Bow-net digital twin wear prediction method and system based on cross-domain multi-model cooperation

Abstract

This invention discloses a cross-domain, multi-model collaborative method and system for predicting pantograph-catenary digital twin wear. The method includes the following steps: photographing the actual operating pantograph and converting it into real-time wear data as input to the digital space; fusing a geometric model, a pantograph-catenary coupling dynamics model, a multi-roughness peak current-carrying friction wear model, a variational N-BEATS surrogate model considering the current-carrying wear mechanism, and a time-series probabilistic graphical model in the digital space, embedding the pantograph current-carrying wear model under the influence of multi-roughness peaks into the trend basis function of the surrogate model, enabling the model to be trained and predicted according to the current-carrying wear mechanism; and establishing a wear state transition network using the time-series probabilistic graphical model to predict the wear degradation of the pantograph-catenary system. This technical solution, through multi-model fusion, achieves a comprehensive digital mapping from geometric morphology and dynamic contact to wear mechanism, and uses a variational inference algorithm to update and dynamically evolve model parameters, thereby realizing the prediction of wear degradation in the pantograph-catenary system.

Description

Technical Field

[0001] This invention belongs to the field of bearing fault diagnosis technology, and relates to a cross-domain multi-model collaborative digital twin wear prediction method and system for bow and catenary systems. Background Technology

[0002] With the rapid development of urban rail transit networks, urban rail trains have become an important component of urban transportation systems, and their operational safety and reliability are directly related to the stable operation of urban public transportation. Urban rail trains operate in complex environments, undergo variable operating conditions, and have sophisticated system structures. Once a key component fails, it can easily lead to serious economic losses and social impacts.

[0003] Therefore, conducting research on predictive and health management technologies based on the operation and maintenance needs of high-end equipment is of great significance for ensuring the long-term safe and stable operation of equipment, reducing the operation and maintenance costs throughout the entire life cycle, and avoiding major accidents.

[0004] In the critical systems of urban rail trains, the pantograph-catenary system is responsible for obtaining electrical energy for the train, and its operating status directly affects the continuity and stability of the train's power supply. The pantograph's carbon contact plate, as a consumable component in the pantograph-catenary system, is in a dynamic contact state for extended periods under high-speed friction and continuous current-carrying conditions. With the combined effects of mechanical and electrical forces, its wear accumulates continuously. When the carbon contact plate wear exceeds a safe threshold, it may lead to structural deformation or even breakage. In severe cases, this can cause widespread damage to the pantograph and overhead contact system, ultimately resulting in train shutdown.

[0005] Conducting degradation modeling and prediction research on the wear mechanism of pantographs, and realizing accurate assessment of the remaining life of carbon sliding plates and scientific formulation of replacement cycles, is a key issue in improving the safety and operation and maintenance efficiency of pantograph-catenary systems.

[0006] The wear evolution of the pantograph carbon contact plate exhibits significant multi-physics coupling characteristics, with its degradation behavior simultaneously influenced by mechanical loads, current, and thermal effects. During actual operation, dynamic fluctuations in the pantograph-catenary contact force alter the contact interface state. Current carrying and arcing effects, coupled with temperature rise, accelerate material degradation, while temperature changes further affect the material's mechanical and electrical properties, forming a complex interactive mechanism of force-heat-electric multi-field coupling. This coupling effect results in a wear process characterized by randomness, nonlinearity, and non-stationary evolution.

[0007] Existing modeling methods mainly rely on pure data-driven modeling approaches. Although they can fit historical data, they lack physical consistency constraints, making it difficult to ensure that the predicted results match the actual wear mechanism. The models also lack generalization ability and engineering interpretability.

[0008] Furthermore, existing methods struggle to directly embed key physical parameters such as contact force, current, and thermal effects, along with their inherent laws, into the wear prediction process. This results in a disconnect between the multi-field coupling mechanism and data prediction, making it difficult to accurately predict long-term degradation trends while ensuring computational efficiency.

[0009] Therefore, there is an urgent need to construct a modeling framework that can integrate multiple field coupling factors and take into account both physical mechanism expression and computational efficiency, so as to improve the accuracy and engineering applicability of pantograph-catenary system wear prediction. Summary of the Invention

[0010] The purpose of this invention is to address the aforementioned problems in existing technologies by proposing a cross-domain, multi-model collaborative digital twin wear prediction method and system for pantograph-catenary circuits.

[0011] To achieve the above objectives, the basic solution of this invention is: a cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method, comprising the following steps:

[0012] S1, The pantograph condition detection system takes pictures of the pantograph in actual operation, and the pantograph images are converted into real-time wear data through image processing, and the real-time wear data is used as the input of the digital space;

[0013] S2, the digital space fusion geometric model, pantograph-catenary coupling dynamics model, multi-roughness peak current-carrying friction and wear model, variational N-BEATS surrogate model considering current-carrying wear mechanism, and time-series probabilistic graphical model, through the surrogate model, realizes the fusion and order reduction calculation of multi-domain mechanism models, and drives the dynamic evolution of the pantograph-catenary body over time according to the time-series probabilistic graphical model, specifically:

[0014] The geometric model constructs the spatial morphology of the pantograph-catenary system using a parametric modeling method, providing a spatial morphological benchmark for the pantograph-catenary system to support subsequent dynamic simulations and wear analysis.

[0015] The pantograph-catenary coupling dynamic model simulates dynamic contact force based on the spatial topography of the pantograph-catenary system, generating real-time contact force data as input variables for mechanical and electrical coupling, driving subsequent dynamic wear prediction.

[0016] The multi-rough peak current-carrying tribo-wear model decomposes dynamic contact force into mechanical friction terms and current wear terms, quantifies the contribution of mechanical friction and current thermal effects to wear depth, and provides a basis for embedding current-carrying wear mechanisms into proxy models;

[0017] The variational N-BEATS surrogate model of the current-carrying wear mechanism embeds the pantograph current-carrying wear model under the influence of multiple rough peaks into the trend basis function of the surrogate model. The dynamic contact force data simulated by the velocity, current and pantograph-catenary coupling dynamic model are used as input variables of the surrogate model, so that the model is trained and predicted according to the current-carrying wear mechanism.

[0018] A time-series probabilistic graphical model was used to establish a wear state transition network. The model parameters were updated and dynamically evolved through variational inference algorithms, thus enabling the prediction of wear degradation in the pantograph-catenary system.

[0019] The working principle and beneficial effects of this basic solution are as follows: This technical solution constructs a complete "data acquisition-multi-model fusion-dynamic prediction" technical framework. By building a comprehensive digital space that includes geometry, physics, data-driven principles, and temporal logic, isolated models are coordinated. The dynamic model provides key contact force inputs, the mechanistic model embeds physical constraints for the surrogate model, and the temporal model endows the system with "self-evolution" capabilities. It solves the problems of existing prediction models being static, singular, and lacking physical meaning, and achieves cross-domain, dynamic, and interpretable prediction from microscopic mechanisms to macroscopic behavior.

[0020] Furthermore, the method for converting pantograph images into real-time wear data through image processing is as follows:

[0021] Multi-angle imaging units deployed along both sides of the track are used to acquire multi-angle image data of the carbon sliding plate as the pantograph passes.

[0022] The acquired multi-angle images are stitched together and their angles adjusted to generate a complete image of the carbon skateboard.

[0023] The stitched carbon skateboard image is denoised and grayscale enhanced to improve the contrast between the target and the background;

[0024] The target region was extracted by adaptive binarization and appropriate morphological processing, and the key structure of the pantograph was located by connected component filtering and edge detection.

[0025] Calculate the feature lines or centroid positions of the upper and lower edges as a reference, and achieve geometric alignment through straight line fitting or affine transformation to complete the cropping and stitching of the left and right regions, thereby obtaining stable and comparable standardized image results.

[0026] Finally, the thickness of the carbon slide plate is identified to obtain real-time wear depth data.

[0027] By using multi-angle imaging units on both sides of the track to collect data collaboratively, the problem of blind spots in single-view imaging was solved. Through image stitching and angle adjustment, a complete image of the carbon skateboard was generated. Then, through image preprocessing and feature extraction, automatic, real-time, and accurate identification of the carbon skateboard thickness was achieved, providing high-quality, high-frequency real-time wear data input for the digital twin system, ensuring the accuracy and timeliness of subsequent predictions.

[0028] Furthermore, the geometric model is a digital representation composed of various physical components, including the pantograph, carbon sliding plate, contact wire, and support structure. The geometric model determines the geometric dimensions, spatial positions, and connection and motion constraints between each component. The geometric information ensures that the digital model is consistent with the shape and arrangement of the actual system, providing a foundation for kinematic analysis and dynamic modeling.

[0029] By constructing a complete geometric model that includes the pantograph, carbon sliding plate, contact wire, and support structure, the size, position, and motion constraints of each component were accurately determined, ensuring the consistency of the digital twin and the physical entity in terms of spatial form.

[0030] Furthermore, the pantograph-catenary coupling dynamics model includes the contact wire model, the pantograph model, and the pantograph-catenary coupling model;

[0031] Both the overhead contact line model and the pantograph model are modeled based on the geometric dimensions and spatial structural relationships determined in the geometric model, and the dynamic equations are established according to the actual structural dimensions.

[0032] The dynamic model of the overhead contact line and pantograph is as follows:

[0033] ,

[0034] in, , , These represent the global displacement vector, global velocity vector, and global acceleration vector of the overhead contact system, respectively. , , M represents the global displacement vector, global velocity vector, and global acceleration vector of the pantograph system, respectively. P(C) K P(C) and C P(C) These are the equivalent mass matrix, damping matrix, and stiffness matrix of the pantograph or overhead contact line, respectively. The superscript P represents the pantograph, and the superscript C represents the overhead contact line. c and F p These are the equivalent power matrices for the overhead contact line and the pantograph, respectively.

[0035] Using the penalty function method to couple the two structures, the bow-catenary coupling model is obtained as follows:

[0036] ,

[0037] in, Indicates the contact pressure between the bow and the catenary. This indicates the vertical displacement of the bow head. This indicates the vertical displacement of the contact line at the contact point. The contact stiffness in the penalty function is represented by ; the Newmark-β method is used to solve the model.

[0038] The penalty function method is used for pantograph-catenary coupling, and contact force is simulated through contact stiffness, which can effectively reflect the dynamic interaction between the pantograph and the catenary. The Newmark-β method is used for numerical solution, ensuring computational efficiency and stability. This enables the efficient and accurate generation of dynamic contact force data that reflects real working conditions, providing key input variables for subsequent wear prediction.

[0039] Furthermore, a multi-roughness peak current-carrying friction and wear model is used, in which wear includes mechanical wear, electrical wear, and arc wear, to calculate the power dissipation:

[0040] ,

[0041] in, This represents the total power dissipation (J·s⁻¹). , and These represent the power dissipation due to mechanical friction, Joule heat, and arc heat between the slide and the contact wire, respectively. Indicates the offline rate. Indicates the coefficient of friction. This represents the normal contact force (N) of the skateboard, i.e., the contact pressure of the catenary. This represents the relative sliding speed (m·s⁻¹) between the skateboard and the contact line. Indicates contact resistance (Ω). This represents the current intensity (A) passing through the pantograph-catenary interface. This represents the voltage drop (V) during arc discharge.

[0042] The total dissipated power is equivalent to the mechanical friction dissipation power generated by a normal contact force. The contact resistance is calculated in advance using Holm's electrical contact theory. Based on Hertz's contact theory and the GW contact model, the relationship between the contact radius and the normal contact force is established, and the equivalent normal contact force is calculated. for:

[0043] ,

[0044] in, This represents the equivalent elastic modulus of the slide and the contact line. Indicates the surface roughness of the skateboard;

[0045] Substitute wear depth and time:

[0046] ,

[0047] in, The (GW) model assumes that the material surface consists of the radii of curvature of multiple randomly distributed spherical micro-protrusions. The normal load at the contact point, i.e., the equivalent normal phase contact force. ;

[0048] When considering the effects of mechanical friction, Joule heating, and electric arc, the relationship between wear depth and other physical quantities is as follows:

[0049] ,

[0050] in, Indicates the depth of wear. This represents the ratio of the dimensionless wear coefficient to the hardness of the softer material (i.e., the skateboard). A1 represents the equivalent resistivity between the slide plate and the contact wire; t represents time; A1, A2, and A3 are intermediate parameters related to the friction coefficient, equivalent resistivity, equivalent elastic modulus, and surface roughness of the slide plate, respectively, when considering different wear effects.

[0051] If only mechanical friction is considered during the wear process of the skateboard, then:

[0052] ,

[0053] If only Joule heating is considered during the wear process of the skateboard, then:

[0054] ,

[0055] If only the effect of electric arc is considered during the wear process of the skateboard, then:

[0056] .

[0057] The nonlinear coupling contributions of mechanical friction, Joule heating, and electric arc to total wear were quantitatively revealed by the energy dissipation method. The explicit mathematical relationship between wear depth h and contact force, current, velocity, material properties, and surface roughness was given, which is beneficial for subsequent use.

[0058] Furthermore, the proxy model comprises a four-layer structure, specifically:

[0059] The first layer is a stack layer, consisting of m stacks. Each stack has two outputs: one output serves as the input to the next stack, and the other output is aggregated to form the prediction output of the entire model. The mathematical form of the stack layer is:

[0060] ,

[0061] in, This represents the predicted output of the entire model, where i = 1, 2, ..., m represents the index of the stack. This represents the predicted output of the i-th stack;

[0062] The second layer is the block layer, representing a stack composed of n blocks. Each block contains two outputs: backward prediction and forward prediction. The input of the current block and the residual of its backward prediction serve as the input of the next block, and the sum of the forward predictions serves as the output of the stack. The prediction task of the entire model is decomposed into multiple blocks. The residual structure is used to remove the portion reconstructing the input from the input. The operations of the second layer are described by the following equation:

[0063] ,

[0064] in, This represents the input to the entire model. Indicates the index of the block. Indicates the first The first stack The input of each block, Indicates the first The first stack Backcasting of individual blocks, used to reconstruct the input. Indicates the first The first stack Forward prediction of each block;

[0065] The third layer consists of the block's internal components, including encoders and decoders, which process the input... As input to the encoder, the data is mapped to the latent space, resampled, and then input into the corresponding basis functions to obtain the back-prediction and forward-prediction outputs. The trend basis functions are:

[0066] ,

[0067] Among them, intermediate parameters , and The coefficient of friction, equivalent resistivity, equivalent elastic modulus and surface roughness of the slide plate are related to the coefficient of friction, equivalent resistivity, equivalent elastic modulus and the surface roughness of the slide plate. The coefficient of friction is indirectly generated through latent variables and the appropriate value is obtained by Bayesian optimization. In the internal structure of the block, the latent space is resampled to obtain the response A1A2A3 and then physical variables are input to construct the trend basis function.

[0068] After the wear depth data is input into the model, trend modeling is performed in the trend block according to the physical inductive bias formula (i.e. trend basis function) embedded in the current-carrying wear mechanism to obtain trend characteristics that conform to the current-carrying wear mechanism.

[0069] The periodic variation features in the wear sequence are extracted in the periodic block, and the remaining nonlinear and complex features are learned in the general block. Each block outputs the back prediction and forward prediction results respectively. The interpreted part is eliminated layer by layer by residual method and the forward prediction output is accumulated to form a stack-level prediction result. Finally, the final prediction output of wear depth is obtained by the step-by-step residual transfer and prediction summation of multiple stacks.

[0070] By utilizing stack and block residual structures, complex time series prediction tasks can be efficiently decomposed and progressively refined, improving model learning efficiency and prediction accuracy. This enables the model to model trends according to physical laws, ensuring that prediction results not only conform to physical mechanisms but also capture complex patterns in the data.

[0071] Furthermore, the wear state transition network in the time-series probabilistic graphical model This indicates the physical state of the pantograph slider. This represents the observed data of the skateboard, specifically the wear data. Represents the posterior distribution of the encoding process , This indicates that in the IV-NBEATS model, the posterior distribution... Latent variables obtained from sampling This represents the predicted output of the proxy model. This represents the prior distribution of the latent variables at the corresponding time point. Represents the loss function of the proxy model;

[0072] By Posterior distribution at time 1 As the prior distribution at time t, that is:

[0073] ,

[0074] in, Let represent the prior distribution of the latent variables at time t. express The posterior distribution of the latent variables at time step. and They represent The mean and standard deviation of the posterior distribution of the latent variables at time points.

[0075] The loss function of the surrogate model at time t is expressed as:

[0076] ,

[0077] Where J represents the number of samples. Since direct calculation of the expectation is not feasible, Monte Carlo sampling is used to approximate the expectation.

[0078] Through the The physical state at time is Wear detection of the pantograph was performed to obtain the corresponding observation variables. After being processed by the encoder, the corresponding latent variables are generated. Latent variables The corresponding predicted output is obtained after processing by the decoder. By the mean square error of the output and The model's loss function is constructed using divergence, and the model's parameters are updated using gradient descent. At the same time, the prior distribution of the latent variables is dynamically updated to achieve accurate prediction.

[0079] A pantograph-catenary digital twin wear prediction is constructed based on a time-series probabilistic graphical model. The posterior distribution of the latent variables at the previous time step is used as the prior distribution at the current time step, thereby realizing the recursive update of the wear status in the time dimension.

[0080] By combining Monte Carlo sampling and gradient descent algorithms, the model parameters are iteratively optimized. In actual operation, every time new observation data is received, the Bayesian update method is used to take the posterior distribution of the latent variables at the previous time step as the prior at the current time step and dynamically correct the distribution of the latent variables.

[0081] The optimization of the parameters themselves is based on the distribution of latent variables, and is continuously adjusted through gradient descent to make the model predictions consistent with the observed data.

[0082] By constraining the distribution of latent variables using KL divergence, the stability of the prediction is guaranteed, as well as the robustness and accuracy of long-term predictions, thus truly realizing the synchronous evolution of the digital twin and the physical entity.

[0083] The present invention also provides a cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction system, including a pantograph motion status detection system, a control unit and a display unit;

[0084] The pantograph status detection system takes pictures of the pantograph in actual operation and transmits them to the control unit. The control unit converts the pantograph images into real-time wear data through image processing. The real-time wear data is used as input to the digital space. The control unit executes the method described in this invention to predict pantograph-catenary wear and displays it through the display unit.

[0085] By combining a machine vision acquisition system with a control unit embedded with a multi-model collaborative algorithm, a fully automated closed-loop system was constructed, encompassing automatic data acquisition, processing, analysis, and visualization of prediction results. This system can be directly deployed at urban rail train operation and maintenance sites, achieving end-to-end intelligent monitoring and prediction of pantograph-catenary wear status, and providing a direct, reliable, and operable intelligent tool for actual operation and maintenance decision-making.

[0086] Furthermore, the pantograph dynamic detection system is installed where the train passes at low speed to photograph the pantograph carbon strip. The pantograph dynamic detection system has two cameras on each side of the track, one in front and one behind. Each camera is mainly responsible for photographing half of the pantograph, and each camera is equipped with a flash to provide sufficient light during shooting to ensure that the camera can obtain a clear and bright image of the carbon strip.

[0087] When the train enters the station, the magnet / infrared sensor is triggered, which in turn triggers the two front cameras and the two rear cameras to acquire images in sequence.

[0088] By coordinating multiple cameras on both sides of the track and using flash lighting, comprehensive and high-quality imaging of the pantograph's sliding plate was achieved, effectively avoiding blind spots and insufficient illumination. Utilizing magnet / infrared triggering, automatic, orderly, and precise image acquisition was realized during low-speed train entry into the station, ensuring the reliability and consistency of the data source and laying a solid data foundation for accurate predictions by the entire digital twin system. Attached Figure Description

[0089] Figure 1 This is a flowchart illustrating the cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method of the present invention;

[0090] Figure 2 This is a schematic diagram of the structure of the cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method of the present invention;

[0091] Figure 3 This is a schematic diagram of the contact wire structure of the cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method of the present invention;

[0092] Figure 4 This is a schematic diagram of the pantograph structure of the pantograph-catenary digital twin wear prediction method of the present invention, which is based on cross-domain multi-model collaboration.

[0093] Figure 5 This is a schematic diagram of the variational N-BEATS surrogate model of the cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method of the present invention;

[0094] Figure 6 This is a schematic diagram of the pantograph dynamic detection structure of the cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction system of the present invention. Detailed Implementation

[0095] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0096] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0097] In the description of this invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to mechanical or electrical connections, or internal connections between two components. They can be direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0098] This invention discloses a cross-domain, multi-model collaborative digital twin wear prediction method for pantographs and catenary systems. It is primarily used for predicting carbon contact plates on pantographs, and can also be applied to wear caused by microscopic roughness peak contact under current-carrying conditions. Addressing the shortcomings of traditional pure data-driven models in terms of insufficient generalization ability and lack of physical consistency constraints, the physical wear mechanism formula is constructed as an inductive bias term and explicitly embedded into the data-driven modeling process. This provides physical constraints to guide wear depth prediction, thereby improving prediction accuracy and model robustness. Figure 1 and Figure 2 As shown, the cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method includes the following steps:

[0099] S1, using the pantograph status detection system to monitor the actual operating pantograph (e.g., Figure 4 (As shown) Take pictures, and convert the pantograph images into real-time wear data through image processing, and use the real-time wear data as input to the digital space;

[0100] S2, digital space fusion geometric model, pantograph-catenary coupling dynamic model, multi-roughness peak current-carrying friction and wear model, variational N-BEATS surrogate model considering current-carrying wear mechanism (such as...) Figure 5 As shown in the figure, the temporal probabilistic graphical model is used to achieve the fusion and order reduction calculation of multi-domain mechanism models through a proxy model, and the dynamic evolution of the pantograph-catenary body over time is driven by the temporal probabilistic graphical model, specifically:

[0101] The geometric model constructs the spatial morphology of the pantograph-catenary system using parametric modeling methods, providing a spatial morphological benchmark for the system to support subsequent dynamic simulations and wear analysis. The geometric model also elucidates the geometric structure and kinematic relationship of the pantograph-catenary coupling system, ensuring geometric consistency between the model and the physical entity, thus providing a foundation for accurate modeling of the pantograph-catenary system in subsequent dynamic analysis.

[0102] The pantograph-catenary coupling dynamics model simulates dynamic contact forces based on the spatial topography of the pantograph-catenary system, generating real-time contact force data as input variables for mechanical and electrical coupling, driving subsequent dynamic wear prediction. The pantograph-catenary coupling dynamics model outputs key physical quantities such as dynamic contact forces, and the multi-rough peak current-carrying friction and wear model characterizes the wear mechanism under the coupling effect of mechanical friction and current thermal effect. On this basis, a variational N-BEATS surrogate model with embedded dynamic parameters and explicit formulas of current-carrying wear mechanism is used to fuse and reduce the order of multi-domain mechanism models, realizing the mapping of cross-domain physical information to a unified prediction framework.

[0103] Furthermore, by combining a time-series probabilistic graphical model, the random variables and degradation process are modeled in a time-series correlation, driving the dynamic evolution of the pantograph-catenary body state and the prediction of long-term wear trends in the digital space.

[0104] The multi-rough-peak current-carrying tribo-wear model decomposes dynamic contact force into mechanical friction terms and current wear terms, quantifies the contribution of mechanical friction and current thermal effects to wear depth, and provides a basis for embedding current-carrying wear mechanisms into surrogate models. The multi-rough-peak current-carrying tribo-wear model is constructed based on energy dissipation theory, in which dissipated power characterizes the effects of mechanical tribo-wear, electrical wear, and arc wear.

[0105] By equating the multi-physics coupling effect to the total dissipated power generated by a single equivalent normal contact force, a unified characterization of different wear mechanisms is achieved. The equivalent normal contact force is decomposed into three parts: mechanical friction contribution, Joule heating contribution, and arc contribution. The contribution relationship of each physical action to the wear depth is quantified, and the wear depth-time evolution formula is substituted into the formula for solution, resulting in an expression that the wear depth is proportional to one-third of the time. This expression is embedded in the surrogate model as a depth wear formula with physical induction bias, providing a theoretical basis for introducing current-carrying wear mechanism constraints into the surrogate model.

[0106] The variational N-BEATS surrogate model of the current-carrying wear mechanism embeds the pantograph current-carrying wear model under the influence of multiple rough peaks into the trend basis function of the surrogate model. The dynamic contact force data simulated by the velocity, current and pantograph-catenary coupling dynamic model are used as input variables of the surrogate model, so that the model is trained and predicted according to the current-carrying wear mechanism.

[0107] A time-series probabilistic graphical model was used to establish a wear state transition network. The model parameters were updated and dynamically evolved through variational inference algorithms, thus enabling the prediction of wear degradation in the pantograph-catenary system.

[0108] In a preferred embodiment of the present invention, the method for converting pantograph images into real-time wear data through image processing is as follows:

[0109] Multi-angle imaging units deployed along both sides of the track are used to acquire multi-angle image data of the carbon sliding plate as the pantograph passes.

[0110] The acquired multi-angle images are stitched together and their angles adjusted to generate a complete image of the carbon skateboard.

[0111] The stitched carbon skateboard image is denoised and grayscale enhanced to improve the contrast between the target and the background;

[0112] The target region was extracted by adaptive binarization and appropriate morphological processing, and the key structure of the pantograph was located by connected component filtering and edge detection.

[0113] Calculate the feature lines or centroid positions of the upper and lower edges as a reference, and achieve geometric alignment through straight line fitting or affine transformation to complete the cropping and stitching of the left and right regions, thereby obtaining stable and comparable standardized image results.

[0114] Finally, the thickness of the carbon slide plate is identified to obtain real-time wear depth data.

[0115] In a preferred embodiment of the present invention, the geometric model is a digital representation composed of various physical components, including the pantograph, carbon sliding plate, and overhead contact line (e.g., ...). Figure 3 As shown, the conductor and support structure, the geometric model determines the geometric dimensions, spatial position of each component, and the connection and motion constraints between them. The geometric information ensures that the digital model is consistent with the shape and layout of the actual system, providing a basis for kinematic analysis and dynamic modeling.

[0116] In a preferred embodiment of the present invention, the pantograph-catenary coupling dynamics model includes a catenary model, a pantograph model, and a pantograph-catenary coupling model;

[0117] Both the overhead contact line model and the pantograph model are modeled based on the geometric dimensions and spatial structural relationships determined in the geometric model, and the dynamic equations are established according to the actual structural dimensions.

[0118] The dynamic model of the overhead contact line and pantograph is as follows:

[0119] ,

[0120] in, , , These represent the global displacement vector, global velocity vector, and global acceleration vector of the overhead contact system, respectively. , , M represents the global displacement vector, global velocity vector, and global acceleration vector of the pantograph system, respectively. P(C) K P(C) and C P(C) These are the equivalent mass matrix, damping matrix, and stiffness matrix of the pantograph or overhead contact line, respectively. The superscript P indicates the pantograph, and the superscript C indicates the overhead contact line. Fc and Fp are the equivalent mass matrices of the overhead contact line and the pantograph, respectively.

[0121] Using the penalty function method to couple the two structures, the bow-catenary coupling model is obtained as follows:

[0122] ,

[0123] in, Indicates the contact pressure between the bow and the catenary. This indicates the vertical displacement of the bow head. This indicates the vertical displacement of the contact line at the contact point. The contact stiffness in the penalty function is represented; the Newmark-β method is used to solve the model (the Newmark-β method is a commonly used implicit time integration method in structural dynamics analysis in this field, and is widely used in solving the transient dynamic response of structures. This method is a conventional numerical calculation method well known to those skilled in the art. In this application, it is only used as a conventional calculation method for solving the model, and is not an innovation or improvement of this application. Therefore, its specific algorithm process is not further limited or explained).

[0124] In a preferred embodiment of the present invention, a multi-roughness peak current-carrying friction and wear model is used, where wear includes mechanical wear, electrical wear, and arc wear, and the power dissipation is calculated as follows:

[0125] ,

[0126] in, This represents the total power dissipation (J·s⁻¹). , and These represent the power dissipation due to mechanical friction, Joule heat, and arc heat between the slide and the contact wire, respectively. Indicates the offline rate. Indicates the coefficient of friction. This represents the normal contact force (N) of the skateboard, also known as the pantograph-catenary contact pressure (the pantograph-catenary contact pressure and the normal contact force of the skateboard are essentially the same parameter; the difference in expression is due to the dynamics model emphasizing the overall force vector while the wear model emphasizes the pressure distribution, but the physical meaning is the same). This represents the relative sliding speed (m·s⁻¹) between the skateboard and the contact line. Indicates contact resistance (Ω). This represents the current intensity (A) passing through the pantograph-catenary interface. This represents the voltage drop (V) during arc discharge.

[0127] The total dissipated power is equivalent to the mechanical friction dissipation power generated by a normal contact force, which is the equivalent normal contact force. for:

[0128] ,

[0129] in, This represents the equivalent elastic modulus of the slide and the contact line. Indicates the surface roughness of the skateboard;

[0130] Substitute wear depth and time:

[0131] ,

[0132] in, The (GW) model assumes that the material surface consists of the radii of curvature of multiple randomly distributed spherical micro-protrusions. The normal load at the contact point, i.e., the equivalent normal phase contact force. ;

[0133] When considering the effects of mechanical friction, Joule heating, and electric arc, the relationship between wear depth and other physical quantities is as follows:

[0134] ,

[0135] in, Indicates the depth of wear. This represents the ratio of the dimensionless wear coefficient to the hardness of the softer material (i.e., the skateboard). A1 represents the equivalent resistivity between the slide plate and the contact wire; t represents time; A1, A2, and A3 are intermediate parameters related to the friction coefficient, equivalent resistivity, equivalent elastic modulus, and surface roughness of the slide plate, respectively, when considering different wear effects.

[0136] If only mechanical friction is considered during the wear process of the skateboard, then:

[0137] ,

[0138] If only Joule heating is considered during the wear process of the skateboard, then:

[0139] ,

[0140] If only the effect of electric arc is considered during the wear process of the skateboard, then:

[0141] .

[0142] In a preferred embodiment of the present invention, the proxy model comprises a four-layer structure, specifically:

[0143] The first layer is a stack layer, consisting of m stacks. Each stack has two outputs: one output serves as the input to the next stack, and the other output is aggregated to form the prediction output of the entire model. The mathematical form of the stack layer is:

[0144] ,

[0145] in, This represents the predicted output of the entire model, where i = 1, 2, ..., m represents the index of the stack. This represents the predicted output of the i-th stack;

[0146] The second layer is the block layer, representing a stack composed of n blocks. Each block contains two outputs: backward prediction and forward prediction. The input of the current block and the residual of its backward prediction serve as the input of the next block, and the sum of the forward predictions serves as the output of the stack. The prediction task of the entire model is decomposed into multiple blocks. The residual structure is used to remove the portion reconstructing the input from the input. The operations of the second layer are described by the following equation:

[0147] ,

[0148] in, This represents the input to the entire model. Indicates the index of the block. Indicates the first The first stack The input of each block, Indicates the first The first stack Backcasting of individual blocks, used to reconstruct the input. Indicates the first The first stack Forward prediction of each block;

[0149] The third layer consists of the block's internal components, including an encoder and a decoder. The encoder employs a standard VAE structure, while the decoder embeds the physical wear formula based on the multi-micro-protrusion contact assumption of the pantograph-catenary slide plate into the trend basis function of N-BEATS through inductive bias. This ensures that the prediction simultaneously satisfies data fitting and physical constraints, significantly improving interpretability. The input... As input to the encoder, the data is mapped to the latent space, resampled, and then input into the corresponding basis functions to obtain the back-prediction and forward-prediction outputs. The trend basis functions are:

[0150] ,

[0151] Among them, intermediate parameters , and The coefficient of friction, equivalent resistivity, equivalent elastic modulus and surface roughness of the slide plate are related to the coefficient of friction, equivalent resistivity, equivalent elastic modulus and the surface roughness of the slide plate. The coefficient of friction is indirectly generated through latent variables and the appropriate value is obtained by Bayesian optimization. In the internal structure of the block, the latent space is resampled to obtain the response A1A2A3 and then physical variables are input to construct the trend basis function.

[0152] After the wear depth data is input into the model, trend modeling is performed in the trend block according to the physical inductive bias formula (i.e. trend basis function) embedded in the current-carrying wear mechanism to obtain trend characteristics that conform to the current-carrying wear mechanism.

[0153] The periodic variation features in the wear sequence are extracted in the periodic block, and the remaining nonlinear and complex features are learned in the general block. Each block outputs the back prediction and forward prediction results respectively. The interpreted part is eliminated layer by layer by residual method and the forward prediction output is accumulated to form a stack-level prediction result. Finally, the final prediction output of wear depth is obtained by the step-by-step residual transfer and prediction summation of multiple stacks.

[0154] Trend blocks, periodic blocks, and general blocks are essentially different network stack structures designed to model different data features. They are used to learn trend information, periodic information, and other complex residual information in time series data, respectively. Their function is to decompose and represent different types of features through structural division of labor, which is a common modular design approach for this type of model.

[0155] In Variational N-BEATS, the trend block, periodic block, and general block are standard functional module divisions within the N-BEATS model framework. The trend block characterizes low-frequency trend components in the time series, the periodic block models periodic or seasonal components, and the general block learns residual information or complex patterns not explicitly modeled. This module division is a conventional structural design of the N-BEATS model; the N-BEATS model consists of a trend stack, a periodic stack, and a general stack, and is widely used in academia. The innovation of this invention lies primarily in the unique structural innovation of the trend block within the trend stack, specifically, reconstructing the trend block output according to physical formulas.

[0156] In a preferred embodiment of the present invention, the wear state transition network in the time-series probabilistic graphical model... This represents the physical state of the pantograph skateboard (the actual state of the carbon skateboard is further obtained through the image recognition described above, which leads to the following x). i (i.e., observing wear data, wear depth). This represents the observed data of the skateboard, specifically the wear data. Represents the posterior distribution of the encoding process (encoding within the surrogate model). , The IV-NBEATS model (NBEATS structure is essentially a purely predictive model, specifically designed to output future wear predictions y) indicates that the model is a predictive model. i ), just input the observed wear data x i N-BEATS can directly provide the predicted output y. i However, the initial predictions may not be accurate. Using Bayesian methods to analyze the data... i Input the model, first calculate the probability distribution and the predicted value y. i ; the predicted value y i By comparing with actual wear data, a total loss value L is calculated. i This loss considers two things simultaneously: the accuracy of the prediction and the reasonableness of the probability distribution. The system automatically adjusts the parameters in the N-BEATS model based on the magnitude and direction of the loss value. After repeated updates, the predicted output y of N-BEATS... i This will increasingly approximate the actual wear trend, and the probability distribution will become more reasonable. (This is the method of parameter updating in the surrogate model, from the posterior distribution.) Latent variables obtained from sampling This represents the predicted output of the proxy model. This represents the prior distribution of the latent variables at the corresponding time point. Represents the loss function of the proxy model;

[0157] By Posterior distribution at time 1 As the prior distribution at time t, that is:

[0158] ,

[0159] in, Let represent the prior distribution of the latent variables at time t. express The posterior distribution of the latent variables at time step. and They represent The mean and standard deviation of the posterior distribution of the latent variables at time points.

[0160] The loss function of the surrogate model at time t is expressed as:

[0161] ,

[0162] Where J represents the number of samples. Since direct calculation of the expectation is not feasible, Monte Carlo sampling is used to approximate the expectation.

[0163] Through the The physical state at time is Wear detection of the pantograph was performed to obtain the corresponding observation variables. After being processed by the encoder, the corresponding latent variables are generated. Latent variables The corresponding predicted output is obtained after processing by the decoder. By the mean square error of the output and The model's loss function is constructed using divergence, and the model's parameters are updated using gradient descent. At the same time, the prior distribution of the latent variables is dynamically updated to achieve accurate prediction.

[0164] A pantograph-catenary digital twin wear prediction is constructed based on a time-series probabilistic graphical model. The posterior distribution of the latent variables at the previous time step is used as the prior distribution at the current time step, thereby realizing the recursive update of the wear status in the time dimension.

[0165] By combining Monte Carlo sampling and gradient descent algorithms, the model parameters are iteratively optimized. In actual operation, every time new observation data is received, the Bayesian update method is used to take the posterior distribution of the latent variables at the previous time step as the prior at the current time step and dynamically correct the distribution of the latent variables.

[0166] The optimization of the parameters themselves is based on the distribution of latent variables, and is continuously adjusted through gradient descent to make the model predictions consistent with the observed data.

[0167] The present invention also provides a cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction system, including a pantograph motion status detection system, a control unit, and a display unit.

[0168] The pantograph status detection system takes pictures of the pantograph in actual operation and transmits them to the control unit. The control unit converts the pantograph images into real-time wear data through image processing. The real-time wear data is used as input to the digital space. The control unit executes the method described in this invention to predict pantograph-catenary wear and displays it through the display unit.

[0169] In a preferred embodiment of the present invention, the pantograph dynamic detection system is installed where the train passes at low speed and is used to photograph the pantograph carbon strip. The pantograph dynamic detection system has two cameras on each side of the track, one in front and one behind. Each camera is mainly responsible for photographing half of the pantograph, and each camera is equipped with a flash to provide sufficient light during the shooting to ensure that the camera can obtain a clear and bright image of the carbon strip.

[0170] When the train enters the station, the magnet / infrared sensor is triggered, which in turn triggers the two front cameras and the two rear cameras to acquire images in sequence.

[0171] By coordinating multiple cameras on both sides of the track and using flash lighting, comprehensive and high-quality imaging of the pantograph's sliding plate was achieved, effectively avoiding blind spots and insufficient illumination. Utilizing magnet / infrared triggering, automatic, orderly, and precise image acquisition was realized during low-speed train entry into the station, ensuring the reliability and consistency of the data source and laying a solid data foundation for accurate predictions by the entire digital twin system.

[0172] This invention uses a dataset of measured thicknesses of the carbon sliding plate from a pantograph for evaluation. The pantograph thickness is collected by installing a dynamic monitoring system to obtain wear data for the carbon sliding plate. The proposed model is used to predict and analyze the wear trend of the carbon sliding plate, and the results are compared with those of LSTM, Deepstate, DLSSM, and IV-NBEATS models.

[0173] The pantograph dynamic detection system is installed where urban rail trains are about to arrive at low speed to photograph the pantograph's carbon strip. The system has two cameras on each side of the track, one in front and one behind. Each camera is responsible for photographing half of the pantograph, and each camera is equipped with a flash to provide sufficient light for capturing clear and bright images of the carbon strip. When the train enters the station, it triggers a magnet / infrared sensor, sequentially activating the two front cameras and the two rear cameras to acquire images, identifying forward / reverse orientation, and adjusting the carbon strip images accordingly. Figure 6 As shown.

[0174] Wear data was collected from eight pantograph sliders. The data collection time was not fixed; sometimes data was collected multiple times a day, and sometimes only once every few days. Since the daily wear variation of the pantograph is very small, and the differences between multiple measurements within the same day are not significant, the wear data from multiple measurements each day were averaged, and the average value was used as the wear data for that day. For days when data was collected only once, linear interpolation was used to fill in the missing data on those days, ultimately forming a new dataset of wear data in "days," with each new dataset containing 176 data points. The initial thickness of the pantograph slider was approximately 37mm. If the thickness fell below 22mm, the slider was replaced promptly to prevent further damage or even accidents. Therefore, the wear data for the pantograph slider ranged from 22 to 37mm.

[0175] Based on the design parameter of 110N initial static pantograph-catenary contact force for urban rail trains, the dynamic contact force of the pantograph-catenary system at different speeds was simulated and analyzed as the train traveled a certain distance.

[0176] The EN 50367

[30] standard clarifies the reasonable range of simulation results for the pantograph-catenary coupling dynamic model and provides the calculation method for this range, as follows:

[0177] (1) Maximum average contact force: ;

[0178] (2) Minimum average contact force: ;

[0179] (3) Maximum contact force: When the speed is less than 200 km / h, ;

[0180] (4) Minimum contact force: ;

[0181] (5) Maximum standard deviation of contact force: .

[0182] The simulation results of the contact force of the pantograph-catenary coupling model at four different speeds are compared with the EN 50367 standard, as shown in Table 1. Since the upper and lower limits of the average contact force vary with speed, a unified standard range is used in the table, namely, the intersection range satisfying the four different speeds. The results show that the simulation results of the contact force of the established pantograph-catenary coupling model all meet the range of the EN 30567 standard, indicating that the constructed pantograph-catenary coupling dynamic model is reasonable.

[0183] Table 1 Comparison of simulation results with EN30567 standard

[0184]

[0185] The LSTM model predicts using a purely data-driven approach, the DeepState model predicts using a framework that combines state-space models with deep learning, and the DLSSM model introduces latent variables to capture the potential features in the input data. Compared to linear models, all three can predict the wear trend of skateboards better, but the prediction results are slightly worse in terms of stability and accuracy.

[0186] The prediction results of the model were evaluated using MSE and MAE, as shown in Table 2. Table 2 shows that the system proposed in this invention performs best in both MSE and MAE on the four skateboard datasets, and its average prediction error is also superior to other models. The results demonstrate that the digital twin system can effectively predict the wear trend of skateboards and has higher accuracy and robustness.

[0187] Table 2. Prediction errors of various models on the skateboard wear dataset

[0188]

[0189] The specific embodiments described herein are merely illustrative examples of the present invention. Those skilled in the art can make various modifications or additions to the described embodiments or use similar methods to substitute them, without departing from the technology of the present invention or exceeding the scope defined by the appended claims.

Claims

1. A cross-domain, multi-model collaborative method for predicting wear using a pantograph-catenary digital twin, characterized in that, Includes the following steps: S1, The pantograph condition detection system takes pictures of the pantograph in actual operation, and the pantograph images are converted into real-time wear data through image processing, and the real-time wear data is used as the input of the digital space; S2, the digital space fusion geometric model, pantograph-catenary coupling dynamic model, multi-roughness peak current-carrying friction and wear model, variational N-BEATS surrogate model considering current-carrying wear mechanism, and time-series probabilistic graphical model, realize the fusion and order reduction calculation of multi-domain mechanism models through the surrogate model, and drive the dynamic evolution of the pantograph-catenary body over time according to the time-series probabilistic graphical model, specifically: The geometric model constructs the spatial morphology of the pantograph-catenary system using a parametric modeling method, providing a spatial morphological benchmark for the pantograph-catenary system to support subsequent dynamic simulations and wear analysis. The pantograph-catenary coupling dynamic model simulates dynamic contact force based on the spatial topography of the pantograph-catenary system, generating real-time contact force data as input variables for mechanical and electrical coupling, driving subsequent dynamic wear prediction. The multi-rough peak current-carrying tribo-wear model decomposes dynamic contact force into mechanical friction terms and current wear terms, quantifies the contribution of mechanical friction and current thermal effects to wear depth, and provides a basis for embedding current-carrying wear mechanisms into proxy models. The variational N-BEATS surrogate model of the current-carrying wear mechanism embeds the pantograph current-carrying wear model under the influence of multiple rough peaks into the trend basis function of the surrogate model. The dynamic contact force data simulated by the velocity, current and pantograph-catenary coupling dynamic model are used as input variables of the surrogate model, so that the model is trained and predicted according to the current-carrying wear mechanism. A time-series probabilistic graphical model was used to establish a wear state transition network. The model parameters were updated and dynamically evolved through variational inference algorithms, thus enabling the prediction of wear degradation in the pantograph-catenary system.

2. The cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method according to claim 1, characterized in that, The method for converting pantograph images into real-time wear data through image processing is as follows: Multi-angle imaging units deployed along both sides of the track are used to acquire multi-angle image data of the carbon sliding plate as the pantograph passes. The acquired multi-angle images are stitched together and their angles adjusted to generate a complete image of the carbon skateboard. The stitched carbon skateboard image is denoised and grayscale enhanced to improve the contrast between the target and the background; The target region was extracted by adaptive binarization and appropriate morphological processing, and the key structure of the pantograph was located by connected component filtering and edge detection. Calculate the feature lines or centroid positions of the upper and lower edges as a reference, and achieve geometric alignment through straight line fitting or affine transformation to complete the cropping and stitching of the left and right regions, thereby obtaining stable and comparable standardized image results. Finally, the thickness of the carbon slide plate is identified to obtain real-time wear depth data.

3. The cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method according to claim 1, characterized in that, The geometric model is a digital representation of various physical components, including the pantograph, carbon sliding plate, contact wire, and support structure. The geometric model determines the geometric dimensions, spatial positions, and connection and motion constraints between each component. The geometric information ensures that the digital model is consistent with the shape and layout of the actual system, providing a foundation for kinematic analysis and dynamic modeling.

4. The cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method according to claim 1, characterized in that, The pantograph-catenary coupling dynamics model includes the catenary model, the pantograph model, and the pantograph-catenary coupling model; Both the overhead contact line model and the pantograph model are modeled based on the geometric dimensions and spatial structural relationships determined in the geometric model, and the dynamic equations are established according to the actual structural dimensions. The dynamic model of the overhead contact line and pantograph is as follows: ， in, , , These represent the global displacement vector, global velocity vector, and global acceleration vector of the overhead contact system, respectively. , , M represents the global displacement vector, global velocity vector, and global acceleration vector of the pantograph system, respectively. P(C) K P(C) and C P(C) These are the equivalent mass matrix, damping matrix, and stiffness matrix of the pantograph or overhead contact line, respectively. The superscript P indicates the pantograph, and the superscript C indicates the overhead contact line; F c and F p These are the equivalent power matrices for the overhead contact line and the pantograph, respectively. Using the penalty function method to couple the two structures, we obtain the bow-net coupling model, which is: ， in, Indicates the contact pressure between the bow and the catenary. This indicates the vertical displacement of the bow head. This indicates the vertical displacement of the contact line at the contact point. The contact stiffness in the penalty function is represented by ; the Newmark-β method is used to solve the model.

5. The cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method according to claim 4, characterized in that, A multi-rough peak current-carrying tribo-wear model is used, where wear includes mechanical wear, electrical wear, and arc wear. Power dissipation is calculated. ， in, This represents the total power dissipation. , and These represent the power dissipation due to mechanical friction, Joule heat, and arc heat between the slide and the contact wire, respectively. Indicates the offline rate. Indicates the coefficient of friction. This represents the normal contact force of the skateboard, i.e., the contact pressure of the catenary. This indicates the relative sliding speed between the skateboard and the contact line. Indicates contact resistance. This indicates the current intensity passing through the pantograph-catenary interface. This represents the voltage drop during an electric arc discharge. The total dissipated power is equivalent to the mechanical friction dissipation power generated by a normal contact force, which is the equivalent normal contact force. for:

6. Among them, This represents the equivalent elastic modulus of the slide and the contact line. Indicates the surface roughness of the skateboard; Substitute wear depth and time: ， in, The (GW) model assumes that the material surface consists of the radii of curvature of multiple randomly distributed spherical micro-protrusions. The normal load at the contact point, i.e., the equivalent normal phase contact force. ; When considering the effects of mechanical friction, Joule heating, and electric arc, the relationship between wear depth and other physical quantities is as follows: ， in, Indicates the depth of wear. This represents the ratio of the dimensionless wear coefficient to the hardness of the softer material (i.e., the skateboard). A1 represents the equivalent resistivity between the slide plate and the contact wire; t represents time; A1, A2, and A3 are intermediate parameters related to the friction coefficient, equivalent resistivity, equivalent elastic modulus, and surface roughness of the slide plate, respectively, when considering different wear effects. If only mechanical friction is considered during the wear process of the skateboard, then: ， If only Joule heating is considered during the wear process of the skateboard, then: ， If only the effect of electric arc is considered during the wear process of the skateboard, then: 。 7. The cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method according to claim 5, characterized in that, The proxy model comprises a four-layer structure, specifically: The first layer is a stack layer, consisting of m stacks. Each stack has two outputs: one output serves as the input to the next stack, and the other output is aggregated to form the prediction output of the entire model. The mathematical form of the stack layer is: ， in, This represents the predicted output of the entire model, where i = 1, 2, ..., m represents the index of the stack. This represents the predicted output of the i-th stack; The second layer is the block layer, representing a stack composed of n blocks. Each block contains two outputs: backward prediction and forward prediction. The input of the current block and the residual of its backward prediction serve as the input of the next block, and the sum of the forward predictions serves as the output of the stack. The prediction task of the entire model is decomposed into multiple blocks. The residual structure is used to remove the portion reconstructing the input from the input. The operations of the second layer are described by the following equation: ， in, This represents the input to the entire model. Indicates the index of the block. Indicates the first The first stack The input of each block, Indicates the first The first stack Backcasting of individual blocks, used to reconstruct the input. Indicates the first The first stack Forward prediction of each block; The third layer consists of the block's internal components, including encoders and decoders, which process the input... As input to the encoder, the data is mapped to the latent space, resampled, and then input into the corresponding basis functions to obtain the back-prediction and forward-prediction outputs. The trend basis functions are: ， Among them, intermediate parameters , and The friction coefficient, equivalent resistivity, equivalent elastic modulus, and surface roughness of the slide plate are related to the latent variables, which are indirectly generated through latent variables and then optimized by Bayesian methods to obtain appropriate values. In the internal structure of the block, the latent space is resampled to obtain the response A1A2A3, and then physical variables are input to construct the trend basis function. After the wear depth data is input into the model, the trend is modeled in the trend block according to the physical inductive bias formula (i.e., the trend basis function) embedded in the current-carrying wear mechanism to obtain the trend characteristics that conform to the current-carrying wear mechanism. The periodic variation features in the wear sequence are extracted in the periodic block, and the remaining nonlinear and complex features are learned in the general block. Each block outputs the back prediction and forward prediction results respectively. The interpreted part is eliminated layer by layer by residual method and the forward prediction output is accumulated to form a stack-level prediction result. Finally, the final prediction output of wear depth is obtained by the step-by-step residual transfer and prediction summation of multiple stacks.

8. The cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction method according to claim 1, characterized in that, The wear state transition network in the time-series probabilistic graphical model This indicates the physical state of the pantograph slider. This represents the observed data of the skateboard, specifically the wear data. Represents the posterior distribution of the encoding process , This indicates that in the IV-NBEATS model, the posterior distribution... Latent variables obtained from sampling This represents the predicted output of the proxy model. This represents the prior distribution of the latent variables at the corresponding time point. Represents the loss function of the proxy model; By Posterior distribution at time 1 As the prior distribution at time t, that is: ， in, Let represent the prior distribution of the latent variables at time t. express The posterior distribution of the latent variables at time step. and They represent The mean and standard deviation of the posterior distribution of the latent variables at time points. The loss function of the surrogate model at time t is expressed as: ， Where J represents the number of samples. Since direct calculation of the expectation is not feasible, Monte Carlo sampling is used to approximate the expectation. Through the The physical state at time is Wear detection of the pantograph was performed to obtain the corresponding observation variables. After being processed by the encoder, the corresponding latent variables are generated. Latent variables The corresponding predicted output is obtained after processing by the decoder. By the mean square error of the output and The model's loss function is constructed using divergence, and the model's parameters are updated using gradient descent. At the same time, the prior distribution of the latent variables is dynamically updated to achieve prediction. A pantograph-catenary digital twin wear prediction is constructed based on a time-series probabilistic graphical model. The posterior distribution of the latent variables at the previous time step is used as the prior distribution at the current time step, thereby realizing the recursive update of the wear status in the time dimension. By combining Monte Carlo sampling and gradient descent algorithms, the model parameters are iteratively optimized. In actual operation, every time new observation data is received, the Bayesian update method is used to take the posterior distribution of the latent variables at the previous time step as the prior at the current time step and dynamically correct the distribution of the latent variables. The optimization of the parameters themselves is based on the distribution of latent variables, and is continuously adjusted through gradient descent to make the model predictions consistent with the observed data.

9. A cross-domain, multi-model collaborative digital twin wear prediction system for pantograph-catenary systems, characterized in that, Includes a pantograph motion status detection system, a control unit, and a display unit; The pantograph status detection system takes pictures of the pantograph in actual operation and transmits them to the control unit. The control unit converts the pantograph images into real-time wear data through image processing. The real-time wear data is used as input to the digital space. The control unit executes the method described in any one of claims 1-7 to predict pantograph-catenary wear and displays it through the display unit.

10. The cross-domain multi-model collaborative pantograph-catenary digital twin wear prediction system according to claim 8, characterized in that, The pantograph dynamic detection system is installed where the train passes at low speed and is used to photograph the pantograph carbon strip. The pantograph dynamic detection system has two cameras on each side of the track, one in front and one behind. Each camera is mainly responsible for photographing half of the pantograph, and each camera is equipped with a flash to provide light during the shooting process to ensure that the camera can acquire images of the carbon strip. When the train enters the station, the magnet / infrared sensor is triggered, which in turn triggers the two front cameras and the two rear cameras to acquire images in sequence.

Images