Wireless charging efficiency optimization method and system based on data analysis

Abstract

The application provides a wireless charging efficiency optimization method and system based on data analysis, and belongs to the technical field of data analysis optimization. The method first creates a magnetic coupling three-dimensional model containing a transmitting coil and a receiving coil, determines the optimal size parameters of the coil by solving the maximum coupling coefficient through finite element simulation analysis. Then, electromagnetic field simulation is performed within the determined coil turn range, the offset condition of the unmanned aerial vehicle is simulated, and simulation data containing the offset and coil inductance data are collected. Based on these data, a multi-objective optimization algorithm is used to determine the optimal coil turns. Finally, the transmitting coil and the receiving coil are adjusted in combination with the optimal size parameters and the optimal coil turns, and the wireless charging efficiency is optimized. The application has the effect of improving the wireless charging efficiency of the unmanned aerial vehicle.

Description

Technical Field

[0001] This invention belongs to the field of data analysis technology, specifically relating to a method and system for optimizing wireless charging efficiency based on data analysis. Background Technology

[0002] Drone technology has experienced explosive growth in recent years and is now widely used in surveying, agriculture, logistics, security, disaster relief, and many other fields. With the continuous expansion of application scenarios, the demand for long-duration, autonomous operation of drones is increasing. Especially in scenarios such as remote monitoring, continuous inspection, and emergency rescue, drones need to complete long-duration tasks without human intervention, which places higher demands on their energy supply systems.

[0003] Traditional drone power supply relies primarily on battery swapping or wired charging. Battery swapping requires manual intervention, hindering truly autonomous operation; wired charging necessitates precise docking of the drone with the charging interface, which is technically challenging and limits reliability. These limitations severely restrict the application potential of drones in scenarios requiring extended autonomous operation. The introduction of wireless charging technology offers a new possibility for solving this problem. Utilizing principles such as electromagnetic induction and magnetic resonance, wireless charging systems can achieve energy transfer without physical contact, greatly simplifying the drone charging process and improving the system's autonomy.

[0004] However, the low efficiency of wireless charging is a particularly prominent issue in practical applications. The efficiency of a wireless charging system is mainly affected by the degree of coupling between the transmitter and receiver. In drone applications, the design of coil parameters, such as size and number of turns, directly impacts the system's transmission efficiency. Parameter optimization for wireless charging systems is a complex problem involving multiple variables and objectives. Parameters such as coil size, number of turns, material, and spacing have complex interrelationships, making it difficult to find the globally optimal solution using traditional single-parameter optimization or empirical design methods. Without a systematic optimization approach, engineers often have to rely on experience or repeated trial and error to determine these parameters, which is not only time-consuming and labor-intensive but also unlikely to yield the optimal solution. Summary of the Invention

[0005] This invention provides a method and system for optimizing wireless charging efficiency based on data analysis, in order to solve the problem of low wireless charging efficiency for drones.

[0006] In a first aspect, the present invention provides a wireless charging efficiency optimization method based on data analysis, applied to a drone wireless charging system. The drone wireless charging system includes a transmitting coil disposed on a wireless charging platform and a receiving coil disposed at the bottom of the drone landing gear. The method includes the following steps:

[0007] Create a magnetically coupled 3D model that includes a transmitting coil and a receiving coil;

[0008] Based on the magnetic coupling three-dimensional model and using the finite element simulation analysis method to solve for the maximum coupling coefficient, the optimal size parameters of the transmitting coil and the receiving coil are obtained.

[0009] The range of coil turns is determined based on the optimal size parameters. Electromagnetic field simulation is performed on the magnetically coupled three-dimensional model within the range of coil turns. During the simulation, the UAV offset is simulated and simulation data is collected. The simulation data includes the UAV offset and coil inductance data.

[0010] The optimal number of coil turns was determined based on simulation data and a multi-objective optimization algorithm.

[0011] Adjust the transmitting and receiving coils by combining the optimal size parameters and the optimal number of coil turns.

[0012] Optionally, the step of solving for the maximum coupling coefficient based on the magnetically coupled three-dimensional model and using the finite element simulation analysis method to obtain the optimal size parameters of the transmitting coil and the receiving coil includes the following steps:

[0013] A finite element simulation environment is constructed based on a magnetically coupled three-dimensional model, and the magnetic insulation boundary condition is used as the boundary condition of the finite element simulation environment.

[0014] A constant frequency AC current excitation is applied to the simulated transmitting coil in the magnetically coupled three-dimensional model. The coil size parameters of the magnetically coupled three-dimensional model are scanned and the simulated coupling coefficient is calculated.

[0015] A functional relationship model between coil size parameters and simulation coupling coefficients is established using the response surface methodology.

[0016] Using the maximum coupling coefficient of the magnetically coupled three-dimensional model as the optimization objective, the optimal size parameters of the transmitting and receiving coils are obtained by solving a functional relationship model and using the gradient descent method.

[0017] Optionally, the step of determining the coil turn range based on the optimal size parameters, performing electromagnetic field simulation on the magnetically coupled three-dimensional model within the coil turn range, and simulating UAV offset and collecting simulation data during the simulation process includes the following steps:

[0018] The maximum and minimum number of Litz wire turns for the transmitting and receiving coils are calculated based on the optimal size parameters, thus obtaining the range of coil turns.

[0019] The optimal size parameters and the magnetic coupling three-dimensional model are imported into the simulation software. For each combination of coil turns within the range of coil turns, the magnetic field distribution of the magnetic coupling three-dimensional model under standard magnetic coupling state is simulated by the simulation software. The maximum magnetic induction intensity and the initial leakage magnetic field intensity of the simulated receiving coil in the magnetic coupling three-dimensional model are calculated based on the magnetic field distribution.

[0020] The simulation receiving coil is controlled by a preset translation step size to perform step translation to simulate the drone's deviation until the maximum magnetic induction intensity is greater than or equal to the saturation magnetic induction intensity or leakage magnetic intensity of the simulated magnetic core in the magnetic coupling three-dimensional model, which exceeds the preset intensity threshold.

[0021] After each step translation, the coil inductance data of the magnetically coupled three-dimensional model is calculated, and the displacement value between the simulated receiving coil and the original position is used as the drone offset amount to simulate the drone offset.

[0022] Optionally, the method further includes the following steps:

[0023] The simulation data is organized into a structured dataset and then normalized.

[0024] A generative adversarial network model is constructed using a multilayer perceptron and a convolutional neural network.

[0025] A generative adversarial network (GAN) model is trained by combining the coil turns range, optimal size parameters, and a normalized structured dataset. The trained GAN model then outputs enhanced simulation data.

[0026] The enhanced simulation data is filtered using a preset physical verification function, and the filtered enhanced simulation data is then merged into the simulation data.

[0027] Optionally, determining the optimal number of coil turns based on simulation data and using a multi-objective optimization algorithm includes the following steps:

[0028] Determine the decision variables for multi-objective optimization based on the range of coil turns;

[0029] The optimization objective function is set according to the preset indicators, and the constraint conditions are set according to the physical constraints of coil inductance. The optimization objective function includes maximizing coil energy transmission efficiency, minimizing coil total mass, and maximizing UAV offset tolerance.

[0030] Based on all decision variables, an initial solution space is constructed using an adaptive grid Latin hypercube sampling method;

[0031] A simplified solution set is obtained by rapidly searching within the initial solution space using a binary particle swarm optimization method based on magnetic coupling sensing.

[0032] With the objective function as the optimization objective, under constraints, the simplified solution set is solved by multi-objective optimization using the NSGAII algorithm guided by electromagnetic field sensitivity, and the Pareto optimal solution set is obtained.

[0033] The comprehensive performance index of each Pareto solution in the Pareto optimal solution set is calculated based on the optimization objective function, and the optimal Pareto solution with the highest comprehensive performance index is analyzed as the optimal number of coil turns.

[0034] Optionally, the construction of the initial solution space based on all decision variables using the adaptive grid Latin hypercube sampling method includes the following steps:

[0035] A non-uniform decision space grid is constructed based on all decision variables and the optimal turns ratio relationship predicted by electromagnetic field theory.

[0036] Pre-defined prior knowledge of electromagnetic coupling degree is introduced into a non-uniform decision space grid to sample samples and obtain an initial sample set;

[0037] The target sample set is obtained by minimizing the correlation of all initial sample points in the initial sample set. The optimization objective function value of all target sample points in the target sample set is calculated to form the initial solution space.

[0038] Optionally, the step of using a magnetically coupled sensing-based binary particle swarm optimization method to quickly search within the initial solution space to obtain a simplified solution set includes the following steps:

[0039] Encode all initial solutions in the initial solution space into binary bit strings;

[0040] Initialize the particle swarm optimization algorithm parameters in a binary bit string;

[0041] The fitness of the initial particles in the initial particle swarm is calculated by combining the optimization objective function and the magnetic coupling coefficient corresponding to the coil turns combination.

[0042] The velocity and position of all particles are updated iteratively based on fitness. During the position update of all particles, a mutation probability is added to each particle. The mutation probability is linearly related to the magnetic coupling coefficient of the particle's current position.

[0043] When the number of iterations reaches the preset maximum number of iterations, the iteration update stops, and the particles in the global optimal position and their corresponding fitness values ​​are used as the simplified solution set.

[0044] Optionally, the step of using the objective function as the optimization objective and, under constraints, performing multi-objective optimization on the simplified solution set using the NSGAII algorithm guided by electromagnetic field sensitivity to obtain the Pareto optimal solution set includes the following steps:

[0045] Use the simplified solution set as the initial population for the NSGAII algorithm;

[0046] After initializing the algorithm parameters of the NSGAII algorithm, the NSGAII algorithm process is executed iteratively to update the population under constraints, with the objective function as the optimization target.

[0047] In the population mutation operation of the NSGAII algorithm, the sensitivity matrix of the optimization objective function to the number of coil turns is calculated, and the sensitivity matrix is ​​used to guide the population mutation.

[0048] After iteratively updating the population using the NSGAII algorithm, the first frontier in the final population is output as the Pareto optimal solution set.

[0049] In a second aspect, the present invention also provides a wireless charging efficiency optimization system based on data analysis, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the wireless charging efficiency optimization method based on data analysis as described in the first aspect.

[0050] Thirdly, the present invention also provides a computer-readable storage medium storing instructions that, when executed by a processor, configure the processor to perform the wireless charging efficiency optimization method based on data analysis as described in the first aspect.

[0051] The beneficial effects of this invention are:

[0052] This invention determines the optimal coil parameters through a magnetically coupled three-dimensional model and finite element simulation analysis, enabling the system to achieve maximum energy transfer efficiency under ideal conditions. Secondly, this invention significantly enhances the system's robustness. By simulating UAV landing offsets and collecting a large amount of simulation data, the coil parameters determined by a multi-objective optimization algorithm maintain high charging efficiency under various offset conditions, effectively solving the problem of charging efficiency fluctuations caused by insufficient UAV landing accuracy in practical applications. Furthermore, this invention establishes a systematic design process, replacing the traditional design approach that relies on experience or repeated trial and error, greatly shortening the development cycle and reducing R&D costs. Simultaneously, the optimized wireless charging system improves the autonomous operation capability of UAVs, reduces the need for human intervention, and enables UAVs to perform long-term missions in remote and harsh environments. Attached Figure Description

[0053] Figure 1 This is a system circuit topology diagram of a drone wireless charging system according to one embodiment of this application.

[0054] Figure 2This is a flowchart illustrating a data analysis-based wireless charging efficiency optimization method in one embodiment of this application.

[0055] Figure 3 This is a three-view drawing of a magnetically coupled three-dimensional model in one embodiment of this application.

[0056] Figure 4 This is an electromagnetic field distribution diagram of a magnetically coupled three-dimensional model in one embodiment of this application.

[0057] Figure 5 This is a schematic diagram showing the relationship between the self-inductance of the transmitting coil and the horizontal offset distance in one embodiment of this application.

[0058] Figure 6 This is a schematic diagram illustrating the relationship between the self-inductance of the receiving coil and the horizontal offset distance in one embodiment of this application.

[0059] Figure 7 This is a schematic diagram illustrating the relationship between coil mutual inductance and horizontal offset distance in one embodiment of this application.

[0060] Figure 8 This is a schematic diagram of the coil moving device in one embodiment of this application. Detailed Implementation

[0061] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0062] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0063] This invention discloses a data analysis-based method for optimizing wireless charging efficiency, which is applied to a wireless charging system for unmanned aerial vehicles (UAVs). Figure 1The drone wireless charging system includes a transmitting coil located on the wireless charging platform and a receiving coil located at the bottom of the drone's landing gear. The electrical energy is generated from the power grid, rectified and filtered to convert the mains power into DC power, and then converted into AC power of a set frequency via a high-frequency inverter. An impedance compensation circuit is also included. Figure 1 L1 is the compensation inductor, C1 is the compensation capacitor), and the transmitting coil inductance ( Figure 1 The LP coil resonates, transferring the transmitting energy to the receiving coil via magnetic field coupling. Figure 1 In the middle LS), the transmitting coil and the receiving coil form mutual inductance ( Figure 1 According to the law of electromagnetic induction, the receiving coil on the receiving side generates an induced electromotive force, thereby realizing the wireless transmission of energy from the transmitting side to the receiving side. The receiving coil induces an alternating current, which is then compensated for by impedance (M). Figure 1 C2 is a compensation capacitor. It is rectified and filtered to convert DC power to charge the drone battery.

[0064] Reference Figure 2 , Figure 2 This is a flowchart illustrating a data analysis-based wireless charging efficiency optimization method in one embodiment. It should be understood that, although... Figure 2 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 2 At least some steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps. For example Figure 2 As shown, the wireless charging efficiency optimization method based on data analysis disclosed in this invention specifically includes the following steps:

[0065] S101. Create a magnetically coupled 3D model containing the transmitting coil and the receiving coil.

[0066] The process begins by determining the geometry of the transmitting and receiving coils. In this embodiment, a rectangular helical structure is used. Initial parameters such as coil diameter, wire diameter, number of turns, and spacing are then set. A geometric model of the coil is constructed using 3D modeling software (such as COMSOL or ANSYS Maxwell), and material properties are defined, such as the conductivity (5.8 × 10^7 S / m) and permeability (μr ≈ 1) of copper wire. The model also needs to include the nonlinear BH curve characteristics of the core material (such as ferrite) and the air medium region. To improve computational efficiency, a symmetric simplification model, such as axisymmetric simplification, can be used. Furthermore, a suitable mesh generation strategy is required, employing a finer mesh in regions with drastic electromagnetic field changes (such as near the coil). The final 3D model will serve as the basis for subsequent simulation analysis, accurately reflecting the electromagnetic field distribution and energy transfer characteristics of the UAV wireless charging system, providing a reliable theoretical basis for optimized design.

[0067] S102. Based on the magnetic coupling three-dimensional model and using the finite element simulation analysis method, the maximum coupling coefficient is solved to obtain the optimal size parameters of the transmitting coil and the receiving coil.

[0068] In this simulation, magnetic insulation boundary conditions are set to ensure that the electromagnetic field does not leak outside the computational domain. Then, a constant frequency (typically 85 kHz) AC current excitation, typically 1 A, is applied to the transmitting coil. The coil geometry parameters, including the core lengths of the transmitting and receiving coils, are systematically changed using a parameter sweep method. For each parameter combination, the coupling coefficient is calculated. Where M is the mutual inductance, and L1 and L2 are the self-inductances of the transmitting and receiving coils, respectively. Then, the response surface methodology is used to establish a functional relationship model between the coil size parameters and the coupling coefficient: k = f(D T D R Finally, with the maximum coupling coefficient as the optimization objective, the optimal size parameters are solved using the gradient descent method. The optimal combination of size parameters for the transmitting and receiving coils is obtained through iterative calculations, achieving preliminary optimization of the coil geometry and laying the foundation for subsequent turns optimization.

[0069] S103. Determine the range of coil turns based on the optimal size parameters, and perform electromagnetic field simulation on the magnetically coupled three-dimensional model within the range of coil turns. During the simulation, simulate the drone's offset and collect simulation data.

[0070] The simulation data includes UAV offset and coil inductance data. Specifically, this step calculates the maximum number of Litz wire turns N for the transmitting and receiving coils based on optimal dimensional parameters. max =πD / (d w +s) and minimum number of winding turns N min (Typically 3-5 turns), where D is the coil diameter, dw Here, 's' represents the wire diameter, and 's' represents the wire spacing. After determining the range of coil turns, the optimal dimensional parameters are imported into simulation software (such as ANSYS Maxwell). For each combination of coil turns within the range, the magnetic field distribution under standard magnetic coupling is simulated, and the maximum magnetic flux density and leakage flux density are calculated. Subsequently, the receiving coil is controlled to perform step translation based on a preset translation step size (usually 1-5 mm) to simulate the UAV's offset in the x, y, and z directions. After each translation, the coil inductance data, including self-inductance L1, L2, and mutual inductance M, is measured, and the displacement values ​​between the receiving coil and the original position are recorded as the UAV offset Δx, Δy, and Δz. Translation is stopped when the maximum magnetic flux density is greater than or equal to the core saturation magnetic flux density or the leakage flux density exceeds a preset threshold (usually 20 μT). Through this process, coil inductance data with different combinations of turns and different offsets are collected, forming a simulation dataset that provides data support for subsequent multi-objective optimization.

[0071] S104. Determine the optimal number of coil turns based on simulation data and a multi-objective optimization algorithm.

[0072] The process begins by defining the decision variables as the number of turns in the transmitting and receiving coils. The objective functions include maximizing coil energy transfer efficiency, minimizing the total coil mass, and maximizing UAV offset tolerance. Constraints include physical constraints related to coil inductance. An initial solution space is then constructed using an adaptive grid Latin hypercube sampling method, sampling within a non-uniform decision space grid based on prior knowledge of electromagnetic coupling. Next, a rapid search is performed using a binary particle swarm optimization method based on magnetic coupling sensing. The solutions are encoded as binary bit strings, and particle positions are iteratively updated, with the mutation probability linearly correlated with the magnetic coupling coefficient. Then, multi-objective optimization is performed using the NSGAII algorithm guided by electromagnetic field sensitivity, calculating the sensitivity matrix to guide population mutation. Finally, the optimal Pareto solution is selected based on comprehensive performance indicators, determining the optimal combination of coil turns and achieving precise optimization of the coil turn count.

[0073] S105. Adjust the transmitting and receiving coils by combining the optimal size parameters and the optimal number of coil turns.

[0074] Based on the optimal dimensional parameters (including the diameter of the transmitting coil, the diameter of the receiving coil, and the coil spacing) and the optimal number of coil turns obtained in the preceding steps, a coil winding scheme is designed. During the actual winding process, the coil's geometric dimensions must be precisely controlled to ensure consistency with the optimization results. For the transmitting coil, Litz wire (multi-strand insulated fine wires connected in parallel) is typically used to reduce the skin effect at high frequencies; for the receiving coil, considering the drone's payload limitations, a lighter wire material can be selected. After the coil winding is completed, electrical parameter tests are performed, including self-inductance (L1, L2), mutual inductance (M), and quality factor, to ensure that the error between the actual parameters and the simulation results is within an acceptable range (usually requiring an error of <5%). If necessary, parameter correction can be performed by fine-tuning the number of coil turns or adding compensation capacitors. Finally, the adjusted transmitting coil is installed on the wireless charging platform, and the receiving coil is installed at the bottom of the drone's landing gear, completing the physical construction of the entire wireless charging system. Through this series of optimizations and adjustments, the wireless charging efficiency is significantly improved, while the system's tolerance to drone landing position deviations is enhanced.

[0075] In one embodiment, the optimal size parameters of the transmitting and receiving coils are obtained by solving for the maximum coupling coefficient based on a magnetically coupled three-dimensional model and using finite element simulation analysis, including the following steps:

[0076] A finite element simulation environment is constructed based on a magnetically coupled three-dimensional model, and the magnetic insulation boundary condition is used as the boundary condition of the finite element simulation environment.

[0077] A constant frequency AC current excitation is applied to the simulated transmitting coil in the magnetically coupled three-dimensional model. The coil size parameters of the magnetically coupled three-dimensional model are scanned and the simulated coupling coefficient is calculated.

[0078] A functional relationship model between coil size parameters and simulation coupling coefficients is established using the response surface methodology.

[0079] Using the maximum coupling coefficient of the magnetically coupled three-dimensional model as the optimization objective, the optimal size parameters of the transmitting and receiving coils are obtained by solving a functional relationship model and using the gradient descent method.

[0080] In this embodiment, an accurate three-dimensional magnetic coupling model needs to be constructed, and a finite element simulation environment needs to be established based on it. This model contains two key components: a transmitting coil mounted on the wireless charging platform and a receiving coil mounted on the bottom of the drone's landing gear. Both coils adopt a rectangular helical structure design. Compared to traditional circular coils, this structure provides higher area utilization within a limited space, making it particularly suitable for applications like drones where weight and space are strictly limited. The geometric parameters of the rectangular helical coil include the core length and core width, which directly affect the coupling efficiency of the system. When constructing the finite element simulation environment, the geometry of the coil needs to be accurately modeled in three-dimensional space. The rectangular helical coil can be represented by parametric equations, where the coordinates of the nth turn can be expressed as: for the x-coordinate, a constant an·d (where a is the initial length and d is the wire diameter plus the turn spacing) along the length direction; and a variable along the width direction; for the y-coordinate, a constant bn·d (where b is the initial width) along the width direction; and a variable along the length direction. Coil materials are usually chosen to be copper with high conductivity. In the model, its physical properties such as conductivity (about 5.8×10^7 S / m) and relative permeability (about 1) need to be defined.

[0081] In finite element mesh generation, special attention needs to be paid to the mesh density in the coil region. Due to the large current density and magnetic field gradient in the coil, the mesh size in these regions should be controlled within the range of 0.1-0.5 mm, while regions far from the coil can use larger mesh sizes (5-20 mm) to improve computational efficiency. The entire computational domain typically needs to be divided into hundreds of thousands to millions of tetrahedral or hexahedral elements to ensure computational accuracy. The most critical aspect of finite element simulation is the setting of boundary conditions. In this embodiment, a magnetically insulated boundary condition is used as the boundary condition for the finite element simulation environment. The magnetically insulated boundary condition is mathematically expressed as: n×H=0, where n is the normal vector of the boundary surface and H is the magnetic field strength vector. This condition ensures that the magnetic field lines are parallel to the boundary surface at the boundary and do not cross the boundary, thus simulating the magnetic field distribution in open space. The size of the computational domain is typically set to 5-10 times the maximum coil size to ensure that the boundary conditions do not significantly affect the calculation results of the core region.

[0082] After constructing the finite element simulation environment for the magnetic coupling 3D model, the next step is to apply a constant-frequency alternating current excitation to the simulated transmitting coil and obtain the coupling coefficient under different coil size combinations through systematic parameter scanning. The alternating current excitation adopts a sinusoidal form, and its mathematical expression is: I(t)=I0sin(2πft), where I0 is the current amplitude and f is the frequency. For drone wireless charging systems, the frequency is usually selected in the range of 85kHz to 6.78MHz, which conforms to international wireless charging standards (such as the Qi standard or A4WP standard). The current amplitude is set according to the power requirements of the drone. During the parameter scanning process, it is necessary to systematically change the key dimensional parameters of the rectangular helical coil. For the transmitting coil, the main parameters include: length, width, wire diameter, and turn spacing; for the receiving coil, the main parameters include: length, width, wire diameter, and turn spacing.

[0083] The parameter scanning employs an orthogonal experimental design method, dividing each parameter into multiple discrete levels to form a multidimensional parameter space. If a full-factor experimental design were used, with 5 parameters and 5 levels per parameter, 5^5 = 3125 simulations would be required, resulting in a massive computational load. However, the orthogonal experimental design reduces the number of experiments to approximately 25, significantly improving computational efficiency. For each parameter combination, the electromagnetic field distribution of the system is calculated using a finite element solver. The solution process is based on Maxwell's equations, expressed in the frequency domain as: and Where E is the electric field strength, B is the magnetic flux density, H is the magnetic field strength, J is the current density, D is the electric displacement, and ω is the angular frequency. Solving these equations yields the electromagnetic field distribution throughout the computational domain.

[0084] Based on the electromagnetic field distribution, the coupling coefficient between the transmitting and receiving coils is calculated. The formula for calculating the coupling coefficient k is: Where M is the mutual inductance, and L1 and L2 are the self-inductances of the transmitting and receiving coils, respectively. Self-inductance can be calculated using the energy method: Among them W m Mutual inductance can be calculated in two ways: one is through the energy method; the other is through the open-circuit voltage method, where current is passed through the transmitting coil, the induced electromotive force in the receiving coil is calculated, and then the relationship is used. Please provide a solution.

[0085] After obtaining the correlation data between the coil size parameters and the coupling coefficient, a mathematical model needs to be established to describe the functional relationship between them. Response Surface Methodology (RSM) is an effective mathematical statistical method that can construct a continuous functional relationship between input variables and output response based on a limited number of sampling points. In this implementation, the input variables are the coil size parameters (including the length, width, wire diameter, and turn spacing of the transmitting coil, and the length, width, wire diameter, and turn spacing of the receiving coil), and the output response is the coupling coefficient k. The core idea of ​​RSM is to fit the sampled data points using a polynomial function. Commonly used response surface models include first-order, second-order, and higher-order models. Considering that the relationship between coil size parameters and the coupling coefficient usually exhibits nonlinear characteristics, a second-order polynomial model is a more suitable choice. The general form of a second-order response surface model is:

[0086]

[0087] Where k is the coupling coefficient, x i β is the size parameter of the i-th coil, β0 is a constant term, and β i It is the coefficient of the first-order term, β ii It is the coefficient of the second-order term, β ij Here, ε is the interaction term coefficient, ε is the error term, and n is the total number of parameters. To determine these coefficients, the least squares method is needed to fit the sampled data. The goal of the least squares method is to minimize the sum of squares error between the predicted and actual values. Where y k It is the actual coupling coefficient value of the k-th sampling point. Here, is the coupling coefficient value predicted by the model, and m is the total number of sampling points. In practical applications, various numerical methods can be used to solve this minimization problem, such as the Gauss-Newton method and the Levenberg-Marquardt algorithm. These algorithms iteratively adjust the coefficient values ​​until the convergence condition is met.

[0088] The functional relationship model established using the response surface methodology can predict the coupling coefficient within a continuous parameter space without requiring additional finite element simulation calculations. This significantly improves the efficiency of subsequent optimization processes. Furthermore, the model can reveal the interactions between parameters, thus helping to understand the mechanisms by which different parameters affect the coupling coefficient. For example, it might reveal an optimal matching relationship between the aspect ratios of the transmitting and receiving coils, or that the ratio of wire diameter to turn spacing has a significant impact on the coupling coefficient.

[0089] After establishing the functional relationship model between the coil size parameters and the coupling coefficient, the next step is to find the optimal combination of size parameters that maximizes the coupling coefficient. In this implementation, gradient descent is used as the optimization algorithm, with the maximum coupling coefficient of the magnetically coupled three-dimensional model as the optimization objective. The optimal size parameters of the transmitting and receiving coils are obtained by solving the functional relationship model. Gradient descent is an iterative optimization algorithm whose core idea is to move along the negative gradient direction of the function to find a local minimum. Since the goal in this case is to maximize the coupling coefficient, it is necessary to move along the positive gradient direction of the function, or equivalently, minimize the negative coupling coefficient. The iterative formula for gradient descent is: Where x t Let be the parameter vector for the t-th iteration, and α be the learning rate (step size). The function f at point x t The gradient at the given point. In this case, f represents the coupling coefficient k, and x represents the coil size parameter vector, including parameters such as the length, width, wire diameter, and number of turns of the transmitting and receiving coils.

[0090] Calculating the gradient is a crucial step in the gradient descent method. For response surface models, the gradient can be obtained by taking the partial derivatives of the model function, and its i-th component is:

[0091]

[0092] During optimization, parameter constraints must also be considered. Coil size parameters are typically subject to physical and engineering limitations, specifically: the size of the transmitting coil cannot exceed the available space on the charging platform; the size of the receiving coil cannot exceed the available space on the bottom of the drone; the wire diameter and turn spacing must meet manufacturing process requirements; and the total length of the coil is limited by resistance. There are various methods for handling these constraints, including the projected gradient method, the penalty function method, and the barrier function method. Taking the penalty function method as an example, the constraints can be quantified and transformed into penalty terms, which are then added to the objective function.

[0093]

[0094] Among them, g i (x)≤0 is the i-th constraint, and λ is the penalty coefficient.

[0095] When the iteration process reaches the preset maximum number of iterations, the algorithm stops iterating and outputs the current parameter values ​​as the optimal solution. The optimal coil size parameters obtained by solving the gradient descent method enable the wireless charging system to achieve the maximum coupling coefficient under given constraints.

[0096] In one embodiment, reference is made to Figure 3 , Figure 3The three-view diagram shown illustrates the magnetic coupling 3D model of the drone wireless charging system of this invention. This magnetic coupling structure employs a transformer-like design concept, achieving efficient energy transfer. The transmitting coil uses a manganese-zinc ferrite magnetic block as the core of the magnetic circuit, with multiple turns of Litz wire precisely wound on its surface, forming the source of energy transfer. Protruding rectangular magnetic bases are specially designed on the upper left and right sides of the magnetic block. These bases not only serve as landing platforms for the drone but also form an integral structure with the bottom magnetic block, enhancing the system's mechanical stability. This design extends the magnetic bases along the horizontal plane, giving the coupling device significant anti-displacement capability, allowing an effective energy transfer channel to be established even with some positional deviation during drone landing, greatly improving the system's practicality and reliability.

[0097] The receiving coil uses a lightweight manganese-zinc ferrite rod as the magnetic circuit carrier, horizontally fixed to the landing support beam of the micro-UAV. Its surface is also wound with multi-turn Litz wire, and its winding process is consistent with that of the transmitting coil, ensuring magnetic field coupling compatibility. The upper and lower surfaces of the ferrite rod adopt a planar structure design. This design fully utilizes the gravity of the UAV during landing, allowing the receiving unit to fit tightly against the transmitting coil's magnet base, maximizing magnetic field coupling efficiency. When the UAV needs to recharge, it simply lands on the ground transmitting unit. The ferrite rod on the landing support contacts the rectangular magnet base of the ground transmitting coil, and the two parts of the manganese-zinc ferrite form a tight contact. Viewed from the side, the entire coupling device exhibits typical transformer-like structural characteristics. After the transmitting coil is energized, the magnetic field forms a closed loop within the magnet of the entire coupling device, significantly improving magnetic field coupling capability and effectively reducing leakage magnetic interference, ensuring efficient and safe energy transmission.

[0098] Based on the aforementioned magnetic coupling 3D model, the key dimensional parameters that need to be determined after constructing the finite element simulation environment include the length, width, and height of the transmitting coil magnetic block; the length and width of the protruding part of the transmitting coil magnetic block; the wire diameter and turn spacing of the transmitting coil; and the length and width of the receiving coil, as well as the wire diameter and turn spacing of the receiving coil. According to the finite element simulation analysis, the following optimal parameter combinations are obtained: the length L1 of the transmitting coil magnetic block is 120mm, the width W1 is 45mm, the height H1 is 20mm; the length L2 of the protruding part of the transmitting coil magnetic block is 100mm, the width W2 of the protruding part of the transmitting coil magnetic block is 20mm, the wire diameter of the transmitting coil is 1.6mm, and the turn spacing is 1.2mm. The length L3 of the receiving coil is 160mm, the width W3 of the receiving coil is 8mm, the wire diameter of the receiving coil is 0.7mm, and the turn spacing of the receiving coil is 0.5mm.

[0099] The above process determines the optimal size parameters of the magnetic coupling device, thereby obtaining the highest coupling coefficient. A higher coupling coefficient signifies higher energy transfer efficiency, reducing charging time and energy loss. Furthermore, improved energy transfer efficiency reduces coil heat generation, enhancing system reliability and safety. These improvements are significant for enhancing the endurance and operational efficiency of drones. This coil size optimization method based on response surface methodology and gradient descent provides a systematic solution for the efficient design of wireless charging systems, significantly shortening product development cycles and improving design quality.

[0100] In one embodiment, the range of coil turns is determined based on optimal size parameters, and electromagnetic field simulation is performed on the magnetically coupled three-dimensional model within this range. The simulation process, which includes simulating UAV displacement and collecting simulation data, includes the following steps:

[0101] The maximum and minimum number of Litz wire turns for the transmitting and receiving coils are calculated based on the optimal size parameters, thus obtaining the range of coil turns.

[0102] The optimal size parameters and the magnetic coupling three-dimensional model are imported into the simulation software. For each combination of coil turns within the range of coil turns, the magnetic field distribution of the magnetic coupling three-dimensional model under standard magnetic coupling state is simulated by the simulation software. The maximum magnetic induction intensity and the initial leakage magnetic field intensity of the simulated receiving coil in the magnetic coupling three-dimensional model are calculated based on the magnetic field distribution.

[0103] The simulation receiving coil is controlled by a preset translation step size to perform step translation to simulate the drone's deviation until the maximum magnetic induction intensity is greater than or equal to the saturation magnetic induction intensity or leakage magnetic intensity of the simulated magnetic core in the magnetic coupling three-dimensional model, which exceeds the preset intensity threshold.

[0104] After each step translation, the coil inductance data of the magnetically coupled three-dimensional model is calculated, and the displacement value between the simulated receiving coil and the original position is used as the drone offset amount to simulate the drone offset.

[0105] In this embodiment, Litz wire is a conductor made of multiple strands of insulated fine wire twisted in parallel. It has the advantages of reducing skin effect and proximity effect, and is widely used in high-frequency circuits. When calculating the maximum number of turns, it is first necessary to determine the effective winding area of ​​the coil, which is equal to the internal area of ​​the coil frame minus the necessary edge allowance. For Figure 3For rectangular coils, the effective winding area width is the coil width minus the allowance at both edges, typically 2-5mm on each side. The effective diameter of the Litz wire includes the diameter of the conductor itself and the thickness of the insulation layer, and the gap between the wires during winding must also be considered. The maximum number of turns is equal to the effective winding area width divided by the effective diameter of the Litz wire, rounded down. The minimum number of turns must consider electrical performance requirements, typically no less than 3-5 turns, to ensure sufficient inductance and coupling effect. Furthermore, the coil's resistance and inductance requirements must be considered; too many turns increase coil resistance, leading to increased energy loss; while too few turns may result in insufficient inductance, affecting energy transfer efficiency. In practical applications, the coil's self-resonant frequency must also be considered, ensuring it is higher than the system's operating frequency to avoid energy loss due to resonance. The coil turn range calculated using this method provides clear parameter boundaries for subsequent simulation analysis, effectively reducing the parameter search space and improving optimization efficiency.

[0106] Importing the optimal dimensional parameters and the magnetically coupled 3D model into simulation software for electromagnetic field analysis is a crucial step in designing a wireless charging system. Commonly used electromagnetic field simulation software includes ANSYS Maxwell, COMSOL Multiphysics, and CST Studio Suite, all of which support 3D electromagnetic field solving and parametric modeling. Mesh generation is a key factor in simulation accuracy; a denser mesh (minimum mesh size approximately 1 / 5 of the wire diameter) is needed for the coil region, while a sparser mesh can be used for the far-field region to improve computational efficiency. For each coil turn combination within the range of coil turns, a parametric scan simulation is required, which can be achieved using the parameter scan function of the simulation software. For example, if the transmitting coil has 8-20 turns and the receiving coil has 5-15 turns, two parameter variables need to be set and a two-dimensional parameter scan needs to be performed, totaling approximately 100 simulations. In each simulation, the software solves Maxwell's equations to calculate the magnetic field distribution in three-dimensional space. (Refer to...) Figure 4 , Figure 4 This is a simulation diagram of the electromagnetic field distribution when the transmitting coil has 14 turns and the receiving coil has 13 turns. Next, using post-processing functions, magnetic field strength data at key locations can be extracted, particularly the maximum magnetic field strength at the receiving coil and the leakage magnetic field strength in the surrounding environment. The maximum magnetic field strength usually occurs near the magnetic core and can be calculated using the field calculator function; the leakage magnetic field strength needs to be measured at a preset safe distance (usually 1.5-2 times the distance from the coil center).

[0107] Next, the simulated receiving coil needs to be controlled to perform step translation based on a preset translation step size to simulate the drone's offset. In actual operation, the translation step size needs to be determined first, usually chosen as 1%-5% of the coil's characteristic dimensions (such as diameter or side length). The translation direction usually considers two main directions: the X-axis (horizontal direction) and the Y-axis (horizontal direction), as well as the diagonal direction in the XY plane. Step translation can be implemented through the parametric modeling function of the simulation software, setting the position coordinates of the receiving coil as variables and incrementing these variables in each simulation. For example, if the initial position is (0,0,20mm) and the step size is 2mm, then the translation sequence in the X direction is (2mm,0,20mm), (4mm,0,20mm), (6mm,0,20mm), etc. After each translation, the electromagnetic field distribution needs to be re-solved, and two key indicators need to be extracted: maximum magnetic flux density and leakage flux density. The translation process continues until termination conditions are met: first, the maximum magnetic flux density reaches or exceeds the core's saturation magnetic flux density (typically 0.3-0.5T), at which point the core enters saturation and energy transfer efficiency significantly decreases; second, the leakage magnetic flux density exceeds a preset safety threshold, at which point the system no longer meets safety requirements. To improve computational efficiency, an adaptive step-size strategy can be adopted, using a larger step size (e.g., 5mm) when far from the critical point and a smaller step size (e.g., 1mm) when approaching the critical point, to obtain a more accurate critical offset value. Furthermore, the response surface methodology can be combined to construct a response surface model between the magnetic field strength and the offset using a small number of simulation points, thereby quickly predicting the magnetic field distribution under different offsets and further improving computational efficiency.

[0108] After each translational step, the coil inductance data of the magnetically coupled 3D model is calculated, and the displacement value between the simulated receiving coil and the original position is used as the drone offset for simulating the drone's movement. The coil inductance data includes the self-inductance L1 of the transmitting coil, the self-inductance L2 of the receiving coil, and the mutual inductance M. These parameters directly determine the system's coupling coefficient k and energy transfer efficiency. In the simulation software, these inductance values ​​can be calculated using the energy method or circuit parameter extraction function. At each offset position, these inductance parameters need to be recalculated, and the corresponding displacement value recorded. The displacement value is typically represented by coordinates (Δx, Δy), where Δx and Δy represent the horizontal offset.

[0109] The following is a record of one of the simulation processes in this embodiment:

[0110] This simulation aims to evaluate the performance of a UAV wireless charging system using 3D electromagnetic field simulation software (ANSYS Maxwell). The focus is on the initial performance under different coil turn combinations and the impact of receiver coil position offset on coupling characteristics and magnetic field distribution. The simulation objective is to obtain coil inductance parameters (L1, L2, M), coupling coefficient (k), maximum magnetic flux density, and leakage flux density under different operating conditions, providing data support for system design and safety assessment.

[0111] First, a 3D model is constructed. The model includes a transmitting coil (Tx), a receiving coil (Rx), an optional magnetic core structure (explicit core saturation analysis is not included in this simulation, but a saturation threshold monitoring is set), and an air domain encompassing the entire coupling region and part of the far field. The transmitting coil is set as a planar helical coil with an outer diameter of 100mm and an inner diameter of 70mm, and the receiving coil is set as a planar helical coil with an outer diameter of 80mm and an inner diameter of 50mm. The diameter of the coil wires is 1mm. Initially, the two coils are coaxially aligned, with a vertical spacing (Z-axis direction) of 20mm. For material properties, the coil material is set to copper, and the surrounding environment is set to air. For the coil wire region, a fine tetrahedral mesh is used, with a minimum mesh size of 0.2mm (approximately 1 / 5 of the wire diameter) to accurately capture current distribution and proximity effects. For the coupling region between the coils, a moderate mesh density is used. At the boundary of the air domain far from the coils (set as a radiation boundary or a sufficiently large air box), a gradually thinning mesh is used to reduce computational resource consumption and improve solution efficiency. After the overall mesh was generated, a quality check was performed to ensure that the element quality met the solution requirements.

[0112] Next, a parameter scan was performed to optimize the coil turns. The number of turns of the transmitting coil was set as a parameter variable, with a scan range of 8 to 20 turns and a step size of 1 turn; the number of turns of the receiving coil was set as a parameter variable, with a scan range of 5 to 15 turns and a step size of 1 turn. A two-dimensional parameter scan was performed, with the solver set to a frequency domain solver and the operating frequency set to 100kHz (a typical wireless charging frequency). For each combination of turns (a total of (20-8+1)*(15-5+1)=13*11=143 simulations), the inductance parameters (L1, L2, M) and coupling coefficient k were calculated under the initial alignment condition. Based on the preliminary scan results, a combination of 14 turns for the transmitting coil and 13 turns for the receiving coil was selected for subsequent offset analysis. This combination showed good potential coupling performance during initial alignment. Figure 4 The diagram shows the magnetic field distribution cloud map under the aligned state with this combination of turns, and it can be seen that the magnetic field lines are mainly concentrated in the area between the coils.

[0113] Subsequently, a simulation of the receiving coil's step translation was performed to simulate the positional shift during UAV landing. Based on a configuration of Tx = 14 turns and Rx = 13 turns, the position of the transmitting coil was kept fixed, and the position coordinates of the receiving coil were parameterized. First, a translation along the X-axis was performed, with an initial position of (0, 0, 20 mm). The translation step size was set to 5 mm (a relatively large initial step size was chosen, approximately 5% of the coil's characteristic size), with a translation range from 0 mm to 30 mm. In the parameter scan settings, the X-coordinate of the receiving coil was set as a variable, taking values ​​of 0 mm, 5 mm, 10 mm, 15 mm, 20 mm, 25 mm, and 30 mm sequentially. At each offset position (Δx, 0, 20 mm), the frequency domain solution was rerun.

[0114] After each solution is obtained, perform post-processing operations:

[0115] 1. Inductance parameter extraction: Using the energy method or circuit parameter extraction function, calculate the self-inductance L1 of the transmitting coil, the self-inductance L2 of the receiving coil, and the mutual inductance M between them at this offset position. Record the corresponding displacement value Δx.

[0116] 2. Coupling coefficient calculation: Calculate the coupling coefficient k according to the formula.

[0117] Magnetic field strength analysis: Extract three-dimensional magnetic field distribution data. Use the field calculator function to find the maximum magnetic flux density in the receiving coil region (especially near the center or where the wires are densely packed) and compare it with a preset core saturation threshold (e.g., 0.4T). Simultaneously, measure the average or maximum magnetic flux density as leakage magnetic flux density on a preset safety assessment circle at a specific radius from the system center (e.g., 50 mm horizontally from the center point) and compare it with safety standards (e.g., ICNIRP's public exposure limit of 6.25 μT).

[0118] Simulation results show that as the offset Δx in the X direction increases, the mutual inductance M and coupling coefficient k decrease significantly. The self-inductance L1 of the transmitting coil remains basically unchanged, and the self-inductance L2 of the receiving coil also changes little (assumed to be constant in this simulation). Within the tested offset range (0-30mm), the maximum magnetic flux density B_max is always below the saturation threshold of 0.4T, and the leakage flux density B_leakage does not exceed the set safety limit. The L1, L2, M, and k values ​​corresponding to each Δx are recorded. Although detailed translation simulations in the Y and diagonal directions were not performed, their trends are expected to be similar to those in the X direction: the larger the offset, the worse the coupling performance. The entire simulation process utilizes parametric modeling and automatic post-processing functions to effectively evaluate the system performance under different turns and offset conditions. The simulation data is compiled to plot the curves of L1 / L2, M, and k as a function of offset, visually demonstrating the system's sensitivity to displacement. The specific simulation data is shown in Table 1.

[0119] Table 1. Simulation data of UAV offset

[0120]

[0121]

[0122] Table 1 shows the simulated inductance parameters and coupling coefficients of the receiving coil under different offsets (Δx) along the X-axis, with a selected number of coil turns (Tx = 14, Rx = 13) and a fixed vertical spacing (20 mm). L1 and L2 are treated as constants in this offset simulation, which is a common simplification in actual simulations, or to indicate that their changes are much smaller than the changes in M. The mutual inductance M decreases significantly with increasing offset Δx, reflecting the decrease in the degree of magnetic coupling between the coils. The coupling coefficient k is calculated according to a preset formula, and its trend is consistent with that of M. To comprehensively evaluate the system performance, curves of self-inductance and mutual inductance as a function of offset can be plotted, as detailed in [reference needed]. Figures 5 to 7 This directly reflects the system's offset tolerance. Furthermore, it's necessary to calculate the energy transfer efficiency η under different offsets. This efficiency is related to the coupling coefficient k, the coil quality factors Q1 and Q2, and the load matching degree, and can be calculated using the formula η = k. 2 Q1Q2 / ((1+k 2 Q1Q2) 2 Estimate the value.

[0123] In one embodiment, the data analysis-based wireless charging efficiency optimization method further includes the following steps:

[0124] The simulation data is organized into a structured dataset and then normalized.

[0125] A generative adversarial network model is constructed using a multilayer perceptron and a convolutional neural network.

[0126] A generative adversarial network (GAN) model is trained by combining the coil turns range, optimal size parameters, and a normalized structured dataset. The trained GAN model then outputs enhanced simulation data.

[0127] The enhanced simulation data is filtered using a preset physical verification function, and the filtered enhanced simulation data is then merged into the simulation data.

[0128] In this implementation, organizing the simulation data into a structured dataset and normalizing it are key steps in data preprocessing. The simulation data can be organized in tabular form, with each row representing a set of simulation results and each column representing a feature or label. After the dataset is constructed, normalization is required to transform features of different dimensions to the same scale, preventing certain features from dominating model training due to their large values. Common normalization methods include min-max normalization and Z-score standardization. Different normalization methods may be needed for different types of features. For example, geometric parameters are suitable for min-max normalization, while physical quantities such as magnetic field strength are suitable for Z-score standardization. After normalization, feature selection or dimensionality reduction is also required to reduce data redundancy and computational complexity. Common methods include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Recursive Feature Emission (RFE). Finally, the processed dataset is divided into training, validation, and test sets, typically in a 70%:15%:15% ratio, to support subsequent model training and evaluation.

[0129] The core technology for achieving simulation data augmentation is to construct a generative adversarial network (GAN) model using a multilayer perceptron and a convolutional neural network. A GAN consists of a generator and a discriminator, which generate data through adversarial training. In the simulation data augmentation of a wireless charging system, the generator is responsible for generating realistic simulation data, while the discriminator is responsible for distinguishing between real and generated simulation data. The generator typically uses a multilayer perceptron (MLP) structure, containing an input layer, multiple hidden layers, and an output layer. The input layer receives a random noise vector z (usually following a standard normal distribution N(0,1)) and a condition vector c (containing conditional information such as coil parameters); the hidden layers consist of multiple fully connected layers, each followed by batch normalization and an activation function; the number of neurons in the output layer is equal to the dimension of the target simulation data, and the activation function is selected based on the data range (e.g., the sigmoid function maps the output to the [0,1] interval). In this embodiment, the generator structure includes an input layer (100 noise neurons + 10 condition neurons), three hidden layers (with 256, 512 and 256 neurons respectively), and an output layer (20 neurons, corresponding to the dimension of the simulation result).

[0130] The discriminator employs a convolutional neural network (CNN) structure, effectively capturing spatial correlations and physical laws within the simulation data. The discriminator's input consists of simulation data and a conditional vector *c*. The network structure comprises multiple convolutional layers, each followed by batch normalization and activation functions. Finally, a fully connected layer outputs a scalar representing the probability that the input data is real data. For example, the discriminator might contain three convolutional layers (3×3 kernel size, with 64, 128, and 256 channels respectively) and two fully connected layers (with 128 and 1 neuron respectively). GAN training utilizes an adversarial training strategy, with the generator and discriminator optimizing alternately. Furthermore, to generate simulation data that satisfies physical constraints, a physical constraint term can be added to the generator's loss function. Through this combination of deep learning and physical knowledge, the constructed GAN model can generate simulation data that conforms to both statistical distributions and physical laws.

[0131] The training process of a Generative Adversarial Network (GAN) model first requires preparing a condition vector containing the coil turns range and optimal size parameters. These parameters, after normalization, are used as input to the generator along with a random noise vector z. Training employs mini-batch gradient descent, with each batch containing 32-128 samples. In each training iteration, the generator parameters are first fixed, and the discriminator parameters are updated; then, the discriminator parameters are fixed again, and the generator parameters are updated once. The learning rate is typically set to 0.0001-0.0002, and the Adam optimizer is used for parameter updates. After training, the generator is used to generate augmented simulation data. Specifically, multiple turns combinations are first uniformly sampled within the coil turns range. These combinations are then combined with the optimal size parameters to form the condition vector. Finally, a random noise vector z is generated and input into the generator along with the condition vector to obtain the augmented simulation data. To increase data diversity, small perturbations can be introduced into the condition vector to simulate minor parameter changes. For example, adding ±2% random perturbation to the optimal size parameters generates more diverse simulation scenarios. Furthermore, the diversity and innovativeness of the generated data can be controlled by adjusting the distribution characteristics of the noise vector z. For example, increasing the variance of the noise vector can generate more diverse but potentially less accurate data, while decreasing the variance generates more conservative but more reliable data. This method can generate a large amount of enhanced simulation data, significantly expanding the size and coverage of the original simulation dataset. This enhanced data can fill in the gaps in the original simulation data, providing more comprehensive data support for subsequent optimization designs, while simultaneously reducing the computational cost of high-precision simulations.

[0132] Finally, the enhanced simulation data needs to be filtered using preset physical verification functions, and the filtered enhanced simulation data is then merged into the simulation data. Physical verification functions are mathematical functions designed based on electromagnetic principles and engineering experience, used to evaluate whether the generated data conforms to physical laws. These functions typically include verification in several aspects: First, inductance consistency verification, checking whether the relationship between self-inductance L1, L2, and mutual inductance M meets physical constraints, such as the mutual inductance value should not exceed the geometric mean of self-inductance; second, coupling coefficient verification, checking whether the calculated coupling coefficient k is within a reasonable range and monotonically decreases with increasing offset; third, magnetic field distribution verification, checking whether the maximum magnetic flux density and leakage flux density conform to physical laws, such as the maximum magnetic flux density should increase with increasing coil turns and decrease with increasing offset; fourth, energy conservation verification, checking whether the input power, output power, and power loss satisfy the law of conservation of energy. Physical verification functions can be represented as a series of inequality constraints. For each generated data point, the values ​​of these constraint functions are calculated, and thresholds are set to determine whether the physical constraints are met. The data filtering process typically removes 20%-40% of the generated data, retaining only high-quality data that conforms to both statistical distribution and physical constraints. The filtered enhanced simulation data needs to be merged with the original simulation data to form an expanded dataset. During merging, attention must be paid to data balance to avoid excessive data in certain parameter regions, which could lead to bias. Stratified sampling or weighted merging methods can be used to ensure that the final dataset is evenly distributed in the parameter space. The final merged dataset is not only larger and more comprehensive but also maintains physical consistency and data quality, providing a reliable data foundation for subsequent coil turns optimization and anti-offset strategy design, thus improving the correctness of these optimization and design.

[0133] In one implementation, determining the optimal number of coil turns based on simulation data and using a multi-objective optimization algorithm includes the following steps:

[0134] Determine the decision variables for multi-objective optimization based on the range of coil turns;

[0135] The optimization objective function is set according to the preset indicators, and the constraint conditions are set according to the physical constraints of coil inductance. The optimization objective function includes maximizing coil energy transmission efficiency, minimizing coil total mass, and maximizing UAV offset tolerance.

[0136] Based on all decision variables, an initial solution space is constructed using an adaptive grid Latin hypercube sampling method;

[0137] A simplified solution set is obtained by rapidly searching within the initial solution space using a binary particle swarm optimization method based on magnetic coupling sensing.

[0138] With the objective function as the optimization objective, under constraints, the simplified solution set is solved by multi-objective optimization using the NSGAII algorithm guided by electromagnetic field sensitivity, and the Pareto optimal solution set is obtained.

[0139] The comprehensive performance index of each Pareto solution in the Pareto optimal solution set is calculated based on the optimization objective function, and the optimal Pareto solution with the highest comprehensive performance index is analyzed as the optimal number of coil turns.

[0140] In this embodiment, the theoretical range of the number of turns that can be wound on the transmitting and receiving coils is first calculated based on the optimal size parameters obtained in the previous embodiment. Since the number of turns must be an integer, the decision variable space is a discrete two-dimensional integer space. For example, if the number of turns of the transmitting coil N_T∈[5,25] and the number of turns of the receiving coil N_R∈[3,15] are calculated, then the decision variable space contains (25-5+1)×(15-3+1)=273 possible combinations of turns. These combinations of turns constitute the decision variable space, and each decision variable point is represented as a vector (N_T,N_R). Next, three optimization objective functions are set according to the preset indicators: (1) maximize the coil energy transmission efficiency η; (2) minimize the total mass m of the coil, the calculation formula of which is m=ρ·π·(N T ·D T ·S T +N R ·D R ·S R ), where ρ is the wire density, D is the coil diameter, and S is the wire cross-sectional area; (3) Maximize the UAV offset tolerance T, defined as T=min(Δx_max,Δy_max), which represents the maximum allowable offset of the UAV in the horizontal direction under the premise of maintaining the energy transmission efficiency not lower than the threshold. At the same time, the constraints include: physical constraints of coil inductance L1≥L_min and L2≥L_min to ensure that the coil inductance meets the requirements of the resonant circuit; coil resistance constraints R1≤R_max and R2≤R_max to control coil loss; and magnetic field strength constraints B_max≤B_sat to prevent magnetic core saturation.

[0141] Next, a non-uniform decision space grid is constructed based on the optimal turns ratio predicted by electromagnetic field theory, with denser grid points placed near the theoretically optimal ratio. Then, prior knowledge of electromagnetic coupling is introduced into the non-uniform grid for sample sampling, prioritizing regions with higher theoretical coupling coefficients (k). Specifically, the decision space is divided into m×n grid cells, and a sample point is randomly selected from each cell to form an initial sample set. Next, correlation minimization is performed on all sample points in the initial sample set. By iteratively swapping the positions of sample points, the correlation between them is minimized to obtain the target sample set. Finally, the optimization objective function values ​​for all sample points in the target sample set are calculated, forming the initial solution space. This sampling method ensures the diversity and representativeness of the initial solution space, providing a high-quality starting point for subsequent optimization algorithms.

[0142] Then, all initial solutions in the initial solution space are encoded into binary bit strings. Next, a particle swarm is initialized, containing P particles (usually P = 50), each representing a possible combination of coil turns, and the particle swarm optimization algorithm parameters are set. Then, the fitness of the initial particles in the initialized particle swarm is calculated by combining the optimization objective function and the magnetic coupling coefficient k corresponding to the coil turn combination. During iteration, the velocity and position of all particles are iteratively updated based on the fitness, and mutation probabilities are added to the particles. Iteration stops when the number of iterations reaches the preset maximum number of iterations, and the particles at the global optimum and their corresponding fitness values ​​are output as a simplified solution set.

[0143] The simplified solution set obtained in the previous step is used as the initial population for the NSGAII algorithm, and then the parameters of the NSGAII algorithm are initialized. During the execution of the NSGAII algorithm, the optimization objectives are to maximize the coil energy transfer efficiency η, minimize the total coil mass m, and maximize the UAV offset tolerance T. Under the constraints of coil inductance, the initial population is iteratively updated using the NSGAII algorithm process. Specifically, the population is sorted by non-dominated sorting and crowding calculation, and high-quality individuals are selected for crossover and mutation operations to generate offspring populations. In the population mutation operation, the sensitivity matrix of the optimization objective function to the number of coil turns is calculated. Based on the sensitivity matrix, the mutation operation prioritizes adjusting the number of turns variable with higher sensitivity, and the change in turn length is proportional to the sensitivity. After multiple iterations, the first frontier (non-dominated solution set) in the final population is output as the Pareto optimal solution set. These solutions represent the best trade-offs among the three optimization objectives. Finally, the comprehensive performance index of each Pareto solution in the Pareto optimal solution set is calculated based on the optimization objective function, and the selection of the optimal solution is the last step of multi-objective optimization. Then, the Pareto solution with the highest comprehensive performance index is selected as the optimal solution, and it is analyzed as the optimal number of coil turns.

[0144] In one implementation, constructing the initial solution space based on all decision variables using the adaptive grid Latin hypercube sampling method includes the following steps:

[0145] A non-uniform decision space grid is constructed based on all decision variables and the optimal turns ratio relationship predicted by electromagnetic field theory.

[0146] Pre-defined prior knowledge of electromagnetic coupling degree is introduced into a non-uniform decision space grid to sample samples and obtain an initial sample set;

[0147] The target sample set is obtained by minimizing the correlation of all initial sample points in the initial sample set. The optimization objective function value of all target sample points in the target sample set is calculated to form the initial solution space.

[0148] In this embodiment, based on electromagnetic field theory, the turns ratio of the transmitting and receiving coils in a wireless charging system directly affects the energy transfer efficiency. When constructing a non-uniform decision space grid, the range of turns for the transmitting coil is first calculated based on the optimal size parameters. and the range of the number of turns of the receiving coil A two-dimensional integer space is formed. Then, based on the optimal turns ratio relationship in electromagnetic field theory... (Where L1 and L2 are the self-inductances of the transmitting and receiving coils, respectively) A non-uniform grid is constructed in this space. In practice, the region near the theoretically optimal ratio is divided into denser grid points, for example, in N... T / N R Within a region of 3 ± 0.5, the grid spacing is set to 1, while in other regions the grid spacing is set to 2 or greater. This non-uniform grid design ensures more sampling points in areas where theoretically more efficient turns combinations are more likely to be obtained, improving the efficiency and accuracy of subsequent optimization.

[0149] Based on the constructed non-uniform decision space grid, prior knowledge of electromagnetic coupling is introduced for sample sampling. During the sampling process, the theoretical coupling coefficient k corresponding to each grid point (N_T, N_R) is first calculated. t Then according to k t The size of the sampling probability is assigned so that k t Higher sampling probabilities are obtained for areas with higher elevations. In practice, the probability density function P(N) is used. T N R )∝exp(α·k t (N T N R Importance sampling is performed, where α is a control parameter. In this way, m×n sample points are selected from the decision space to form an initial sample set, ensuring that high-potential areas are fully explored.

[0150] Finally, the initial sample set is subjected to correlation minimization processing to improve the representativeness and diversity of the samples. Specifically, the maximum-minimum distance algorithm is used, which iteratively swaps sample point positions to maximize the minimum distance between sample points. The algorithm flow is as follows: First, calculate the distance matrix D between all sample point pairs in the initial sample set, where D_ij represents the Euclidean distance between sample points i and j; then iteratively execute: find the sample point pair (i,j) with the smallest distance, randomly select a new position in the decision space to replace one of the points. If the minimum distance of the new sample set increases, accept the replacement; otherwise, keep it as is; repeat this process until the preset number of iterations is reached or the minimum distance no longer increases significantly. After processing, the target sample set is obtained. Subsequently, the optimization objective function value corresponding to each target sample point is calculated, including the coil energy transmission efficiency η, the total coil mass m, and the UAV offset tolerance T. For example, for sample point (N_T=12, N_R=4), electromagnetic field simulation calculations yield η=0.85, m=120g, and T=5cm. All sample points and their objective function values ​​together constitute the initial solution space, providing a high-quality, uniformly distributed starting point for subsequent optimization algorithms.

[0151] In one implementation, the simplified solution set is obtained by rapidly searching the initial solution space using a magnetically coupled sensing-based binary particle swarm optimization method, including the following steps:

[0152] Encode all initial solutions in the initial solution space into binary bit strings;

[0153] Initialize the particle swarm optimization algorithm parameters in a binary bit string;

[0154] The fitness of the initial particles in the initial particle swarm is calculated by combining the optimization objective function and the magnetic coupling coefficient corresponding to the coil turns combination.

[0155] The velocity and position of all particles are updated iteratively based on fitness. During the position update of all particles, a mutation probability is added to each particle. The mutation probability is linearly related to the magnetic coupling coefficient of the particle's current position.

[0156] When the number of iterations reaches the preset maximum number of iterations, the iteration update stops, and the particles in the global optimal position and their corresponding fitness values ​​are used as the simplified solution set.

[0157] In this embodiment, encoding all initial solutions in the initial solution space into binary bit strings is a key preprocessing step in the optimization algorithm. The purpose is to transform continuous or discrete decision variables into a form suitable for processing by the binary particle swarm optimization algorithm. In the optimization of a wireless charging system, the decision variables are the number of turns in the transmitting coil and the number of turns in the receiving coil, both of which are integer values. The encoding process first requires determining the number of bits required for each variable. For the number of turns in the transmitting coil, the required number of bits is... Similarly, the number of binary bits required for the number of turns of the receiving coil is

[0158] During encoding, for each initial solution (N_T, N_R), first map N_T to... Values ​​within the range, i.e., N T '=N T -N Tmin Then N T Convert ′ to b T A binary number. Similarly, N... R Mapped to And convert to b R Two binary numbers are then concatenated to form a single binary number of length b. T +b R The binary bit string encoding method offers several advantages: First, it ensures the reversibility of the encoding and decoding process, allowing any binary bit string to be uniquely decoded back into the original combination of turns; second, it maps each point in the decision space to a fixed-length binary string, facilitating subsequent particle swarm optimization (PSO) operations; and finally, binary encoding enables the algorithm to perform complex search behaviors, such as crossover and mutation, through simple bit operations. This encoding transformation converts the original integer optimization problem into a binary optimization problem, providing a standardized input format for subsequent PSO algorithms.

[0159] Particle Swarm Optimization (PSO) is a swarm intelligence algorithm that simulates the foraging behavior of birds, searching for optimal solutions through the cooperative search of multiple particles in the solution space. In binary PSO, each particle represents a possible combination of coil turns, represented as a binary bit string. When initializing the particle swarm, the number of particles, P, is first determined. Too few particles will lead to insufficient searching, while too many will increase the computational burden. Each particle contains three key attributes: its current position X. i (a binary string), speed V i (A real vector representing the probability of each bit being flipped) and the individual's historical best position pbest i (The best solution ever found for this particle). The initial position of the particle can be set in two ways: one is completely random initialization, that is, randomly generating a position of length b. T +b R The first approach is to use a binary bit string as the initial position; the second approach is to select a high-quality solution from the initial solution space as the initial position, which can accelerate the convergence of the algorithm. In this embodiment, the second approach is adopted, randomly selecting P solutions from the initial solution space obtained in the previous steps and encoding them as binary bit strings as the initial positions of the particles.

[0160] The initial velocity V of the particlei It is a real-number vector with the same length as the bit string, where each element represents the probability of the corresponding bit being flipped. The initial velocity is usually randomly generated within a preset range. Besides initializing the particle swarm, key parameters of the algorithm need to be set: inertia weight w, cognitive coefficient c1, and social coefficient c2. The inertia weight w controls the degree to which particles maintain their original velocity, and is usually set to a value between 0.7 and 0.9. A larger w is beneficial for global search, while a smaller w is beneficial for local search. A common strategy is to linearly decrease the value of w with each iteration, initially setting it to 0.9 and eventually reducing it to 0.4. This allows for extensive exploration in the early stages of the algorithm and fine-grained search in the later stages. The cognitive coefficient c1 controls the tendency of particles to move towards their individual historical best position, and the social coefficient c2 controls the tendency of particles to move towards the group's historical best position; both are usually set to 2.0. Finally, the maximum number of iterations T is set. max As a termination condition for the algorithm.

[0161] Next, the fitness of the initial particles needs to be calculated by combining the objective function and the magnetic coupling coefficient corresponding to the coil turns combination. The design of the fitness function directly determines the direction of optimization and the characteristics of the final solution, which is particularly important in the optimization of wireless charging systems. For each particle, its binary bit string first needs to be decoded into the actual coil turns combination (N_T, N_R), and then multiple performance indicators are calculated based on these parameters to comprehensively evaluate its fitness. The decoding process is the reverse of the encoding process: the binary bit string is divided into the first b... T Position and after b R Each bit is converted to a decimal number N. T ′ and N R ′, then calculate and The actual number of coil turns is obtained.

[0162] After obtaining the actual number of turns, three optimization objective function values ​​are calculated: coil energy transfer efficiency η, total coil mass m, and UAV offset tolerance T. Additionally, the magnetic coupling coefficient k needs to be calculated. After obtaining these performance indicators, a comprehensive fitness function needs to be designed to evaluate the quality of each particle. Considering the characteristics of multi-objective optimization, the fitness function is usually in the form of a weighted sum: F = w1·η + w2·(1 / m) + w3·T + w4·k, where w1, w2, w3, and w4 are weight coefficients, controlling the importance of each objective in the fitness. Through the above process, each particle is assigned a fitness value, directly reflecting its quality as a candidate solution. The higher the fitness value, the better the coil turn combination represented by the particle. These initial fitness values ​​are not only used to evaluate the quality of the initial particle swarm but also serve as a benchmark for subsequent iterative optimization, guiding particles to move towards better solutions.

[0163] Introducing the magnetic coupling coefficient as a key parameter for calculating particle fitness is of great significance. The magnetic coupling coefficient k directly characterizes the energy transfer capability between the transmitting and receiving coils, and its introduction provides a physical basis for fitness evaluation. Since the energy transfer efficiency η of a wireless charging system is directly related to the magnetic coupling coefficient k, calculating the magnetic coupling coefficient corresponding to different coil turn combinations allows for accurate evaluation of the energy transfer performance of each particle's design, ensuring the optimization process is based on reliable electromagnetic theory. Furthermore, the magnetic coupling coefficient is highly sensitive to the coil turn count, making it a crucial bridge in the optimization process. The coil turn count affects the coil's self-inductance and mutual inductance, thus influencing the magnetic coupling coefficient. By adding the magnetic coupling coefficient, the optimization algorithm can capture the nonlinear impact of coil turn count variations on system performance, avoiding potential misleading effects from simplified models.

[0164] The next step, iteratively updating the velocity and position of all particles based on fitness, is the particle swarm optimization (PSO) algorithm. Through this process, the particle swarm gradually moves towards a better solution. In binary PSO, the particle's position is represented by a binary bit string, while the velocity is expressed as the probability of bit flips. In each iteration, the particles adjust their velocity and position based on their own experience and the swarm's experience, gradually exploring the solution space and converging to the optimal solution. Velocity updates are crucial for particle movement, and the classic PSO velocity update formula is used:

[0165] V i (t+1)=w·V i (t)+c1·r1·(pbest i -X i (t))+c2·r2·(gbest-X i (t))

[0166] Where V i (t) is the velocity vector of particle i in the t-th iteration, r1 and r2 are random numbers between [0,1], and gbest is the global optimal position. This formula consists of three parts: the inertial term w·V i (t) ensures the particle maintains its original motion tendency; cognitive term c1·r1·(pbest) i -X i (t) guides the particle to move towards its historical best position; social term c2·r2·(gbest-X) i(t) guides particles to move towards the optimal position in the swarm. In binary PSO, position updates differ from continuous PSO. First, the velocity is converted into a position flip probability using the sigmoid function. Then, a random number between [0,1] is generated for each bit. If the random number is less than the position flip probability, the position is flipped; otherwise, it remains unchanged. This mechanism ensures that the larger the absolute value of the velocity, the closer the bit flip probability is to 1, thus realizing "movement" in binary space.

[0167] Another innovation in this implementation is the introduction of a mutation mechanism related to the magnetic coupling coefficient. Traditional PSO is prone to getting trapped in local optima, while the mutation operation can increase the algorithm's exploratory ability. The mutation probability P... m Designed to be linearly related to the magnetic coupling coefficient k of the particle's current position: P m =P m0 ·(1-k / k max ), where P m0 It is the basic mutation probability, k max This is the theoretical maximum coupling coefficient. This means that particles with low coupling coefficients have a higher mutation probability, while particles with high coupling coefficients have a lower mutation probability. The mutation operation is performed after the position update. This adaptive mutation mechanism has significant advantages: regions with low coupling coefficients often correspond to suboptimal solutions, and increasing the mutation probability in these regions can help the algorithm escape local optima; while regions with high coupling coefficients may be close to the global optimum, and reducing the mutation probability helps the algorithm perform fine-grained searches in these regions. Through this adaptive mutation mechanism, the algorithm can achieve a good balance between global exploration and local exploitation. When a particle is in a low coupling coefficient region, the higher mutation probability gives it a chance to escape local optimum traps; when a particle is close to a high coupling coefficient region, the lower mutation probability helps with fine-grained searches and convergence. This strategy is particularly suitable for wireless charging system optimization problems because the magnetic coupling coefficient directly reflects energy transfer efficiency and is an important indicator for evaluating solution quality.

[0168] After each iteration, the individual best position and the global best position of each particle need to be updated. If the fitness of particle i at its new position is better than its historical best fitness, then pbest is updated. i The current position is set; if a better position than the current gbest appears among all particles, then gbest is updated. Fitness evaluation uses the comprehensive fitness function described in S3, ensuring that the optimization process always moves towards improving energy transfer efficiency, reducing coil mass, and enhancing offset tolerance. Through this iterative update mechanism, the particle swarm can efficiently search the solution space, gradually approaching the optimal combination of coil turns. The mutation mechanism related to the magnetic coupling coefficient enhances the algorithm's exploration capability, enabling it to escape local optima while maintaining a fine search for high-quality solution regions.

[0169] The iteration update stops when the preset maximum number of iterations is reached, and the particle at the global optimum and its corresponding fitness value are used as the simplified solution set. The maximum number of iterations is an important control parameter of the algorithm and needs to be set reasonably according to the complexity of the problem and the limitations of computational resources. For the coil turns optimization problem of wireless charging system, the maximum number of iterations is usually set between 100 and 200. Too few iterations may lead to insufficient convergence of the algorithm and the acquisition of suboptimal solutions; too many iterations will increase the computational cost, while the benefit may be negligible. When the algorithm terminates, the global optimum position gbest represents the optimal combination of coil turns found during the search process. gbest is decoded into the actual number of coil turns, and the corresponding performance indicators are calculated: energy transfer efficiency, total coil mass, offset tolerance, and magnetic coupling coefficient. These data constitute the simplified solution set.

[0170] In one implementation, with the objective function as the optimization objective, the simplified solution set is solved using the NSGAII algorithm guided by electromagnetic field sensitivity under constraints to obtain the Pareto optimal solution set. The steps include:

[0171] Use the simplified solution set as the initial population for the NSGAII algorithm;

[0172] After initializing the algorithm parameters of the NSGAII algorithm, the NSGAII algorithm process is executed iteratively to update the population under constraints, with the objective function as the optimization target.

[0173] In the population mutation operation of the NSGAII algorithm, the sensitivity matrix of the optimization objective function to the number of coil turns is calculated, and the sensitivity matrix is ​​used to guide the population mutation.

[0174] After iteratively updating the population using the NSGAII algorithm, the first frontier in the final population is output as the Pareto optimal solution set.

[0175] In this implementation, using the simplified solution set as the initial population for the NSGAII algorithm is an efficient optimization strategy. By leveraging the high-quality solutions obtained from previous particle swarm optimization as a starting point, the multi-objective optimization process is accelerated. Specifically, the optimal coil turns combination and its corresponding performance metrics are first extracted from the simplified solution set output by the particle swarm optimization algorithm. To construct the initial population for NSGAII, a diverse set of individuals needs to be generated based on this optimal solution. This can be achieved by applying small perturbations around the optimal solution. Simultaneously, to ensure population diversity, a certain proportion of individuals can be randomly generated, with their coil turns evenly distributed within a preset range. Each individual is represented as a chromosome, encoded using real-number encoding (directly using the coil turns value) or binary encoding (converting the turns into a binary bit string). For real-number encoding, the chromosome length is 2 bits; for binary encoding, if the range of transmit coil turns requires 8 bits and the range of receive coil turns requires 7 bits, the total chromosome length is 15 bits. The initial population size is typically set between 50 and 200, depending on the problem complexity and computational resources. This "hot start" strategy significantly improves the convergence speed of the NSGAII algorithm because the initial population already contains high-quality solutions. The algorithm can start searching directly from promising regions instead of starting from random states, greatly reducing the number of iterations required to reach convergence. It is particularly suitable for scenarios with limited computing resources.

[0176] Next, key parameters are set: population size N, maximum number of iterations, crossover probability, and mutation probability. The optimization objective function is set as three conflicting objectives: maximizing energy transfer efficiency, minimizing total coil mass, and maximizing offset tolerance. Constraints include: a range of coil turns, a minimum energy transfer efficiency requirement (η≥η_min), and a maximum coil mass limit. The NSGAII algorithm iterative process includes: (1) Non-dominated sorting: The population is divided into frontiers of different levels according to the Pareto dominance relationship. The solutions in the first frontier are not dominated by any other solutions; (2) Crowding calculation: The crowding degree is calculated for the solutions in the same frontier, which represents the sparseness of the solution distribution in the target space; (3) Selection operation: Binary tournament selection is used to select parent individuals based on frontier level and crowding degree. Those with lower frontier level are given priority, and those with higher crowding degree are given priority when the levels are the same; (4) Crossover operation: Simulated binary crossover (SBX) is performed on the selected parent individuals to generate two offspring individuals; (5) Mutation operation: Polynomial mutation is performed on the offspring individuals to introduce random perturbation; (6) Elite retention: The parent and offspring are merged, and non-dominated sorting and crowding degree calculation are performed again to select the top N best individuals to form a new generation of population. Through this iterative update mechanism, the NSGAII algorithm can optimize multiple conflict objectives at the same time and gradually approach the Pareto optimal frontier.

[0177] Introducing a sensitivity matrix as a guide in the population mutation operation of the NSGAII algorithm is an innovative strategy to improve search efficiency. The sensitivity matrix reflects the degree to which the optimization objective function is sensitive to changes in the number of coil turns. It is calculated by numerically estimating the partial derivatives of each objective function with respect to the number of coil turns. Specifically, for each individual i, the sensitivity of the three objective functions to two decision variables is first calculated: Numerical estimation can be performed using the central difference method: Where h is the small step size. The calculated sensitivity matrix... Used to guide mutation operations. After introducing sensitivity, the mutation formula is modified as follows:

[0178]

[0179] Where the weighting factor w T and w R The result is calculated based on the sensitivity matrix. This sensitivity-guided mutation mechanism makes the variable turn length proportional to the sensitivity of the objective function, allowing for a larger-scale exploration in directions of high sensitivity and a smaller-scale fine-tuning in directions of low sensitivity. This method can explore the decision space more effectively, accelerate convergence to the Pareto front, and improve the diversity and uniformity of solution distribution. It is particularly suitable for problems such as coil turn optimization, which involve different sensitivity directions.

[0180] When the algorithm reaches its maximum number of iterations, the final population is non-dominated and sorted, and all solutions in the first front are extracted as the Pareto optimal solution set. These solutions achieve the best trade-off among the three optimization objectives (energy transfer efficiency η, total coil mass m, and offset tolerance T), where improvement in any one objective inevitably leads to the deterioration of at least one other objective. The Pareto optimal solution set typically contains multiple solutions, each corresponding to a different set of coil turns combinations and their performance indices.

[0181] In one embodiment, the drone wireless charging system further includes a coil moving device disposed on the wireless charging platform, as shown in the reference. Figure 8 The coil moving device is a sophisticated mechatronic system designed specifically for wireless charging platforms to achieve precise positioning and dynamic adjustment of the transmitting coil. Figure 8 As can be seen, the device employs a dual-axis Cartesian coordinate mechanism, consisting of a frame structure composed of four lead screws (lead screw 1, lead screw 2, lead screw 3, and lead screw 4) and four push rods (push rod 1, push rod 2, push rod 3, and push rod 4), mounted on the landing plane, with the transmitting coil positioned at the center of the coil moving device. The entire device constitutes an XY plane coordinate system, enabling precise two-dimensional movement of the transmitting coil within the horizontal plane.

[0182] In the coil moving device, the lead screw mechanism is the core transmission component. Lead screws 1 and 3 are located above and below the device, parallel to the X-axis, respectively; lead screws 2 and 4 are located on the left and right sides, parallel to the Y-axis, respectively. These four lead screws are connected to the push rods via high-precision ball screw pairs, converting rotational motion into linear motion. Each lead screw is driven by an independent stepper motor, and its speed and direction are precisely controlled by a microcontroller, thereby achieving precise displacement control of the push rods. The push rod structure forms a movable rectangular frame, with push rods 1 and 3 moving along the Y-axis and push rods 2 and 4 moving along the X-axis. A transmitting coil bracket is installed at the intersection of the four push rods to fix the transmitting coil of the wireless charging system. The push rods are made of lightweight, high-strength aluminum alloy, ensuring structural rigidity while reducing overall weight. The push rods and lead screws are connected by sliders with built-in ball bearings to reduce friction and improve motion accuracy.

[0183] In terms of operation, when the position of the transmitting coil needs to be adjusted, the control system first calculates the required rotation angle of each lead screw based on the target position. Then, the stepper motor drives the lead screw to rotate according to preset parameters, and the rotational motion of the lead screw is converted into the linear motion of the push rod through the ball screw pair. The movement in the X-axis direction is controlled collaboratively by lead screw 1 and lead screw 3, while the movement in the Y-axis direction is controlled collaboratively by lead screw 2 and lead screw 4. Through the precise coordination of the four motors, the transmitting coil can be moved to any position in the plane. The device is also equipped with high-precision position sensors, including photoelectric encoders and limit switches, to monitor the position status of each push rod in real time, forming a closed-loop control system. The microcontroller continuously adjusts the motor output based on the sensor feedback information to ensure the accuracy of the transmitting coil position. In addition, the device integrates an anti-collision protection mechanism; when abnormal resistance is detected, the system will immediately stop moving to prevent mechanical damage. The entire coil moving device is connected to the host computer through a communication interface to receive position adjustment commands and return to the execution state. During the drone charging process, the device can dynamically adjust the position of the transmitting coil according to the actual landing position of the drone to ensure maximum charging efficiency and effectively solve the problem of reduced charging efficiency caused by drone landing deviation.

[0184] Based on the above-described coil moving device, in one embodiment, the wireless charging efficiency optimization method based on data analysis further includes the following steps:

[0185] Extract the target simulation data corresponding to the optimal number of coil turns, and construct a mathematical mapping model between coil inductance data and UAV offset based on the target simulation data;

[0186] Constructing an inverse mapping function for UAV position estimation based on a mathematical mapping model;

[0187] An optimal path planning algorithm is deployed in the coil moving device to enable the coil moving device to generate an anti-offset strategy based on the position estimation result of the inverse mapping function.

[0188] In this embodiment, firstly, the target simulation data corresponding to the optimal coil turns combination obtained from the previous optimization is extracted. After data augmentation, the accuracy of the mathematical mapping model is greatly improved. These data constitute a multidimensional dataset (x i ,y i ,L Ti ,L Ri M i ,k i Z i Q i ), where (x i y i The coordinates () represent the offset coordinates of the UAV. Next, a mathematical mapping model is constructed using methods such as multinomial regression, radial basis function networks, or neural networks. Taking multinomial regression as an example, the following mapping relationship can be established:

[0189] L T (x,y)=a o +a1x+a2y+a3x 2 +a4xy+α5y 2 +...

[0190] L R (x, y) = b o +b1x+b2y+b3x 2 +b4xy+b5y 2 +...

[0191] M(x,y)=co + c1x + c2y + c3x 2 +c4xy+c5y 2 +...

[0192] The coefficients a0~a5, b0~b5, and c0~c5 are determined using the least squares method to minimize the mean square error between the model's predicted values ​​and the simulation data. The resulting mathematical mapping model accurately describes the relationship between the UAV's offset and the coil inductance parameters.

[0193] Next, an inverse mapping function for UAV position estimation is constructed based on a mathematical mapping model. The goal of the inverse mapping function is to infer the actual position coordinates of the UAV from the real-time measured coil inductance parameters. In specific implementation, a high-precision inductance measurement circuit is first integrated into the coil moving device. Using the principle of impedance analyzer, a small signal of known frequency is injected into the transmitting coil, and the voltage and current across the coil are measured simultaneously to calculate the real-time self-inductance, mutual inductance, and induced voltage of the receiving coil. The measurement circuit uses a 16-bit ADC for data acquisition with a sampling rate of no less than 1MHz to ensure a measurement accuracy within 0.1%. Since the inverse mapping relationship is usually difficult to express analytically, a lookup table (LUT) combined with interpolation can be used to achieve this.

[0194] Specifically, the forward mapping model constructed in the above steps is used to calculate the inductance parameter values ​​on a predefined XY plane grid, forming a lookup table. When the measured inductance value is obtained, the best-matching position coordinates are found in the lookup table using bilinear interpolation or higher-order interpolation methods. Another more advanced method uses machine learning techniques, such as Support Vector Regression (SVR) or Deep Neural Networks (DNNs), to directly learn the mapping relationship from inductance parameters to position coordinates. Taking a neural network as an example, a feedforward network containing 2-3 hidden layers (20-50 neurons per layer) can be constructed, with the measured inductance parameters as input and the estimated XY coordinates as output.

[0195] Based on the UAV's position estimation results, the target position that the transmitting coil needs to move to is calculated. Finally, an optimal path is planned and the coil moving device is controlled to execute it. In specific implementation, the system adopts a real-time closed-loop control architecture with a control cycle of 10ms to ensure rapid response to changes in the UAV's position. The path planning algorithm is an improved version of the A* algorithm, taking into account the kinematic constraints and dynamic characteristics of the coil moving device. First, the objective function is defined as: J = w1·d(P c P t )+w2·t m +w3·E c Where d(P) c P t ) represents the Euclidean distance from the current position to the target position, t m E represents the time of travel. cThe values ​​w1, w2, and w3 represent energy consumption and are weighting coefficients that can be dynamically adjusted according to the application scenario. To avoid interference from mechanical vibration during the charging process, path planning also needs to consider acceleration and jerk constraints, employing an S-shaped velocity curve to ensure smooth motion. Specifically, the coil's trajectory uses fifth-order polynomial interpolation. To handle potential continuous drift of the drone, the device also implements a predictive control strategy, predicting the drone's future position trend based on its most recent position estimates and adjusting the transmitting coil position in advance. Once the drone's position is detected to be stable (position change less than the threshold ε, typically set to 2mm), the system enters a fine alignment mode, using a proportional-integral-derivative (PID) controller to fine-tune the transmitting coil position, maximizing the magnetic coupling coefficient k. Throughout the entire anti-drift strategy execution, the device continuously monitors the charging efficiency. When the efficiency reaches a preset threshold (typically 95% of the rated efficiency), alignment is considered successful. The coil movement device based on the anti-drift strategy can increase the charging efficiency from less than 30% to over 90% even when the drone's landing drift reaches 80mm, significantly extending the drone's endurance and improving the overall operational efficiency of the drone system.

[0196] The present invention also provides a wireless charging efficiency optimization system based on data analysis, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the wireless charging efficiency optimization method based on data analysis as described in any of the above embodiments.

[0197] The processor can be a central processing unit (CPU). Of course, depending on the actual use, it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0198] The memory can be an internal storage unit of a computer device, such as a hard disk or RAM, or an external storage device, such as a plug-in hard disk, smart memory card (SMC), secure digital card (SD), or flash memory card (FC) provided on the computer device. Furthermore, the memory can be a combination of internal storage units and external storage devices of a computer device. The memory is used to store computer programs and other programs and data required by the computer device. The memory can also be used to temporarily store data that has been output or will be output. This application does not limit this.

[0199] The present invention also provides a computer-readable storage medium storing instructions that, when executed by a processor, configure the processor to perform the data analysis-based wireless charging efficiency optimization method as described in any of the preceding claims.

[0200] The computer program can be stored in a machine-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file or certain middleware, etc. The machine-readable medium includes any entity or device capable of carrying computer program code, recording medium, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electrical carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the machine-readable medium includes, but is not limited to, the above-mentioned components.

[0201] The transmission line integrated fault detection method in the above embodiments is stored in the computer-readable storage medium and loaded and executed on the processor to facilitate the storage and application of the above method.

[0202] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of protection of this application is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of one or more embodiments of this application as described above, which are not provided in detail for the sake of brevity.

[0203] One or more embodiments in this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments in this application should be included within the protection scope of this application.

Claims

1. A method for optimizing wireless charging efficiency based on data analysis, characterized in that, An application is made to a wireless charging system for unmanned aerial vehicles (UAVs). The UAV wireless charging system includes a transmitting coil disposed on a wireless charging platform and a receiving coil disposed at the bottom of the UAV landing gear. The method includes the following steps: Create a magnetically coupled 3D model that includes a transmitting coil and a receiving coil; Based on the magnetic coupling three-dimensional model and using the finite element simulation analysis method to solve for the maximum coupling coefficient, the optimal size parameters of the transmitting coil and the receiving coil are obtained. The maximum and minimum number of Litz wire turns for the transmitting and receiving coils are calculated based on the optimal size parameters, thus obtaining the range of coil turns. The optimal size parameters and the magnetic coupling three-dimensional model are imported into the simulation software. For each combination of coil turns within the range of coil turns, the magnetic field distribution of the magnetic coupling three-dimensional model under standard magnetic coupling state is simulated by the simulation software. The maximum magnetic induction intensity and the leakage magnetic field intensity at the simulated receiving coil in the magnetic coupling three-dimensional model are calculated based on the magnetic field distribution. The simulation receiving coil is controlled by a preset translation step size to perform step translation to simulate the drone's deviation until the maximum magnetic induction intensity is greater than or equal to the saturation magnetic induction intensity or leakage magnetic intensity of the simulated magnetic core in the magnetic coupling three-dimensional model, which exceeds the preset intensity threshold. After each step translation, the coil inductance data of the magnetically coupled three-dimensional model is calculated, and the displacement value between the simulated receiving coil and the original position is used as the drone offset amount to simulate the drone offset. Determine the decision variables for multi-objective optimization based on the range of coil turns; The optimization objective function is set according to the preset indicators, and the constraint conditions are set according to the physical constraints of coil inductance. The optimization objective function includes maximizing coil energy transmission efficiency, minimizing coil total mass, and maximizing UAV offset tolerance. Based on all decision variables, an initial solution space is constructed using an adaptive grid Latin hypercube sampling method; A simplified solution set is obtained by rapidly searching within the initial solution space using a binary particle swarm optimization method based on magnetic coupling sensing. With the objective function as the optimization objective, under constraints, the simplified solution set is solved by multi-objective optimization using the NSGAII algorithm guided by electromagnetic field sensitivity, and the Pareto optimal solution set is obtained. The comprehensive performance index of each Pareto solution in the Pareto optimal solution set is calculated based on the optimization objective function, and the optimal Pareto solution with the highest comprehensive performance index is analyzed as the optimal number of coil turns. Adjust the transmitting and receiving coils by combining the optimal size parameters and the optimal number of coil turns.

2. The wireless charging efficiency optimization method based on data analysis according to claim 1, characterized in that, The process of solving for the maximum coupling coefficient based on a magnetically coupled three-dimensional model and using finite element simulation analysis to obtain the optimal size parameters of the transmitting and receiving coils includes the following steps: A finite element simulation environment is constructed based on a magnetically coupled three-dimensional model, and the magnetic insulation boundary condition is used as the boundary condition of the finite element simulation environment. A constant frequency AC current excitation is applied to the simulated transmitting coil in the magnetically coupled three-dimensional model. The coil size parameters of the magnetically coupled three-dimensional model are scanned and the simulated coupling coefficient is calculated. A functional relationship model between coil size parameters and simulation coupling coefficients is established using the response surface methodology. Using the maximum coupling coefficient of the magnetically coupled three-dimensional model as the optimization objective, the optimal size parameters of the transmitting and receiving coils are obtained by solving a functional relationship model and using the gradient descent method.

3. The wireless charging efficiency optimization method based on data analysis according to claim 1, characterized in that, The method further includes the following steps: The simulation data is organized into a structured dataset and then normalized. A generative adversarial network model is constructed using a multilayer perceptron and a convolutional neural network. A generative adversarial network (GAN) model is trained by combining the coil turns range, optimal size parameters, and a normalized structured dataset. The trained GAN model then outputs enhanced simulation data. The enhanced simulation data is filtered using a preset physical verification function, and the filtered enhanced simulation data is then merged into the simulation data.

4. The wireless charging efficiency optimization method based on data analysis according to claim 1, characterized in that, The construction of the initial solution space based on all decision variables using the adaptive grid Latin hypercube sampling method includes the following steps: A non-uniform decision space grid is constructed based on all decision variables and the optimal turns ratio relationship predicted by electromagnetic field theory. Pre-defined prior knowledge of electromagnetic coupling degree is introduced into a non-uniform decision space grid to sample samples and obtain an initial sample set; The target sample set is obtained by minimizing the correlation of all initial sample points in the initial sample set. The optimization objective function value of all target sample points in the target sample set is calculated to form the initial solution space.

5. The wireless charging efficiency optimization method based on data analysis according to claim 1, characterized in that, The method of using magnetically coupled sensing-based binary particle swarm optimization to quickly search within the initial solution space and obtain a simplified solution set includes the following steps: Encode all initial solutions in the initial solution space into binary bit strings; Initialize the particle swarm optimization algorithm parameters in a binary bit string; The fitness of the initial particles in the initial particle swarm is calculated by combining the optimization objective function and the magnetic coupling coefficient corresponding to the coil turns combination. The velocity and position of all particles are updated iteratively based on fitness. During the position update of all particles, a mutation probability is added to each particle. The mutation probability is linearly related to the magnetic coupling coefficient of the particle's current position. When the number of iterations reaches the preset maximum number of iterations, the iteration update stops, and the particles in the global optimal position and their corresponding fitness values ​​are used as the simplified solution set.

6. The wireless charging efficiency optimization method based on data analysis according to claim 1, characterized in that, The process of optimizing the simplified solution set using the NSGAII algorithm guided by electromagnetic field sensitivity under constraints, with the objective function as the optimization goal, to obtain the Pareto optimal solution set includes the following steps: Use the simplified solution set as the initial population for the NSGAII algorithm; After initializing the algorithm parameters of the NSGAII algorithm, the NSGAII algorithm process is executed iteratively to update the population under constraints, with the objective function as the optimization target. In the population mutation operation of the NSGAII algorithm, the sensitivity matrix of the optimization objective function to the number of coil turns is calculated, and the sensitivity matrix is ​​used to guide the population mutation. After iteratively updating the population using the NSGAII algorithm, the first frontier in the final population is output as the Pareto optimal solution set.

7. A wireless charging efficiency optimization system based on data analysis, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the wireless charging efficiency optimization method based on data analysis as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing instructions thereon, characterized in that, When executed by a processor, this instruction causes the processor to be configured to perform the wireless charging efficiency optimization method based on data analysis according to any one of claims 1 to 6.

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