Underwater wireless power eddy current loss calculation method and system based on CGAN and physical constraints

Abstract

The underwater wireless power eddy current loss calculation method and system based on CGAN and physical constraints aim to solve the problems of low calculation efficiency and insufficient precision of seawater eddy current loss in underwater wireless power transmission. The present application constructs a seawater electric field distribution cloud atlas dataset under multiple sets of system parameters through finite element simulation, and builds a CGAN model composed of a Res-UNet generator and a layered conditional batch normalization discriminator. In the generator loss function, an eddy current loss energy norm error loss term based on electromagnetic field energy conservation is introduced to form a hybrid loss function, and an alternating training strategy is used to optimize the model to convergence. The system contains five modules: dataset construction, CGAN, hybrid loss calculation, model training and eddy current loss prediction. The generator outputs the electric field distribution cloud atlas by inputting the parameters to be predicted, and the eddy current loss is calculated by volume integration. The present application considers both calculation efficiency and physical rationality, efficiently and accurately evaluates the eddy current loss, and is suitable for engineering parameter iteration optimization.

Description

Technical Field

[0001] This invention relates to the field of underwater wireless power transmission technology, and in particular to a method and system for calculating underwater wireless power eddy current loss based on CGAN and physical constraints. Background Technology

[0002] With the continuous deepening of marine exploration and development activities, underwater equipment such as Autonomous Underwater Vehicles (AUVs) are increasingly widely used in marine observation, resource exploration, and underwater operations. However, the endurance of these devices is limited by the capacity of their onboard batteries, becoming a key bottleneck restricting their long-term continuous operation. To solve this problem, underwater wireless power transfer technology has emerged. It provides continuous power supply to underwater equipment in a non-contact manner, effectively extending the equipment's operating time. It is a core technology for building long-term marine observation networks and ensuring the continuous operation of underwater equipment, and has significant research and application value.

[0003] However, underwater wireless power transfer systems face challenges due to the high conductivity of seawater. Under the influence of the system's high-frequency alternating magnetic field, seawater generates a strong eddy current effect, resulting in considerable eddy current losses. These losses not only significantly reduce the system's transmission efficiency and distance but may also cause safety hazards due to localized overheating, severely restricting the high-performance design and safe operation of underwater wireless power transfer systems with magnetic cores. Therefore, accurately and efficiently quantifying the eddy current losses of underwater wireless power transfer systems in seawater environments is a crucial prerequisite for optimizing system parameters, improving overall performance, and ensuring operational safety.

[0004] In existing technologies, engineering applications primarily rely on the finite element method (FEM) for eddy current field simulation to calculate eddy current losses in underwater wireless power transmission systems. For example, CN118054574A discloses a method and system for calculating coil eddy current losses in underwater wireless power transmission, proposing to calculate the total eddy current loss by combining coil parameters and system operating frequency, and verifying it through an equivalent model using finite element simulation. However, the finite element method has significant drawbacks: its modeling process is complex, requiring detailed establishment of the system's electromagnetic field simulation model and parametric scanning of key system parameters; it consumes large computational resources, with high-frequency electromagnetic field simulation requiring substantial resources, resulting in low computational efficiency when handling multi-parameter, large-scale system design spaces; and it struggles to support rapid parameter iteration optimization, as the long computation time makes rapid scanning and iteration of system parameters difficult, leading to low design efficiency.

[0005] Analytical methods calculate eddy current losses by establishing loss calculation formulas, offering fast computation speeds. However, their derivation processes are often based on idealized assumptions, such as infinitely large magnetic cores or neglecting the magnetic core, which differ significantly from the finite-size structure and complex electromagnetic environment of actual underwater wireless power transmission systems. This leads to difficulties in guaranteeing prediction accuracy and significant limitations in engineering applications. For example, when dealing with complex coil structures (such as DD (Double-D) coils and Bipolar coils), analytical methods struggle to accurately calculate eddy current losses, resulting in substantial errors.

[0006] In recent years, the successful application of deep learning technology, especially Conditional Generative Adversarial Networks (CGANs), in image generation and processing has provided new ideas for solving the problem of eddy current loss calculation in underwater wireless power transmission systems. However, directly applying deep learning models to prediction problems with strong physical constraints, such as eddy current fields, still faces many challenges. On the one hand, data acquisition is costly, especially in the complex electromagnetic environment of underwater wireless power transmission systems, where obtaining sufficient multi-dimensional training data is expensive. On the other hand, models are prone to overfitting; with limited training samples, models are susceptible to overfitting, resulting in insufficient generalization ability for unknown system parameter combinations. Furthermore, traditional data-driven models lack constraints from electromagnetic physics, easily generating visually plausible but violating fundamental electromagnetic equations, thus losing physical meaning. For example, CN121615419A discloses a parameter identification method for underwater wireless power transmission systems based on machine learning. This method proposes a parameter identification method based on machine learning, which predicts key electromagnetic parameters of the system, including eddy current loss, by constructing multiple independent XGBoost (Extreme Gradient Boosting) regression models. However, this method may still result in inaccurate predictions due to a lack of physical constraints.

[0007] Although CGAN performs well in image generation, when applied to underwater electric field distribution prediction, it suffers from insufficient network structure adaptability. The lack of a network structure specifically designed for the characteristics of underwater electric field distribution results in prediction accuracy and stability that cannot meet engineering requirements. At the same time, the lack of physical constraints may cause the prediction results to violate the basic equations of electromagnetic fields and lose physical consistency.

[0008] In summary, existing technologies for calculating eddy current losses in underwater wireless power transmission systems suffer from low computational efficiency, insufficient prediction accuracy, and a lack of physical consistency, making them unsuitable for practical engineering applications. With the continuous development of marine activities such as marine resource exploration, underwater environmental monitoring, and underwater vehicle operations, underwater wireless power transmission technology has become a core supporting technology for ensuring the long-term stable operation of underwater equipment. Therefore, developing a precise, efficient, and physically consistent method for calculating eddy current losses in underwater wireless power transmission systems has significant practical importance and application value. Summary of the Invention

[0009] The technical problem this invention aims to solve is to provide a method and system for calculating underwater wireless power eddy current losses based on CGAN and physical constraints, addressing the issues of low calculation efficiency and insufficient prediction accuracy in the field of underwater wireless power transmission technology. Specifically, while the traditional finite element method can obtain accurate field distribution results, its modeling process is complex and computationally resource-intensive, making it difficult to support rapid scanning and optimization of system parameters. Analytical methods, although fast, often rely on idealized assumptions, resulting in significant differences from the complex electromagnetic environment of actual systems and making it difficult to guarantee prediction accuracy. This invention overcomes the limitations of traditional methods in terms of computational efficiency and prediction accuracy.

[0010] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: This paper presents a method and system for calculating underwater wireless power eddy current loss based on CGAN and physical constraints. While ensuring computational efficiency, it introduces physical constraints to improve the physical rationality and accuracy of the prediction results, achieving efficient and accurate rapid assessment of eddy current loss. The details are as follows: I. A method for calculating underwater wireless power eddy current loss based on CGAN and physical constraints, including the following steps: Step 1: Construct a training dataset: Obtain the electric field intensity distribution cloud map of the sea area under multiple combinations of different system parameters through finite element simulation. The system parameters include transmission distance, number of coil turns, coil inner diameter and resonant frequency. Normalize the electric field intensity data and save it as a fixed-size grayscale image, and divide it into training set and test set according to the ratio.

[0011] Step 2: Construct a Conditional Generative Adversarial Network (CGAN) model, which consists of a generator and a discriminator. The generator adopts a Res-UNet architecture, replacing standard convolutional blocks with residual blocks in the encoder, decoder, and bottleneck module of the U-Net. Skip connections are set between corresponding layers in the encoder and decoder, and a Dropout operation is added before the activation function of the bottleneck module. The discriminator adopts a hierarchical Conditional Batch Normalization (CBN) structure, with standard batch normalization used in shallow convolutional layers and conditional batch normalization used in deep convolutional layers. The system parameters are converted into scaling parameters through a mapping network. With offset parameter The feature map is modulated.

[0012] Step 3: Input the system parameters into the generator to generate a predicted electric field intensity distribution cloud map; input the actual cloud map or predicted cloud map and the system parameters into the discriminator to complete the determination of authenticity and condition consistency.

[0013] Step 4: Introduce an eddy current loss energy norm error loss term based on the law of conservation of electromagnetic field energy into the generator loss function to form a hybrid loss function: Eddy current loss energy norm error loss term: (4); In the formula, This refers to the energy norm error loss due to eddy current loss. This represents the total number of pixels in the electric field intensity contour map. The pixel number in the electric field intensity contour map; Binary masking for areas of interest in marine waters; The electrical conductivity of seawater; The model predicts the first The magnitude of the electric field intensity at each pixel; The first finite element simulation obtained The magnitude of the electric field intensity at each pixel.

[0014] Generator total loss function: (5); In the formula, This represents the total loss of the generator; To combat loss in generators; This refers to the physical loss weighting coefficient; This refers to the energy norm error loss due to eddy current loss.

[0015] Step 5: Optimize the generator and discriminator parameters using an alternating training strategy until the model converges: train the discriminator with the generator parameters fixed, then train the generator with the discriminator parameters fixed, and repeat this process until the loss function stabilizes.

[0016] Step 6: Input the system parameters to be predicted into the trained generator, output the electric field intensity distribution cloud map, and calculate the eddy current loss value through volume integral in cylindrical coordinates. (6); In the formula, Power loss due to seawater eddy currents; The electrical conductivity of seawater; The electric field intensity vector; The magnitude of the electric field intensity; This is the volume integral.

[0017] II. An underwater wireless power eddy current loss calculation system based on CGAN and physical constraints, including: Dataset building module: Used to perform step 1, completing the generation, preprocessing and partitioning of the training dataset; Conditional Generative Adversarial Network (CGN) module: used to execute steps 2 and 3, and to build the Res-UNet generator and the hierarchical CBN discriminator; Hybrid loss calculation module: used to execute step 4, realizing the weighted fusion of adversarial loss and physical constraint loss; Model training module: used to execute step 5, completing the alternating optimization of the generator and discriminator; Eddy current loss prediction module: used to execute step 6, realize electric field distribution prediction and eddy current loss volume integral calculation.

[0018] The underwater wireless power eddy current loss calculation method and system based on CGAN and physical constraints provided by this invention have the following beneficial effects: 1. This invention establishes an end-to-end mapping relationship from system design parameters to electric field intensity distribution by constructing a conditional generative adversarial network model. This overcomes the limitations of traditional finite element method's repeated modeling and calculation and analytical method's insufficient accuracy due to ideal assumptions, and achieves rapid and accurate calculation of eddy current loss, greatly improving calculation efficiency and accuracy.

[0019] 2. The Res-UNet generator network designed in this invention introduces the residual learning mechanism into the U-Net architecture. By leveraging cross-layer connections, it effectively solves the gradient vanishing and degradation problems in deep network training, and significantly improves the model's convergence speed and feature representation ability while maintaining the ability to capture spatial details.

[0020] 3. The hierarchical conditional batch normalization discriminator proposed in this invention adopts a hierarchical strategy of shallow standard normalization and deep conditional normalization, which not only ensures the stability of basic visual feature extraction, but also realizes the deep fusion of conditional information at the feature distribution level, thereby enhancing the ability to constrain the generated results.

[0021] 4. The innovative eddy current loss energy norm error loss function of this invention is based on the law of conservation of electromagnetic field energy. It explicitly embeds physical priors into the model optimization process, so that the generator strictly follows physical laws during adversarial training, thereby improving the model's generalization ability and the physical rationality of the prediction results under limited sample conditions.

[0022] 5. This invention introduces Dropout operation into the generator bottleneck module, which effectively prevents model overfitting, enhances prediction stability under unknown parameter combinations, provides reliable assurance for practical engineering applications, and reduces prediction risks caused by data bias.

[0023] 6. The method of this invention significantly reduces computational costs, shortening the computation time from several hours to seconds compared to the traditional finite element method, while maintaining an accuracy level comparable to high-fidelity simulation, providing strong technical support for the rapid design and parameter optimization of underwater wireless power transmission systems.

[0024] 7. This invention organically combines physical constraints and data-driven approaches, achieving physical consistency of prediction results while ensuring computational efficiency. It provides a novel solution for engineering calculation problems in complex electromagnetic environments, breaking through the limitations of traditional methods.

[0025] 8. The technical solution of this invention has good scalability. It can be adapted to different underwater wireless power transmission system configurations and marine environmental conditions by adjusting the network structure and loss function. It can be effectively applied regardless of different transmission distances, coil parameters, or complex marine environments.

[0026] 9. This invention provides a complete technical path for the intelligent design of underwater wireless power transmission systems. By deeply integrating deep learning with traditional numerical methods, it promotes technological innovation in the field of electromagnetic computing and leads the industry's development direction.

[0027] 10. The invention has been verified by a large number of simulations. The proposed method is significantly better than traditional methods in terms of prediction accuracy, computational efficiency and generalization ability. It provides reliable technical support for the energy system optimization design of marine equipment and ensures the efficient and stable operation of marine equipment.

[0028] 11. The improved computational efficiency of this invention enables rapid scanning and optimization of system parameters, greatly shortening the R&D cycle, accelerating product launch time, and enhancing the company's competitiveness in the market.

[0029] 12. The accuracy of the prediction provided by this invention allows designers to understand system performance more accurately, identify potential problems in advance, reduce the cost of later debugging and improvement, and improve product quality and reliability.

[0030] 13. The powerful generalization ability of this invention enables the model to work stably in different scenarios, reducing the need for remodeling and calculation due to environmental changes or system configuration adjustments, and lowering research and development and maintenance costs.

[0031] 14. The broad application prospects of this invention lay the foundation for the large-scale application of underwater wireless power transmission technology in fields such as marine exploration and marine resource development, and promote the development of marine science and technology.

[0032] 15. The reliable technical guarantee of this invention allows marine equipment energy systems to fully consider eddy current loss factors during the design phase, optimize energy distribution, improve energy utilization efficiency, and reduce operating costs. Attached Figure Description

[0033] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart illustrating an embodiment of the calculation method of the present invention; Figure 2 This is a structural diagram of the Res-UNet generator of the present invention; Figure 3 This is a schematic diagram of the residual block structure of the present invention; Figure 4 This is a structural diagram of the hierarchical conditional batch normalization discriminator of the present invention; Figure 5 This is a comparison chart showing the prediction effect of the cloud map of electric field intensity distribution in sea areas according to the present invention. Detailed Implementation

[0034] The technical solutions of the present invention will be further described below with reference to the embodiments and accompanying drawings: Example 1 like Figure 1 As shown, this embodiment provides a method for calculating underwater wireless power eddy current loss based on CGAN and physical constraints, specifically including the following steps: Step 1: Constructing the training dataset: Using COMSOL Multiphysics finite element simulation software, an electromagnetic field model of the underwater wireless power transmission system is established, and cloud maps of the electric field intensity distribution in the sea area under multiple combinations of different system parameters are obtained. The system parameters include transmission distance, number of coil turns, coil inner diameter, and resonant frequency. The electric field intensity data is normalized and saved as a 128×256 fixed-size grayscale image, and divided into training and test sets at a ratio of 4:1.

[0035] Step 2: Construct a Conditional Generative Adversarial Network (CGAN) model, which consists of a generator and a discriminator; like Figure 2As shown, the generator adopts a Res-UNet (Residual U-Net) architecture, replacing standard convolutional blocks in the encoder, decoder, and bottleneck modules of the U-Net with... Figure 3 The residual block shown has skip connections between corresponding levels of the encoder and decoder, and a Dropout operation is added before the activation function of the bottleneck module; the output of the residual block satisfies: (1); In the formula, and These represent the input and output vectors of the residual block, respectively. It is based on the weight The nonlinear residual mapping consists of convolutional layers, batch normalization layers, and activation functions; These are the weight parameters for the convolutional layer.

[0036] Note: Figure 2 In this context, Dropout stands for Random Deactivation; ReLU stands for Rectified Linear Unit. Figure 3 In this context, Conv2D stands for 2D convolution; BN stands for batch normalization; and ReLU stands for rectified linear unit.

[0037] like Figure 4 As shown, the discriminator employs a hierarchical conditional batch normalization (CBN) structure. Shallow convolutional layers use standard batch normalization, while deep convolutional layers use conditional batch normalization. A mapping network transforms the system parameters into scaling parameters. With offset parameter The feature map is modulated; the calculation process and modulation formula for the conditional batch normalization are as follows: (2); (3); In the formula, , These are the condition-driven scaling parameters and the offset parameters, respectively. It is a conditional vector; To generate the weight matrix for scaling parameters, used to divide the condition vector Mapped to scaling parameter space; Generate a bias vector for the scaling parameters, providing a learnable baseline offset for the scaling parameters; To generate the weight matrix for the offset parameters, used to incorporate the condition vector Mapped to offset parameter space; Generate an offset vector for the offset parameters, providing a learnable baseline offset for the offset parameters; To conditionally batch normalize the output feature map; Input feature map; The batch mean of the input feature maps; The batch standard deviation of the input feature map.

[0038] Note: Figure 4 In this context, Conv2D stands for 2D convolution; BN for standard batch normalization; LeakyReLU for leaky linear rectifier unit; CBN for conditional batch normalization; and Sigmoid for sigmoid function.

[0039] Step 3: Input the system parameters into the generator network and generate a predicted electric field intensity distribution cloud map based on the Res-UNet structure; input the real finite element simulation cloud map or the generated predicted cloud map and the system parameters into the discriminator network, and complete the authenticity and condition consistency judgment based on the hierarchical conditional batch normalization structure.

[0040] Step 4: Introduce an eddy current loss energy norm error loss term based on the law of conservation of electromagnetic field energy into the generator loss function to form a hybrid loss function: Eddy current loss energy norm error loss term: (4); In the formula, This refers to the energy norm error loss due to eddy current loss. This represents the total number of pixels in the electric field intensity contour map. The pixel number in the electric field intensity contour map; Binary masking for areas of interest in marine waters; The electrical conductivity of seawater; The model predicts the first The magnitude of the electric field intensity at each pixel; The first finite element simulation obtained The magnitude of the electric field intensity at each pixel; The generator's total loss function is a weighted sum of adversarial loss and eddy current loss energy norm error loss: (5); In the formula, This represents the total loss of the generator; To combat loss in generators; This refers to the physical loss weighting coefficient; This refers to the energy norm error loss due to eddy current loss.

[0041] Step 5: Optimize the generator and discriminator parameters using an alternating training strategy until the model converges: Train the discriminator with fixed generator parameters, then train the generator with fixed discriminator parameters. Update the network parameters using the Adam (Adaptive Moment Estimation) optimizer and cosine annealing learning rate, and iterate until the loss function converges stably.

[0042] Step 6: Input the system parameters to be predicted into the trained generator, which will output an electric field intensity distribution cloud map, such as... Figure 5 The image shows a comparison of the predicted electric field intensity distribution cloud map results for the sea area using this invention; and the eddy current loss power is calculated using volume integrals in cylindrical coordinates. (6); In the formula, Power loss due to seawater eddy currents; The electrical conductivity of seawater; The electric field intensity vector; The magnitude of the electric field intensity; This is the volume integral.

[0043] Example 2 In another preferred embodiment, based on Embodiment 1, this embodiment provides an underwater wireless power eddy current loss calculation system based on CGAN and physical constraints. This system is used to implement the underwater wireless power eddy current loss calculation method based on CGAN and physical constraints described in Embodiment 1, and includes: Dataset construction module: Used to obtain the electric field intensity distribution cloud map of the sea area under multiple system parameter combinations through finite element simulation, and to complete preprocessing operations such as data normalization, image format conversion, and dataset partitioning.

[0044] Conditional Generative Adversarial Network (GAN) modules include, for example: Figure 2 The Res-UNet generator shown is similar to... Figure 4 The hierarchical conditional batch normalization discriminator shown is used to receive system parameters and generate electric field intensity distribution cloud maps, while simultaneously determining the authenticity and conditional consistency of the generated results.

[0045] Hybrid loss calculation module: used to calculate the eddy current loss energy norm error loss and weighted fusion with the adversarial loss to obtain the generator's total loss function.

[0046] Model training module: Used to employ an alternating training strategy to iteratively optimize the parameters of the generator and discriminator, and save the optimal model weights after convergence.

[0047] Eddy current loss prediction module: Used to load the trained model, input the system parameters to be predicted, and output as follows. Figure 5 The electric field intensity distribution cloud map is shown, and the final eddy current loss value is obtained by volume integration in cylindrical coordinate system.

[0048] Each of the above modules corresponds to one of the steps in Example 1, enabling rapid and accurate calculation of end-to-end eddy current losses.

[0049] Example 3 In another preferred embodiment, based on embodiments 1 and 2, this embodiment provides an electronic device, including a processor, a memory, a communication interface, and a bus; the processor, memory, and communication interface all communicate with each other through the bus.

[0050] The memory is used to store computer program instructions; the processor is used to execute the program instructions to implement all the steps of the underwater wireless power eddy current loss calculation method based on CGAN and physical constraints described in Embodiment 1.

[0051] The electronic devices include, but are not limited to, industrial control computers, simulation workstations, servers, portable computers, and embedded computing platforms, and can be adapted to engineering scenarios such as underwater wireless power transmission system design, simulation, and parameter optimization.

[0052] Example 4 In another preferred embodiment, based on embodiments 1 to 3, this embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements all the steps of the underwater wireless power eddy current loss calculation method based on CGAN and physical constraints described in embodiment 1.

[0053] The computer-readable storage medium is a non-transitory computer-readable storage medium, including but not limited to: read-only memory (ROM), random access memory (RAM), magnetic disk, optical disk, USB flash drive, solid state hard drive (SSD), etc., which can be used for the deployment and operation of simulation software, design platforms, and control systems.

[0054] Example 5 In another preferred embodiment, this embodiment is based on embodiment 1, such as... Figure 1 As shown, this embodiment provides a method for calculating underwater wireless power eddy current loss based on CGAN and physical constraints, specifically including the following steps: Step 1: Construct dataset: Obtain the distribution cloud map of electric field intensity in the sea area under multiple combinations of different system parameters through finite element simulation.

[0055] In practical applications, the following data processing is performed: (1) Finite element simulation setup. An electromagnetic field simulation model of the underwater wireless power transmission system was established using COMSOL Multiphysics finite element simulation software. The model includes a transmitting coil, a receiving coil, a magnetic core structure, and seawater and air medium domains. Mesh generation parameters were set to ensure that the mesh density in the seawater region was high enough to accurately capture the eddy current effect.

[0056] (2) Parametric scanning. A parametric scan is performed on key system parameters, including transmission distance. Number of coil turns Coil inner diameter and resonant frequency High-frequency electromagnetic field simulations were performed under each parameter combination to calculate the steady-state electric field intensity distribution and its corresponding eddy current loss values.

[0057] (3) Data preprocessing. The electric field intensity data obtained from the finite element simulation is normalized, and the normalization coefficient is... The electric field intensity is determined by calculating the maximum electric field intensity value across all training samples. The electric field intensity distribution data is saved as a 128×256 pixel grayscale image, where the pixel value represents the normalized electric field intensity magnitude.

[0058] (4) Dataset partitioning. The generated data is divided into training set and test set in a 4:1 ratio. The training set is used for model parameter learning, and the test set is used for model performance evaluation.

[0059] Step 2: Construct a conditional generative adversarial network model; The model includes a generator and a discriminator. The generator adopts a Res-UNet architecture, and the discriminator adopts a hierarchical conditional batch normalization structure. The Res-UNet architecture of the generator replaces standard convolutional blocks with residual blocks in the encoder, decoder, and bottleneck module of the U-Net. Skip connections are set between corresponding layers in the encoder and decoder, and a Dropout operation is added before the activation function of the bottleneck module. The hierarchical conditional batch normalization structure of the discriminator is as follows: shallow convolutional layers use standard batch normalization, and deep convolutional layers use conditional batch normalization. Conditional batch normalization converts system parameters into scaling parameters through a mapping network. With offset parameter The feature map is modulated.

[0060] Step 3: Input the system parameters into the generator network to generate the predicted electric field intensity distribution cloud map based on the Res-UNet structure.

[0061] The generator using step 2 above employs a Res-UNet network structure, such as... Figure 2 As shown, this structure deeply integrates the encoder-decoder architecture of U-Net with the residual learning mechanism of ResNet, forming a deep generative network specifically for physics prediction. The specific network architecture and data flow of the generator are as follows: Step 3.1: Input Layer Processing System parameter condition vector (Dimension 4, corresponding to transmission distance, number of coil turns, inner diameter of coil, and resonant frequency) is expanded to 128×256=32768 dimensions through a fully connected layer, and then reshaped into a 1×128×256 feature map through an anti-flattening operation, which serves as the initial input to the generator.

[0062] Step 3.2: Encoder Path The encoder contains three cascaded downsampling modules, each consisting of a residual block and a max-pooling layer: The first encoding module: Input channel 1, processed through a 64-channel residual block. The residual block contains two 3×3 convolutional layers, each followed by batch normalization and ReLU activation. The output feature map size is 128×256×64, downsampled to 64×128×64 by 2×2 max pooling.

[0063] The second encoding module has 64 input channels, which are processed by a 128-channel residual block to output a feature map of size 64×128×128. This feature map is then downsampled to 32×64×128 using 2×2 max pooling.

[0064] The third encoding module has 128 input channels, which are processed by a 256-channel residual block to output a feature map of size 32×64×256. This feature map is then downsampled to 16×32×256 using 2×2 max pooling.

[0065] Each residual block achieves identity mapping through cross-layer shortcut connections, and the residual block structure is as follows: Figure 3 As shown, its core calculation formula is: the output of the residual block satisfies: (1); In the formula, and These represent the input and output vectors of the residual block, respectively. It is based on the weight The nonlinear residual mapping consists of convolutional layers, batch normalization layers, and activation functions; These are the weight parameters of the convolutional layer; in this embodiment... It is represented by the residual transformation learned by two 3×3 convolutional layers, which effectively alleviates the gradient vanishing problem in deep networks.

[0066] Step 3.3: Bottleneck Module The module receives a 16×32×256 feature map from the encoder output and performs deep feature extraction using a 512-channel residual block. A Dropout operation is introduced before the activation function of this module, with a dropout rate set to 0.5, randomly disabling some neurons to enhance the model's generalization ability and prevent overfitting.

[0067] Step 3.4: Skip Connection Mechanism A direct feature transfer path is established between corresponding layers of the encoder and decoder. The shallow features rich in spatial details extracted by the encoder are concatenated with the deep features rich in semantic information recovered by the decoder along the channel dimension, which effectively solves the problem of information loss during downsampling.

[0068] Step 3.5: Decoder Path The decoder contains three cascaded upsampling modules that gradually restore spatial resolution through transposed convolution: The first decoding module: The 16×32×512 feature map output from the input bottleneck layer is upsampled to 32×64×256 through transposed convolution (kernel 4×4, stride 2, padding 1), and concatenated with the output of the third encoding module in the channel dimension (total channels 512), and then processed by a 256-channel residual block.

[0069] The second decoding module takes a 32×64×256 feature map as input, upsamples it to 64×128×128 through transposed convolution, concatenates it with the output of the second encoding module (total 256 channels), and processes it through a 128-channel residual block.

[0070] The third decoding module takes a 64×128×128 feature map as input, upsamples it to 128×256×64 through transposed convolution, concatenates it with the output of the first encoding module (total 128 channels), and processes it through a 64-channel residual block.

[0071] Step 3.6: Output Layer Processing Finally, the 64-channel feature map is reduced to a single channel by 1×1 convolution, and the output value is constrained to the range of [0, 1] by the Sigmoid activation function to generate a 128×256 electric field intensity distribution prediction map that strictly corresponds to the input system parameters.

[0072] Step 3.7: Input the real finite element simulation cloud map or the generated fake map and the underwater wireless power transmission system parameters into the discriminator network, and perform authenticity and consistency discrimination based on the hierarchical conditional batch normalization structure.

[0073] The discriminator in step 4 above employs an innovative hierarchical conditional batch normalization structure, such as... Figure 4 As shown, this discriminator achieves multi-level deep fusion of conditional information and visual features through a normalization strategy that differentiates between shallow and deep layers.

[0074] The discriminator network described above consists of three convolutional normalization activation modules. The kernel size of all convolutional layers is set to 4, the padding is 1, and the stride is 2. The normalization layer uses standard batch normalization (BN) in the first module and conditional batch normalization (CBN) in the second and third modules.

[0075] Standard batch normalization layer: performs standardization processing at the batch level; the calculation formula is as follows: (7); In the formula, To output feature maps that are normalized for the standard batch; For scaling parameters; Input feature map; The batch mean of the input feature maps; The batch standard deviation of the input feature maps; This is the offset parameter.

[0076] The specific implementation of conditional batch normalization uses a dedicated mapping network to transform the 4-dimensional conditional vector... Dynamically convert to normalized parameters: (2); in, , These are the condition-driven scaling parameters and the offset parameters, respectively. It is a conditional vector; To generate the weight matrix for scaling parameters, used to divide the condition vector Mapped to scaling parameter space; Generate a bias vector for the scaling parameters, providing a learnable baseline offset for the scaling parameters; To generate the weight matrix for the offset parameters, used to incorporate the condition vector Mapped to offset parameter space; Generate an offset vector for the offset parameters, providing a learnable baseline offset for the offset parameters.

[0077] The modulation process of the feature map is as follows: (3); This mechanism enables the discriminator to adjust the feature distribution according to specific system parameters, enhancing its conditional consistency discrimination capability; among which... The output feature map is conditionally batch normalized.

[0078] In practical applications, the electric field intensity distribution prediction map generated by the generator and the real finite element simulation cloud map form an image pair. The input passes through the first convolutional normalization activation module, the second convolutional normalization activation module, and the third convolutional normalization activation module in sequence. Then, the output discriminant probability is obtained through a flattening layer, a fully connected layer, and a Sigmoid (S-shaped function) activation function.

[0079] The hierarchical normalization strategy proposed in this invention conforms to the cognitive laws of feature learning—shallow learning of general features maintains stability, while deep integration of conditional information achieves precise modulation. Through this progressive conditional fusion approach, the discriminator can not only determine the authenticity of an image but also assess the physical consistency between the generated result and the system parameters, providing the generator with more physically meaningful gradient guidance.

[0080] Step 4: Calculate the loss based on the outputs of the generator and discriminator, and update the network parameters of the generator and discriminator using the gradient descent method to obtain the electric field intensity distribution prediction model.

[0081] Step 4 above involves setting relevant parameters during network training until the network converges, and then saving the network training weights, as detailed below: Step 4.1: Training Parameter Settings. Set the total number of training epochs, batch size, initial learning rate, and physical loss weight coefficients obtained after hyperparameter tuning. A cosine annealing learning rate scheduling strategy is adopted, with the learning rate linearly decaying from the initial value to 1% of the initial value. The total number of training steps is the product of the total number of epochs and the number of steps per epoch.

[0082] Step 4.2: Training Process. An alternating training strategy is adopted, first updating the discriminator network parameters, and then updating the generator network parameters. In each training batch, the discriminator loss is first calculated and backpropagated to update the discriminator, and then the generator loss is calculated and backpropagated to update the generator.

[0083] Step 4.3: Optimizer and Loss Function. Adam is used as the optimizer. The momentum parameter betas of the generator optimizer is set to (0.5, 0.999), and the momentum parameter betas of the discriminator optimizer is set to (0.5, 0.9). During optimization, a hybrid loss function is used, where the generator's total loss function is a weighted sum of the adversarial loss and the physical information loss, calculated as follows: (5); in, This represents the total loss of the generator; The generator adversarial loss represents the loss incurred by the generator in adversarial training to deceive the discriminator. It is calculated using the binary cross-entropy loss function, and its goal is to make the electric field intensity distribution cloud map G(c) generated by the generator appear as realistic as possible to the discriminator D. It is the eddy current loss energy norm error loss, which is a physical information loss term designed based on the physical laws of electromagnetic fields. It is used to constrain the consistency between the electric field intensity distribution predicted by the generator and the finite element simulation results at the physical energy level. It is a preset physical loss weighting coefficient, which is used as one of the hyperparameters to balance the relative importance of adversarial loss and physical information loss in the total loss.

[0084] The formula for calculating the eddy current loss energy norm error loss function is as follows: (4); The discriminator loss function can be a traditional adversarial loss; among which, This refers to the energy norm error loss due to eddy current loss. This represents the total number of pixels in the electric field intensity contour map. The pixel number in the electric field intensity contour map; Binary masking for areas of interest in marine waters; The electrical conductivity of seawater; The model predicts the first The magnitude of the electric field intensity at each pixel; The first finite element simulation obtained The magnitude of the electric field intensity at each pixel; Step 4.4: Model Saving and Evaluation. After each training cycle, evaluate the model performance on the test set. The main evaluation metrics include mean absolute error in the symmetric domain, null domain accuracy, mean square error in the non-null domain, and peak hold exponent. When the mean square error in the non-null domain reaches its historical best, save the current generator model parameters. Repeat the training process until the network converges, obtaining the electric field intensity distribution prediction model.

[0085] Step 5: Input the system parameters to be predicted into the trained generator, output the electric field intensity distribution cloud map, and calculate the eddy current loss value through volume integral.

[0086] The specific steps are as follows: Step 5.1: Electric Field Intensity Distribution Prediction. Input the parameters of the underwater wireless power transmission system to be predicted (transmission distance, number of coil turns, coil inner diameter, resonant frequency) into the trained generator network, and directly output the corresponding electric field intensity distribution cloud map.

[0087] Step 5.2: Region of Interest Extraction. A region of interest mask is generated based on the transmission distance parameter to extract the electric field intensity value of the seawater region. The calculation of the region of interest mask is determined based on the ratio between the image size (128×256 pixels) and the actual physical size (65mm×130mm).

[0088] Step 5.3: Eddy Current Loss Calculation. Based on the predicted electric field intensity distribution cloud map, the eddy current loss value of the system is calculated using volume integral. Considering the axisymmetric characteristics of the system, the integral calculation is performed in cylindrical coordinates. The integral formula is: (6); The integration area is the entire sea area. Power loss due to seawater eddy currents; The electrical conductivity of seawater; The electric field intensity vector; The magnitude of the electric field intensity; This is the volume integral.

[0089] Step 5.4: Result Verification. The predicted eddy current loss value is compared with the finite element simulation results to calculate the relative error and verify the prediction accuracy of the model. Experimental results show that the relative error between the predicted eddy current loss value and the finite element simulation result is within 5%, while the calculation time is reduced from several hours in the traditional finite element method to seconds.

[0090] Applying the above design to practice, this invention can quickly and accurately predict the distribution cloud map of the electric field intensity in the sea area under different system parameters, and then calculate the eddy current loss value. For example... Figure 5 As shown, (a) is the electric field intensity distribution cloud map obtained by finite element simulation, (b) is the electric field intensity distribution cloud map predicted by the model of this invention, and (c) is the percentage relative error distribution map. It can be seen that the prediction results are visually highly consistent with the simulation results, and the relative error is mainly concentrated in the low electric field intensity region.

[0091] Compared with the traditional finite element method, the computational efficiency of this invention is significantly improved. Under the same hardware conditions, the finite element method requires remodeling and recalculating to handle different system parameters, while the model of this invention can directly input system parameters for prediction, thus improving computational efficiency while maintaining an accuracy level comparable to finite element simulation.

[0092] In the preferred embodiment, the system parameters mentioned in step 1 include transmission distance, number of coil turns, coil inner diameter, and resonant frequency. These settings comprehensively cover the key factors affecting eddy current losses in underwater wireless power transmission systems. Transmission distance affects the attenuation of electromagnetic signals, the number of coil turns and inner diameter determine the distribution of the electromagnetic field, and the resonant frequency affects energy transmission efficiency. By comprehensively considering these parameters, a more accurate system model can be established, providing a solid foundation for subsequent accurate calculations of eddy current losses. This facilitates in-depth analysis of the impact of different parameter combinations on eddy current losses and provides a strong basis for system optimization design.

[0093] In the preferred embodiment, the generator in step 2 adopts a Res-UNet architecture, and the discriminator adopts a hierarchical conditional batch normalization structure. This configuration allows the Res-UNet architecture of the generator to better capture spatial features, utilizes residual connections to solve the training challenges of deep networks, and improves feature extraction capabilities. The hierarchical conditional batch normalization structure of the discriminator ensures stable basic feature extraction through shallow standard batch normalization, while deep conditional batch normalization achieves deep fusion of conditional information. The combination of these two approaches makes the generative adversarial network more stable and efficient during training, improves the quality and accuracy of the generated results, and provides a reliable model for accurately calculating eddy current loss.

[0094] In the preferred scheme, the Res-UNet architecture of the generator replaces standard convolutional blocks with residual blocks in the encoder, decoder, and bottleneck module of the U-Net. Skip connections are set between corresponding layers in the encoder and decoder, and a Dropout operation is added before the activation function of the bottleneck module. These settings address the vanishing gradient problem in deep networks by using residual blocks, enabling the network to learn more complex features. Skip connections promote feature fusion across different layers, preserving more detailed information. The Dropout operation prevents overfitting and enhances the model's generalization ability. These improvements make the generator perform better when processing complex underwater electromagnetic environment data, generating more accurate electric field intensity distributions and providing high-quality input for subsequent eddy current loss calculations.

[0095] In a preferred embodiment, the hierarchical conditional batch normalization structure of the discriminator is as follows: shallow convolutional layers use standard batch normalization, and deep convolutional layers use conditional batch normalization; conditional batch normalization converts system parameters into scaling parameters through a mapping network. With offset parameter The feature maps are modulated. The above settings include shallow standard batch normalization to ensure the stability of basic visual feature extraction, and deep conditional batch normalization to integrate system parameter information into the feature distribution, enabling the discriminator to better distinguish between real and generated data. A mapping network converts system parameters into scaling and offset parameters, flexibly adjusting the feature maps. This structure improves discriminator performance, strengthens constraints on the generated results, prompts the generator to produce results that better conform to physical laws, and improves the accuracy of eddy current loss calculation.

[0096] In the preferred embodiment, the generator's total loss function in step 3 is a weighted sum of the adversarial loss and the eddy current loss energy norm error loss. This setting ensures that the adversarial loss makes the data generated by the generator more closely resemble the real data in terms of distribution, thus making the generated results more reasonable. The eddy current loss energy norm error loss is based on the law of conservation of electromagnetic field energy, embedding physical priors into the model optimization to guarantee that the generated results conform to physical laws. The weighted sum of these two losses serves as the total loss function, balancing the reasonableness of the data distribution and physical consistency, guiding the generator to continuously optimize during training, generating a more accurate electric field intensity distribution, and providing a guarantee for the accurate calculation of eddy current losses.

[0097] In the preferred embodiment, when constructing the training dataset for model training in step 4, the electric field intensity data is normalized and saved as fixed-size grayscale images, and then proportionally divided into training and test sets. This normalization process eliminates the influence of data dimensions, making different data comparable and accelerating model convergence. Saving as fixed-size grayscale images facilitates unified model processing and improves training efficiency. Proportionally dividing the training and test sets allows for reasonable evaluation of model performance and avoids overfitting. By scientifically constructing the training dataset, high-quality training samples are provided for the model, enabling it to learn more accurate features and patterns, and improving its ability to predict eddy current losses in underwater wireless power transmission systems.

[0098] In the preferred embodiment, the eddy current loss value calculation in step 6 uses volume integration in cylindrical coordinates, with the integration region being the sea area. This setting ensures that the cylindrical coordinate system better matches the actual geometry of the underwater wireless power transmission system, providing a more accurate description of the electromagnetic field distribution in seawater. Using the sea area as the integration region allows for precise calculation of eddy current losses in seawater, avoiding the omission of critical regions. This calculation method fully considers the actual physical environment and geometric characteristics, making the calculation results more consistent with reality. It provides an accurate basis for evaluating the performance and optimizing the design of the underwater wireless power transmission system, contributing to improved energy transmission efficiency and stability.

[0099] In summary, the underwater wireless power eddy current loss calculation method and system based on CGAN and physical constraints proposed in this invention effectively solves the problems of low calculation efficiency and insufficient prediction accuracy of seawater eddy current loss in the field of underwater wireless power transmission technology, successfully overcoming the limitations of traditional methods in terms of computational efficiency and prediction accuracy. This scheme establishes an end-to-end mapping relationship from system design parameters to electric field intensity distribution by constructing a conditional generative adversarial network model. Unlike the traditional finite element method's iterative modeling and calculation and the analytical method's assumption of idealization, this approach significantly improves computational efficiency while ensuring prediction accuracy, providing reliable technical support for the rapid design and optimization of underwater wireless power transmission systems.

[0100] In terms of model design, the scheme designs a Res-UNet generator network, introduces the residual learning mechanism into the U-Net architecture, and solves the problem of deep network training by leveraging cross-layer connections; proposes a hierarchical conditional batch normalization discriminator, and adopts a hierarchical strategy of shallow standard normalization and deep conditional normalization; innovates the eddy current loss energy norm error loss function, and explicitly embeds physical priors into the model optimization process based on the law of conservation of electromagnetic field energy; introduces Dropout operation in the generator bottleneck module to prevent model overfitting and enhance the prediction stability under unknown parameter combinations.

[0101] This invention organically combines physical constraints with data-driven approaches, achieving physical consistency of prediction results while ensuring computational efficiency, providing a novel approach to engineering computation problems in complex electromagnetic environments. Its designed network structure and loss function exhibit excellent scalability, adapting to different underwater wireless power transmission system configurations and marine environmental conditions, thus demonstrating broad applicability. Simultaneously, it provides a complete technical path for the intelligent design of underwater wireless power transmission systems, driving technological innovation in the field of electromagnetic computation through the deep integration of deep learning and traditional numerical methods.

[0102] Furthermore, the loss function and model design proposed in this invention significantly improve the model's generalization ability and the physical rationality of the prediction results under limited sample conditions, solving the problems of accuracy and generalization in traditional methods. The overall solution improves computational efficiency, accuracy, and generalization ability in multiple aspects, providing reliable assurance for the optimized design of marine equipment energy systems and promoting the large-scale application of underwater wireless power transmission technology in multiple fields.

Claims

1. A method for calculating underwater wireless power eddy current loss based on CGAN and physical constraints, characterized in that, Includes the following steps: Step 1: Construct a training dataset and obtain ocean electric field intensity distribution cloud maps under multiple combinations of system parameters through finite element simulation; Step 2: Construct a conditional generative adversarial network model, which includes a generator and a discriminator; Step 3: Input the system parameters into the generator to generate a predicted electric field intensity distribution cloud map; input the actual cloud map or predicted cloud map and the system parameters into the discriminator to complete the authenticity and condition consistency judgment; Step 4: Introduce an eddy current loss energy norm error loss term based on the law of conservation of electromagnetic field energy into the generator loss function to form a hybrid loss function; Step 5: Optimize the generator and discriminator parameters using an alternating training strategy until the model converges; Step 6: Input the system parameters to be predicted into the trained generator, output the electric field intensity distribution cloud map, and calculate the eddy current loss value through volume integral.

2. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 1, characterized in that: The system parameters mentioned in step 1 include transmission distance, number of coil turns, coil inner diameter, and resonant frequency.

3. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 1, characterized in that: The generator described in step 2 adopts the Res-UNet architecture, and the discriminator adopts a hierarchical conditional batch normalization structure. The Res-UNet architecture of the generator replaces the standard convolutional blocks with residual blocks in the encoder, decoder and bottleneck module of U-Net. Skip connections are set between corresponding layers of the encoder and decoder, and a Dropout operation is added before the activation function of the bottleneck module.

4. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 3, characterized in that, The output of the residual block satisfies: （1）； In the formula, and These represent the input and output vectors of the residual block, respectively. It is based on the weight The nonlinear residual mapping consists of convolutional layers, batch normalization layers, and activation functions; These are the weight parameters for the convolutional layer.

5. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 3, characterized in that, The discriminator's hierarchical conditional batch normalization structure is as follows: shallow convolutional layers use standard batch normalization, while deep convolutional layers use conditional batch normalization. Conditional batch normalization transforms system parameters into scaling parameters through a mapping network. With offset parameter The feature map is modulated.

6. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 5, characterized in that, The calculation process and modulation formula for conditional batch normalization are as follows: （2）； （3）； In the formula, , These are the condition-driven scaling parameters and the offset parameters, respectively. It is a conditional vector; To generate the weight matrix for scaling parameters; Generate a bias vector for the scaling parameters; To generate the weight matrix for the offset parameters; Generate the offset vector for the offset parameters; To conditionally batch normalize the output feature map; Input feature map; The batch mean of the input feature maps; The batch standard deviation of the input feature map.

7. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 1, characterized in that, The formula for calculating the eddy current loss energy norm error loss term in step 3 is as follows: （4）； In the formula, This refers to the energy norm error loss due to eddy current loss. This represents the total number of pixels in the electric field intensity contour map. The pixel number in the electric field intensity cloud map; Binary masking for areas of interest in marine waters; The electrical conductivity of seawater; The model predicts the first The magnitude of the electric field intensity at each pixel; The first finite element simulation obtained The magnitude of the electric field intensity at each pixel; The generator's total loss function in step 3 is a weighted sum of adversarial loss and eddy current loss energy norm error loss: （5）； In the formula, This represents the total loss of the generator; To combat loss in generators; This refers to the physical loss weighting coefficient; This refers to the energy norm error loss due to eddy current loss.

8. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 1, characterized in that: When constructing the training dataset for model training in step 4, the electric field intensity data is normalized and saved as a fixed-size grayscale image, and then divided into a training set and a test set according to the proportion.

9. The underwater wireless power eddy current loss calculation method based on CGAN and physical constraints according to claim 1, characterized in that, The eddy current loss value calculated in step 6 is performed using a volume integral in cylindrical coordinates, with the integration region being the sea area. （6）； In the formula, Power loss due to seawater eddy currents; The electrical conductivity of seawater; The electric field intensity vector; The magnitude of the electric field intensity; This is the volume integral.

10. An underwater wireless power eddy current loss calculation system based on CGAN and physical constraints, characterized in that, It is a computing system for implementing the underwater wireless power eddy current loss calculation method based on CGAN and physical constraints as described in any one of claims 1 to 9, comprising: a dataset construction module, a conditional generative adversarial network module, a hybrid loss calculation module, a model training module, and an eddy current loss prediction module; each module is used to execute each step of the underwater wireless power eddy current loss calculation method based on CGAN and physical constraints.

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