Underwater wireless power transmission system parameter identification method based on machine learning

Abstract

The invention discloses an underwater wireless power transmission system parameter identification method based on machine learning, which comprises the following steps: constructing a data set through finite element simulation, and obtaining original input parameters including geometry, electromagnetism and position offset and corresponding key output parameters; feature engineering is executed, and derived features with physical significance are extracted; performing standardized preprocessing on the data; for each key output parameter, independently training an XGBoost regression model; carrying out five-fold cross validation on the training set by adopting a Bayesian optimization algorithm, and carrying out independent hyper-parameter optimization on each XGBoost model; and carrying out interpretability analysis on the trained agent model by utilizing SHAP analysis, quantifying the contribution degree of each input feature to a prediction result, and providing physical insight. According to the method, high-precision prediction of the electromagnetic parameters under the complex working condition is achieved, complex electromagnetic field calculation is avoided, the system design efficiency is remarkably improved, and the efficiency and interpretability of intelligent optimization design of the UWPT system are remarkably improved.

Description

Technical Field

[0001] This invention relates to wireless power transmission technology, and more specifically to a method for parameter identification of underwater wireless power transmission systems based on machine learning. Background Technology

[0002] In underwater wireless power transfer (UWPT) systems, the magnetic coupling mechanism is the core component for energy transmission. Its electromagnetic parameters, such as mutual inductance, resistance, eddy current losses, and coil losses, directly determine the system's transmission efficiency and power. Seawater is a conductive medium; when an alternating magnetic field propagates through it, significant eddy currents are inevitably generated. This eddy current effect in a conductive medium leads to additional power losses, reducing system efficiency and causing the medium to heat up. Furthermore, the underwater environment is complex and variable; transmission system parameters (such as mutual inductance) are influenced by a combination of factors, including seawater conductivity and the relative position of the coils, making accurate modeling difficult using traditional analytical methods. Currently, there are three main approaches to obtaining these electromagnetic parameters:

[0003] 1. Theoretical Formula Method: For simple air-core coils, theoretical formulas can provide some estimation. However, in UWPT system applications, complex multi-turn coils (such as DD coils and bipolar coils) are commonly used to improve coupling performance and shield leakage. In this case, eddy current losses become extremely complex, and traditional theoretical formulas are difficult to calculate accurately, resulting in huge errors.

[0004] 2. Finite Element Method (FEM): Finite element simulation software can simulate complex electromagnetic field distributions with high precision and calculate accurate coil parameters. However, FEM is extremely computationally expensive. A single simulation analysis often takes minutes, hours, or even days. In the design optimization process of UWPT systems (e.g., using multi-objective optimization algorithms to optimize structural parameters), it is usually necessary to evaluate thousands of different parameter combinations. If relying on FEM for evaluation, its high time cost makes the entire optimization cycle impractical.

[0005] 3. Experimental measurement method: Making a physical prototype and measuring it is the most direct way, but this requires high manufacturing and time costs, cannot be done in the early stages of design, and is difficult to cover all possible working conditions.

[0006] Therefore, there is an urgent need in this field for a new technical means that can achieve both FEM-level high precision and near-instantaneous computing speed, thereby solving the problems faced by complex underwater magnetic coupling mechanisms in the design and optimization stage, and providing the possibility for accurate identification and real-time optimization of system parameters. Summary of the Invention

[0007] In view of this, the purpose of this invention is to overcome the limitations of existing methods for calculating the parameters of magnetic coupling mechanisms in underwater wireless power transmission technology, namely, the insufficient accuracy of theoretical formula methods and the excessive time consumption of finite element methods. This invention proposes a rapid prediction method for electromagnetic parameters of magnetic coupling mechanisms based on machine learning. By integrating Bayesian optimization and SHAP (SHapley Additive exPlanations) interpretability analysis with the XGBoost (eXtreme Gradient Boosting) intelligent prediction system, the invention achieves rapid and accurate prediction of key coil parameters in underwater wireless power transmission systems, thereby enabling rapid iteration and intelligent optimization design of underwater wireless power transmission systems.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A method for parameter identification of underwater wireless power transfer systems based on machine learning, the key of which includes the following steps:

[0010] S1: Construct a data-driven model that includes multiple independent XGBoost regression models. Use finite element simulation software to build an underwater wireless power transfer system dataset. The model input is the original input parameters and derived features of the coil, and the model output is the key electromagnetic parameters of the system.

[0011] S2: The dataset is divided into training and test sets, in a 4:1 ratio. Then, 5-fold cross-validation is performed on the training set using the Bayesian optimization algorithm. Hyperparameter optimization is performed on each independent XGBoost regression model in the data-driven model to ensure prediction accuracy.

[0012] S3: Perform SHAP interpretability analysis on the trained data-driven model to quantify the contribution of input features to the prediction results.

[0013] Preferably, the training set data comes from Ansys Maxwell. A three-dimensional model of the DD coil magnetic coupling mechanism is built in the software, and a series of key original input parameters are systematically scanned. The original input parameters include: the geometric dimensions of the transmitting coil, the geometric dimensions of the receiving coil, the number of coil turns, the turn spacing, the excitation current, the operating frequency, and the relative position offset between the coils.

[0014] Preferred approach: For each combination of original input parameters, perform finite element simulation to obtain the corresponding key output parameters, including: internal resistance of the transmitting coil, internal resistance of the receiving coil, mutual inductance of the coils, eddy current loss, and coil loss, which together with the original input parameters form a dataset.

[0015] Preferably, the method includes a feature engineering step, which extracts or calculates a set of derived features with clear physical meaning from the original input parameters, such as coil area, total offset distance, and turns product, and merges the derived features with the original input parameters into an extended feature set, which is used as the final input of the XGBoost model to improve model training efficiency and prediction accuracy.

[0016] Preferably, the method employs a multi-model independent training strategy, that is, for each key output parameter, a dedicated and independent XGBoost regression model is constructed to form a model suite containing multiple independent models.

[0017] Preferably, in step S2, the Bayesian optimization algorithm is used to optimize the hyperparameters of each independent XGBoost regression model. The hyperparameters include the number of iterations, the maximum depth of the tree, and the regularization coefficient. The Bayesian optimization algorithm uses minimizing the mean absolute error (MAE) obtained by cross-validation of the model on the training set as the optimization index to search for the optimal combination in the hyperparameter space.

[0018] The structural objective function Obj of the XGBoost regression model when constructing the t-th regression tree during training is... (t) The calculation formula is:

[0019]

[0020] Where t represents the current iteration round, i.e., the t-th regression tree currently being built; n is the number of training samples; and l is the loss function used to measure the true value y. i The difference between the current model prediction and the predicted value, specifically in the form of squared error; This represents the cumulative prediction results for the first t-1 trees; For the t-th tree, pair of sample x i The predicted output; The regularization term controls the complexity of the tree model; constant is a constant term.

[0021] Preferably, the method further includes a model interpretability analysis step, namely, using the SHAP analysis method to analyze the trained high-fidelity surrogate model; quantifying whether the contribution of each input feature to a single prediction is positive or negative, and the magnitude of the contribution, by calculating the SHAP value; and providing intuitive and reliable physical insights for coil design optimization by generating SHAP summary maps and feature importance maps, thus freeing the data-driven model from the "black box" limitation.

[0022] Preferably, the method is particularly suitable for UWPT systems and can effectively handle the eddy current effect generated by high-frequency alternating magnetic fields in seawater conductive media; the eddy current effect leads to additional power loss. This necessitates that UWPT system modeling must consider the equivalent resistance of eddy current losses. and and its impact on mutual inductance This invention reproduces these complex electromagnetic phenomena with high precision by learning FEM simulation data.

[0023] Where α is the coefficient for the change in mutual inductance between air and seawater, and θ represents... and The phase difference between them.

[0024] Preferably, the method further includes a model evaluation step, which verifies the accuracy of the data-driven model by testing evaluation metrics on a test set, the evaluation metrics including:

[0025] Coefficient of determination R 2 The calculation formula is as follows: Where n is the number of samples, The value to be fitted, The mean, These are the fitted values;

[0026] The mean absolute error (MAE) is calculated using the following formula: ;

[0027] The root mean square error (RMSE) is calculated using the following formula: ;

[0028] The Mean Absolute Percentage Error (MAPE) is calculated using the following formula: Where n is the number of samples, For the true value, These are the model's predicted values.

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] 1. This invention, by learning from high-fidelity FEM simulation data and combining optimized feature engineering with a Bayesian-optimized XGBoost algorithm, achieves prediction accuracy far exceeding that of traditional theoretical formulas. In a preferred embodiment, the prediction R² value for key parameters such as mutual inductance can reach over 0.9, achieving an accuracy essentially consistent with that of FEM simulation itself.

[0031] 2. This invention reduces the computation time required for FEM simulation, which can take minutes or even hours, to millisecond-level model inference time. This significant speed improvement enables real-time prediction and large-scale design optimization.

[0032] 3. This invention effectively solves complex problems that are difficult to model accurately using traditional theoretical formulas, such as the complex underwater eddy current loss and strong nonlinear problems of underwater mutual inductance of DD coils.

[0033] 4. The XGBOOST model constructed in this invention can be directly embedded into the fitness function of multi-objective optimization algorithms (such as NSGA-II), enabling designers to evaluate tens of thousands of design schemes within minutes, thereby quickly finding the Pareto optimal solution and greatly shortening the development cycle and design cost of the UWPT system.

[0034] 5. The introduction of SHAP analysis transforms data-driven models from "black boxes." This invention not only provides prediction results but also analyzes the impact of various input parameters on output loss and mutual inductance, offering designers intuitive and reliable physical insights. Attached Figure Description

[0035] Figure 1 This is a flowchart of the XGBoost prediction method based on Bayesian optimization and SHAP analysis described in this invention.

[0036] Figure 2 This is a diagram of the intelligent prediction system architecture for electromagnetic parameters of the UWPT magnetic coupling mechanism described in this invention.

[0037] Figure 3 This is a schematic diagram of the DD coil structure and its key input parameters used in a preferred embodiment of the present invention;

[0038] Figure 4 This is a scatter plot comparing the predicted and simulated values ​​of the output parameters in a preferred embodiment of the present invention.

[0039] Figure 5 This is a residual distribution diagram of the predicted values ​​of the output parameters in this invention;

[0040] Figure 6 This is a SHAP summary diagram illustrating the impact of key features in this invention on the prediction results.

[0041] Figure 7 This is the input feature importance ranking graph based on SHAP analysis in this invention. Detailed Implementation

[0042] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0043] Example

[0044] Reference Figure 1and Figure 2 This invention provides a method for parameter identification of underwater wireless power transfer systems based on machine learning. Its core is the construction of a high-precision, high-speed electromagnetic parameter prediction model, which is based on a high-fidelity dataset and specifically includes the following steps:

[0045] S1: Construct a data-driven model that includes multiple independent XGBoost regression models. Use finite element simulation software to build an underwater wireless power transfer system dataset. The model input is the original input parameters and derived features of the coil, and the model output is the key electromagnetic parameters of the system.

[0046] S2: Divide the dataset into training and test sets, perform 5-fold cross-validation on the training set using the Bayesian optimization algorithm, and optimize the hyperparameters of each independent XGBoost regression model in the data-driven model to ensure prediction accuracy;

[0047] S3: Perform SHAP interpretability analysis on the trained data-driven model to quantify the contribution of input features to the prediction results.

[0048] In this embodiment, the high-fidelity dataset is constructed using finite element simulation software. For the complex operating conditions of the underwater DD coil magnetic coupling mechanism, a series of original input parameters are systematically changed through parametric scanning, including coil geometry, number of turns, turn spacing, excitation current, operating frequency, and relative offset, such as... Figure 3 As shown in the figure. In one specific embodiment, a total of 34,432 valid data sample points were generated. For each sample point, the simulation software calculated and derived five key output parameters: internal resistance of the transmitting coil, internal resistance of the receiving coil, mutual inductance, eddy current loss, and coil loss.

[0049] To improve the model's prediction accuracy and its ability to learn physical laws, this invention performs feature engineering on the original input parameters before model training. By calculating derived features with clear physical meaning, such as coil area, total offset distance, and turns product, the original input parameters are expanded into an extended feature set containing 38 features. These derived features pre-capture some nonlinear relationships, significantly improving model performance.

[0050] One of the core features of this invention lies in its unique model suite architecture. Instead of employing a single multi-output regression model, this invention constructs five dedicated and independent XGBoost regression models for five key output parameters with different physical causes.

[0051] Before model training, the generated extended feature set is standardized to eliminate the influence of dimensions and divided into 4:1 ratios (27,545 training samples and 6,887 test samples in this embodiment).

[0052] To ensure optimal performance for each individual model, this invention employs a Bayesian optimization algorithm to independently optimize the hyperparameters of each of the five XGBoost models. Specifically, the hyperparameters include the number of iterations, the maximum depth of the tree, and the regularization coefficient. The Bayesian optimization algorithm uses minimizing the mean absolute error (MAE) obtained from cross-validation on the training set as the optimization metric, searching for the optimal combination within the hyperparameter space.

[0053] The structural objective function Obj of the XGBoost regression model when constructing the t-th regression tree during training is... (t) The calculation formula is:

[0054]

[0055] Where t represents the current iteration round, i.e., the t-th regression tree currently being built; n is the number of training samples; and l is the loss function used to measure the true value y. i The difference between the current model prediction and the predicted value, specifically in the form of squared error; This represents the cumulative prediction results for the first t-1 trees; For the t-th tree, pair of sample x i The predicted output; The regularization term controls the complexity of the tree model; constant is a constant term.

[0056] Through the above design, the algorithm intelligently searches for the optimal combination of hyperparameters. For example, for the model used to predict "mutual inductance," Bayesian optimization finds the optimal parameter combination as n_estimators=1500, max_depth=12, etc.; while for the model used to predict "eddy current loss," it finds n_estimators=698, max_depth=10, etc. This targeted independent optimization is the key to achieving high accuracy.

[0057] After training, the five optimized XGBoost models and the standardized processor were packaged and solidified into a single model. This model can be used by a UWPT design optimization platform. When the designer inputs a new set of coil parameters, the prediction system can return all five high-precision electromagnetic parameters within milliseconds, perfectly replacing time-consuming FEM simulations and solving the "simulation bottleneck" problem. Figure 4 and Figure 5 It can be seen that the predicted values ​​of the output parameters in this embodiment are basically the same as the software simulation values.

[0058] Another key innovation of this invention lies in the introduction of SHAP interpretability analysis, such as... Figure 6 , Figure 7As shown. Data-driven models are often criticized as "black boxes," but this invention, through SHAP analysis, can quantify the specific contribution of each input feature to the prediction result. This interpretable analysis can help understand the physical mechanisms behind the model's decisions, providing intuitive guidance for design optimization.

[0059] In summary, this invention successfully constructs a high-precision, highly interpretable electromagnetic parameter identification model for underwater magnetic coupling mechanisms by combining finite element simulation, feature engineering with physical information enhancement, the Bayesian-optimized XGBoost model suite, and SHAP interpretability analysis. It effectively solves the problems of inaccurate theory and slow simulation faced in the design of complex coils in the UWPT field, providing strong technical support for the automated and intelligent design optimization of UWPT systems.

[0060] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for parameter identification of an underwater wireless power transmission system based on machine learning, characterized in that, The method comprises the following steps: S1: constructing a data-driven model comprising a plurality of independent XGBoost regression models, constructing an underwater wireless power transmission system dataset by using a finite element simulation software, the model input being original input parameters and derived features of a coil, and the model output being key electromagnetic parameters of the system; S2: dividing the dataset into a training set and a test set, performing 5-fold cross-validation on the training set according to a Bayesian optimization algorithm, and performing hyperparameter optimization on each independent XGBoost regression model in the data-driven model to ensure prediction accuracy; S3: performing SHAP explainability analysis on the trained data-driven model to quantify the contribution of input features to the prediction result.

2. The method of claim 1, wherein, The system key electromagnetic parameters include the transmitting coil internal resistance R1, the receiving coil internal resistance R2, the mutual inductance value M between the coils, the eddy current loss P eddy and the coil loss P coil .

3. The method according to claim 1 or 2, characterized in that, The original input parameters include the geometric size of the transmitting coil, the geometric size of the receiving coil, the number of turns of the coil, the turn spacing, the excitation current, the operating frequency, and the relative positional offset between the coils.

4. The method of claim 3, wherein, The derived features include the coil area, the total offset distance, and the turn product.

5. The method according to claim 2 or 4, characterized in that, In step S1, for each key output parameter, an exclusive and independent XGBoost regression model is constructed.

6. The method of claim 5, wherein, In step S2, the Bayesian optimization algorithm is used to perform hyperparameter optimization on each independent XGBoost regression model, the hyperparameters including the number of iterations, the maximum depth of the tree, and the regularization coefficient; the Bayesian optimization algorithm takes the minimum average absolute error of the model obtained by cross-validation on the training set as the optimization index, and searches for the optimal combination in the hyperparameter space; The structure objective function Obj of the XGBoost regression model when constructing the tth regression tree in the training process (t) The calculation formula is: ， where t represents the current iteration round, i.e., the tth regression tree being constructed; n is the number of training samples; l is a loss function used to measure the difference between the true value y i and the prediction value of the current model, specifically in the form of squared error; is the cumulative prediction result of the first t-1 trees; is the prediction output of the tth tree for the sample x i ; and is a regularization term used to control the complexity of the tree model; and constant is a constant term.

7. The method of claim 6, wherein, The evaluation index of the data-driven model is tested by the test set to verify its accuracy, and the evaluation index includes: coefficient of determination R 2 , and the calculation formula is: ; wherein n is the sample number, is the to-be-fitted value, is the mean value, is the fitted value; The mean absolute error MAE is calculated as follows: ; Root Mean Square Error, RMSE, is calculated as: ; The mean absolute percentage error MAPE is calculated as follows: ; wherein n is the number of samples, is the true value, is the model prediction.

Images