Pantograph-catenary physical variable prediction method, device and system and storage medium

Abstract

The invention relates to the technical field of rail transit, and discloses a pantograph-catenary physical variable prediction method, device and system and a storage medium, which are used for capturing a complex mapping relation of parameters in a pantograph-catenary system kinetic model from a frequency domain through a Fourier neural operator. And a complex association relationship among pantograph-catenary system parameters is simulated through the residual connection network, so that the prediction result of the target neural operator is improved. The pantograph-catenary physical variable prediction method comprises the following steps: acquiring a pantograph-catenary system input parameter corresponding to a target prediction task; inputting the input parameters of the pantograph-catenary system into the first full-connection layer for conversion to obtain an initial time domain state; inputting the initial time domain state into a plurality of target neural operators of a feature extraction layer for iteration to perform frequency domain feature extraction to obtain a target time domain state; inputting the target time domain state into a second full connection layer for conversion to obtain an initial bow net physical variable set; and inputting the initial pantograph-catenary physical variable set into the residual connection network layer for correction to obtain a target pantograph-catenary physical variable set.

Description

Technical Field

[0001] The present application relates to the field of rail transit technology, and in particular to a method, device, system and storage medium for predicting physical variables of a pantograph and a catenary. Background Art

[0002] The pantograph-contact system (PCS) is an important link between the train and the power supply system. Its performance directly affects the stable current collection and driving safety of the train. The good interaction performance between the pantograph and the contact network in the pantograph-contact system is crucial to the safe operation of rail vehicles. The effective analysis of the respective motion states and coupling responses in the pantograph-contact system is of great significance to the optimal design of the pantograph-contact system, improving operational stability, and preventing potential faults.

[0003] In related technologies, the interaction between the pantograph and the contact network is extremely complex. The analysis of the pantograph-catenary interaction relationship through the pantograph-catenary interaction analysis model relies on big data drive, resulting in poor generalization ability. The overall dynamic behavior of the pantograph-catenary system is affected by parameters such as mass distribution, stiffness and damping. However, under actual operating conditions, the input parameters of the pantograph-catenary system have time-varying characteristics and are difficult to measure, making it difficult for the pantograph-catenary dynamics model to accurately characterize the dynamic behavior of the pantograph-catenary system. The traditional pantograph-catenary interaction analysis model has poor robustness and generalization ability for the response prediction and state identification of the pantograph-catenary system. Summary of the invention

[0004] The present application provides a method, device, system and storage medium for predicting physical variables of a pantograph and a contact network, which are used to improve the accuracy of the interaction analysis task between the pantograph and the contact network in the pantograph-catenary system, that is, the robustness and generalization capability of response prediction and state identification.

[0005] The first aspect of the present application provides a method for predicting a physical variable of a pantograph-catenary system, comprising: obtaining a pantograph-catenary system input parameter corresponding to a target prediction task; Inputting the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state; Inputting the initial time domain state into a plurality of target neural operators of a feature extraction layer of the target PhyFnoNet model iteratively performs frequency domain feature extraction to obtain a target time domain state, wherein the target neural operator at least includes a Fourier neural operator; Input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial bow-net physical variable set; The initial bow-net physical variable set is input into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

[0006] A second aspect of the present application provides a pantograph-catenary physical variable prediction device, comprising: a first acquisition module, for acquiring a pantograph-catenary system input parameter corresponding to a target prediction task; A first conversion module is used to input the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state; A feature extraction module, used for inputting the initial time domain state into a plurality of target neural operators of the feature extraction layer of the target PhyFnoNet model to iteratively perform frequency domain feature extraction to obtain a target time domain state, wherein the target neural operator at least includes a Fourier neural operator; A second conversion module is used to input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial bow network physical variable set; The correction module is used to input the initial bow-net physical variable set into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

[0007] The third aspect of the present application provides a bow-catcher system, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor calls the instructions in the memory so that the bow-catcher system executes the above-mentioned bow-catcher physical variable prediction method.

[0008] A fourth aspect of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores instructions, which, when executed on a computer, enable the computer to execute the above-mentioned method for predicting the physical variables of a bow-catwalk.

[0009] In the technical solution provided by the present application, a physical-driven and data-driven physical Fourier neural operator network (Physics Fourier neural operator Network, PhyFnoNet) is proposed to solve the state identification and response prediction problems of PCS. The Fourier neural operator is used to replace the integral operation, avoiding the need for integral discretization, thereby eliminating the discretization and truncation errors, and can effectively capture high-frequency and low-frequency features in the frequency domain, thereby comprehensively describing the dynamic behavior of the bow-net system. A novel residual connection network (Physics-Informed Residual Network, PIRN) is designed, which uses the prior knowledge of the existence of these physical variables to implicitly execute physical laws, thereby establishing soft constraint relationships between the characteristics of physical variables to correct the prediction results of the target neural operator, significantly enhancing the performance of the model in solving complex PCS environments. The model can adapt to different bow-net parameters and conditions and has a strong ability to learn physical coupling equation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 Schematic diagram of the prediction framework of the PhyFnoNet model in this application; Figure 2 A schematic diagram of an embodiment of a method for predicting physical variables of a pantograph and catenary in the present application; Figure 3 This is a schematic diagram of a second embodiment of the method for predicting physical variables of a bow-catwalk in this application; Figure 4 Schematic diagram of the residual connection structure based on physical information based on the PhyFnoNet model in this application; Figure 5 This is a schematic diagram of a third embodiment of the method for predicting physical variables of a bow-catwalk in this application; Figure 6 This is a schematic diagram of the overall framework based on the PhyFnoNet model in this application; Figure 7 This is a schematic diagram of the Fourier operator framework based on local features and global features in the PhyFnoNet model in this application; Figure 8 A schematic diagram of an embodiment of a bow-cat system prediction device in the present application; Fig. 9 It is a schematic diagram of another embodiment of the bow-cat system prediction device in the present application; Fig.10 It is a schematic diagram of an embodiment of the bow-net system in the present application. DETAILED DESCRIPTION

[0011] The present application provides a method, device, system and storage medium for predicting physical variables of a bow-catcher, which are used to solve the problem that the traditional bow-catcher interaction analysis model has poor robustness and generalization ability for bow-catcher system response prediction and state identification.

[0012] The terms "first", "second", "third", "fourth", etc. (if any) in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" or "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0013] Reference Figure 1 The PhyFnoNet model of this application is based on a prediction framework of physics-driven (i.e., dynamics model) and data-driven (deep learning model), in which: is the equivalent mass of the pantograph-catenary system, is the equivalent stiffness of the pantograph-catenary system, is the equivalent damping of the pantograph-catenary system, is the internal force of the pantograph-catenary system, is the displacement matrix of the pantograph-catenary system, is the velocity matrix of the pantograph-catenary system, is the acceleration matrix of the pantograph-catenary system, For the PhyFnoNet model, Represents the output of the PhyFnoNet model.

[0014] In order to analyze the state identification and response prediction of the pantograph-network system, this application needs to establish a dynamic model. The system dynamic model is divided into a rigid network dynamic model, a pantograph dynamic model and a PCS coupling dynamic model.

[0015] The above rigid network dynamics model can discretize the beam into several plane beam units based on its structural characteristics. When longitudinal vibration and transverse vibration exist at the same time, the beam unit has longitudinal vibration and transverse vibration at the same time, and the node coordinates are determined by the axial displacement. and lateral displacement Therefore, we can use the interpolation function Displacement coordinate matrix for beam elements Establish and The relationship between them is calculated as shown in the formula:

[0016] in, is the displacement matrix of axial coordinate i, is the displacement matrix of the lateral coordinate j.

[0017] The above method can establish the dynamic equation of the rigid contact network: .

[0018] The above pantograph dynamics model can adopt a simplified model of three mass blocks. This model equates the pantograph head, upper frame, and lower frame to three mass blocks respectively, and connects them with spring-damper elements. The advantage of this simplified method is that the structure is simple, which is convenient for analytical calculation, and the accuracy meets the requirements of engineering applications. According to Newton's second law, the dynamic equation of the pantograph can be established:

[0019] Among them, the mass matrix Includes the equivalent mass of the bow head , the equivalent mass of the upper frame and the equivalent mass of the lower frame; the stiffness matrix Including the equivalent stiffness of the bow head , upper frame equivalent stiffness and the equivalent stiffness of the lower frame; damping matrix Including bow head equivalent damping , upper frame equivalent damping and the lower frame equivalent damping ; Displacement matrix Indicates bow head displacement , upper frame displacement and lower frame displacement ; Force matrix Static lift and contact force .

[0020] pass The pantograph and the contact network system can be coupled together, but when the pantograph slides on the rigid contact network, it may be offline, resulting in the possibility of penetration between the pantograph and the contact network. In order to deal with this contact problem, the penalty function method is used. Specifically, the axial displacement of the contact network is calculated in each time step. The axial displacement of the bow head at the same time The difference is taken as the penetration displacement . equal Contact stiffness However, when the bow head is below the overhead wire, The strain is zero. Therefore, the calculation formula of the PCS coupled dynamics model is:

[0021] The boundary conditions and initial conditions of the rigid contact network are as follows: and ), the vertical displacement is zero; at the initial moment ( ), the contact network is in a static state, that is, the displacement and velocity are both zero, that is:

[0022] Therefore, the above rigid grid dynamics model, pantograph dynamics model and PCS coupling dynamics model can be expressed as follows To unify the statement:

[0023] in, , , , , , , .

[0024] In practical applications, the pantograph and rigid catenary are composed of multiple components, and there are complex geometric relationships and mechanical couplings between the components, resulting in the interaction between the pantograph and the catenary usually being controlled by multiple ordinary differential equations (ODEs) and partial differential equations (PDEs). This limits the test conditions, especially the key parameters (such as pantograph-catenary contact force, displacement, velocity and acceleration) are difficult to measure directly. Relying solely on physical models to fully characterize the dynamic behavior of the pantograph-catenary system becomes insufficient in practical applications, especially in the case of discrete material parameters, uncertainty of boundary conditions and noise interference, the accuracy of the model is easily affected. Contact force, and use the system dynamics model to solve the vibration state. However, since the contact force and other key parameters are difficult to obtain directly, response prediction becomes an effective method to infer these unknown parameters. First, the pantograph-catenary dynamics usually exhibit strong nonlinearity and non-stationarity. Most of these methods are purely data-driven black box models, which rely too much on big data and may lead to poor generalization ability. Secondly, since the overall dynamic behavior of PCS, such as vibration and deformation, is affected by factors such as mass distribution, stiffness and damping, and exhibits different frequency characteristics, data-driven deep learning methods also face model robustness challenges in the system response prediction and state identification solution of PCS, that is, sensitivity to input data noise or outliers. To solve the above technical problems, this application provides a method for predicting physical variables of a pantograph: 201. Obtain the input parameters of the bow-net system corresponding to the target prediction task.

[0025] It is understandable that the execution subject of the present application can be a bow-net physical variable prediction device, or a bow-net system, a terminal or a server, which is not limited here. The present application embodiment takes the bow-net system as an example to illustrate. For ease of understanding, the specific process of the present application embodiment is described below. Please refer to Figure 1 , 2 An embodiment of the method for predicting physical variables of a bow-net in the present application includes: The target prediction task of the present application is response prediction or state identification, wherein state identification is the task of predicting the state of the pantograph and the rigid contact network according to the force between the pantograph and the contact network in the pantograph-network system, for example, deriving the vibration acceleration through the known contact force; response prediction is the task of predicting the response information of the pantograph and the contact network (such as contact force) according to the current vibration acceleration of the pantograph (such as displacement, velocity and acceleration).

[0026] The input parameters of the pantograph-catenary system of this embodiment may include but are not limited to the following: lifting force and contact force , displacement of the bow head and frame of the pantograph system ,speed , acceleration The combination of several parameters in the above example can specifically determine the corresponding input parameters according to the corresponding prediction task, and this embodiment does not impose any specific limitation.

[0027] 202. Input the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state.

[0028] Enter the parameters of the pantograph system Through the fully connected layer Perform local transformation and map it to a high-dimensional expression ,in, represents the initial time domain state; Indicates that all lengths are The set of real number vectors, in this embodiment, the bow network system input parameters are converted into Mapping to a higher-dimensional space helps the model capture complex features in the input data.

[0029] It is understandable that in state identification, the input parameters of the pantograph-catenary system are Includes lifting force and contact force ; In response prediction, the input parameters of the pantograph-catenary system are Includes the displacement of the bow head and frame ,speed , acceleration .

[0030] 203. Input the initial time domain state into multiple target neural operators of the feature extraction layer of the target PhyFnoNet model, iteratively perform frequency domain feature extraction, and obtain the target time domain state, wherein the target neural operator at least includes a Fourier neural operator.

[0031] In practical applications, the bow-net system has complex frequency domain and exhibits diverse response characteristics under different working conditions. In particular, accurately capturing the frequency domain information of high-frequency and low-frequency features is crucial for state identification and response prediction. To this end, this application designs a new Fourier neural operator that can capture high-frequency and low-frequency features in the frequency domain to output data. Can be The Fourier neural operator takes the input data , established from arrive The mapping relationship.

[0032] It can be understood that based on the physical properties of the pantograph, the above initial timing state The impact function and other response related functions The integral of the product is:

[0033] therefore, and The relationship between them can be established through the integral form of the following formula: .

[0034] in, It is the transfer function of the structural impact response, covering changes in multiple factors such as displacement, velocity and acceleration. , can be expressed in matrix form:

[0035] in, and It can be further interpreted as the number of response points and excitation points. This application uses Fourier neural operator to perform to reduce the impact of disturbances on the pantograph-catenary system.

[0036] Specifically, the initial time domain state is subjected to a Fast Fourier Transform (FFT) to obtain the initial frequency domain state ; Learning the transfer matrix through the Fourier neural operator of the first target neural operator ,use Determine the frequency domain signal for the next iteration , through the Inverse Fast Fourier Transform (IFFT) Convert to time domain And pass it to the Fourier neural operator of the second target neural operator for learning, and cycle in sequence until the last target neural operator to obtain the target time domain state The Fourier neural operator FNO of the present application can effectively capture high-frequency and low-frequency features in the frequency domain, avoiding the frequency domain discretization and truncation error problems in traditional methods.

[0037] 204. Input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial bow network physical variable set.

[0038] Specifically, through the fully connected layer Learning Transfer Matrix , the target time domain state Transformed into , and obtain the initial set of pantograph-catenary physical variables.

[0039] 205. Input the initial bow-net physical variable set into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

[0040] In practical applications, there are correlations between variables in the bow-net system. The present application captures the correlation between physical variables through a residual connection network layer, and continuously corrects the initial set of bow-net physical variables through residual mapping, so that the initial set of bow-net physical variables approaches the set of true values ​​of physical variables. The constraints are strengthened by embedding additional output conditions that conform to the physical laws of the bow-net in the neural network, so as to improve the accuracy of the target set of bow-net physical variables output by the model, and reduce the problems of high-dimensional integral calculation complexity, numerical instability and difficulty in selecting integral kernel functions that are still faced in pure data-driven fusion of physical information.

[0041] Specifically, each initial physical variable in the initial pantograph-catenary physical variable set is input into the corresponding building block for processing, and by performing residual connection with the associated physical variables, each building block is traversed to obtain the target pantograph-catenary physical variable set.

[0042] It can be understood that in state identification, the output target pantograph physical variable set is Includes the displacement of the bow head and frame of the bow-net system ,speed , acceleration and the axial displacement of the rigid contact network ; In response prediction, the output target pantograph physical variable set includes Lifting force and contact force and axial displacement .

[0043] In this embodiment, a physical Fourier neural operator network driven by physics and data is proposed to solve the state identification and response prediction problems of PCS. By replacing the integral operation with the Fourier neural operator, not only the need for integral discretization is avoided, thereby eliminating the discretization and truncation errors, but also the high-frequency and low-frequency characteristics can be effectively captured in the frequency domain, thereby comprehensively describing the dynamic behavior of the bow-net system. A novel residual connection network is designed to implicitly execute the physical laws using the prior knowledge of the existence between these physical variables, thereby establishing a soft constraint relationship between the characteristics of the physical variables to correct the prediction results of the target neural operator, significantly enhancing the performance of the model in solving the prediction of spatiotemporal dynamics in complex PCS environments, and can adapt to different bow-net parameters and conditions, with a strong ability to learn physical coupling equation systems.

[0044] In practical applications, traditional operator regression problems mainly deal with a single partial differential equation (PDE), making weight setting relatively straightforward. However, the pantograph system is more complex. Usually multiple ordinary differential equations (ODE) and partial differential equations (PDE) are involved, which describe the motion of different degrees of freedom. In this case, during the neural network training process, the data loss caused by each equation may be similar, but the impact on the model is different. This may lead to uneven magnitude of gradients during the backpropagation of the neural network, affecting the effective update of model parameters. It is worth noting that some equations may dominate the overall model training loss due to their large impact on the accuracy of the solution. The influence of these "sensitive" equations may mask the importance of other equations, but this sensitivity is only a mathematical property of the equation and does not fully represent its physical importance. To address this issue, please refer to Figure 3 , 4 The second embodiment of the method for predicting the physical variables of the pantograph-catwalk in the present application includes: 301. Obtain a sample data set.

[0045] The sample data set of the present application is used to indicate sample data for training the initial PhyFnoNet model, which may be a numerical simulation data set and / or a circuit data set.

[0046] The numerical simulation data set can be a numerical simulation data set for training DNN generated by using a pantograph-contact network interaction model based on a finite element numerical model (Finite Element Models, FEMs). The reasonable parameter range that complies with international design specifications is considered when generating the data set. For example, 2000 sets of data are generated as training sets by using the parameters obtained from the line test of the pantograph model DSA250. In addition, multiple sets of data of different pantograph models CX-018 and CED125D are collected as test sets, covering a variety of key parameters, including equivalent mass, stiffness and damping of the bow head, upper frame and lower frame.

[0047] The line data set can collect actual line data from multiple monitoring points on the real track line to cover different environmental conditions, operating speeds and system types. The data set can be divided into a training set and a test set, and the performance of the model in real applications can be evaluated by testing the actual data.

[0048] 302. The preset initial PhyFnoNet model is trained through the sample data set, and a multi-stage joint optimization is performed through a multi-dimensional loss function to obtain a target PhyFnoNet model.

[0049] Among them, the expression of the multidimensional loss function is:

[0050] in, represents a multidimensional loss function; Represents the data loss function, which is used to indicate the deviation between the model output and the actual true value; Represents the physical equation loss function, which is used to indicate the deviation between the model output result and the bow-catenary coupling dynamic equation; represents the partial derivative loss function, which is used to perform numerical partial derivative of the displacement signal in the contact network; Represents the weight coefficient of the corresponding loss function.

[0051] Specifically, the deviation between the model output result and the actual true value is determined by a preset data loss function to obtain a first loss value; the deviation between the model output result and the coupling equation is determined by a preset physical equation loss function to obtain a second loss value; the displacement signal in the model output result is numerically derived by a preset partial derivative function loss function to obtain a third loss value; a dynamic weighted balance adjustment is performed based on the first loss value, the second loss value, and the third loss value to obtain a target loss value; back propagation optimization is performed based on the target loss value to obtain a target PhyFnoNet model. This application aims to ensure that the model can fully consider the authenticity of the data, the accuracy of physics, and the accuracy of prediction during the learning process through a multi-dimensional loss function design.

[0052] Optionally, the expression of the data loss function is:

[0053] Optionally, the expression of the physical equation loss function is:

[0054] Optionally, the expression of the partial derivative loss function is:

[0055] This embodiment uses a dynamic weighted balance algorithm to dynamically balance the loss weight through the gradient of the physical equation loss. , putting the gradient norms of different physical equation losses on the same scale. Through this scale, the gradient norm can be dynamically adjusted so that different physical equation losses can be trained at a similar rate. The calculation method is:

[0056] Each physical equation in time The normalized loss rate . The lower the value, the faster the training speed of the equation. This normalized loss rate is calculated by Equations in time Loss With initial loss Compared and multiplied by the shared layer weight Next, calculate the relative loss rate for each physical equation , used to balance the gradients of the equations. Relative loss By normalizing the loss rate The average normalized loss rate of all equations Then, for each physical equation, calculate its weighted loss Relative to the shared layer weights The gradient norm of , and the average gradient norm of all equations Through these gradient norms, the loss weights of each physical equation are dynamically adjusted to keep different physical equations balanced during training, avoiding insufficient or excessive model parameter updates due to uneven gradient magnitudes. In this way, the training speed of the physical equations can be coordinated to ensure that the model has good performance on each equation.

[0057] When the loss of a physical equation is too large (i.e. ), its gradient Increase, resulting in weight To this end, this application calculates the loss gradient To adjust the weight Among them, the hyperparameter Used to pull the loss of different physical equations back to the normal training rate, you can set ,exist middle, The smaller the value of The greater the gradient of the physical equation, the greater the weight Reduce. And calculate the relative loss rate by the following formula To update the weights ,

[0058] in, Represents the global learning rate. In order to prevent the weight is equal to zero, When seeking the derivative, After each training batch, in order to The derivation process and the global learning rate of the neural network Decoupling, this application re-regularizes the weights , so that ,in is the total number of physical equations, which can be set .

[0059] 303. Obtain the input parameters of the bow-net system corresponding to the target prediction task.

[0060] 304. Input the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state.

[0061] Steps 303 and 304 may be performed with reference to steps 201 and 202 and will not be described in detail here.

[0062] 305. The initial time domain state is input into multiple target neural operators of the feature extraction layer of the target PhyFnoNet model to iteratively perform frequency domain feature extraction to obtain the target time domain state.

[0063] The target neural operator of this embodiment includes at least a Fourier neural operator, and a Transformer neural operator and / or a convolution neural operator may be set as required to improve the accuracy of the prediction, which is not specifically limited in this embodiment.

[0064] Specifically, the initial time domain state is fast Fourier transformed to obtain the initial frequency domain state; the initial frequency domain state is input into the first target neural operator for feature extraction to obtain the first frequency domain feature; the first frequency domain feature is input into the second target neural operator for feature extraction to obtain the second frequency domain feature; the frequency domain features extracted by the previous target neural operator are input into the next target neural operator for feature extraction in turn to obtain the target frequency domain features output by the last target neural operator; the target frequency domain features are inversely fast Fourier transformed to obtain the target time domain state.

[0065] Optional, the current initial time domain state , use fast Fourier transform FFT to convert it to the frequency domain and get the frequency domain representation ; The frequency domain signal Input target neural operator , learn the transfer matrix ; Using the learned transfer matrix Calculate the frequency domain signal for the next iteration ; Through IFFT Convert back to the time domain and get the new time domain state ; Repeat the above until the preset number of iterations is reached , and obtain the final time domain state ;pass Learn, will Transformed into .

[0066] 306. Input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial set of bow network physical variables.

[0067] Step 306 can be performed with reference to step 204 and will not be described in detail here.

[0068] 307 Input each initial physical variable in the initial bow-net physical variable set into the corresponding building block for processing, and traverse each building block by performing residual connection with the associated physical variable to obtain the target bow-net physical variable set.

[0069] Reference Figure 4This application uses residual connections to learn the implicit functional relationship between physical variables to describe the connection between physical information. In order to more effectively control the incoming amount of residual features, a learnable gating variable is introduced to adjust the degree of influence between different physical features and enhance the adaptability and flexibility of the model to different physical features. Finally, considering that the pantograph-catenary system is a complex dynamic system and there is a strong coupling interaction between the pantograph and the contact network, this application embeds multiple ODEs and PDEs in PCS into the neural network through the loss function. These equations describe the dynamic behavior of PCS, such as the vibration of the pantograph, the deformation of the contact network, and the propagation of waves.

[0070] In the set of physical variable truth values The physical variables can affect each other. In order to make the physical variable feature set This paper designs a physics-informed residual network (PIRN) to implicitly solve the correlation between physical variables. PIRN continuously modifies the feature set of physical variables through residual mapping. ,make Approximate the corresponding set of true values ​​of physical variables PIRN is composed of The same basic building blocks Composition, each Contains two fully connected layers, Gelu activation function , and by parameter To optimize, can be expressed by the following formula:

[0071] At each discrete time step Down, Using Impact Features The feature set Features in To correct ,in, The training process of a deep residual network can be viewed as the discretization of a dynamic system controlled by ordinary differential equations, where the network layers Corresponding time step, network parameters is considered as the control variable to be optimized. A diffeomorphic transformation is constructed The transformation is done by building blocks , gradually learn the feature set With features The residual mapping relationship between , so that it can more accurately fit the target physical variables :

[0072] in, , It represents the gating mechanism layer, which can adaptively learn the gating variables according to the different influences between physical features. The range of the learned gating variables is between [0,1]. A gating variable of 0 means that the residual input is completely closed, and a gating variable of 1 means that the residual input is completely open. Compared with the traditional residual network, the time-varying , and optimize its fitting error. To this end, assume that the number of blocks , thus the optimization process of the loss function is expressed as:

[0073] Among them, for ,have ; represents the initial residual mapping, represents the final residual mapping change, It represents the change of the residual map at the intermediate moment. is a set of functions that approximate the characteristics of physical variables in the network. The second term is the regularization term, which means that arrive The trajectory length ensures that the optimization process is carried out with the optimal strategy; is a weight factor used to balance the data fitting terms and the influence of the regularization term.

[0074] The PIRN of this application can be described as the following steps: (1) Characteristics of physical variables and its associated physical variable feature set Perform diffeomorphic transformations respectively; (2) Initialize network parameters ; (3) Use the loss functions in the above two formulas to continuously optimize the corrected features and obtain the final physical variables .

[0075] In this embodiment, a dynamic weighted balance algorithm is proposed to achieve dynamic adjustment of the losses of different physical equations to ensure the balance of physical information during training. By proposing a physical Fourier neural operator network driven by physics and data to solve the state identification and response prediction problems of PCS, the Fourier neural operator is used to replace the integral operation. Not only does PhyFnoNet avoid the need for integral discretization, thereby eliminating discretization and truncation errors, but it can also effectively capture high-frequency and low-frequency features in the frequency domain, thereby comprehensively describing the dynamic behavior of the bow-net system. A novel residual connection network is designed to implicitly execute physical laws using the prior knowledge of the existence of these physical variables, thereby establishing soft constraint relationships between the characteristics of physical variables, adjusting the degree of influence between different physical characteristics through gating variables, enhancing the adaptability and flexibility of the model to different physical characteristics, and correcting the prediction results of the target neural operator. The performance of the model in solving complex PCS environments in predicting spatiotemporal dynamics is significantly enhanced, and it can adapt to different bow-net parameters and conditions, and has a strong ability to learn physical coupling equation systems.

[0076] In practical applications, the FNO neural operator of the PhyFnoNet model can effectively extract high-frequency and low-frequency features in the frequency domain, but it has certain limitations in capturing global dependencies and local feature information. To solve this problem, please refer to Figure 5-7 The third embodiment of the method for predicting the physical variables of the bow-net in the present application includes: 501. Obtain input parameters of the bow-net system corresponding to the target prediction task.

[0077] 502. Input the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state.

[0078] Specifically, refer to Figure 6 The structural framework of the target PhyFnoNet model of this application can be expressed as:

[0079] in, represents a FOLGP-based network, Fully connected Map the input parameters of the bow-cat system into high-dimensional space vectors.

[0080] 503. Perform a fast Fourier transform on the initial time domain state to obtain an initial frequency domain state.

[0081] 504. The initial frequency domain state is sequentially input into the Fourier neural operator of the target neural operator to extract high-frequency features and low-frequency features, the global frequency domain features are extracted through the Transformer neural operator, and the local frequency domain features are extracted through the convolution neural operator to obtain the target frequency domain features output by the last target neural operator.

[0082] Reference Figure 7 Each target neural operator in this implementation includes a Fourier neural operator, a Transformer neural operator, and a convolution neural operator, where R represents the application of a learnable linear transformation. The iterative process of multiple target neural operators can be performed with reference to the above step 305. This embodiment takes the processing process of one of the target neural operators FOLGP as an example for explanation: The FOLGP of this application can capture features in global and local scopes and learn the frequency domain characteristics of the pantograph-catenary system mechanics. In each iteration process, Can be defined as the target neural operator And the activation function The compound calculation method is:

[0083] Among them, the target neural operator The formula can be:

[0084] in, represents the Fourier neural operator, represents the Fourier-based neural operator represents the Transformer-based neural operator, represents a convolution-based neural operator; It can enhance the model's ability to capture different frequency components. The expression of the Fourier neural operator is:

[0085] in, represents Fourier-based neural operator; Indicates the current pantograph-catenary system input parameters; Represents the current model parameters; Indicates The frequency domain characteristics of the iteration; Represents each input position All belong to a bounded open set ; represents fast Fourier transform; represents the inverse fast Fourier transform, is a periodic function The Fast Fourier Transform result of .

[0086] The Transformer neural operator can effectively model global features (Global Perceptron) in the frequency domain and capture the correlation between different frequency bands in parallel, especially showing significant advantages in feature extraction of high-frequency and low-frequency components. Therefore, this paper introduces the Transformer to improve the global modeling capability of frequency domain information, so as to achieve more accurate feature capture and representation between different frequency components. The calculation method is:

[0087] in, Represents the Transformer neural operator; Express The fast Fourier transform result is passed as input to the Transformer neural operator for processing. Represents the inverse fast Fourier transform.

[0088] Transformer may lose local structural features when extracting local frequency domain details. To make up for this shortcoming, this application introduces four parallel convolution layers to assist in learning local priors. The designed convolution kernel sizes are 1, 3, 5, and 7 respectively, and the padding is set to To keep the output resolution consistent, thereby enhancing the ability to extract local frequency domain information, the expression of the convolutional neural operator is:

[0089] in, represents the convolutional neural operator; Express The fast Fourier transform result is passed as input to the convolutional neural operator for processing. Represents the inverse fast Fourier transform.

[0090] Repeat the above process until the last layer of feature expression is obtained. .

[0091] The FNO of this embodiment can effectively capture high-frequency and low-frequency features in the frequency domain, avoiding the frequency domain discretization and truncation error problems in traditional methods. The Transformer module can effectively model global features and capture the correlation between different frequency bands by modeling global context information in the frequency domain, thereby improving the ability to capture correlation between different frequency bands. Conv focuses on extracting local frequency domain features to ensure that the internal dependencies between features are maintained.

[0092] 505. Perform inverse fast Fourier transform on the target frequency domain features to obtain the target time domain state.

[0093] 506. Input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial set of bow network physical variables.

[0094] 507. Input the initial bow-net physical variable set into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

[0095] The goal of the residual connection network layer in this application is to make , by optimizing the neural network parameters Establish and The mapping relationship between

[0096] in, Represents a FOLGP-based network.

[0097] In this embodiment, a physically driven and data-driven physical Fourier neural operator network is proposed to solve the state identification and response prediction problems of PCS. The Fourier neural operator is used instead of the integral operation, which not only avoids the need for integral discretization, thereby eliminating the discretization and truncation errors, but also can effectively capture high-frequency and low-frequency features in the frequency domain, and can better capture frequency domain feature information. By adding the Transformer neural operator, the global dependencies in the frequency domain features can be effectively supplemented by adding parallel convolution layers, that is, the convolution neural operator further enhances the ability to capture local features in the frequency domain. The PhyFnoNet model of this application is particularly outstanding in identifying the detailed features of a specific frequency band, thereby comprehensively describing the dynamic behavior of the bow-net system. The residual connection network uses the prior knowledge between these physical variables to implicitly execute physical laws, thereby establishing soft constraint relationships between the characteristics of physical variables. The gated variables are used to adjust the degree of influence between different physical characteristics, enhance the adaptability and flexibility of the model to different physical characteristics, and correct the prediction results of the target neural operator. This significantly enhances the performance of the model in predicting spatiotemporal dynamics in complex PCS environments. It can adapt to different bow-net parameters and conditions and has a strong ability to learn physical coupling equation systems.

[0098] The above describes the method for predicting the physical variables of the bow-net in the present application. The following describes the device for predicting the physical variables of the bow-net in the present application. Figure 8 In this embodiment, an embodiment of the pantograph-catwalk physical variable prediction device includes: The first acquisition module 801 is used to acquire the input parameters of the bow-net system corresponding to the target prediction task; The first conversion module 802 is used to input the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state; A feature extraction module 803 is used to iteratively perform frequency domain feature extraction on multiple target neural operators of a feature extraction layer of a target PhyFnoNet model by inputting the initial time domain state to obtain a target time domain state, wherein the target neural operator includes at least a Fourier neural operator; The second conversion module 804 is used to input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial bow network physical variable set; The correction module 805 is used to input the initial bow-net physical variable set into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

[0099] In this embodiment, a physical Fourier neural operator network driven by physics and data is proposed to solve the state identification and response prediction problems of PCS. By replacing the integral operation with the Fourier neural operator, PhyFnoNet not only avoids the need for integral discretization, thereby eliminating the discretization and truncation errors, but also can effectively capture high-frequency and low-frequency features in the frequency domain, thereby comprehensively describing the dynamic behavior of the bow-net system. A novel residual connection network is designed to implicitly execute physical laws using the prior knowledge of the existence between these physical variables, thereby establishing a soft constraint relationship between the physical variable characteristics to correct the prediction results of the target neural operator, significantly enhancing the performance of the model in solving complex PCS environments in predicting spatiotemporal dynamics, and can adapt to different bow-net parameters and conditions, with a strong ability to learn physical coupling equation systems.

[0100] See also Fig. 9 Another embodiment of the pantograph-catwalk physical variable prediction device in the present application includes: The first acquisition module 801 is used to acquire the input parameters of the bow-net system corresponding to the target prediction task; The first conversion module 802 is used to input the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state; A feature extraction module 803 is used to iteratively perform frequency domain feature extraction on multiple target neural operators of a feature extraction layer of a target PhyFnoNet model by inputting the initial time domain state to obtain a target time domain state, wherein the target neural operator includes at least a Fourier neural operator; The second conversion module 804 is used to input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial bow network physical variable set; The correction module 805 is used to input the initial bow-net physical variable set into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

[0101] Optionally, the feature extraction module 803 includes: The frequency domain conversion unit 8031 ​​is used to perform a fast Fourier transform on the initial time domain state to obtain an initial frequency domain state; The feature extraction unit 8032 is used to input the initial frequency domain state into the first target neural operator for feature extraction to obtain a first frequency domain feature; input the first frequency domain feature into the second target neural operator for feature extraction to obtain a second frequency domain feature; input the frequency domain feature extracted by the previous target neural operator into the next target neural operator for feature extraction in sequence to obtain a target frequency domain feature output by the last target neural operator; The time domain conversion unit 8033 is used to perform inverse fast Fourier transform on the target frequency domain features to obtain the target time domain state.

[0102] The feature extraction unit 8032 is specifically used to: sequentially input the frequency domain features extracted by the previous target neural operator into the Fourier neural operator of the next target neural operator to extract high-frequency features and low-frequency features, and obtain the target frequency domain features output by the last target neural operator; The expression of Fourier neural operator is:

[0103] in, represents Fourier-based neural operator; Indicates the current pantograph-catenary system input parameters; Represents the current model parameters; Indicates The frequency domain characteristics of the iteration; Represents each input position All belong to a bounded open set ; represents fast Fourier transform; represents the inverse fast Fourier transform, is a periodic function The Fast Fourier Transform result of .

[0104] The feature extraction unit 8032 is specifically used to: input the frequency domain features extracted by the previous target neural operator into the Transformer neural operator of the next target neural operator to extract the global frequency domain features. The expression of the Transformer neural operator is:

[0105] in, Represents the Transformer neural operator; Express The fast Fourier transform result is passed as input to the Transformer neural operator for processing.

[0106] And / or, the frequency domain features extracted by the previous target neural operator are input into the convolution neural operator of the next target neural operator to extract the local frequency domain features. The expression of the convolution neural operator is:

[0107] in, represents the convolutional neural operator; Express The fast Fourier transform result is passed as input to the convolutional neural operator for processing.

[0108] Optionally, the pantograph-catenary physical variable prediction device further includes: The second acquisition module 806 is used to acquire a sample data set; The training module 807 is used to train the preset initial PhyFnoNet model through the sample data set, and perform multi-stage joint optimization through a multi-dimensional loss function to obtain the target PhyFnoNet model.

[0109] Optionally, the training module 807 is specifically used for: the multi-dimensional loss function is obtained by dynamically weighted balancing the data loss function, the physical equation loss function, and the partial derivative function loss function, and its expression is:

[0110] in, represents a multidimensional loss function; Represents the data loss function, which is used to indicate the deviation between the model output and the actual true value; Represents the physical equation loss function, which is used to indicate the deviation between the model output result and the bow-catenary coupling dynamic equation; represents the partial derivative loss function, which is used to perform numerical partial derivative of the displacement signal in the contact network; Represents the weight coefficient of the corresponding loss function.

[0111] In this embodiment, a dynamic weighted balance algorithm is proposed to realize dynamic adjustment of the losses of different physical equations to ensure the balance of physical information during the training process. A physically driven and data-driven physical Fourier neural operator network is proposed to solve the state identification and response prediction problems of PCS. By replacing the integral operation with the Fourier neural operator, PhyFnoNet not only avoids the need for integral discretization, thereby eliminating the discretization and truncation errors, but also can effectively capture high-frequency and low-frequency features in the frequency domain. By adding the Transformer neural operator, the global dependencies in the frequency domain features can be effectively supplemented. The addition of parallel convolutional layers further enhances the ability to capture local features in the frequency domain. The PhyFnoNet model of this application is particularly outstanding in identifying the detailed features of specific frequency bands, thereby comprehensively describing the dynamic behavior of the bow-net system. A novel residual connection network is designed to utilize the prior knowledge of the existence between these physical variables to implicitly execute physical laws, thereby establishing soft constraint relationships between the characteristics of physical variables. The degree of influence between different physical characteristics is adjusted by gating variables, thereby enhancing the adaptability and flexibility of the model to different physical characteristics, and correcting the prediction results of the target neural operator. The performance of the model in predicting spatiotemporal dynamics in complex PCS environments is significantly enhanced. It can adapt to different bow-net parameters and conditions and has a strong ability to learn physical coupling equation systems.

[0112] above Figure 8 and Fig. 9 The bow-cat physical variable prediction device of the present application is described in detail from the perspective of modular functional entities, and the bow-cat system of the present application is described in detail from the perspective of hardware processing.

[0113] See also Fig.10 As shown, the bow-cat system includes a processor 1000 and a memory 1001, wherein the memory 1001 stores machine executable instructions that can be executed by the processor 1000, and the processor 1000 executes the machine executable instructions to implement the above-mentioned bow-cat physical variable prediction method.

[0114] Further, Fig.10 The shown pantograph-catenary system further includes a bus 1002 and a communication interface 1003 , and the processor 1000 , the communication interface 1003 and the memory 1001 are connected via the bus 1002 .

[0115] Among them, the memory 1001 may include a high-speed random access memory (RAM), and may also include a non-volatile memory (non-volatile memory), for example, at least one disk storage. The communication connection between the system network element and at least one other network element is realized through at least one communication interface 1003 (which can be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. can be used. The bus 1002 can be an ISA bus, a PCI bus or an EISA bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Fig.10 Only one bidirectional arrow is used in the diagram, but this does not mean that there is only one bus or only one type of bus.

[0116] The processor 1000 may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the hardware integrated logic circuit or software instructions in the processor 1000. The above processor 1000 can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The disclosed methods, steps and logic block diagrams in the embodiments of the present disclosure can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in conjunction with the embodiments of the present disclosure can be directly embodied as a hardware decoding processor for execution, or a combination of hardware and software modules in the decoding processor for execution. The software module may be located in a storage medium mature in the art, such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory 1001, and the processor 1000 reads the information in the memory 1001 and completes the method steps of the above-mentioned embodiment in combination with its hardware.

[0117] The present application also provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium. Instructions are stored in the computer-readable storage medium. When the instructions are executed on a computer, the computer executes the steps of the bow-net physical variable prediction method.

[0118] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0119] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk and other media that can store program codes.

[0120] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some of the technical features therein by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for predicting physical variables of a pantograph and a catenary, characterized in that: The method for predicting the physical variables of the pantograph and catenary comprises: Obtain the input parameters of the bow-net system corresponding to the target prediction task; Inputting the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state; Inputting the initial time domain state into a plurality of target neural operators of a feature extraction layer of the target PhyFnoNet model iteratively performs frequency domain feature extraction to obtain a target time domain state, wherein the target neural operator at least includes a Fourier neural operator; Input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial bow-net physical variable set; The initial bow-net physical variable set is input into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

2. The method for predicting pantograph-catenary physical variables according to claim 1, characterized in that: The step of inputting the initial time domain state into the multiple target neural operators of the feature extraction layer of the target PhyFnoNet model sequentially performs frequency domain feature extraction to obtain the target time domain state, including: Performing a fast Fourier transform on the initial time domain state to obtain an initial frequency domain state; Inputting the initial frequency domain state into a first target neural operator for feature extraction to obtain a first frequency domain feature; Inputting the first frequency domain feature into a second target neural operator for feature extraction to obtain a second frequency domain feature; The frequency domain features extracted by the previous target neural operator are sequentially input into the next target neural operator for feature extraction, and the target frequency domain features output by the last target neural operator are obtained; The target frequency domain features are subjected to inverse fast Fourier transform to obtain the target time domain state.

3. The method for predicting pantograph-catenary physical variables according to claim 2, characterized in that: The frequency domain features extracted by the previous target neural operator are sequentially input into the next target neural operator for feature extraction to obtain the target frequency domain features output by the last target neural operator, including: Sequentially inputting the frequency domain features extracted by the previous target neural operator into the Fourier neural operator of the next target neural operator to extract high-frequency features and low-frequency features, and obtaining the target frequency domain features output by the last target neural operator; The expression of the Fourier neural operator is: in, represents Fourier-based neural operator; Indicates the current pantograph-catenary system input parameters; Represents the current model parameters; Indicates Frequency domain characteristics of iterations; Represents each input position All belong to a bounded open set ; represents fast Fourier transform; represents the inverse fast Fourier transform, is a periodic function The Fast Fourier Transform result of .

4. The method for predicting pantograph-catenary physical variables according to claim 3, characterized in that: The target neural operator also includes a Transformer neural operator and / or a convolutional neural operator; After sequentially inputting the frequency domain features extracted by the previous target neural operator into the Fourier neural operator of the next target neural operator to extract high-frequency features and low-frequency features, the method further includes: The frequency domain features extracted by the previous target neural operator are input into the Transformer neural operator of the next target neural operator to extract the global frequency domain features. The expression of the Transformer neural operator is: in, Represents the Transformer neural operator; Express The fast Fourier transform result is passed as input to the Transformer neural operator for processing; And / or, the frequency domain features extracted by the previous target neural operator are input into the convolution neural operator of the next target neural operator to extract local frequency domain features, and the expression of the convolution neural operator is: in, represents the convolutional neural operator; Express The fast Fourier transform result is passed as input to the convolutional neural operator for processing.

5. The method for predicting pantograph-catenary physical variables according to claim 1, characterized in that: The residual connection network layer includes a plurality of building blocks; The initial set of pantograph-net physical variables is input into the residual connection network layer of the target PhyFnoNet model for correction to obtain a target set of pantograph-net physical variables, including: Each initial physical variable in the initial pantograph-catenary physical variable set is input into a corresponding building block for processing, and a residual connection is performed with the associated physical variable to traverse each building block to obtain a target pantograph-catenary physical variable set.

6. The method for predicting pantograph-catenary physical variables according to any one of claims 1 to 5, characterized in that: Before obtaining the pantograph-catenary system input parameters corresponding to the target prediction task, it also includes: Get a sample data set; The preset initial PhyFnoNet model is trained by the sample data set, and a multi-stage joint optimization is performed by a multi-dimensional loss function to obtain a target PhyFnoNet model.

7. The method for predicting pantograph-catenary physical variables according to claim 6, characterized in that: The multidimensional loss function is obtained by dynamically weighting and balancing the data loss function, the physical equation loss function, and the partial derivative function loss function, and its expression is: in, represents a multidimensional loss function; Represents the data loss function, which is used to indicate the deviation between the model output and the actual true value; Represents the physical equation loss function, which is used to indicate the deviation between the model output result and the bow-catenary coupling dynamic equation; represents the partial derivative loss function, which is used to perform numerical partial derivative of the displacement signal in the contact network; Represents the weight coefficient of the corresponding loss function.

8. A pantograph-catenary physical variable prediction device, characterized in that: The pantograph-catenary physical variable prediction device comprises: The first acquisition module is used to obtain the input parameters of the bow-net system corresponding to the target prediction task; A first conversion module is used to input the input parameters of the bow-net system into the first fully connected layer of the pre-trained target PhyFnoNet model for conversion to obtain an initial time domain state; A feature extraction module, used for inputting the initial time domain state into a plurality of target neural operators of the feature extraction layer of the target PhyFnoNet model to iteratively perform frequency domain feature extraction to obtain a target time domain state, wherein the target neural operator at least includes a Fourier neural operator; A second conversion module is used to input the target time domain state into the second fully connected layer of the target PhyFnoNet model for conversion to obtain an initial bow network physical variable set; The correction module is used to input the initial bow-net physical variable set into the residual connection network layer of the target PhyFnoNet model for correction to obtain the target bow-net physical variable set.

9. A pantograph-catenary system, characterized in that: The pantograph-catenary system comprises: a memory and at least one processor, wherein instructions are stored in the memory; The at least one processor calls the instructions in the memory so that the pantograph-catenary system executes the pantograph-catenary physical variable prediction method according to any one of claims 1 to 7.

10. A computer-readable storage medium having instructions stored thereon, characterized in that: When the instruction is read and executed, the method for predicting the physical variables of the pantograph-catenary system as described in any one of claims 1 to 7 is executed.

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