Pantograph-catenary time history prediction method, device and system and storage medium

Abstract

The invention relates to the technical field of rail transit, discloses a pantograph-catenary time history prediction method, device and system and a storage medium, and is used for solving the problem that a pantograph-catenary system state prediction model established in the prior art cannot be compatible with prediction of pantograph-catenary systems under different catenaries. The method comprises the following steps: acquiring current state data and structure parameters of the pantograph-catenary system; inputting the structure parameters into a condition encoder of a pre-trained target GDPINN model for encoding to obtain physical constraint conditions; inputting the current state data into an AttnFNO layer of the target GDPINN model to perform multi-stage Fourier neural operator iteration to extract frequency domain features, and obtaining target frequency domain features; and inputting the target frequency domain feature and the physical constraint condition into a QKV de-noising network layer of the target GDPINN model for de-noising processing to obtain a target pantograph-catenary time history set.

Description

Technical Field

[0001] This application relates to the field of rail transit technology, and in particular to a method, device, system and storage medium for predicting pantograph-catenary time-history. Background Technology

[0002] The pantograph-contact system (PCS) is a crucial link between the train and the power supply system. Its performance directly affects the train's stable current collection and driving safety. Therefore, good interaction performance between the pantograph and the overhead contact line in the PCS is essential for the safe operation of rail vehicles.

[0003] With the intelligent development of railways, the integration of trunk railways, intercity railways, suburban railways, and urban rail transit has become a key technology for improving railway efficiency and ensuring system stability. Under this integration, predicting the state of the pantograph-catenary system using models faces new challenges. For example, pantograph-catenary systems composed of flexible and rigid contact wires exhibit significant differences in their dynamic characteristics. Existing modeling methods for predicting the state of pantograph-catenary systems mostly focus on a single contact wire type, failing to adapt to different contact wires simultaneously, leading to inaccurate predictions of the pantograph-catenary system's state. Summary of the Invention

[0004] This application provides a method, apparatus, system, and storage medium for predicting pantograph-catenary system time history, aiming to solve the problem that existing pantograph-catenary system state prediction models are incompatible with predictions for pantograph-catenary systems under different contact wire systems.

[0005] The first aspect of this application provides a method for predicting pantograph-catenary time histories, including: Obtain the current status data and structural parameters of the pantograph-catenary system; The structural parameters are input into the conditional encoder of the pre-trained target GDPINN model for encoding to obtain the physical constraints. The current state data is input into the AttnFNO layer of the target GDPINN model to extract frequency domain features through multi-stage Fourier neural operator iteration, thereby obtaining the target frequency domain features. The target frequency domain features and the physical constraints are input into the QKV denoising network layer of the target GDPINN model for denoising processing, resulting in the target pantograph-catenary time history set.

[0006] In one feasible implementation of the first aspect, the step of inputting the current state data into the AttnFNO layer of the target GDPINN model for multi-stage Fourier neural operator iteration to extract frequency domain features and obtain target frequency domain features includes: The current state data is input into the first fully connected layer for transformation to obtain the initialization vector of the current state data; The initialization vector is input into the first attention-based Fourier neural network to perform the first Fourier transform and inverse transform to obtain the first vector; The first vector is input into a second attention-based Fourier neural network for a second Fourier transform and inverse transform to obtain the second vector; The vector obtained by the previous Fourier neural network based on the attention mechanism is sequentially input into the next Fourier neural network based on the attention mechanism for Fourier transform and inverse transform, so as to obtain the vector output by the last Fourier neural network based on the attention mechanism. The last output vector is input into the second fully connected layer for inverse transformation to obtain the target frequency domain features.

[0007] In one feasible implementation of the first aspect, the step of sequentially inputting the vector obtained from the previous attention-based Fourier neural network transformation into the next attention-based Fourier neural network for Fourier transform and inverse transform, to obtain the vector output by the last attention-based Fourier neural network, includes: The vectors obtained from the previous Fourier neural network transformation based on the attention mechanism are sequentially input into the next Fourier neural network based on the attention mechanism for fast Fourier transform. The weight vector is determined based on the result of the Fast Fourier Transform, and then convolved with the result of the Fast Fourier Transform to generate the residual. The residual is multiplied by the result of the Fast Fourier Transform and then normalized. The result of the normalization is then subjected to the Fast Inverse Fourier Transform to obtain the vector output by the last Fourier neural network based on the attention mechanism. The computational expression for the attention-based Fourier neural network is as follows: , in, Represents the target's frequency domain characteristics; Represents status data; For the parameter set of AttnFNO; Indicates the first The vector of the next iteration; This represents the inverse Fast Fourier Transform; For periodic kernel The tensor composed of frequency domain coefficients; Indicates Fast Fourier Transform; Represents the residual.

[0008] In one feasible implementation of the first aspect, determining the weight vector based on the result of the fast Fourier transform includes: The result of the Fast Fourier Transform is convolved, and the result of the convolution is then subjected to global average pooling. The SoftMax function is used to convert the result of the fast Fourier transform after pooling into a weight vector.

[0009] In one feasible embodiment of the first aspect, prior to acquiring the current state data and structural parameters of the pantograph-catenary system, the method further includes: Acquire historical operational data of the pantograph-catenary system, and construct a sample data set based on the historical operational data; The preset initial GDPINN model is trained using the sample data set and optimized using a loss function to obtain the target GDPINN model, wherein the initial GDPINN model is obtained by combining a denoising diffusion probability model and a physical information neural network.

[0010] In one feasible implementation of the first aspect, the expression for the loss function is:

[0011] in, Represents a multidimensional loss function; This represents the data loss function, used to indicate the deviation between the model output and the actual true value; This represents the loss function of the physical equations, used to indicate the deviation between the model output and the bow-catenary coupling dynamics equations; This represents the partial derivative loss function, used to perform numerical partial derivatives on the displacement signal in the overhead contact system. This represents the weighting coefficients of the corresponding loss function.

[0012] In one feasible implementation of the first aspect, constructing a sample data set based on the historical operational data includes: Under the structural parameters of the pantograph-catenary system, a Gaussian-distributed state data sample is obtained by gradually injecting small-amplitude Gaussian noise into the historical state data of the pantograph-catenary system in T steps through a Markov chain. A sample data set is constructed based on the state data samples and the structural parameters of the pantograph-catenary system.

[0013] In one feasible embodiment of the first aspect, before constructing the sample data set based on the state data samples and the structural parameters of the pantograph-catenary system, the method further includes: Calculate the prior probability and posterior probability of each state data in the state data sample; Based on the prior probability and the posterior probability, the Kullback-Leibler divergence is obtained by approximating the solution using a Gaussian function; Based on the Kullback-Leibler divergence, the injected Gaussian noise for each state data is adjusted.

[0014] A second aspect of this application provides a pantograph-catenary time history prediction device, comprising: The acquisition module is used to acquire the current status data and structural parameters of the pantograph-catenary system; The encoding module is used to input the structural parameters into the conditional encoder of the pre-trained target GDPINN model for encoding to obtain the physical constraints. The extraction module is used to input the current state data into the AttnFNO layer of the target GDPINN model to extract frequency domain features through multi-stage Fourier neural operator iteration, thereby obtaining the target frequency domain features; The prediction module is used to input the target frequency domain features and the physical constraints into the QKV denoising network layer of the target GDPINN model for denoising processing, so as to obtain the target pantograph-catenary time history set.

[0015] A third aspect of this application provides a pantograph-catenary system, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor invokes the instructions in the memory to cause the pantograph-catenary system to execute the pantograph-catenary time-course prediction method described above.

[0016] A fourth aspect of this application provides a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the above-described pantograph-catenary time-history prediction method.

[0017] The technical solution provided in this application proposes a unified modeling framework—a physical information neural network model based on a guided denoising diffusion probability model. This model combines generative modeling with physical information constraints, enabling it to simultaneously cover the dynamic characteristics of both flexible and rigid contact wires, and accurately identify and predict the state of the pantograph-catenary system under different operating conditions. Then, by introducing an attention-based Fourier neural operator, the model's ability to model in both the time and frequency domains of the pantograph-catenary system is significantly improved. Finally, this paper proposes a Bayesian-based reversible guidance strategy, which can effectively guide the model to learn a state distribution that conforms to physical laws, thereby enhancing the model's stability and accuracy. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of an embodiment of the bow-net time history prediction method in this application; Figure 2This is a schematic diagram of the second embodiment of the bow-net time history prediction method in this application; Figure 3 This is a schematic diagram of the overall framework of the GDPINN model in this application; Figure 4 This is a schematic diagram of the AttnFNO layer in the GDPINN model of this application; Figure 5 This is a schematic diagram of the framework of the attention-based Fourier neural operator in this application; Figure 6 This is a schematic diagram of the framework of the Bayesian-based reversible guidance strategy in this application; Figure 7 This is a schematic diagram of one embodiment of the pantograph-catenary time history prediction device in this application; Figure 8 This is a schematic diagram of one embodiment of the bow-net system in this application. Detailed Implementation

[0019] This application provides a method, apparatus, system, and storage medium for predicting pantograph-catenary system time history, which addresses the problem that existing pantograph-catenary system state prediction models are incompatible with predictions for pantograph-catenary systems under different contact wire systems.

[0020] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a particular order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms “comprising” or “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0021] As a typical high-dimensional, highly nonlinear, and spatiotemporally coupled dynamic system, the accurate modeling of the pantograph-catenary system is crucial for the stability of the traction power supply system and the safety and efficiency of train operation. With the development of intelligent railways, the integration of trunk railways, intercity railways, suburban railways, and urban rail transit has become a key technology for improving railway efficiency and ensuring system stability. Under this integration, modeling the pantograph-catenary system faces new challenges. The significant differences in dynamic characteristics between flexible and rigid catenaries drive the need for a unified modeling framework. Flexible catenaries employ a chain-like suspension structure of "catenary cable-dropper-contact wire," capable of adapting to complex track deformation and high-frequency vibrations, making them particularly suitable for high-speed railways. Rigid catenaries, on the other hand, have the contact wire directly supported by conductive profiles, resulting in a simplified and robust structure suitable for medium- and low-speed railway lines. Existing modeling methods mostly focus on a single catenary type or specific operating conditions, failing to simultaneously address nonlinear and time-varying problems under different catenary forms and complex operating conditions. Therefore, a unified framework is urgently needed to encompass the dynamic characteristics of different catenary types and provide accurate modeling and prediction.

[0022] To address the aforementioned technical problems, this application provides a method for predicting pantograph-catenary time histories, such as... Figure 1 As shown, the method includes the following steps: 101. Obtain the current status data and structural parameters of the pantograph-catenary system.

[0023] It is understood that the executing entity of this application can be a pantograph-catenary time history prediction device, or it can be a pantograph-catenary system, a terminal, or a server; no specific limitation is made here. This application's embodiments use a pantograph-catenary system as an example for illustration.

[0024] In this step, sensors can be used to monitor and collect the parameters of the contact wire and hardware on the pantograph-catenary system. The parameters of the contact wire are actually calculated based on the real-time load conditions and the fixed parameters of the contact wire itself.

[0025] Structural parameters refer to the connection relationships and related parameters of the circuits and structures between the pantograph-catenary system and the overhead contact line.

[0026] 102. Input the structural parameters into the conditional encoder of the pre-trained target GDPINN model to obtain the physical constraints.

[0027] The structural parameters are input into the condition encoder for condition configuration and encoding to output the physical constraints of the pantograph-catenary system, such as the linkage relationship between various devices in the pantograph-catenary system and the condition settings for execution.

[0028] 103. Input the current state data into the AttnFNO layer of the target GDPINN model to perform multi-stage Fourier neural operator iteration to extract frequency domain features and obtain the target frequency domain features.

[0029] In this embodiment, the AttnFNO layer is actually a Fourier neural operator layer based on the attention mechanism. It is mainly used to extract features from the current state data. Specifically, it obtains the target frequency domain features by integrating, iterating the Fourier neural operator multiple times, and then integrating again.

[0030] 104. Input the target frequency domain features and physical constraints into the QKV denoising network layer of the target GDPINN model for denoising processing to obtain the target pantograph-catenary time history set.

[0031] In this step, the target frequency domain features are constrained by physical constraints, and the noise is removed by a QKV noise removal network layer to restore the original state data for output.

[0032] Specifically, the noise reduction network layer actually performs at least one noise reduction process during noise reduction. The specific number of noise reduction processes can be determined based on the logic learned during training. That is, it is through the reverse process of the noise increase logic learned during training to realize the noise pattern of the state data. When processing the actual state data, the original state data can be accurately restored.

[0033] In this embodiment, the unified model target GDPINN model is constructed to extract features and remove noise from the current state data and structural parameters obtained in the pantograph-catenary system in order to restore the original data, thereby realizing the prediction of the time history set of the pantograph-catenary system. This model structure can predict the pantograph-catenary system without considering the catenary type, which solves the problem of incompatibility of single catenary models in the prior art.

[0034] Please see Figure 2-6 The second embodiment of the pantograph-net time history prediction method in this application specifically includes the following steps: 201. Obtain historical operating data of the pantograph-catenary system and construct a sample dataset based on the historical operating data.

[0035] 202. The initial GDPINN model is trained using a sample dataset and optimized using a loss function to obtain the target GDPINN model. The initial GDPINN model is obtained by combining a denoising diffusion probability model and a physical information neural network.

[0036] In this embodiment, when constructing the sample data set, the structural parameters in the historical running data are obtained as constraints, the original state data in the historical running data is noise-enhanced, and the noise-enhanced data is back-introduced to the original data, thereby realizing the construction of state data samples in the sample data.

[0037] Specifically, under the structural parameters of the pantograph-catenary system, small-amplitude Gaussian noise is gradually injected into the historical state data of the pantograph-catenary system through a Markov chain in T steps to obtain a Gaussian distributed state data sample; a sample data set is constructed based on the state data sample and the structural parameters of the pantograph-catenary system.

[0038] For example, in the GDPINN model, a Bayesian-based reversible guidance strategy is used to first construct a sample dataset. The Bayesian-based reversible guidance strategy includes forward diffusion and backward diffusion. During training, forward diffusion is used to construct the sample dataset, while backward diffusion is the opposite of forward diffusion. During training, the model learns the logic of forward diffusion to enable backward diffusion to remove noise, thereby extracting the original state data and enabling the prediction of the time series.

[0039] During training, its forward diffusion, under condition C (pantograph-contact wire structure parameters), occurs through the state data of the pantograph-contact wire system over T steps via a Markov chain. Gradually inject small-amplitude Gaussian noise to make its distribution asymptotically approximate a standard normal distribution. The calculation method is shown in the following formula: , in, Representation and constant Related Gaussian distribution .

[0040] In this embodiment, before constructing the sample data set based on the state data samples and the structural parameters of the pantograph-catenary system, the following steps are further included: Calculate the prior probability and posterior probability of each state data in the state data sample; Based on the prior probability and the posterior probability, the Kullback-Leibler divergence is obtained by approximating the solution using a Gaussian function; Based on the Kullback-Leibler divergence, the injected Gaussian noise for each state data is adjusted.

[0041] Specifically, this is achieved through the Bayesian-based reversible guidance strategy BRG in the GDPINN model, which can better solve for the state consistency of the pantograph-catenary system given the structural parameters C. In the pantograph-catenary system, from the optimization objective... Let's see, in order to make To maximize, we need to optimize the likelihood. and prior probability distribution . However The model can be constrained using a certain empty ratio condition, as shown by the following formula. and .

[0042]

[0043] Based on the above, it can be further modified to predict both conditional and unconditional noise, and the calculation method is shown in the following formula: , This article has undergone multiple trials and adjustments. The value is set to 0.5. In the actual sampling of the GDPINN model, the state can be generated under the structural parameter C of the pantograph-catenary system. , Add Gaussian noise It can be obtained Therefore, the relationship between them can be expressed as However, it seems... Since it cannot be calculated directly, inspired by Yan et al., it can be represented in integral form. The calculation method is shown in the following formula: , in, The likelihood can be calculated because It was calculated under conditions C. And... This can be demonstrated using approximate variational reasoning based on the GDPINN model. However, it is only necessary to... Approximate solution; therefore, this application uses the Gaussian function approximation to minimize... and The Kullback-Leibler (KL) divergence is estimated using a one-step denoising process instead of focusing on the entire GDPINN sampling process. The calculation method is shown in the following formula.

[0044] .

[0045] GDPINN can be defined The standard deviation is a Gaussian function with a mean of 1 / 2. Therefore, the following formula can be used to approximate it. .

[0046] .

[0047] Furthermore, approximation is needed. Because the GDPINN training in this application gradually reduces the parameters under parameter condition C... Adding Gaussian noise transforms it into a Gaussian distribution, and under approximation, it is... It is also a Gaussian approximation, therefore it can be defined in C. The following is also a Gaussian distribution, therefore It can be expressed by the following formula: , in, These are linearly independent matrices. In most cases... ,and yes The Moore-Penrose inverse (pseudo-inverse). However, this paper does not require calculation of the Moore-Penrose inverse. and Because we can assume For functions that incorporate Gaussian noise, and This is a function to remove Gaussian noise. Therefore, the above can be expressed by the following formula: .

[0048] Finally, due to physical information and This application will therefore study the physical information relevant to this. Similarly, the diffusion steps are optimized within GDPINN. After applying constraints, the final optimization method is shown in the following formula: .

[0049] The expression for the loss function is: .

[0050] 203. Obtain the current status data and structural parameters of the pantograph-catenary system.

[0051] 204. Input the structural parameters into the conditional encoder of the pre-trained target GDPINN model to obtain the physical constraints.

[0052] 205. Input the current state data into the AttnFNO layer of the target GDPINN model to perform multi-stage Fourier neural operator iteration to extract frequency domain features and obtain the target frequency domain features.

[0053] In this embodiment, the current state data is input into a first fully connected layer for transformation to obtain an initialization vector of the current state data; the initialization vector is input into a first attention-based Fourier neural network for a first Fourier transform and inverse transform to obtain a first vector; the first vector is input into a second attention-based Fourier neural network for a second Fourier transform and inverse transform to obtain a second vector; the vectors obtained from the previous attention-based Fourier neural network are sequentially input into the next attention-based Fourier neural network for Fourier transform and inverse transform to obtain the vector output by the last attention-based Fourier neural network; the last output vector is input into a second fully connected layer for inverse transformation to obtain the target frequency domain features.

[0054] The process of sequentially inputting the vector obtained from the previous attention-based Fourier neural network transformation into the next attention-based Fourier neural network for Fourier transform and inverse transform, to obtain the vector output by the last attention-based Fourier neural network, includes: The vectors obtained from the previous Fourier neural network transformation based on the attention mechanism are sequentially input into the next Fourier neural network based on the attention mechanism for fast Fourier transform. The weight vector is determined based on the result of the Fast Fourier Transform (FFT) and then convolved with the result of the FFT to generate a residual. It can be understood that when removing the top weight vector, the result of the FFT is convolved and then global average pooling is performed on the result of the convolution. The SoftMax function is used to convert the pooled result of the FFT into a weight vector. The residual is multiplied by the result of the Fast Fourier Transform and then normalized. The result of the normalization is then subjected to the Fast Inverse Fourier Transform to obtain the vector output by the last Fourier neural network based on the attention mechanism. The computational expression for the attention-based Fourier neural network is as follows: , in, Represents the target's frequency domain characteristics; Represents status data; For the parameter set of AttnFNO; Indicates the first The vector of the next iteration; This represents the inverse Fast Fourier Transform; For periodic kernel The tensor composed of frequency domain coefficients; Indicates Fast Fourier Transform; Represents the residual.

[0055] In practical applications, feature extraction is specifically achieved through the attention-based Fourier neural operator AttnFNO, given an input set. Define the function sequence of AttnFNO. And through recursion The updates will be implemented gradually, as follows: (1) First of all Utilizing fully connected layers Perform a transformation to obtain the initialization vector. , .

[0056] (2) Then for each iteration step The AttnFNO module is used. With activation function The composite update state is calculated using the following formula: , in, For bounded open sets; and These represent the (fast) Fourier transform and its inverse transform, respectively. For periodic kernel The tensor composed of frequency domain coefficients; for any frequency mode ,have and In discrete implementation, Considered as periodic discrete modes Its meaning is the current mode. The contribution of the spectrum to the information carried by the spectrum. In addition, to suppress deep frequency domain attenuation and over-smoothing, AttnFNO is equipped with a frequency domain correction module to supplement and correct key spectral information, thereby stabilizing the main frequency and improving prediction accuracy. Specifically, this paper first uses Fourier transform... Obtain the weight vector Then, residuals are generated through convolutional layers. .

[0057]

[0058] in, and These represent global average pooling and the SoftMax function, respectively. The final formula is as follows: This can be expressed as the following formula: .

[0059] 206. Input the target frequency domain features and physical constraints into the QKV denoising network layer of the target GDPINN model for denoising processing to obtain the target pantograph-catenary time history set.

[0060] Understandably, this noise reduction process is actually a reverse diffusion process that deduces the set of time-history quantities, which includes contact force, bow head acceleration, displacement, velocity, and contact wire displacement, etc.

[0061] In the reverse diffusion process, Gaussian noise is gradually eliminated based on Gaussian distribution sampling to generate a distribution that conforms to the target distribution. The calculation method is shown in the following formula: Among them, variance It is a constant, and the mean is... It is a learnable function.

[0062] In this embodiment, a unified physical modeling framework—a Guided Denoising Diffusion Probability Model-Based Physical Information Neural Network (GDPINN)—is proposed, capable of simultaneously encompassing the dynamic behavior of both flexible and rigid overhead contact lines. Based on the different structural characteristics and working principles of rigid and flexible overhead contact lines, this framework combines DDPM and PINN to solve the modeling problems of different overhead contact line-pantograph systems in existing technologies. By introducing a unified numerical solution method, this model can provide efficient and high-precision simulation results across low-speed and high-speed track conditions.

[0063] Furthermore, an attention-based Fourier neural operator (AttnFNO) was designed in DDPM to further enhance the model's ability to express complex frequency domain features. Through generative modeling techniques, this paper not only recovers the dynamic behavior of the pantograph-catenary system under different operating conditions but also effectively captures frequency domain features, providing a more stable and accurate solution for pantograph-catenary state recognition and prediction.

[0064] To further improve the accuracy of state identification in the pantograph-catenary system, this application also proposes a Bayesian-based reversible guided strategy (BRG), which effectively constrains the state consistency of the model under given structural parameters. This strategy significantly improves the inference of complex dynamic features during the generation process by maximizing the posterior probability, combined with prior distribution and physical consistency, ensuring the high accuracy and stability of the model.

[0065] The pantograph-catenary time history prediction method in this application has been described above. The pantograph-catenary time history prediction device in this application is described below. Please refer to [link / reference]. Figure 7 One embodiment of the pantograph-catenary time history prediction device in this example includes: The acquisition module 710 is used to acquire the current status data and structural parameters of the pantograph-catenary system; Encoding module 720 is used to input the structural parameters into the conditional encoder of the pre-trained target GDPINN model for encoding to obtain physical constraints. The extraction module 730 is used to input the current state data into the AttnFNO layer of the target GDPINN model to extract frequency domain features through multi-stage Fourier neural operator iteration, thereby obtaining the target frequency domain features. The prediction module 740 is used to input the target frequency domain features and the physical constraints into the QKV denoising network layer of the target GDPINN model for denoising processing, so as to obtain the target pantograph-catenary time history set.

[0066] Optionally, the feature extraction module 730 is specifically used for: The current state data is input into the first fully connected layer for transformation to obtain the initialization vector of the current state data; The initialization vector is input into the first attention-based Fourier neural network to perform the first Fourier transform and inverse transform to obtain the first vector; The first vector is input into a second attention-based Fourier neural network for a second Fourier transform and inverse transform to obtain the second vector; The vector obtained by the previous Fourier neural network based on the attention mechanism is sequentially input into the next Fourier neural network based on the attention mechanism for Fourier transform and inverse transform, so as to obtain the vector output by the last Fourier neural network based on the attention mechanism. The last output vector is input into the second fully connected layer for inverse transformation to obtain the target frequency domain features.

[0067] Optionally, the feature extraction module 730 is specifically used for: The vectors obtained from the previous Fourier neural network transformation based on the attention mechanism are sequentially input into the next Fourier neural network based on the attention mechanism for fast Fourier transform. The weight vector is determined based on the result of the Fast Fourier Transform, and then convolved with the result of the Fast Fourier Transform to generate the residual. The residual is multiplied by the result of the Fast Fourier Transform and then normalized. The result of the normalization is then subjected to the Fast Inverse Fourier Transform to obtain the vector output by the last Fourier neural network based on the attention mechanism. The computational expression for the attention-based Fourier neural network is as follows: , in, Represents the target's frequency domain characteristics; Represents status data; For the parameter set of AttnFNO; Indicates the first The vector of the next iteration; This represents the inverse Fast Fourier Transform; For periodic kernel The tensor composed of frequency domain coefficients; Indicates Fast Fourier Transform; Represents the residual.

[0068] Optionally, the feature extraction module 730 is specifically used for: The result of the Fast Fourier Transform is convolved, and the result of the convolution is then subjected to global average pooling. The SoftMax function is used to convert the result of the fast Fourier transform after pooling into a weight vector.

[0069] Optionally, the device further includes a training module 750 specifically used for: Acquire historical operational data of the pantograph-catenary system, and construct a sample data set based on the historical operational data; The preset initial GDPINN model is trained using the sample data set and optimized using a loss function to obtain the target GDPINN model, wherein the initial GDPINN model is obtained by combining a denoising diffusion probability model and a physical information neural network.

[0070] Optionally, the training module 750 is specifically used for: Under the structural parameters of the pantograph-catenary system, a Gaussian-distributed state data sample is obtained by gradually injecting small-amplitude Gaussian noise into the historical state data of the pantograph-catenary system in T steps through a Markov chain. A sample data set is constructed based on the state data samples and the structural parameters of the pantograph-catenary system.

[0071] Optionally, the training module 750 is further configured to: Calculate the prior probability and posterior probability of each state data in the state data sample; Based on the prior probability and the posterior probability, the Kullback-Leibler divergence is obtained by approximating the solution using a Gaussian function; Based on the Kullback-Leibler divergence, the injected Gaussian noise for each state data is adjusted.

[0072] In this embodiment, a unified modeling framework is proposed—a physical information neural network model based on a guided denoising diffusion probability model. This model combines generative modeling with physical information constraints, enabling it to simultaneously cover the dynamic characteristics of both flexible and rigid contact wires, and accurately identify and predict the state of the pantograph-catenary system under different operating conditions. Then, by introducing an attention-based Fourier neural operator, the model's ability to model the pantograph-catenary system in both the time and frequency domains is significantly improved. Finally, this paper proposes a Bayesian-based reversible guidance strategy, which effectively guides the model to learn a state distribution that conforms to physical laws, thereby enhancing the model's stability and accuracy.

[0073] above Figure 7 The pantograph-catenary time history prediction device of this application is described in detail from the perspective of modular functional entities. The pantograph-catenary system of this application is described in detail below from the perspective of hardware processing.

[0074] See Figure 8As shown, the pantograph-catenary system includes a processor 800 and a memory 801. The memory 801 stores machine-executable instructions that can be executed by the processor 800. The processor 800 executes the machine-executable instructions to implement the pantograph-catenary time-history prediction method described above.

[0075] Furthermore, Figure 8 The pantograph-catenary system shown also includes a bus 802 and a communication interface 803. The processor 800, the communication interface 803, and the memory 801 are connected via the bus 802.

[0076] The memory 801 may include high-speed random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 803 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc. The bus 802 may be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 8 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0077] The processor 800 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of the processor 800 or by software instructions. The processor 800 may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may 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 gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this disclosure. The general-purpose processor may be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this disclosure can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules may reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in memory 801. Processor 800 reads the information in memory 801 and, in conjunction with its hardware, completes the method steps of the aforementioned embodiment.

[0078] This application also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, storing instructions that, when executed on a computer, cause the computer to perform the steps of the pantograph-catenary time history prediction method.

[0079] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0080] If the integrated unit is implemented as 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 this application, in essence, 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. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0081] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for predicting pantograph-catenary time history quantities, characterized in that, The pantograph-catenary time history prediction method includes: Obtain the current status data and structural parameters of the pantograph-catenary system; The structural parameters are input into the conditional encoder of the pre-trained target GDPINN model for encoding to obtain the physical constraints. The current state data is input into the AttnFNO layer of the target GDPINN model to extract frequency domain features through multi-stage Fourier neural operator iteration, thereby obtaining the target frequency domain features. The target frequency domain features and the physical constraints are input into the QKV denoising network layer of the target GDPINN model for denoising processing, resulting in the target pantograph-catenary time history set.

2. The pantograph-catenary time history prediction method according to claim 1, characterized in that, The step of inputting the current state data into the AttnFNO layer of the target GDPINN model for multi-stage Fourier neural operator iteration to extract frequency domain features, thereby obtaining the target frequency domain features, includes: The current state data is input into the first fully connected layer for transformation to obtain the initialization vector of the current state data; The initialization vector is input into the first attention-based Fourier neural network to perform the first Fourier transform and inverse transform to obtain the first vector; The first vector is input into a second attention-based Fourier neural network for a second Fourier transform and inverse transform to obtain the second vector; The vector obtained by the previous Fourier neural network based on the attention mechanism is sequentially input into the next Fourier neural network based on the attention mechanism for Fourier transform and inverse transform, so as to obtain the vector output by the last Fourier neural network based on the attention mechanism. The last output vector is input into the second fully connected layer for inverse transformation to obtain the target frequency domain features.

3. The pantograph-catenary time history prediction method according to claim 2, characterized in that, The process of sequentially inputting the vector obtained from the previous attention-based Fourier neural network transformation into the next attention-based Fourier neural network for Fourier transform and inverse transform, to obtain the vector output by the last attention-based Fourier neural network, includes: The vectors obtained from the previous Fourier neural network transformation based on the attention mechanism are sequentially input into the next Fourier neural network based on the attention mechanism for fast Fourier transform. The weight vector is determined based on the result of the Fast Fourier Transform, and then convolved with the result of the Fast Fourier Transform to generate the residual. The residual is multiplied by the result of the Fast Fourier Transform and then normalized. The result of the normalization is then subjected to the Fast Inverse Fourier Transform to obtain the vector output by the last Fourier neural network based on the attention mechanism. The computational expression for the attention-based Fourier neural network is as follows: ， in, Represents the frequency domain characteristics of the target; Represents status data; For the parameter set of AttnFNO; Indicates the first The vector of the next iteration; This represents the inverse Fast Fourier Transform; For periodic kernel The tensor composed of frequency domain coefficients; Indicates Fast Fourier Transform; Represents the residual.

4. The pantograph-catenary time history prediction method according to claim 3, characterized in that, The determination of the weight vector based on the results of the Fast Fourier Transform includes: The result of the Fast Fourier Transform is convolved, and the result of the convolution is then subjected to global average pooling. The SoftMax function is used to convert the result of the fast Fourier transform after pooling into a weight vector.

5. The pantograph-catenary time history prediction method according to any one of claims 1-4, characterized in that, Before acquiring the current state data and structural parameters of the pantograph-catenary system, the following steps are also included: Acquire historical operational data of the pantograph-catenary system, and construct a sample data set based on the historical operational data; The preset initial GDPINN model is trained using the sample data set and optimized using a loss function to obtain the target GDPINN model, wherein the initial GDPINN model is obtained by combining a denoising diffusion probability model and a physical information neural network.

6. The pantograph-catenary time history prediction method according to claim 5, characterized in that, The construction of the sample data set based on the historical operational data includes: Under the structural parameters of the pantograph-catenary system, a Gaussian-distributed state data sample is obtained by gradually injecting small-amplitude Gaussian noise into the historical state data of the pantograph-catenary system in T steps through a Markov chain. A sample data set is constructed based on the state data samples and the structural parameters of the pantograph-catenary system.

7. The pantograph-catenary time history prediction method according to claim 6, characterized in that, Before constructing the sample data set based on the state data samples and the structural parameters of the pantograph-catenary system, the method further includes: Calculate the prior probability and posterior probability of each state data in the state data sample; Based on the prior probability and the posterior probability, the Kullback-Leibler divergence is obtained by approximating the solution using a Gaussian function; Based on the Kullback-Leibler divergence, the injected Gaussian noise for each state data is adjusted.

8. A pantograph-catenary time history prediction device, characterized in that, The pantograph-catenary time history prediction device includes: The acquisition module is used to acquire the current status data and structural parameters of the pantograph-catenary system; The encoding module is used to input the structural parameters into the conditional encoder of the pre-trained target GDPINN model for encoding to obtain the physical constraints. The extraction module is used to input the current state data into the AttnFNO layer of the target GDPINN model to extract frequency domain features through multi-stage Fourier neural operator iteration, thereby obtaining the target frequency domain features; The prediction module is used to input the target frequency domain features and the physical constraints into the QKV denoising network layer of the target GDPINN model for denoising processing, so as to obtain the target pantograph-catenary time history set.

9. A pantograph-catenary system, characterized in that, The pantograph-catenary system includes: a memory and at least one processor, wherein the memory stores instructions; The at least one processor invokes the instructions in the memory to cause the pantograph-catenary system to perform the pantograph-catenary time-course prediction method as described in any one of claims 1-7.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When the instruction is read and executed, it performs the pantograph-catenary time-history prediction method as described in any one of claims 1-7.

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