph networks according to claim 5, characterized in that, The damped oscillation propagation calculation is determined by the following formula: ; in, This is the current response status. Frequency domain representation after performing a fast Fourier transform along the time dimension; For the trend of propagation and evolution Frequency domain representation after performing a fast Fourier transform along the time dimension; The equivalent propagation frequency, The equivalent damping ratio is given. For virtual communication depth, For the damped propagation frequency, It is a numerically stable term.

7. The pantograph parameter identification method integrating dispersive physical coding and hypergraph networks according to claim 1, characterized in that, When the multiple parameter vertex features are input into an adaptive soft hypergraph network, and bidirectional message passing between parameter vertices and soft hyperedges is performed through the adaptive soft hypergraph network, the process includes: The adaptive soft hypergraph network generates soft hyperedges and a soft participation matrix based on the features of the multiple parameter vertices. The elements in the soft participation matrix represent the degree to which the parameter vertices participate in the soft hyperedge. The parameter vertex features are aggregated into soft hyperedge features by transposing the soft participation matrix, and then the soft hyperedge features are propagated back to the parameter vertices by the soft participation matrix. The propagation results are then residually connected and normalized with the original parameter vertex features to obtain enhanced parameter vertex features.

8. The pantograph parameter identification method according to claim 7, characterized in that, When generating soft hyperedges and soft participation matrices using the adaptive soft hypergraph network based on the multiple parameter vertex features, the process includes: A globally learnable soft hyperedge prototype is set up to provide a basic hyperedge representation. Generate global context features based on the vertex features of the multiple parameters; Based on the global context features, the globally learnable soft hyperedge prototype is adaptively corrected using samples to obtain the sample-adaptive soft hyperedge prototype. The similarity between the parameter vertex features and the sample adaptive soft hyperedge prototype is calculated and normalized to obtain the soft participation matrix, where the elements of the soft participation matrix represent the degree to which the parameter vertex participates in the soft hyperedge.

9. The pantograph parameter identification method according to claim 8, characterized in that, When performing bidirectional message passing between parametric vertices and soft hyperedges, it includes: Based on the soft participation matrix, the parameter vertex features are aggregated into soft hyperedge features; The soft hyperedge features are propagated back to the parameter vertices using the soft participation matrix, and the propagation results are residually connected and normalized with the original parameter vertex features to obtain the enhanced parameter vertex features.

10. The pantograph parameter identification method according to claim 1, characterized in that, When the method is executed through a pre-trained parameter recognition model, it includes: The parameter identification model is trained using a joint loss function, which includes data loss and physical loss. The data loss is used to constrain the error between the predicted structural state parameters and the actual structural state parameters, and the physical loss is used to constrain the predicted structural state parameters to satisfy the dynamic equations of the pantograph's three mass blocks. The physical loss is obtained by substituting the predicted structural state parameters into the dynamic equation of the three mass blocks of the pantograph to obtain the dynamic residual, and the physical loss is constructed based on the dynamic residual.

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