A wireless power transmission mutual inductance online identification method based on PINN and nonlinear load compensation

Abstract

This invention relates to an online identification method for wireless power transfer mutual inductance based on PINN and nonlinear load compensation, belonging to the field of parameter identification for wireless power transfer systems. It includes: acquiring time-domain waveform data of the WPT system; calculating the true equivalent load resistance, including harmonics and diode voltage drop, offline based on an accurate nonlinear model; embedding this true equivalent resistance as a deterministic physical constraint into the system's time-domain ordinary differential equations to construct a differentiable forward physical model; reconstructing the theoretical waveform using this physical model and establishing a loss function to drive a one-dimensional convolutional neural network for self-supervised offline training; and using the trained network to instantly output high-precision mutual inductance parameters through pure forward computation. This invention solves the problem of equivalent model distortion under waveform distortion and light load conditions in traditional methods, overcomes the limitations of long online iterative optimization time and poor physical generalization of pure black-box neural networks, and improves the speed and accuracy of parameter identification.

Description

Technical Field

[0001] This invention belongs to the field of parameter identification of wireless power transmission systems, and relates to an online identification method for wireless power transmission mutual inductance based on physical information neural network (PINN) and nonlinear load compensation. Background Technology

[0002] In wireless power transfer (WPT) systems, mutual inductance M and load R are the core parameters determining system transmission efficiency optimization, output power regulation, and soft-switching control. In real-world dynamic charging scenarios (such as wireless charging for electric vehicles and powering mobile robots), the parameters of WPT systems exhibit strong time-varying characteristics due to the continuous shift in the relative positions of the coils and the dynamic changes in the battery's equivalent load. Therefore, achieving real-time, accurate online identification of key parameters is crucial for the closed-loop stable control of the system.

[0003] Currently, the mainstream methods for parameter identification in WPT systems mainly include frequency domain analytical methods based on fundamental frequency approximation, iterative optimization methods based on time domain models, and purely data-driven machine learning methods. However, these methods all face insurmountable limitations in practical engineering applications. Traditional mechanistic modeling and frequency domain analytical methods are typically based on the fundamental approximation principle of Fourier analysis, equating the nonlinear sub-circuit containing the rectifier bridge and filter capacitor to a purely linear resistor. However, this simplified analytical method relies on the strict assumption that the rectifier bridge is in continuous conduction mode (CCM) and the input current is a perfect sine wave. In actual operation, when the system is under light load, the rectifier bridge is prone to entering discontinuous conduction mode (DCM). Simultaneously, due to hardware non-ideal factors such as inverter dead time, parasitic capacitance of power switches, and nonlinear forward voltage drop of diodes, the secondary voltage and current inevitably experience severe distortion. At this point, higher harmonics and harmonic phase shifts significantly participate in the energy transfer process. If the traditional linear equivalent formula is continued, huge amplitude and phase errors will occur, leading to a significant deviation in the final identified mutual inductance result.

[0004] To correct the aforementioned nonlinear errors, some scholars have proposed high-order analytical models that incorporate harmonic compensation and parasitic parameter correction. While these models theoretically improve accuracy, implementing online identification requires the controller to perform a Fast Fourier Transform (FFT) on the acquired waveform in real time to extract the amplitude and phase difference of each harmonic, followed by inverse calculations using extremely complex algebraic equations. This not only significantly increases the computational burden on the underlying hardware (such as FPGAs or DSPs), making millisecond-level real-time control difficult to achieve, but also heavily relies on ideal measurement conditions and is highly susceptible to interference from high-frequency electromagnetic noise in actual industrial environments.

[0005] Secondly, parameter identification methods based on time-domain state-space models (such as modern heuristic algorithms like genetic algorithms and particle swarm optimization) can handle complex nonlinear ordinary differential equations (ODEs). These methods do not require frequency-domain approximation, but they essentially rely on online iterative solutions to approximate the true parameters. The extremely high online computational complexity means that a single identification process typically takes several seconds or even minutes, which is completely unacceptable for the real-time tracking requirements of dynamic WPT systems.

[0006] On the other hand, while traditional data-driven neural network methods that have emerged in recent years have achieved extremely fast online inference, they treat the WPT system as a complete "black box." The training of such models relies excessively on pre-labeled, large-scale datasets with precise physical labels, while accurately measuring the real mutual inductance and equivalent load under dynamic conditions in the real world is extremely difficult and costly. More fatally, pure black-box models, detached from the constraints of the underlying physical mechanisms, have extremely poor generalization ability when faced with the difference between simulation data and real hardware physics (Sim-to-Real Gap), and are prone to outputting invalid solutions that completely violate the fundamental physical laws of electromagnetism under unexpected operating conditions (e.g., producing negative mutual inductance values ​​or divergent prediction results).

[0007] In summary, existing WPT system parameter identification technologies struggle to achieve a balance between "extremely high accuracy under non-ideal operating conditions," "millisecond-level real-time performance on the underlying hardware," and "strong consistency with physical laws." Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide an online identification method for wireless power transmission mutual inductance based on PINN and nonlinear load compensation, which aims to solve the problem of equivalent model distortion under light load and waveform distortion in traditional analytical methods, while overcoming the limitations of online iterative solution computational bottleneck and poor physical consistency of pure black box neural networks.

[0009] To achieve the above objectives, the present invention provides the following technical solution: An online identification method for wireless power transfer mutual inductance based on PINN and nonlinear load compensation, the method comprising: Collect multi-channel time-domain waveform data of a wireless power transmission system under different operating conditions to construct a training dataset; In offline mode, based on the accurate nonlinear modeling method, harmonic analysis and feature extraction are performed on the sampled waveform to calculate the true equivalent load resistance including harmonic compensation and diode voltage drop compensation. A one-dimensional convolutional neural network is constructed, and the real equivalent load resistance calculated offline is used as a known physical constraint to be implanted into the time-domain ordinary differential equation of the WPT system. A differentiable forward physical model is constructed, and the theoretical waveform is reconstructed using the physical model and a loss function is established to drive the one-dimensional convolutional neural network to perform self-supervised offline training. A lightweight one-dimensional convolutional neural network with trained and fixed weights is deployed to an embedded hardware platform. Pure forward inference is performed directly using real-time sampled time-domain waveforms to achieve online, fast, and high-precision mutual inductance identification.

[0010] Furthermore, the acquired multi-channel time-domain waveform data is preprocessed to form a training dataset. The preprocessing includes: Perform median filtering and Criterion-based anomaly detection removes isolated spikes from waveform data; A fourth-order Butterworth low-pass filter is used to smooth the cleaned data sequence; A software phase detection and timestamp alignment compensation algorithm based on zero-crossing detection is used to eliminate static channel delay caused by hardware traces of data acquisition sensors. Long waveform sequences are sliced ​​using a dynamic sliding window truncation mechanism, and discrete sampling is performed within a single sliding window to construct an initial matrix for four-channel time-domain waveform observation. Normalization is performed on each row vector in the initial matrix of the four-channel time-domain waveform observation, so that all voltage and current input features are stretched and mapped to... The dimensionless interval is used to obtain the standardized waveform input matrix.

[0011] Furthermore, the true equivalent load resistance is obtained in the following way: In offline mode, the measured secondary current is expanded using FFT series:

[0012] in, The fundamental angular frequency; For the first The amplitude of the second harmonic; For the first Phase difference of the subharmonic relative to the fundamental frequency The highest harmonic order; Considering the nonlinear behavior of the rectifier bridge, the rectifier input voltage is expressed as a function of the output DC voltage. Diode equivalent forward voltage drop The relationship for determining:

[0013] in, It is a symbolic function; Will Perform a Fourier expansion and substitute the active power into the secondary side. In the calculation formula, the power transmission of the fundamental frequency and higher harmonics is combined:

[0014] in, For the system fundamental frequency operating period, This represents the fundamental amplitude of the secondary current. The harmonic distortion compensation coefficient is defined as follows: ; According to the law of conservation of energy, the active power input to the rectifier bridge is equal to the sum of the power consumed by the load and the diode losses:

[0015] in, For diode losses, This represents the true equivalent load resistance. Combining the above equations and eliminating intermediate variables, we obtain the true equivalent load resistance, which includes hardware non-ideal factors. The expression is: .

[0016] Furthermore, the constructed one-dimensional convolutional neural network includes: The network input layer takes a standardized waveform input matrix as input. The multi-scale feature extraction layer employs at least three cascaded one-dimensional convolutional modules with different kernel sizes. The convolutional module with a larger kernel size is used to initially extract the fundamental energy flow features and macroscopic phase delay across multiple sampling periods. The convolutional module with a medium kernel size is used to capture the local waveform distortion features caused by dead time and non-ideal switching characteristics of the inverter. The convolutional module with a smaller kernel size is used to extract higher-order harmonic features and the small waveform fluctuation patterns caused by parameter changes. The global feature fusion and fully connected layer flatten and reshapes the multi-dimensional feature map output by the multi-scale feature extraction layer into a one-dimensional feature vector, and then outputs the dimensionless predicted value of the mutual inductance parameter through the fully connected layer. The physical boundary mapping activation layer introduces a physical boundary mapping mechanism that combines the hyperbolic tangent function, which limits the final predicted mutual inductance to the theoretical physical limit.

[0017] The multi-scale feature extraction layer includes a cascaded first convolutional module, a second convolutional module, and a third convolutional module; the first convolutional module uses a large-sized convolutional kernel, the second convolutional module uses a medium-sized convolutional kernel, and the third convolutional module uses a small-sized convolutional kernel.

[0018] Furthermore, the loss function can be constructed by: based on the KCL and KVL laws, constructing a set of time-domain differential equations for a single-input single-output (SS) topology wireless power transfer system.

[0019] in, The primary-side parasitic resistance, For secondary-side parasitic resistance, This is the voltage across the primary-side compensation capacitor. This is the voltage across the secondary-side compensation capacitor; Introducing the differential relationship of capacitance and And define a continuous-time state vector. , It is the primary-side capacitor. It is the secondary capacitor; Let the inductively coupled determinant The time-domain differential equations are inverted and simplified algebraically to reconstruct the standard state-space equations. The system matrix and input matrix Specifically, it can be elaborated as follows:

[0020] The actual equivalent load resistance As a matrix of known physical constraints ; Using a differentiable ordinary differential equation solver to measure voltage As input, for the state-space equation Perform numerical integration to obtain the network prediction variables. Theoretical simulation of current trajectory and ; Construct the mean square error loss function for the fused time-domain waveforms:

[0021] in, This represents the total number of discrete sampling points within a single observation time window. This is the actual measured current on the primary side. For the actual measured current on the secondary side, The weighting coefficient is used to balance the errors in the primary and secondary currents.

[0022] Furthermore, through the loss function The constructed one-dimensional convolutional neural network is trained offline with self-supervised instruction. During the training phase, the Adam optimizer is used to optimize the set of trainable weights and biases of the network. Iterative updates are performed, and a cosine annealing learning rate decay strategy is used during training.

[0023] Furthermore, the lightweight one-dimensional convolutional neural network, with its trained and weighted components fixed, is deployed on an embedded hardware platform. During online real-time operation, the control system performs a single pure forward inference step to obtain the mutual inductance prediction value. ,in, The standardized waveform input matrix is ​​constructed during online operation. This represents the optimal set of parameters for a one-dimensional convolutional neural network. It is a one-dimensional convolutional neural network.

[0024] The beneficial effects of this invention are as follows: This invention constructs an online identification strategy for wireless power transmission mutual inductance that features "complex offline constraints and ultra-fast online inference." Utilizing the unrestricted computing power in the offline phase, it corrects the theoretical errors caused by the traditional first-order harmonic approximation through an accurate nonlinear model. Furthermore, in self-supervised training, this complex compensation logic is integrated into the weight matrix of the neural network, enabling the neural network to evolve and solidify its accurate identification capability for mutual inductance. In the deployment phase, this invention eliminates the computational burden of online frequency domain analysis and equation solving, stripping away the computationally intensive components such as the ODE solver, FFT analysis module, and nonlinear calculations. This allows the neural network to maintain extremely high identification accuracy under non-ideal operating conditions (light load, distortion, parasitic parameters) and meet the microsecond-level real-time control requirements of underlying hardware such as FPGAs / DSPs.

[0025] This invention effectively solves the problem of equivalent model distortion under waveform distortion and light load conditions in traditional analytical methods. At the same time, it overcomes the limitations of long time consumption of traditional online iterative optimization and poor physical generalization of pure black box neural networks, and significantly improves the speed, accuracy and robustness of parameter identification.

[0026] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0027] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 A schematic flowchart of an online identification method for wireless power transfer mutual inductance based on PINN and nonlinear load compensation provided in an embodiment of the present invention; Figure 2 A schematic diagram of a single-input single-output (SS) topology wireless power transfer system. Figure 3 This is a schematic diagram of the equivalent circuit of a wireless power transmission system. Detailed Implementation

[0028] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0029] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0030] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0031] An embodiment of the present invention provides an online identification method for wireless power transfer mutual inductance based on PINN and nonlinear load compensation, which mainly includes: Data acquisition and feature mapping based on multi-channel waveforms: Collect multi-channel time-domain waveform data of the main and secondary sides of the WPT system under different operating conditions, and construct a training dataset.

[0032] Offline precise nonlinear modeling to construct absolute physical constraints: In the offline data preparation phase, an accurate true equivalent load resistance is calculated using a precise nonlinear model (including diode voltage drop compensation and harmonic phase angle compensation). As the "perfect physics mentor".

[0033] Introducing hard physical boundaries and self-supervised end-to-end training: Setting mutual inductance values ​​for network output The physical hard boundary. and The current trajectory is reconstructed by substituting it into a differentiable ODE solver, with MSE as the physical loss function. This forces the network to autonomously learn and absorb the compensation rules for nonlinear distortions during backpropagation.

[0034] Online ultra-fast inference that abandons complex calculations: The lightweight network with fixed weights is deployed to hardware. When running online, it does not need to perform time-consuming FFT, harmonic calculation or ODE iteration. It relies on pure forward propagation to quickly output high-precision mutual inductance identification values.

[0035] Please see Figure 1 The method is as follows: 1. Build a physical platform or high-fidelity simulation model for the WPT system, and acquire and process multi-channel time-domain waveform data matrices.

[0036] To fully cover the time-varying dynamic characteristics of the WPT system and ensure the strong generalization ability of the offline training dataset, this embodiment employs rigorous engineering design for multi-channel waveform data acquisition, digital filtering and noise reduction, outlier removal, and sliding window truncation mechanisms. The specific data preprocessing and anomaly handling procedures are as follows: (1) Offline full-condition dataset construction strategy: The WPT system faces complex non-ideal factors in actual operation. In order to enable 1D-CNN to fully absorb these physical features in unsupervised learning, multi-dimensional parameter scanning is performed through a high-fidelity physical simulation platform or an automated physical test bench during the offline data acquisition stage.

[0037] Specifically, for the mutual inductance M, the simulation of the receiving coil's translational displacement along the X and Y axes (e.g., displacement distance ranging from 0 mm to 200 mm) and the air gap change along the Z axis is used to obtain the distribution of... to Mutual inductance sample label fields between; for load resistors Simulates the full-cycle impedance change of a power battery as it transitions from constant current charging (CC) to constant voltage charging (CV) (e.g., the load changes from constant current charging (CC) to constant voltage charging (CV)). Dynamic jump to In addition, to enhance the network's noise immunity, a signal-to-noise ratio (SNR) of [value missing] is artificially injected into the acquired raw waveform. Gaussian white noise is used to simulate electromagnetic interference (EMI) generated by hard switching of inverters in industrial settings.

[0038] (2) Sensor sampling and hardware outlier removal: such as Figure 2The single-input single-output (SS) topology wireless power transfer system shown uses a TMS320F28335 DSP or a Xilinx Zynq series FPGA as the control core. It utilizes a high-frequency Hall current sensor and an isolated voltage probe, along with an on-chip or external high-speed analog-to-digital converter (ADC) on the main control chip, configured with a sampling rate of [missing information]. The ADC simultaneously acquires the voltage and current sequences of the primary and secondary sides. In strong electromagnetic environments, ADC sampling is susceptible to spike pulse interference, producing abnormal "glitch" data that far exceeds physical limits (such as 0xFFFF or 0x0000 output from register overflow).

[0039] Therefore, in this embodiment, median filtering is first performed before the data is sent to the buffer pool. Criterion anomaly detection. Let the value of the current sampling point be... ,like (in and If the mean and standard deviation of the data within the preceding time window are respectively, then the point is determined to be a hardware pulse anomaly point. The linear interpolation of the two normal sampling points before and after it is used to replace the anomaly value, thereby completing the hardware-level data cleaning without destroying the timing phase.

[0040] (3) Digital Low-Pass Filtering and Phase Alignment: After removing isolated glitches, although higher harmonics are crucial for the derivation of nonlinear loads, excessively high-frequency broadband white noise can severely affect the network's ability to capture the fundamental phase. Therefore, this embodiment uses a fourth-order Butterworth low-pass filter to smooth the cleaned data sequence. Preferably, the cut-off frequency of this digital filter is set to the system switching frequency. of To ensure that while filtering out sensor noise floor, the first 15 core harmonic characteristics, which play a decisive role in system energy transfer, are preserved, this embodiment employs a software phase detection and timestamp alignment compensation algorithm based on zero-crossing detection. This eliminates the static channel delay caused by hardware traces, ensuring absolute synchronization between the primary and secondary waveforms on the same nanosecond time scale.

[0041] (4) Dynamic Sliding Window Segmentation Mechanism: The high-frequency AC waveform of the WPT system is a continuous, infinitely long sequence, while the 1D-CNN network requires tensor inputs of fixed dimensions. This embodiment uses a dynamic sliding window technique with overlap rate to slice the long sequence. Let the system cycle time be... Time window length The window size is set to include 3-5 complete switching cycles to ensure the network can extract complete steady-state waveform periodic features. For the offline training set, the sliding window step size is set to... (i.e., overlap rate) This overlapping sliding window slicing not only achieves data augmentation, increasing the number of effective training samples, but also endows the network with translation invariance. Furthermore, during the online inference phase, to reduce processor load, the sliding step size is set to... (Non-overlapping) enables real-time, uninterrupted streaming inference. Through the aforementioned sliding window slicing, continuous long-sequence waveforms are divided into multiple independent time windows, thus forming a training dataset containing a large number of samples. For any independent sliding window in this dataset, the number of discrete sampling points within a single window is set to... (For example This sample is used as an input sample for a single forward inference pass of the 1D-CNN network, thereby constructing the initial matrix of a four-channel temporal waveform observation for a single sample. , represented as: (1) in, This represents the instantaneous value of the primary voltage at the Nth discrete sampling moment within the current time window. This represents the instantaneous value of the primary current at the Nth discrete sampling moment within the current time window. This represents the instantaneous value of the secondary voltage at the Nth discrete sampling moment within the current time window. This represents the instantaneous value of the secondary voltage at the Nth discrete sampling moment within the current time window.

[0042] (5) Independent Channel-wise Min-Max Normalization: In WPT systems, the primary-side inverter voltage amplitude can reach hundreds of volts (e.g., The current amplitude is typically in the tens of amperes (e.g., 15 A). If unscaled absolute values ​​are directly fed into the neural network, the voltage characteristics will dominate the gradient calculation during backpropagation, leading to vanishing gradients or difficulty in network convergence. Therefore, this embodiment focuses on the matrix... The maximum and minimum value normalization process is applied based on channel independence. For each row vector in the four channels... (The length representing a certain physical quantity is) The normalization operation for the time series is as follows: (2) in, This represents the original measurement value of the current channel at the k-th discrete sampling time. This represents the maximum observed value of the current channel within the entire time window. This represents the minimum observed value of the current channel within the entire time window.

[0043] Through equation (2), all voltage and current input characteristics are strictly stretched and mapped to... Dimensionless interval. This operation not only completely eliminates the numerical magnitude gap caused by different physical dimensions, but also significantly improves the physical information loss function during the self-supervised training phase. The stability of error backpropagation is used to obtain a high-quality normalized waveform input matrix that is finally fed into subsequent network layers. .

[0044] 2. Based on discrete-time observation data, the true equivalent load resistance is calculated using Fast Fourier Transform (FFT) and an accurate nonlinear compensation model.

[0045] The traditional first-order harmonic approximation (FHA) treats the rectifier bridge as a pure resistor. However, it ignores higher harmonics and diode voltage drop, which will introduce theoretical errors under light load and distortion conditions.

[0046] In this embodiment, the accurate nonlinear compensation model is derived offline: First, the measured current on the secondary side... Perform a Fast Fourier Transform (FFT) series expansion: (3) in: This is the system's fundamental angular frequency; For the first The amplitude of the second harmonic; For the first The phase difference between the subharmonic and the fundamental frequency. This is the highest harmonic order.

[0047] Considering the nonlinear behavior of the rectifier bridge, the rectifier input voltage It can be generated by the output DC voltage Equivalent forward voltage drop of diode Decide: (4) Will Perform a Fourier expansion and substitute the active power into the secondary side. In the calculation formula, the power transmission of the fundamental frequency and higher harmonics is combined: (5) in, The operating period of the system's fundamental frequency. This represents the fundamental amplitude of the measured secondary current.

[0048] The harmonic distortion compensation coefficient is defined as follows: .

[0049] Meanwhile, according to the law of conservation of energy, the active power input to the rectifier bridge is equal to the sum of the power consumed by the load and the diode losses: (6) in, This refers to the equivalent forward conduction loss of the diodes in the secondary-side full-bridge rectifier. This is the actual equivalent load resistance.

[0050] By combining equations (5) and (6) and eliminating intermediate variables, the true equivalent load resistance, which includes hardware non-ideal factors, can be derived. The expression: (7) True equivalent load resistance This will serve as a physical constraint constant in subsequent PINN training, eliminating the pressure of multi-parameter coupled prediction in the network.

[0051] 3. Construct a one-dimensional convolutional neural network (1D-CNN), using the offline calculated real equivalent load resistance as a known physical constraint to be implanted into the time-domain ordinary differential equation of the WPT system, construct a differentiable forward physical model, use this physical model to reconstruct the theoretical waveform and establish a loss function, and drive the one-dimensional convolutional neural network to perform self-supervised offline training.

[0052] This paper designs a self-supervised neural network training framework driven by physical equations. To accurately extract phase difference and amplitude attenuation features from high-frequency time-domain waveforms containing severe distortion and nonlinear noise, this embodiment constructs a lightweight 1D-CNN with multi-scale receptive fields. The specific topology and signal forward propagation process include the following cascaded layers: network input layer, multi-scale feature extraction layer, global feature fusion and fully connected layer, and physical boundary mapping activation layer. The signal forward propagation process is designed as follows: (1) Network Input Layer: The network input is the time-domain waveform matrix obtained in step 1 and normalized. Let the number of sampling points within the time window be... (For example If the input tensor has a dimension of , then the dimension of the input tensor is . These correspond to four independent one-dimensional time series channels: primary side voltage, primary side current, secondary side voltage, and secondary side current.

[0053] (2) Multi-scale Convolutional Layers: In order to take into account both the macroscopic fundamental wave trend and the microscopic high-frequency distortion features of the waveform, the network contains at least three cascaded one-dimensional convolutional modules (Conv1DBlock).

[0054] The first convolutional module uses a relatively large kernel (e.g., kernel size = 7 or 9) with a stride of 2. The large kernel acts like a low-pass filter, initially extracting fundamental energy flow features and macroscopic phase delays across multiple sampling periods. The output channel count (Filters) is set to 16, and the extracted feature map dimensions are downsampled to... After downsampling, a batch normalization (BN) layer is applied to accelerate convergence, and the Leaky ReLU activation function (with the negative half-axis slope set to 0.01) is used to avoid neuron death.

[0055] The second convolutional module uses a medium-sized convolutional kernel (e.g., Kernel Size = 5) with a stride of 1. This second convolutional module aims to capture local waveform distortion features caused by dead time and non-ideal switching characteristics of the inverter. The number of output channels is increased to 32, and further dimensionality reduction is achieved through a max pooling layer (Max Pooling 1D, pooling window size of 2) to preserve the most significant distortion peak features.

[0056] The third convolutional module uses small-sized convolutional kernels (e.g., Kernel Size = 2) and sets the number of output channels to 64. These small kernels focus on extracting higher-order harmonic features and the subtle waveform fluctuations caused by parameter variations. The third convolutional module also includes Batch Normalization (BN) layers, Leaky ReLU activation functions, and max-pooling layers, ultimately outputting a highly abstract temporal feature map.

[0057] (3) Global feature fusion and fully connected layers (Flatten & Dense Layers): After the above multi-layer convolution and pooling operations, the multi-dimensional feature map is input into the flatten layer to reshape it into a one-dimensional feature vector.

[0058] Then connect the two fully connected layers (Fully Connected Layer / Dense Layer): Hidden fully connected layer: Contains 128 neurons and uses the ReLU activation function. To prevent overfitting during offline training and improve the model's generalization ability under unseen conditions, a random dropout layer is introduced after this layer, with a dropout rate set to 0.3~0.5.

[0059] Output fully connected layer: This layer contains only one neuron node and is used to output the dimensionless predicted value of the mutual inductance parameter.

[0060] (4) Physical Boundary Mapping Activation Layer: Traditional pure data-driven networks, lacking physical constraints, are prone to outputting negative mutual inductances or invalid values ​​exceeding theoretical limits under extreme conditions. Therefore, this embodiment abandons conventional linear activation at the network's final output and introduces a layer combining the hyperbolic tangent function (…). The physical boundary mapping mechanism of the above 1D-CNN network. Let the set of all trainable weights and biases of the above 1D-CNN network be denoted as . And the scalar output result of the forward computation of the fully connected layer is Then the final prediction of mutual inductance The mathematical expression is: (8) in, For the original side to feel, For the secondary side's self-perception.

[0061] because The range of the value is strictly limited to (-1, 1), and equation (8) mathematically guarantees the mutual inductance value of the network output. Always safely clamped in The theoretical physical limit (i.e., coupling coefficient) Within the extreme operating conditions, the physical consistency and system safety of the model in practical applications are enhanced.

[0062] (5) Hyperparameter configuration and offline training strategy: In the self-supervised offline training phase, the Adam (Adaptive Moment Estimation) optimizer is used to optimize all trainable weights and biases of the above 1D-CNN network. Perform iterative updates. Initial learning rate (Learning Rate, The learning rate was set to 0.001, and a cosine annealing (LR) learning rate decay strategy was used to ensure that the network could converge precisely near the minimum value in the later stages of training. The batch size was set to 64 or 128, and the maximum number of epochs was set to 500-1000. Through the above-mentioned refined network structure and hyperparameter scheduling, the network's efficient learning and accurate fitting of mutual intuition features were guaranteed.

[0063] Secondly, based on Kirchhoff's voltage and current laws (KVL / KCL), a set of differential equations for the SS topology system in the time domain is constructed: (9) in, The primary-side parasitic resistance, For secondary-side parasitic resistance, Let be the instantaneous voltage of the primary-side compensation capacitor at time t. Let be the instantaneous voltage of the secondary-side compensation capacitor at time t.

[0064] Introducing the differential relationship of capacitance and And define a continuous-time state vector. , It is the primary-side capacitor. This is the secondary capacitor.

[0065] Let the inductively coupled determinant By performing matrix inversion and algebraic simplification on equation (9), it can be rigorously reconstructed into the standard state-space equation. The system matrix and input matrix Specifically, it can be elaborated as follows: (10) In equation (10), the result calculated from equation (7) As a deterministic constant forced implantation matrix The voltage was measured using a differentiable ordinary differential equation solver (ODE Solver). As input, for the state-space equation Perform numerical integration to obtain the network prediction variables. Theoretical simulation of current trajectory and .

[0066] Finally, the mean square error (MSE) loss function for the fused time-domain waveforms is constructed: (11) in, This represents the total number of discrete sampling points within a single observation time window. This is the actual measured current on the primary side. For the actual measured current on the secondary side, These are weighting coefficients used to balance the errors in the primary and secondary currents.

[0067] Calculate the gradient using the Adam optimization algorithm. The network is then updated via backpropagation. To ensure the simulated waveform closely approximates the measured waveform, the network must adjust its hidden layer weights. The system automatically evolves and solidifies its ability to accurately identify mutual inductance.

[0068] 4. Extract the optimal network model and solidify the weights, then deploy it to an embedded underlying hardware platform to achieve ultra-fast forward inference online without iteration or frequency domain analysis.

[0069] Once the loss function converges and the model training is complete, the massive ODE solver, FFT analysis module, and nonlinear calculation formulas (3) to (7) required for offline processing are removed.

[0070] Extracting and solidifying the optimal weights Lightweight 1D-CNN models can be deployed on digital signal processors (DSPs) or field-programmable gate arrays (FPGAs).

[0071] During online real-time operation, the control system only needs to perform one pure forward inference step: (12) This process reduces the large number of matrix inversions and numerical integration operations required by traditional online iterative optimization to deterministic neural network multiply-accumulate operations (MACs), completely eliminating the computational bottleneck and achieving high-precision mutual inductance identification at the millisecond level.

[0072] The complete algorithm flow of the method described in this embodiment is as follows: Input information: Offline sampling dataset: Includes DC-side output voltage and current ; WPT system hardware constants: primary and secondary side self-inductance , ,capacitance , parasitic resistance , ; Neural network hyperparameters: learning rate Maximum number of iterations Batch size Loss function weight coefficients , .

[0073] Output information: The optimal network weights after training: ; Real-time online mutual sensing identification results: .

[0074] Phase 1: Offline Data Preprocessing and Physical Constraint Calculation Calculate the actual load using DC-side data: ; For secondary current Perform FFT to extract the fundamental amplitude. Amplitude of each harmonic and phase difference

[0075] Calculate the harmonic distortion compensation coefficient: ; Calculate the equivalent voltage drop of a diode And calculate the true nonlinear equivalent resistance:

[0076] Construct the observation waveform matrix And after normalization, we obtain .

[0077] Phase Two: Self-Supervised Training of Physical Information Neural Network (PINN) initialization: Randomly initialize 1D-CNN network weights ; Set the initial number of iterations ; for to do: From normalized datasets Extract a batch of data ; Step 1: Network Forward Inference Using 1D-CNN to extract waveform features and apply physical boundary constraints, the predicted mutual inductance is output:

[0078] Step 2: Solving the forward physics model Will With deterministic constants Substitute the coefficient matrix into the system state-space equations and middle:

[0079] Call the differentiable ODE solver to To drive the input, calculate the current Theoretical simulation current and ; Step 3: Calculate the physical information loss function

[0080] Step 4: Backpropagation and Weight Update The Adam optimization algorithm is used to calculate gradients and update network weights:

[0081] end Output the fixed optimal network weights .

[0082] Phase 3: Online Real-Time High-Speed ​​Identification (Deployed on FPGA / DSP) initialization: Loading optimal network weights Down to the underlying controller.

[0083] while the system runs do Collect and normalize multi-channel waveforms within the latest time window to form a real-time input matrix.

[0084] Perform pure forward multiplication and addition operations to quickly output high-precision mutual inductance identification values:

[0085] Will The signal is sent to the closed-loop controller for soft switching frequency or phase shift angle adjustment.

[0086] end Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A wireless power transfer mutual inductance online identification method based on PINN and nonlinear load compensation, characterized in that: Collect multi-channel time-domain waveform data of a wireless power transmission system under different operating conditions to construct a training dataset; In offline mode, based on the accurate nonlinear modeling method, harmonic analysis and feature extraction are performed on the sampled waveform to calculate the true equivalent load resistance including harmonic compensation and diode voltage drop compensation. A one-dimensional convolutional neural network is constructed, and the real equivalent load resistance calculated offline is used as a known physical constraint to be implanted into the time-domain ordinary differential equation of the WPT system. A differentiable forward physical model is constructed, and the theoretical waveform is reconstructed using the physical model and a loss function is established to drive the one-dimensional convolutional neural network to perform self-supervised offline training. A lightweight one-dimensional convolutional neural network with trained and fixed weights is deployed to an embedded hardware platform. Pure forward inference is performed directly using real-time sampled time-domain waveforms to achieve online, fast, and high-precision mutual inductance identification.

2. The method of claim 1, wherein: The acquired multi-channel time-domain waveform data is preprocessed to form a training dataset. The preprocessing includes: performing median filtering and criteria anomaly detection, rejecting isolated glitches from the waveform data; A fourth-order Butterworth low-pass filter is used to smooth the cleaned data sequence; A software phase detection and timestamp alignment compensation algorithm based on zero-crossing detection is used to eliminate static channel delay caused by hardware traces of data acquisition sensors. Long waveform sequences are sliced ​​using a dynamic sliding window truncation mechanism, and discrete sampling is performed within a single sliding window to construct an initial matrix for four-channel time-domain waveform observation. Each row vector in the four-channel time-domain waveform observation initial matrix is normalized, so that all voltage and current input characteristics are stretched and mapped to the dimensionless interval of to obtain a normalized waveform input matrix.

3. The method of claim 2, wherein: The true equivalent load resistance is obtained as follows: In offline mode, the measured secondary current is expanded using FFT series: in, The fundamental angular frequency; For the first The amplitude of the second harmonic; For the first Phase difference of the subharmonic relative to the fundamental frequency The highest harmonic order; Considering the non-linear behavior of the rectifier bridge, the rectifier input voltage is expressed as a function of the output DC voltage , the diode equivalent forward conduction voltage drop , the determined relationship: wherein is a sign function; The Fourier expansion is performed and substituted into the calculation of the secondary side input active power power transmission of the fundamental wave and the high-order harmonic wave: wherein, is the system fundamental operating period, is the fundamental amplitude of the secondary current; The harmonic distortion compensation coefficient is defined as: ; According to the law of conservation of energy, the active power input to the rectifier bridge is equal to the sum of the power consumed by the load and the diode losses: wherein is the diode loss, is the real equivalent load resistance; By combining the above equations and eliminating the intermediate variables, the expression of the real equivalent load resistance including the hardware non-ideal factors is obtained The expression is: .

4. The method of claim 3, wherein, The constructed one-dimensional convolutional neural network includes: The network input layer takes a standardized waveform input matrix as input. The multi-scale feature extraction layer employs at least three cascaded one-dimensional convolutional modules with different kernel sizes. The convolutional module with a larger kernel size is used to initially extract the fundamental energy flow features and macroscopic phase delay across multiple sampling periods. The convolutional module with a medium kernel size is used to capture the local waveform distortion features caused by dead time and non-ideal switching characteristics of the inverter. The convolutional module with a smaller kernel size is used to extract higher-order harmonic features and the small waveform fluctuation patterns caused by parameter changes. The global feature fusion and fully connected layer flatten and reshapes the multi-dimensional feature map output by the multi-scale feature extraction layer into a one-dimensional feature vector, and then outputs the dimensionless predicted value of the mutual inductance parameter through the fully connected layer. The physical boundary mapping activation layer introduces a physical boundary mapping mechanism that combines the hyperbolic tangent function, which limits the final predicted mutual inductance to the theoretical physical limit.

5. The method of claim 4, wherein, The multi-scale feature extraction layer includes a cascaded first convolutional module, a second convolutional module, and a third convolutional module; the first convolutional module uses a large-sized convolutional kernel, the second convolutional module uses a medium-sized convolutional kernel, and the third convolutional module uses a small-sized convolutional kernel.

6. The method of claim 4, wherein, The loss function can be constructed in several ways, including by using the KCL and KVL laws to construct a set of time-domain differential equations for a single-input single-output (SS) topology wireless power transfer system. in, The primary-side parasitic resistance, For secondary-side parasitic resistance, This is the voltage across the primary-side compensation capacitor. The voltage across the secondary-side compensation capacitor; Introducing the differential relation of the capacitance And And define the continuous-time state vector , Cp is the primary capacitor, Cp is the secondary capacitor; Let the inductively coupled determinant The time-domain differential equations are inverted and simplified algebraically to reconstruct the standard state-space equations. The system matrix and input matrix Specifically, it can be elaborated as follows: The actual equivalent load resistance As a matrix of known physical constraints ; Using a differentiable ordinary differential equation solver to measure voltage As input, for the state-space equation Perform numerical integration to obtain the network prediction variables. Theoretical simulation of current trajectory and ; Construct the mean square error loss function for the fused time-domain waveforms: in, This represents the total number of discrete sampling points within a single observation time window. This is the actual measured current on the primary side. For the actual measured current on the secondary side, The weighting coefficient is used to balance the errors in the primary and secondary currents.

7. The method of claim 6, wherein: Through the loss function The constructed one-dimensional convolutional neural network is trained offline with self-supervised instruction. During the training phase, the Adam optimizer is used to optimize the set of trainable weights and biases of the network. Iterative updates are performed, and a cosine annealing learning rate decay strategy is used during training.

8. The method of claim 7, wherein, A lightweight one-dimensional convolutional neural network with trained and fixed weights is deployed on an embedded hardware platform. During online real-time operation, the control system performs a single pure forward inference step to obtain the mutual inductance prediction value. ,in, The standardized waveform input matrix is ​​constructed during online operation. This represents the optimal set of parameters for a one-dimensional convolutional neural network. It is a one-dimensional convolutional neural network.

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