Train ice-melting simulation optimization method based on electromagnetic-thermal coupling model combined with deep learning method

Abstract

The application relates to the technical field of electric digital data processing, and discloses a train ice melting simulation optimization method of an electromagnetic heat coupling model fused with a deep learning method, which comprises the following steps: inputting a geometric characterization tensor and a physical working condition parameter vector containing an electromagnetic excitation frequency and a reference environment temperature into a feature mapping neural network, outputting a double-channel space source term tensor containing a basic heat source power density and a heat source temperature change sensitivity distribution matrix through nonlinear convolution operation; constructing a heat conduction discrete numerical evolution operator configured with a source term linear correction interface; performing time step operation in a heat conduction time scale, and correcting the basic heat source in real time by using Hadamard product of the sensitivity distribution matrix and a temperature deviation, and substituting the basic heat source into the operator for solving; and the mixed architecture of neural network static mapping and numerical operator dynamic correction is adopted, time scale decoupling is realized under the premise of retaining electromagnetic-heat nonlinear coupling characteristics, and the calculation efficiency in high-frequency physical field simulation is effectively solved.

Description

Technical Field

[0001] This invention relates to a simulation optimization method for train de-icing based on an electromagnetic thermal coupling model that integrates deep learning methods, belonging to the field of electronic digital data processing technology. Background Technology

[0002] Current cold-weather design for rail transit employs electromagnetic induction heating technology. Parameter optimization requires multi-physics field coupling numerical simulation of electromagnetic fields, heat conduction, and ice phase transition processes. Traditional methods utilize finite element analysis to iteratively solve Maxwell's equations and heat conduction equations to simulate physical evolution. However, when dealing with electromagnetic-thermal coupling calculations involving phase transitions, existing technologies face a conflict between computational resources and computational limitations. The electromagnetic field changes on the order of microseconds, while the heat conduction and phase transition processes have timescales on the order of seconds. This timescale difference means that traditional fully coupled computational logic, while satisfying the electromagnetic field convergence requirement, necessitates using extremely small time steps to advance the thermal field calculations. This leads to an exponential increase in the number of iterations, generating a large amount of redundant intermediate data and wasting computational resources.

[0003] To address the issue of control parameter adaptation, existing technologies have developed control schemes that combine simulation algorithms. For example, Chinese invention patent application CN120341778A discloses a control device for AC ice melting. This device integrates finite element algorithm functionality, acquires loop parameters in real time for three-dimensional electromagnetic-thermal coupling field simulation, and uses PID algorithm factors to dynamically correct the ice melting current. However, such schemes are still limited to traditional online iterative solution modes. When dealing with complex and irregular structures like train bogies, the computational load is difficult to meet real-time requirements. Furthermore, relying on PID feedback logic and simplified thermal balance equations, when faced with severe nonlinear drift in material conductivity at low temperatures and geometric topological abrupt changes caused by irregular ice shedding, the lack of physical field prediction capabilities leads to lag in control parameter adjustment, making effective ice melting difficult. The phase transition between ice and water is accompanied by the release of latent heat, and the specific heat capacity and thermal property parameters undergo a step change near the phase transition point. The singularity of physical parameters worsens the condition number of the Jacobian matrix in numerical calculations, making it difficult for the Newton iteration method to converge. Manual intervention in mesh generation or the use of relaxation strategies is required, increasing operational complexity and introducing simulation errors.

[0004] Therefore, the technical problem to be solved by this invention is how to construct an efficient simulation data processing method that decouples the time scales of electromagnetic and thermal fields, automatically handles phase transition singularities, and adapts to dynamic changes in geometric topology. Summary of the Invention

[0005] To address the problems mentioned in the background art, the technical solution of this invention is as follows: A simulation optimization method for train de-icing using an electromagnetic thermal coupling model integrating deep learning methods. The method obtains the geometric representation tensor and physical condition parameter vector of the object to be simulated. The physical condition parameter vector includes at least the electromagnetic excitation frequency value and the reference ambient temperature value. The method also includes the following steps:

[0006] Step A: Input the geometric representation tensor and physical condition parameter vector into a pre-set feature mapping neural network. Through the nonlinear convolution operation of the feature mapping neural network, output a spatial source term tensor containing dual-channel data. The first channel data is the basic heat source power density distribution matrix under the reference ambient temperature value, and the second channel data is the sensitivity distribution matrix of the heat source power density with respect to temperature change. The sensitivity distribution matrix represents the gradient value of the heat source power density at each point in space with temperature change.

[0007] Step B: Construct a discrete numerical evolution operator based on the partial differential equation of heat conduction, and configure source term linear correction logic in the numerical evolution operator. The source term linear correction logic is used to perform matrix linear superposition operation based on Hadamard product.

[0008] Step C involves performing a time-step iterative operation with the heat conduction time scale as the step size. In each time step, the following data processing sub-steps are executed: obtain the temperature field distribution matrix of the current time step and calculate its difference matrix with the baseline ambient temperature value; call the source term linear correction logic, perform the Hadamard product operation of the sensitivity distribution matrix and the difference matrix, and superimpose the operation result onto the basic heat source power density distribution matrix to generate the corrected heat source matrix of the current time step; substitute the corrected heat source matrix as the source term parameter into the discrete numerical evolution operator to calculate the temperature field distribution matrix of the next time step.

[0009] Preferably, the sub-step in step C that generates the corrected heat source matrix for the current time step specifically includes performing matrix operations according to the following formula: ,in, This is the corrected heat source matrix for the current time step. Based on the power density distribution matrix of the basic heat source, The sensitivity distribution matrix is... For the Hadamard product operator, This is the temperature field distribution matrix at the current time step. This is a constant matrix of the same dimension constructed using the reference ambient temperature values.

[0010] Preferably, the training process of the feature mapping neural network includes a physical residual constraint step. The physical residual constraint step calculates the residual value after substituting the basic heat source power density distribution matrix and sensitivity distribution matrix of the network output into the differential form of Maxwell's equations, and adds the residual value as a regularization term to the loss function to constrain the gradient convergence direction of the feature mapping neural network on the sensitivity distribution matrix to conform to the physical conservation law of electromagnetic field.

[0011] Preferably, the discrete numerical evolution operator includes continuously differentiable phase transition smoothing logic. The phase transition smoothing logic uses the hyperbolic tangent function to construct an equivalent specific heat capacity curve, and maps the step term corresponding to the latent heat of the ice-water phase transition in the heat conduction control equation to a continuously differentiable numerical interval, thereby establishing an end-to-end differentiable path of the temperature field distribution matrix with respect to the physical condition parameter vector.

[0012] Preferably, the geometric representation tensor is a symbolic distance field matrix based on a three-dimensional Cartesian coordinate system. Each element in the symbolic distance field matrix represents the Euclidean distance from the spatial sampling point to the nearest boundary of the object to be simulated. The symbolic distance field matrix is ​​generated by voxelizing and resampling unstructured point cloud data and normalizing it, and is used to unify the input data format of objects with different topological structures.

[0013] Preferably, in step A, the spatial source term tensor output by the feature mapping neural network also includes a topological evolution basis channel, which contains multiple heat source basis matrices corresponding to different icing thickness states of the simulated object; correspondingly, the time step iteration operation in step C also includes a topological weighting sub-step: calculating the proportion of elements exceeding the phase transition threshold in the temperature field distribution matrix of the current time step to generate a global phase transition progress scalar, performing a linear weighted summation on multiple heat source basis matrices based on the global phase transition progress scalar, and using the summation result as the basic heat source power density distribution matrix to participate in the subsequent source term linear correction logic.

[0014] Preferably, in the topology weighting sub-step, the weight coefficients of the linear weighted summation are calculated through a set of preset basis functions. The basis functions define the nonlinear mapping relationship between the global phase transition progress scalar and the weights of the basis matrices of each heat source, and are used to simulate the distortion of the electromagnetic field spatial distribution caused by the fading of geometric boundaries through algebraic interpolation without performing mesh reconstruction.

[0015] Preferably, the method further includes a reverse gradient optimization step: constructing a loss function with the total simulation time and energy consumption as independent variables, calculating the gradient of the loss function with respect to the physical condition parameter vector using an automatic differentiation algorithm based on the end-to-end differentiable path of the discrete numerical evolution operator, and updating the physical condition parameter vector using the gradient descent method according to the gradient until the loss function converges to a preset minimum value range.

[0016] Preferably, in step C, the sub-step of calculating the temperature field distribution matrix for the next time step uses an alternating direction implicit difference scheme to solve the discrete numerical evolution operator. The step size setting of the heat conduction time scale must satisfy the Courant-Friedrich-Levi convergence condition, and the step size setting is independent of the time scale of the electromagnetic field frequency, so as to achieve time-domain decoupling between high-frequency electromagnetic data and low-frequency heat conduction data.

[0017] Preferably, the method further includes a data dimensionality reduction and storage step: after the time-stepping iterative calculation is completed, principal component analysis is performed on the generated full-time-domain temperature field distribution matrix sequence to extract the leading edge data that characterizes the spatiotemporal evolution of the temperature field. The intrinsic orthogonal decomposition modes and their corresponding time coefficient vectors are identified, and the intrinsic orthogonal decomposition modes and time coefficient vectors are persistently stored as simulation result data.

[0018] Compared with the prior art, the beneficial effects of the present invention are:

[0019] 1. In the electromagnetic-thermal coupling model of deep learning, a mapping architecture from operating parameters to quasi-static heat source distribution characteristics is constructed. At the data processing level, the time scale decoupling of high-frequency electromagnetic variables and low-frequency heat conduction variables is realized. The electromagnetic field equations that need to be solved at high frequency over time are transformed into a one-time static mapping operation in the spatial domain. This allows the subsequent thermal field numerical evolution operator to set the step size according to the second-level time scale of heat conduction. The heterogeneous data stream processing strategy eliminates the computational redundancy caused by the time rigidity problem in multi-physics coupling calculation. While retaining the physical field coupling characteristics, the time complexity of the calculation process is changed from being dominated by electromagnetic field frequency to being dominated by heat diffusion rate, ensuring the efficiency and determinism of the simulation data processing flow.

[0020] 2. By using the feature mapping network to output multi-channel tensor data and the heat source sensitivity distribution matrix to temperature changes, a linear correction mechanism for the source terms based on first-order Taylor expansion is established. The numerical evolution calculation uses matrix Hadamard product operation to compensate the basic heat source terms in real time according to the current temperature field deviation value. This method reduces the dimension of the complex material property nonlinear drift problem into low-overhead matrix linear algebra operation, without repeatedly calling neural network inference, thus improving the simulation system's ability to adaptively correct the dynamic changes of physical parameters under large temperature difference conditions.

[0021] 3. A discrete-state basis manifold interpolation method is adopted to solve the data processing problem caused by geometric boundary topological changes in the ice melting process. The basis matrix corresponding to different coverage states of the heat source is pre-generated. The basis is dynamically weighted and summed according to the global phase change progress scalar, which transforms the complex dynamic mesh reconstruction problem into a fixed mesh algebraic synthesis problem. The de-geometry data processing logic avoids the risk of computational divergence caused by mesh distortion or topological reconnection in traditional methods, and ensures the numerical stability of the simulation system in handling complex dynamic processes with continuous fading of geometric boundaries. It is suitable for deterministic inference in environments with limited edge computing resources. Attached Figure Description

[0022] Figure 1 This is a flowchart of the hybrid simulation calculation of neural network static mapping and numerical dynamic correction in this invention;

[0023] Figure 2 This is a spatiotemporal distribution curve of heat source power density at different times and under different topological evolution states according to the present invention;

[0024] Figure 3 This is a schematic diagram of the closed-loop simulation system architecture of the present invention, which coordinates physical perception and digital twin computing domain. Detailed Implementation

[0025] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0026] This invention provides a simulation optimization method for train de-icing based on an electromagnetic thermal coupling model incorporating deep learning. Based on a hybrid computing architecture, it transforms high-frequency electromagnetic field calculations into quasi-static feature mapping in the spatial domain, while retaining low-frequency heat conduction calculations as numerical evolution in the time domain. Dynamic coupling correction under time-scale decoupling is achieved through a sensitivity matrix. The method comprises data preprocessing, source term decoupling mapping, numerical operator construction, sparse evolution calculation, and inverse gradient optimization. For the complex unstructured geometric features of components such as train bogies, this embodiment performs geometric representation and operating condition parameterization processing to obtain the geometric representation tensor and physical operating condition parameter vector of the simulated object. For the geometric data, the system uses a voxel resampling method to transform unstructured point cloud data into regular mesh data in a three-dimensional Cartesian coordinate system and calculates the Euclidean distance from the center of each voxel to the nearest boundary, generating a signed distance field matrix. This signed distance field matrix serves as the geometric representation tensor, unifying the input format for objects with different topological structures. For the physical operating conditions, the system maps physical parameters such as electromagnetic excitation frequency, coil current density, and reference ambient temperature to... arrive The numerical range is used to construct a normalized physical condition parameter vector.

[0027] After data preparation is complete, step A, source term decoupling mapping, is executed. This step utilizes a pre-trained feature mapping neural network to establish a nonlinear mapping from the geometric-operating condition parameter space to the electromagnetic-thermal source term space. The system inputs the geometric representation tensor and physical operating condition parameter vectors into the feature mapping neural network and employs a fully convolutional architecture, such as a 3D U-Net variant structure. Through multi-layer nonlinear convolution operations, it outputs a spatial source term tensor containing dual-channel data, where the first channel data is the basic thermal source power density distribution matrix under the reference ambient temperature value. The second channel data is the sensitivity distribution matrix of the heat source power density with respect to temperature changes. Each element in the sensitivity distribution matrix represents the spatial location point as temperature increases. At a temperature of 100 degrees Celsius, the incremental value of its heat power density is introduced into the training phase of the feature mapping neural network through a physical residual constraint mechanism. That is, the residual value after substituting the network output field data into the differential form of Maxwell's equations is calculated and added as a regularization term to the loss function to constrain the sensitivity distribution matrix of the network output to conform to the physical conservation law of electromagnetic field. For scenarios with geometric topological changes such as ice melting and shedding, the spatial source term tensor also includes topological evolution basis channels, outputting multiple heat source basis matrices corresponding to the simulated object under different ice thickness states. For example, they correspond to the heat source distribution in the fully iced, partially iced, and ice-free states, respectively. In this way, the influence of continuous geometric boundary changes on the electromagnetic field is characterized by a linear combination of discrete basis.

[0028] Next, step B is executed, constructing a discrete numerical evolution operator based on the partial differential equation of heat conduction. This operator includes continuously differentiable phase transition smoothing logic and utilizes the hyperbolic tangent function to construct an equivalent specific heat capacity curve. This maps the step term corresponding to the latent heat of the ice-water phase transition in the heat conduction governing equation to a continuously differentiable numerical interval. This process eliminates singularities in the numerical calculation, ensures the condition number stability of the Jacobian matrix, and establishes an end-to-end differentiable path for the temperature field distribution matrix with respect to the physical condition parameter vector. Step C, the sparse evolution calculation, is then executed. This step uses the heat conduction time scale as the step size for time-step iterative computation. This step size satisfies the Courant-Friedrich-Lévy convergence condition and is independent of the electromagnetic field frequency time scale. In the calculation of each time step, the system obtains the temperature field distribution matrix for the current time step. And calculate the same-dimensional constant matrix formed by it and the reference ambient temperature value. The difference matrix; in the source term update stage, the system calls the source term linear correction logic to generate the corrected heat source matrix for the current time step. Specifically, the system performs matrix operations according to the following formula: ,in, This is the corrected heat source matrix for the current time step. Based on the power density distribution matrix of the basic heat source, The sensitivity distribution matrix is... For the Hadamard product operator, This is the temperature field distribution matrix at the current time step. This is a constant matrix of the same dimension constructed using the reference ambient temperature values.

[0029] If topological evolution is involved, the formula above... Generated by the topology weighting sub-step, the system statistically analyzes the proportion of elements exceeding the phase transition threshold in the temperature field distribution matrix at the current time step to generate a global phase transition progress scalar. It then calculates weighting coefficients based on a set of preset basis functions, performs a linear weighted summation on multiple heat source basis matrices, and uses the summation result as the basic heat source term for the current moment in the aforementioned linear correction operation. The calculation logic for the linear weighted summation weighting coefficients in the topology weighting sub-step employs a smooth interpolation method based on normalized radial basis functions. The calculation module statistically analyzes the temperature values ​​exceeding the phase transition threshold in the temperature field distribution matrix at the current time step. Mesh cell volume ratio determines the global phase transition progress scalar. , scalar Substitute the characteristic phase transition points corresponding to the substrates of each heat dissipation source. Centered activation function Calculate the original weight values; characteristic phase transition points. Set to fully icing Half-shedding correspondence and complete shedding correspondence Among them, the smoothing bandwidth parameter Value locked in to The interval, determined based on von Neumann stability analysis, covers the transition domain of adjacent topological states. After normalization, the final weight coefficients drive the continuous differentiable numerical transition of the basic heat source term between the electromagnetic responses of different icing geometries, eliminating iterative oscillations of the numerical evolution operator caused by abrupt changes in the geometric boundary mesh. The resulting corrected heat source matrix is ​​calculated. The discrete numerical evolution operator is then substituted, for example, using an alternating direction implicit difference scheme solver, to calculate the temperature field distribution matrix for the next time step. Based on the differentiable calculation process described above, this embodiment performs a reverse gradient optimization step. The system constructs a loss function with the total simulation duration and energy consumption as independent variables, uses an automatic differentiation algorithm to calculate the gradient of the loss function with respect to the physical condition parameter vector, and updates the physical condition parameter vector using gradient descent based on the gradient until the loss function converges to a preset minimum range, thereby obtaining the optimal ice melting process parameters. In addition, to achieve efficient data storage, this embodiment performs a data dimensionality reduction storage step. After the time step iteration calculation is completed, principal component analysis or intrinsic orthogonal decomposition is performed on the generated full-time-domain temperature field distribution matrix sequence to extract the leading edge characteristics representing the spatiotemporal evolution of the temperature field. Each mode and its corresponding time coefficient vector are used, and the mode data and time coefficients are persistently stored as simulation results.

[0030] Example 1: In a real-world deployment scenario for the anti-cold-weather system of high-speed train bogies in cold regions, the train's operating ambient temperature is... Celsius The temperature fluctuates drastically between degrees Celsius, accompanied by rapid accumulation and irregular shedding of ice layers due to strong airflow. Under these conditions, the conductivity of the aluminum alloy vehicle body material drifts with temperature changes, and the real-time changes in the ice-covered geometry cause dynamic jumps in the load impedance of the induction coil. Traditional multiphysics fully coupled simulation methods are limited by the rigid difference in time scale between microsecond-level electromagnetic field changes and second-level heat conduction processes. When dealing with such problems involving large temperature difference nonlinear drift of physical properties and moving mesh boundaries, computational convergence is difficult and time-consuming, failing to meet the timeliness requirements of rapid parameter optimization in engineering design. This embodiment adopts the fusion depth constructed in the aforementioned specific implementation method. The electromagnetic-thermal coupling model is learned, and the de-icing process parameters for key components of the bogie are optimized. The system acquires unstructured geometric point cloud data of the area to be simulated, generates a standardized symbolic distance field matrix using a voxel resampling algorithm, and constructs a normalized physical condition parameter vector by combining the coil excitation frequency, current density, and reference ambient temperature. The above data is input into a pre-set feature mapping neural network, and through nonlinear convolution operations, it directly outputs a spatial source term tensor containing dual-channel data and a heat source basis matrix corresponding to different icing states. The first channel data determines the basic heat source power density distribution matrix under the reference ambient temperature. The second channel data determines the sensitivity distribution matrix of the heat source power density with respect to temperature changes. .

[0031] In the numerical evolution calculation of heat conduction, the system sets the time step using a heat conduction time scale independent of electromagnetic frequency to advance the temperature field evolution. At each time step, the system statistically analyzes the global temperature distribution in real time to generate a global phase transition progress scalar, and performs a linear weighted summation of multiple heat source basis matrices to synthesize a basic heat source term reflecting the current geometric topology. Simultaneously, the system obtains the temperature field distribution matrix for the current time step. And using the sensitivity distribution matrix Perform Hadamard product operation The result of this calculation is directly added to the basic heat source term to generate the corrected heat source matrix for the current time step. This processing logic introduces a sensitivity distribution matrix as a coupling interface between static mapping and dynamic evolution. Mathematically, it uses a first-order Taylor expansion to compensate for the material conductivity drift effect caused by temperature changes in real time, without having to resolve Maxwell's equations at each time step. Simultaneously, through weighted synthesis of discrete substrates, the complex geometric dynamic mesh reconstruction problem is transformed into an algebraic interpolation problem. Based on the end-to-end differentiable path established by this computational architecture, the system uses an automatic differential algorithm to calculate the gradient of melting time and energy consumption with respect to the input operating parameters, and automatically updates the coil frequency and current density parameters. The final results show that, while ensuring that the calculation conforms to the physical conservation laws, this method reduces the calculation time of a single full-process melting simulation from several hours to minutes using traditional methods, and outputs a control strategy that enables key parts of the bogie to meet the requirements of rapid de-icing and minimum energy consumption.

[0032] Example 2: This example verifies the effectiveness, computational efficiency, and numerical convergence of the proposed deep learning-integrated electromagnetic thermal coupling model in handling nonlinear strongly coupled problems by constructing a high-fidelity train de-icing simulation platform. The experimental platform is built based on the actual three-dimensional geometric model of a certain type of high-speed train bogie and simulates a range of... Celsius To reflect the non-uniformity of icing under real-world conditions, the experiment introduced randomly distributed ice thickness perturbations across a wide temperature range of 100 degrees Celsius. The geometric data used in the experiment originated from standard structural point clouds provided by the train manufacturer, while the physical property data were derived from publicly available material thermophysical property databases and measured data from cryogenic laboratories. All calculations were performed on a uniformly configured high-performance computing workstation, and the baseline true value was obtained from the commercial finite element software COMSOL Multiphysics at an extremely small time step (…). The result is obtained through fully coupled transient solution.

[0033] The experiment was designed with three comparative schemes to evaluate the performance differences of different computational strategies. Experimental group A (the sample group of this invention) adopted the static mapping + dynamic correction hybrid architecture of this invention, in which the feature mapping neural network was pre-built in... Training was completed under randomized conditions, with the time step for heat conduction calculations set to [value missing]. Control group B (traditional decoupling group) adopted a sequential weak coupling strategy, calculating the electromagnetic field only at the initial moment and ignoring the feedback effect of temperature on material properties thereafter. Control group C (fully coupled group) used a standard fully coupled solver from commercial software, but relaxed the time step to... To simulate the compromise strategies commonly used in engineering; the experiment targets the initial ambient temperature. Celsius, ice thickness The simulation is started under the operating conditions, and the simulation progresses to... Table 1 shows the temperature prediction data and computational resource consumption of key bogie components (brake caliper surfaces) at any given time.

[0034] Table 1: Comparison of Simulation Performance Data for Ice Melting Process ( (Timetable)

[0035]

[0036] Data shows that control group B had the fastest calculation speed, but its predicted temperature value deviated significantly from the true value. The temperature in degrees Celsius indicates that under low-temperature and large-temperature-difference conditions, neglecting the nonlinear drift of the material's conductivity with temperature will lead to errors in heat source estimation. Although control group C has the highest accuracy, its calculation time is [missing information]. The computation time for experimental group A was only a fraction of that for control group C, and it also had high memory usage. In this case, the temperature deviation is controlled within Within degrees Celsius, this result demonstrates that the present invention, through the sensitivity matrix... The first-order Taylor correction of the source term effectively captures the nonlinear variation characteristics of physical parameters with extremely low computational cost; furthermore, to verify the adaptability of this invention to geometric topological abrupt changes, an experiment simulated ice layer detachment events during the melting process. At a certain moment, the ice layer on the left side of the bogie was completely detached. Under this condition, the control group C experienced a deterioration in the Jacobian matrix condition number due to drastic changes in mesh topology, leading to calculation divergence and termination. In contrast, the experimental group A, by monitoring the global phase transition progress scalar and smoothly adjusting the weighting coefficients of the matrix away from the heat source substrate, did not experience calculation interruption and continued calculation even after the ice detached. A new steady-state thermal field distribution was established, and the transient response curve matched the theoretical expectations.

[0037] Example 3: This example combines Figures 1 to 3 This paper describes the optimization method for train de-icing simulation using an electromagnetic thermal coupling model that integrates deep learning methods. Figure 1As shown, the geometric representation tensor consists of a signed distance field matrix or voxelized resampled data. The physical condition parameter vector includes electromagnetic frequency, current density, and reference ambient temperature values. These two sets of data are input in parallel into the feature mapping neural network. Through nonlinear convolution operations and physical residual constraint mechanisms, the output is a spatial source term tensor containing dual-channel data. Channel 1 is the basic heat source power density matrix, and channel 2 is the sensitivity distribution matrix. The network can also optionally output a topology evolution basis channel. The basic heat source is generated by linear weighted summation of the heat source basis and enters the core source term linear correction logic. The Hadamard product operation and first-order Taylor expansion compensation are performed using real-time temperature deviation feedback and the sensitivity distribution matrix. The generated corrected heat source is substituted into a discrete numerical evolution operator configured with phase transition smoothing and alternating direction implicit difference scheme. Time step iteration is performed under an independent heat conduction time scale. During this period, the operating parameters are updated using an automatic differentiation algorithm and loss function convergence logic through a back gradient optimization step. Finally, the simulation result data containing the full-time domain temperature field distribution matrix and phase transition progress is output.

[0038] like Figure 2 As shown, the unit of heat source power density is... The heat source distribution exhibits dynamic characteristics as the horizontal axis scale changes from 0 to 20 with spatial location and as time evolves. The figure shows the heat source distribution curves at three key moments. The solid line at t=0s represents the heat source power density distribution in the initial state; the dashed line at t=150s corresponds to the transient distribution when ice layer detachment occurs, showing the drift of peak position and intensity; and the dotted line at t=300s represents the steady-state distribution at the end of the simulation. Figure 3 As shown, the overall system architecture is divided into two main parts: the physical sensing and execution domain and the digital twin computing domain. The physical domain includes the physical bogie, infrared thermal imaging, and current sensing devices, which are responsible for collecting real-time data and transmitting it to the edge monitoring terminal. It also performs adaptive data cleaning and online parameter calibration through a pre-processing service. The processed operating data is then uploaded to the digital twin computing domain located in the high-performance simulation workstation. The digital twin computing domain is equipped with a deep learning engine and a physical evolution engine. The former runs a feature mapping neural network to generate spatial source terms, while the latter runs numerical evolution operators and phase transition smoothing logic for high-fidelity calculation. The two achieve millisecond-level data coupling through a source term correction interaction module. At the same time, the inverse gradient optimization module performs automatic differential parameter optimization based on the dimensionality-reduced modal data stored in the simulation results and sends the calculated optimal parameters to the physical domain to complete closed-loop control.

[0039] Example 4: This example discloses a neural network training method based on physical residual constraints. Prior knowledge of Maxwell's equations is embedded into the network's loss function. The network weights converge to a solution space that conforms to physical conservation laws through gradient descent. The training process employs a composite loss function that includes physical residual terms. In each forward propagation, the network outputs the predicted heat source power density matrix. and sensitivity matrix The system synchronously constructs a residual operator based on the differential form of Maxwell's equations and uses automatic differentiation techniques to calculate... The corresponding electric field divergence and magnetic field curl residuals, and the composite loss function Defined as data fitting loss With physical residual loss Weighted sum: ,in, The mean square error between the predicted and true values. Let L2 norm be the residual of the physical equation. and The preset balance weights are used for the sensitivity distribution matrix. Physical gradient attributes are defined, and training samples are constructed using a two-sample difference gradient supervision labeling procedure.

[0040] For each discretized geometric tensor sample, the electromagnetic field solver calculates the true value of the basic heat source distribution at the reference ambient temperature, and applies an amplitude to the input reference ambient temperature. The system physically perturbs and resolves Maxwell's equations, calculating the ratio of the difference in heat source power density distribution before and after the perturbation, and generating a true label matrix of the heat source's rate of change with temperature at the sample point. During the backpropagation phase, the loss function is set to include a gradient regression penalty term, and the Frobenius norm between the output tensor of the second channel of the feature mapping neural network and the true label matrix is ​​calculated. Minimizing the norm forces the weights of the second channel convolution kernel of the network to converge to the manifold of the first-order partial derivative of the heat source power density with respect to temperature, so that the output sensitivity value corresponds to the tangential stiffness characteristics of the electromagnetic-thermal coupling system under the current operating condition.

[0041] During the backpropagation phase, physical residual loss The generated gradient signal directly affects the network weight update, constraining the field distribution of the network output to satisfy the electromagnetic field conservation law. Furthermore, to ensure the sensitivity matrix... The physical meaning of this is to introduce a Jacobi regularization term, which, by penalizing the gradient norm of the output with respect to the input, suppresses the network's oversensitivity to small numerical perturbations and ensures... Characterizes the actual physical gradient response.

[0042] Example 5: To address the model generalization problem under different train bogie structures and differentiated electromagnetic coil parameters, this example discloses a field pre-calibration procedure for feature mapping neural networks. Before deploying the system to a new object, the steady-state temperature distribution of the target object under constant current excitation is obtained through offline benchmark testing. Surface temperature field data is collected using an infrared thermal imager, and coil current, frequency, and ambient temperature are recorded simultaneously. The measured data are used as calibration samples, and the output layer parameters of the feature mapping neural network are fine-tuned using a mini-batch gradient descent algorithm. This process only updates the weights and biases at the network's end, quickly adapting to the thermal response characteristics of the actual physical system.

[0043] In response to potential sensor data loss or noise interference during actual operation, this embodiment integrates an adaptive input data cleaning logic. After receiving the real-time operating condition parameter vector, the system performs statistical filtering based on a sliding window, calculates the mean and variance of the current data and the historical window data, and determines outliers when the real-time data deviates from the mean by more than three times the standard deviation, and replaces them using cubic spline interpolation. At the same time, for low-frequency changing parameters such as ambient temperature, a first-order low-pass filter is introduced to smooth high-frequency noise. This preprocessing step ensures the quality of the input data.

[0044] Example 6: This example establishes a standardized procedure for constructing feature mapping networks and calibrating physical parameters, and imposes deterministic constraints on the model architecture of the neural network. For the feature mapping neural network, the number of channels in its input layer corresponds to the sum of the spatial dimension of voxel resampling and the dimension of the normalized condition parameter vector. The kernel size, stride, and filling strategy of the hidden layer are adaptively matched according to the minimum geometric feature scale of the object to be simulated to ensure that the receptive field covers the key physical domain. The output layer has a dual-channel structure.

[0045] Regarding the key physical parameters involved in the simulation process, this embodiment specifies the following calibration procedure. For the conductivity-temperature variation curve of metallic materials such as aluminum alloys, it is necessary to use the four-probe method in a temperature-controlled experimental chamber. Celsius Within the range of degrees Celsius, Point-by-point measurements are performed using degrees Celsius as the step size, and a continuous resistivity-temperature function is generated by fitting using the least squares method, serving as the physical benchmark for sensitivity matrix calculation. For the dielectric constant and latent heat of phase transition parameters of the ice layer, differential scanning calorimetry (DSC) and dielectric spectrometry are used in a controlled freezing environment to obtain data on their step characteristics near the phase transition point. The width parameter of the hyperbolic tangent smoothing function is adjusted to balance numerical stability and physical accuracy. Furthermore, for the time step of heat conduction calculations, the theoretical maximum step size is calculated based on the mesh size and the material's thermal diffusivity using the von Neumann stability analysis method, and then... The safety factor ensures the unconditional convergence of the explicit difference solver.

[0046] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A simulation optimization method for train de-icing using an electromagnetic thermal coupling model incorporating deep learning, wherein the method obtains the geometric representation tensor and physical condition parameter vector of the object to be simulated, and the physical condition parameter vector includes at least the electromagnetic excitation frequency value and the reference ambient temperature value, characterized in that... It also includes the following steps: Step A: Input the geometric representation tensor and physical condition parameter vector into a pre-set feature mapping neural network. Through the nonlinear convolution operation of the feature mapping neural network, output a spatial source term tensor containing dual-channel data. The first channel data is the basic heat source power density distribution matrix under the reference ambient temperature value, and the second channel data is the sensitivity distribution matrix of the heat source power density with respect to temperature change. The sensitivity distribution matrix represents the gradient value of the heat source power density at each point in space with temperature change. Step B: Construct a discrete numerical evolution operator based on the partial differential equation of heat conduction, and configure source term linear correction logic in the numerical evolution operator. The source term linear correction logic is used to perform matrix linear superposition operation based on Hadamard product. Step C involves performing a time-step iterative operation with the heat conduction time scale as the step size. In each time step, the following data processing sub-steps are executed: obtain the temperature field distribution matrix of the current time step and calculate its difference matrix with the baseline ambient temperature value; call the source term linear correction logic, perform the Hadamard product operation of the sensitivity distribution matrix and the difference matrix, and superimpose the operation result onto the basic heat source power density distribution matrix to generate the corrected heat source matrix of the current time step; substitute the corrected heat source matrix as the source term parameter into the discrete numerical evolution operator to calculate the temperature field distribution matrix of the next time step.

2. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 1, characterized in that, Step C, which generates the corrected heat source matrix for the current time step, specifically includes performing matrix operations according to the following formula: ,in, This is the corrected heat source matrix for the current time step. Based on the power density distribution matrix of the basic heat source, The sensitivity distribution matrix is... For the Hadamard product operator, This is the temperature field distribution matrix at the current time step. This is a constant matrix of the same dimension constructed using the reference ambient temperature values.

3. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 1, characterized in that, The training process of the feature mapping neural network includes a physical residual constraint step. The physical residual constraint step calculates the residual value after substituting the basic heat source power density distribution matrix and sensitivity distribution matrix of the network output into the differential form of Maxwell's equations. The residual value is then added to the loss function as a regularization term to constrain the gradient convergence direction of the feature mapping neural network on the sensitivity distribution matrix to conform to the physical conservation law of electromagnetic field.

4. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 1, characterized in that, The discrete numerical evolution operator contains a continuously differentiable phase transition smoothing logic. The phase transition smoothing logic uses the hyperbolic tangent function to construct an equivalent specific heat capacity curve, mapping the step term in the heat conduction control equation corresponding to the latent heat of the ice-water phase transition to a continuously differentiable numerical interval, thereby establishing an end-to-end differentiable path of the temperature field distribution matrix with respect to the physical condition parameter vector.

5. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 1, characterized in that, The geometric representation tensor is a symbolic distance field matrix based on a three-dimensional Cartesian coordinate system. Each element in the symbolic distance field matrix represents the Euclidean distance from the spatial sampling point to the nearest boundary of the object to be simulated. The symbolic distance field matrix is ​​generated by voxelizing and resampling unstructured point cloud data and normalizing it, and is used to unify the input data format of objects with different topological structures.

6. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 1, characterized in that, In step A, the spatial source term tensor output by the feature mapping neural network also includes a topological evolution basis channel, which contains multiple heat source basis matrices corresponding to different icing thickness states of the simulated object. Correspondingly, the time step iteration operation in step C also includes a topological weighting sub-step: calculating the proportion of elements exceeding the phase transition threshold in the temperature field distribution matrix of the current time step to generate a global phase transition progress scalar, performing a linear weighted summation on multiple heat source basis matrices based on the global phase transition progress scalar, and using the summation result as the basic heat source power density distribution matrix to participate in the subsequent source term linear correction logic.

7. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 6, characterized in that, In the topology weighting sub-step, the weight coefficients of the linear weighted summation are calculated through a set of preset basis functions. The basis functions define the nonlinear mapping relationship between the global phase transition progress scalar and the weights of the basis matrices of each heat source. They are used to simulate the distortion of the electromagnetic field spatial distribution caused by the fading of geometric boundaries through algebraic interpolation without performing mesh reconstruction.

8. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 4, characterized in that, The method also includes a reverse gradient optimization step: constructing a loss function with the total simulation time and energy consumption as independent variables, using an end-to-end differentiable path based on the discrete numerical evolution operator, calculating the gradient of the loss function with respect to the physical condition parameter vector using an automatic differentiation algorithm, and updating the physical condition parameter vector using gradient descent based on the gradient until the loss function converges to a preset minimum range.

9. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 1, characterized in that, Step C is a sub-step that calculates the temperature field distribution matrix for the next time step. The discrete numerical evolution operator is solved using an alternating direction implicit difference scheme. The step size setting of the heat conduction time scale must satisfy the Courant-Friedrich-Levi convergence condition, and the step size setting is independent of the time scale of the electromagnetic field frequency.

10. The train de-icing simulation optimization method based on the electromagnetic thermal coupling model incorporating deep learning methods according to claim 1, characterized in that, The method also includes a data dimensionality reduction and storage step: after the time-stepping iterative calculation is completed, principal component analysis is performed on the generated full-time-domain temperature field distribution matrix sequence to extract the leading edge data that characterizes the spatiotemporal evolution of the temperature field. The intrinsic orthogonal decomposition modes and their corresponding time coefficient vectors are identified, and the intrinsic orthogonal decomposition modes and time coefficient vectors are persistently stored as simulation result data.

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