Method for optimizing electromagnetic energy loss of super magnetostrictive transducer based on SCReg-PGNN

Abstract

The application discloses a kind of based on SCReg-PGNN's giant magnetostrictive transducer electromagnetic energy loss optimization method, builds the magnetic energy loss test platform of giant magnetostrictive rod and carries out test to the magnetic energy loss under different working conditions, then, the electromagnetic loss of excitation coil is accurately calculated by considering skin effect, proximity effect and edge effect, finally, the electromagnetic energy loss model of high-power giant magnetostrictive transducer based on SCReg-PGNN is established, the electromagnetic loss characteristics of giant magnetostrictive transducer are calculated quickly, finally, the best electromagnetic structure parameters of high-power giant magnetostrictive transducer are searched by means of non-dominated sorting particle swarm optimization algorithm.The application can realize high-precision modeling and response prediction of transducer electromagnetic loss under multiple working conditions and multiple variable input conditions, and further realize the collaborative optimization of structure parameters under multiple objectives, so as to improve the overall energy efficiency and working reliability of transducer system.

Description

Technical Field

[0001] This invention relates to the field of high-power giant magnetostrictive transducers, and in particular to a method for optimizing electromagnetic energy loss in giant magnetostrictive transducers based on SCReg-PGNN. Background Technology

[0002] In recent years, the global energy crisis and increasingly stringent carbon emission regulations have placed higher energy efficiency requirements on engineering equipment, making improved energy conversion efficiency a key approach to achieving carbon reduction goals. High-power super magnetostrictive electroacoustic transducers, as core electrical devices widely used in underwater sonar, underwater acoustic communication, and resource exploration, play a crucial role in energy conservation, emission reduction, and efficient energy utilization by improving their energy conversion efficiency. Currently, the electromagnetic losses of a single high-power super magnetostrictive transducer under typical operating conditions can reach tens of kilowatts, necessitating technological means to reduce these losses and achieve energy conservation, emission reduction, and performance improvement.

[0003] In practical applications, high-power magnetostrictive transducers operate in complex environments, influenced by numerous factors such as magnetic field strength, prestress, temperature, frequency, and structural parameters. Their energy loss process exhibits significant nonlinear and multivariate coupling characteristics. However, existing electromagnetic loss modeling methods largely rely on empirical formulas or finite element simulations. These methods suffer from long modeling cycles, high computational costs, strong parameter dependence, and weak generalization ability, making it difficult to effectively reflect the nonlinear response and multivariate coupling characteristics of electromagnetic losses under complex operating conditions. This limits their adaptability and application effectiveness in engineering practice. Furthermore, optimizing the transducer's structural parameters based on electromagnetic loss modeling is also crucial for improving its energy efficiency and operational reliability. However, traditional optimization methods are prone to getting trapped in local optima when facing multi-objective, nonlinear, and coupled constraints, making it difficult to achieve synergistic optimization of energy efficiency and output performance. Therefore, there is an urgent need to develop a modeling and optimization method that has the ability to sense operating conditions, embed physical characteristics, and balance modeling accuracy and computational efficiency, so as to achieve accurate modeling and efficient optimization prediction of electromagnetic energy loss of high-power super magnetostrictive transducers under complex operating conditions.

[0004] Definitions:

[0005] SCReg-PGNN: Similarity Condition Regularized Physics-aware Graph Neural Network, is a physical perception graph neural network model based on similarity condition regularization. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a method for optimizing electromagnetic energy loss in supermagnetostrictive transducers based on SCReg-PGNN.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] The method for optimizing electromagnetic energy loss in giant magnetostrictive transducers based on SCReg-PGNN includes the following steps:

[0009] Step 1: Construct the SCReg-PGNN electromagnetic energy loss model of the high-power super magnetostrictive transducer; the SCReg-PGNN electromagnetic energy loss model of the high-power super magnetostrictive transducer includes a total magnetic energy loss model and a constraint function; the total magnetic energy loss model includes the SCReg-PGNN magnetic energy loss model of the super magnetostrictive rod and the electromagnetic energy loss function of the excitation coil.

[0010] Step 2: Construct a training dataset for supermagnetostrictive rods;

[0011] Step 3: Input the training dataset into the SCReg-PGNN magnetic energy loss model of the giant magnetostrictive rod for training, and obtain the trained SCReg-PGNN magnetic energy loss model of the giant magnetostrictive rod and the corresponding trained SCReg-PGNN electromagnetic energy loss model of the high-power giant magnetostrictive transducer.

[0012] Step 4: Based on the size range of the magnetic circuit and shell of the giant magnetostrictive transducer, range constraints are imposed on the dimensions of each part of the excitation coil and the giant magnetostrictive rod. Then, using a particle swarm optimization algorithm with non-dominated sorting and a trained SCReg-PGNN electromagnetic energy loss model of the high-power giant magnetostrictive transducer, the dimensions of each part of the giant magnetostrictive transducer are optimized to obtain the size data of the giant magnetostrictive rod and the size data of the excitation coil when the electromagnetic energy loss of the high-power giant magnetostrictive transducer is minimized.

[0013] A further improvement is that the constraint function in step one includes the amplitude constraint function of the AC excitation magnetic field. and the amplitude constraint function of the output force of the supermagnetostrictive rod The SCReg-PGNN electromagnetic energy loss model of the high-power super magnetostrictive transducer. as follows:

[0014] in, This is the total magnetic energy loss model; min() represents taking the minimum value.

[0015] Further improvements,

[0016]

[0017] Where min() represents taking the minimum value,

[0018] The constraint functions include The electromagnetic energy loss function of the excitation coil; The SCReg-PGNN magnetic energy loss model for supermagnetostrictive rods; Indicates the thickness of the flat copper wire in the excitation coil. Indicates the width of the flat copper wire in the excitation coil. This indicates the inner diameter of the excitation coil. This indicates the number of turns of a single wire in the radial direction of the excitation coil. This indicates the number of coil turns in the height direction of the excitation coil. This represents the effective value of the excitation current. Indicates ambient temperature. The imaginary part of the complex permeability of a supermagnetostrictive rod is represented by the following expression: Indicates the frequency of the excitation current. Indicates the diameter of the magnetostrictive rod. Indicates the number of kerfs in the magnetostrictive rod. This represents the magnetic flux density of the magnetostrictive rod. This indicates the prestress in the magnetostrictive rod. This represents the bias magnetic field of the giant magnetostrictive rod.

[0019] A further improvement is that the constraint function includes an amplitude constraint function for the AC excitation magnetic field. and the amplitude constraint function of the output force of the supermagnetostrictive rod

[0020] ;

[0021] Where max() represents taking the maximum value; This indicates the total number of turns of the excitation coil. Indicates the outer diameter of the excitation coil. Indicates the coil height. This represents the radial distance from a point inside the giant magnetostrictive rod to the central axis of the coil; Young's modulus of the supermagnetostrictive rod; This represents the cross-sectional area of ​​the supermagnetostrictive rod. The saturation magnetostrictive strain of the supermagnetostrictive rod; This represents the saturation magnetic field strength. The prestress coupling coefficient; The excitation magnetic field for the supermagnetostrictive rod.

[0022] In a further improvement, the SCReg-PGNN magnetic energy loss model of the super magnetostrictive rod adopts the SCReg-PGNN neural network model; the SCReg-PGNN neural network model includes, in the order of data processing, a feature adaptive sparse graph structure module, a feature encoding module, an information transmission and feature fusion module, and a graph recovery module;

[0023] The input to the adaptive sparse graph structure module is the original graph structure information, which includes a node feature matrix constructed from the geometric structure data and working condition data of the giant magnetostrictive rod. The adaptive sparse graph structure module first calculates the working condition cosine similarity between each node, and then determines whether to retain the connection relationship between nodes based on a preset similarity threshold. Node pairs with similarity higher than the threshold retain edges, while node pairs with similarity lower than the threshold have edges pruned, thereby obtaining the sparse graph structure information and outputting the sparse graph structure information matrix.

[0024] The feature encoding module performs high-dimensional embedding mapping on the node features in the output sparse graph structure information matrix through a multilayer perceptron and outputs a node embedding matrix to extract discriminative features and enhance node representation capabilities.

[0025] The information transmission and feature fusion module takes a node embedding matrix as input, including node and neighboring node information, and edge information. Based on the message passing mechanism of graph neural networks, the module iteratively aggregates the node embedding matrix with its corresponding neighboring node information through multiple rounds, while fusing edge feature information to improve the globality and contextual relevance of node features, and outputs a fused node embedding matrix.

[0026] The graph restoration module maps the node embedding features of the node embedding matrix to the specific task target space through the decoder and regression prediction unit, and outputs the node-level prediction results, namely the electromagnetic energy loss values ​​of the giant magnetostrictive rod at each node.

[0027] A further improvement is the introduction of an adaptive sparsification graph structure module based on a cosine similarity-based graph construction strategy, which achieves sparsification of the graph structure and relation filtering:

[0028] ;

[0029] In the formula, Indicates working conditions , Indicates working conditions , Indicates working conditions , Similarity between them This indicates the threshold for similarity between working conditions. Represents the adjacency matrix. Represents the dimension of a vector. express The One portion, express The Each component.

[0030] In a further improvement, the information transmission and feature fusion module introduces a residual connection mechanism to superimpose the node features of the previous layer with the current update result. That is, after completing the message transmission and feature transformation of the current layer, the input features of the previous layer are superimposed with the calculation result of the current layer to form the final output.

[0031] The first step of the residual connection mechanism is to calculate intermediate features for the current layer by passing messages:

[0032] ;

[0033] In the formula, Indicates the current layer. Represents the neighborhood aggregation function. Represents the learnable weight matrix. This represents the input features of the previous layer. This indicates that the current layer is not inactive for output.

[0034] The second step of the residual join mechanism is residual path processing, which involves linear projection if the dimensions do not match.

[0035] ;

[0036] In the formula, Represents the residual path feature matrix. This represents a learnable linear projection matrix.

[0037] The third step of the residual connection mechanism is feature overlay, which adds the current layer result to the residual path features:

[0038] ;

[0039] In the formula, This represents the output of the current layer after residual connection. Indicates the activation function;

[0040] The information transmission and feature fusion module is for connecting nodes and edge The update process consists of two phases: in the message construction phase, node features of the current layer are extracted from the nodes at both ends of the edge. and and the characteristics of the edge itself. Concatenating to form a message vector During the state update phase, the message vector is... The input MLP obtains the updated features of the edges through nonlinear mapping. The specific update process is shown in the following equation:

[0041] ;

[0042] in, Indicates the edge features of the next layer.

[0043] Node features The update depends on the feature aggregation of its adjacent edges and the fusion of its own state. Nodes receive feature information from neighboring nodes through edge connections and, during the update phase, use MLP to process the message vector. The fusion with its own representation is calculated as follows:

[0044] ;

[0045] in, It is the edge feature between nodes; For the set of neighboring nodes; This represents a message passing function; It is an update function; || indicates that the features are concatenated into a tensor; This represents the updated node characteristics.

[0046] Further improvements include the loss function of the SCReg-PGNN magnetic energy loss model for the supermagnetostrictive rod. as follows:

[0047] ;

[0048] in, Indicates working conditions and working conditions Similarity; For working conditions Predicted magnetic energy loss values ​​under the following conditions; The hyperparameters for controlling the regularization strength; This represents the prediction loss of the model nodes; This represents the loss due to physical consistency constraints.

[0049] A further improvement is made to the method for constructing the magnetic energy loss dataset of the supermagnetostrictive rod in step two, as follows:

[0050] 2.1) Construct a magnetic energy loss testing platform for supermagnetostrictive rods;

[0051] 2.2) Determine the calculation method for magnetic energy loss of giant magnetostrictive rods:

[0052] Constitutive relations of supermagnetostrictive rods characterized by complex permeability

[0053] ;

[0054] In the formula, Indicates an excitation magnetic field. This represents the amplitude of the excitation magnetic field. Represents a complex exponential function. Indicates magnetic flux density. The magnitude of the magnetic flux density. Represents a complex exponential function. Indicates an alternating excitation magnetic field and magnetic induction intensity The phase difference between them Indicates angular velocity. Indicates time, The symbol representing the imaginary part of a complex number. Represents the permeability of free space. The real part of the complex permeability of the supermagnetostrictive rod is represented by . denoted by represents the imaginary part of the complex permeability of the supermagnetostrictive rod.

[0055] Furthermore, the magnetic energy loss of the magnetostrictive rod Represented as:

[0056] ;

[0057] In the formula, Indicates the frequency of the excitation magnetic field; This indicates the volume of the supermagnetostrictive rod. This represents the magnetic energy loss per unit volume of a giant magnetostrictive rod.

[0058] ;

[0059] In the formula, Represents the relative permeability of the magnetostrictive rod.

[0060] 2.3) Obtain magnetic energy loss data of supermagnetostrictive rods under different prestress and temperature, different temperature and excitation frequency, different temperature and magnetic induction intensity, different prestress and excitation frequency, different prestress and magnetic induction intensity, and different excitation frequency and magnetic induction intensity respectively, and form a magnetic energy loss dataset.

[0061] 2.4) The magnetic energy loss dataset is constructed to form the training dataset. One data set in the training dataset includes the diameter of the supermagnetostrictive rod. Number of kerfs in supermagnetostrictive rods Excitation frequency of giant magnetostrictive rods Magnetic flux density of supermagnetostrictive rods Temperature of supermagnetostrictive rods Prestressed supermagnetostrictive rods and the bias magnetic field of the supermagnetostrictive rod .

[0062] Further improvements include optimizing the hyperparameters of the SCReg-PGNN magnetic energy loss model of the supermagnetostrictive rod using Bayesian methods during training; setting the hidden layer dimension of the SCReg-PGNN magnetic energy loss model to 128, the message passing steps to 4, and the Dropout rate to 0.005 to suppress overfitting risk; using SUM aggregation and residual connection to alleviate the difficulty of training deep networks and prevent oversmoothing; and iterating the training samples within 100 rounds during the entire training process, with a batch size of 20 and 30 iterations per round.

[0063] The learning rate uses an adaptive learning rate processing method:

[0064] ;

[0065] In the formula, The learning rate at which decay begins. Indicates the attenuation factor. This represents the total number of decay steps. Indicates the current round number. Indicates the number of rounds from which decay begins. This represents the minimum learning rate. This represents the learning rate obtained after the update.

[0066] The beneficial effects of this invention are as follows:

[0067] This invention establishes a magnetic energy loss testing platform for giant magnetostrictive rods to test magnetic energy loss under different operating conditions, comprehensively exploring the distribution law of magnetic energy loss of giant magnetostrictive rods under complex operating conditions. Then, considering the skin effect, proximity effect, and edge effect, the electromagnetic loss of the excitation coil is accurately calculated. Finally, an electromagnetic energy loss model of a high-power giant magnetostrictive transducer based on SCReg-PGNN is established to rapidly calculate the electromagnetic loss characteristics of the giant magnetostrictive transducer. Finally, a particle swarm optimization algorithm with non-dominated sorting is used to search for the optimal electromagnetic structure parameters of the high-power giant magnetostrictive transducer. Compared with the method of manually adjusting parameters and performing finite element calculations, this invention is more efficient and accurate, not only quickly predicting output characteristics but also providing the optimal combination of operating parameters to meet the requirements of real-time simulation. Attached Figure Description

[0068] The invention will be further illustrated with reference to the accompanying drawings, but the contents of the drawings do not constitute any limitation on the invention.

[0069] Figure 1 This invention provides a magnetic energy loss testing platform for supermagnetostrictive rods.

[0070] Figure 2 This is the basic framework of the physical perception graph neural network model based on similarity condition regularization in this invention.

[0071] Figure 3 This is the adaptive sparsification graph structure of the present invention.

[0072] Figure 4 This invention relates to message passing and MLP feature updates.

[0073] Figure 5 This shows the changing trends of training loss and learning rate of the SCReg-PGNN model of this invention.

[0074] Figure 6 This invention compares the actual measured magnetic loss and predicted value of the supermagnetostrictive bar under different prestress, excitation frequency and magnetic flux density conditions, and shows the relative error.

[0075] Figure 7 This invention provides a computer-based theory for the electromagnetic energy loss of the excitation coil under complex operating conditions.

[0076] Figure 8 This is the result of the non-dominated sorting optimization of the electromagnetic structure in this invention. Detailed Implementation

[0077] To make the purpose, technical solution, and advantages of the invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and examples.

[0078] This invention proposes a modeling and optimization method for electromagnetic energy loss in high-power supermagnetostrictive transducers based on SCReg-PGNN. This method enables accurate characterization of the electromagnetic loss of high-power supermagnetostrictive transducers under complex operating conditions and rapidly optimizes the electromagnetic structure of the transducer using a swarm intelligence optimization method with non-dominated sorting. This solves the problems of low efficiency of finite element analysis methods and the blind selection of various structural parameters in the design of high-power supermagnetostrictive transducers.

[0079] Please refer to Figures 1 to 8 The method includes the following steps:

[0080] Step 1: Construct a magnetic energy loss testing platform for giant magnetostrictive rods, including an excitation module, a measurement module, and an output module. The excitation module includes a power amplifier 4, an impedance matching box 2, a giant magnetostrictive rod 11, an excitation coil 10, a heating and insulation device 12, and a pressure holding device 9; the measurement module includes a measurement coil 13, a pressure sensor 6, and a temperature controller 7; the output module includes a host computer 1, a data acquisition card 5, and a data storage recorder 3.

[0081] Step 2: Establish a database of magnetic energy loss of the super magnetostrictive rod under complex working conditions.

[0082] Step 2.1, Calculation method for magnetic energy loss of giant magnetostrictive rod, the calculation formula for magnetic energy loss of giant magnetostrictive rod is shown in equations (1)-(5):

[0083] A method for calculating the magnetic energy loss of a supermagnetostrictive rod is provided, and the calculation formulas for the magnetic energy loss of the supermagnetostrictive rod are shown in equations (1)-(5). Under AC magnetic field excitation, the magnetization process of the supermagnetostrictive rod exhibits a hysteresis phenomenon; therefore, the constitutive relation of the material can be approximately characterized by complex permeability, as shown in equations (1), (2), and (3).

[0084]

[0085]

[0086]

[0087] In the formula, Indicates an excitation magnetic field. This represents the amplitude of the excitation magnetic field. Represents a complex exponential function. Indicates magnetic flux density. The magnitude of the magnetic flux density. Represents a complex exponential function. Indicates an alternating excitation magnetic field and magnetic induction intensity The phase difference between them Indicates angular velocity. Indicates time, The symbol representing the imaginary part of a complex number. Represents the permeability of free space. The real part of the complex permeability of the supermagnetostrictive rod is represented by . Let represent the imaginary part of the complex permeability of the supermagnetostrictive rod. The magnetic energy loss per unit volume of the supermagnetostrictive rod can then be expressed as equation (4):

[0088]

[0089] In the formula, Let represent the relative permeability of the supermagnetostrictive rod. Equation (4) shows that, given a peak magnetic induction intensity, can be used... The magnetic energy loss of the supermagnetostrictive rod is characterized. At this point, the magnetic energy loss of the supermagnetostrictive rod can be expressed as shown in equation (5):

[0090]

[0091] In the formula, Indicates the frequency of the excitation magnetic field; This indicates the volume of the supermagnetostrictive rod.

[0092] Step 2.2: Distribution of Magnetic Energy Loss in Giant Magnetostrictive Rods under Different Prestresses and Temperatures. Under prestress, the internal domain structure, motion path, and magnetization degree of the giant magnetostrictive rod all change significantly. Under constant excitation frequency and magnetic induction intensity, the increase in prestress directly affects the crystal orientation of the domains and the initial spacing of the domain walls, leading to distortion and deflection of the hysteresis loop of the giant magnetostrictive rod, ultimately causing an increase in magnetic energy loss. Furthermore, the giant magnetostrictive rod is highly sensitive to changes in ambient temperature; increased temperature weakens the pinning effect of the domain walls, reducing the domain response hysteresis and thus decreasing dynamic hysteresis loss.

[0093] Step 2.3: Distribution of Magnetic Energy Loss in Giant Magnetostrictive Rods under Different Temperatures and Excitation Frequencies. In giant magnetostrictive rods, magnetic energy loss is significantly affected not only by prestress and temperature, but also by the coupling effect of frequency and temperature. Magnetic energy loss increases exponentially with increasing frequency, due to the accelerated domain reversal rate and broadened hysteresis loop at high frequencies, resulting in increased energy loss per unit time. Increased temperature, to some extent, alleviates the loss increase caused by high frequency, especially in the medium-high temperature region, indicating that temperature weakens domain pinning and friction effects, improving high-frequency response performance. Notably, in the low-temperature high-frequency region, loss rises rapidly, and temperature is insufficient to compensate for the frequency-induced magnetic response hysteresis; while in the high-temperature high-frequency region, temperature, to some extent, "suppresses" the amplification effect of frequency on magnetic energy loss. Overall, excitation frequency is the dominant factor in the increase of magnetic energy loss, while temperature has a bidirectional regulatory effect: its influence is smaller at low frequencies, and it can significantly alleviate the loss caused by hysteresis at high frequencies.

[0094] Step 2.4: Distribution of Magnetic Energy Loss in Giant Magnetostrictive Rods under Different Temperatures and Magnetic Induction Intensities. In giant magnetostrictive materials, magnetic energy loss is affected not only by temperature and excitation frequency, but also significantly by the coupling effect of magnetic induction intensity and temperature. Magnetic energy loss increases significantly with increasing magnetic induction intensity, mainly due to frequent domain reversals and hysteresis loop broadening under stronger magnetic fields, leading to increased energy loss per unit time. Magnetic energy loss exhibits obvious nonlinear coupling characteristics: in the low-temperature, high-magnetic-field region, the loss increases rapidly; while in the high-temperature, high-magnetic-field region, the loss tends to stabilize or even decrease slightly. Overall, magnetic induction intensity is the dominant factor driving the increase in magnetic energy loss; while temperature has a limited effect under low magnetic fields, but can significantly reduce energy loss caused by the magnetic field under high magnetic field conditions.

[0095] Step 2.5: Distribution of magnetic energy loss in giant magnetostrictive rods under different prestresses and excitation frequencies. Magnetic energy loss increases significantly with frequency, especially showing a rapid upward trend in the high-frequency region; simultaneously, the loss also gradually increases with the increase of prestress, exhibiting a coupled enhancement effect, indicating that high frequency and high prestress jointly exacerbate the domain reversal resistance and energy dissipation.

[0096] Step 2.6: Distribution of magnetic energy loss in giant magnetostrictive rods under different prestresses and magnetic induction intensities. Magnetic energy loss increases significantly with increasing magnetic induction intensity, especially in the high prestress region, indicating that the magnetic field is the dominant influencing factor. Simultaneously, increasing prestress also leads to an increase in magnetic energy loss, particularly under high magnetic field conditions, indicating a coupling effect between the two, thus increasing magnetic energy loss.

[0097] Step 2.7: Distribution of magnetic energy loss in giant magnetostrictive rods under different excitation frequencies and magnetic flux densities. Magnetic energy loss increases significantly with increasing frequency and magnetic flux density, especially in the high-frequency and high-magnetic-induction regions, where the loss increases exponentially, demonstrating a strong frequency-magnetic field coupling effect. This indicates that energy loss under alternating magnetic fields is mainly driven by the combined effect of frequency and magnetic flux density.

[0098] Step 3: Establish the SCReg-PGNN magnetic energy loss model for the super magnetostrictive rod.

[0099] Step 3.1: Basic framework of the physical perception graph neural network model based on similarity condition regularization. SCReg-PGNN is based on an Encoder-Process-Decoder structure, using multi-layer GNNs to complete message passing, multi-scale feature extraction and fusion, and partial edge removal based on the similarity of working conditions. It also incorporates skip connections to improve the model's learning ability and generalization performance, achieving efficient processing and prediction. Its overall architecture is as follows: Figure 2As shown, it mainly includes four modules: feature encoding, adaptive sparse graph structure, information transfer and feature fusion, and graph restoration. Furthermore, a residual connection mechanism is introduced to superimpose the node features of the previous layer with the current update result, effectively mitigating feature degradation and gradient vanishing problems.

[0100] Step 3.2: Graph coarsening strategy driven by operating condition similarity. To characterize the magnetic energy loss behavior of giant magnetostrictive rods under different operating conditions, this invention constructs a graph structure with operating condition parameters as nodes to depict the intrinsic correlation between material responses under multiple variables. Considering the wide variety of combinations of operating condition parameters, directly constructing a fully connected graph not only incurs high computational overhead but may also introduce redundant information, affecting the model's learning performance. Therefore, this invention introduces a graph construction strategy based on cosine similarity to achieve sparsity reduction and relation filtering of the graph structure.

[0101] As shown in equation (6), the adjacency matrix between operating conditions is shown in equation (7).

[0102]

[0103]

[0104] In the formula, Indicates working conditions , Indicates working conditions , Indicates working conditions , Similarity between them This indicates the threshold for similarity between working conditions. Represents the adjacency matrix. Represents the dimension of a vector. express The One portion, express The Each component.

[0105] Adaptive sparse graph structure as follows Figure 3 As shown, firstly, cosine similarity is calculated for the feature vectors of each pair of nodes (i.e., different operating conditions) to measure their similarity in the high-dimensional representation space; secondly, a similarity threshold is set. By retaining only edges between highly similar node pairs and eliminating connections with weak physical correlations, a sparser and more physically interpretable graph structure is constructed. This strategy not only effectively reduces the interference caused by weakly correlated connections between different operating conditions and improves the model's ability to represent complex magnetic energy losses, but also avoids the oversmoothing problem caused by an overly dense graph structure, maintaining the distinguishability of node representations, thereby improving the modeling efficiency and accuracy of magnetic energy loss behavior in giant magnetostrictive rods.

[0106] Step 3.3: Information Passing and Feature Fusion. To accurately model the magnetic energy loss behavior of giant magnetostrictive materials under multiple operating conditions, a multi-layer graph neural network structure was constructed, and a high-dimensional feature mapping was performed on the input graph structure data based on a multilayer perceptron (MLP) encoder. Through layer-by-layer message passing, feature updating, and residual connection mechanisms, deep aggregation and expression optimization of high-dimensional features of nodes and their neighbors were achieved. The node representation is continuously updated in each layer, gradually capturing the complex dependencies between operating condition variables, thereby improving the accuracy and generalization ability of magnetic energy loss prediction. To achieve the optimal balance between information aggregation and noise suppression, a Bayesian optimization method was further introduced to adaptively adjust key hyperparameters in the GNN model: message passing steps, number of hidden layers, and cosine similarity threshold, in order to search for the optimal configuration under different graph structures. The message passing mechanism of the graph neural network consists of two stages: "message passing" and "state updating". Figure 4 As shown, in each layer, the edge feature update process aims to improve the model's ability to represent structural and attribute information. For connected nodes... and edge The update process consists of two phases: in the message construction phase, node features of the current layer are extracted from the nodes at both ends of the edge. and and the characteristics of the edge itself. Concatenating to form a message vector During the state update phase, the message vector is... The input MLP obtains the updated features of the edges through nonlinear mapping. The specific update process is shown in Equation (8). The update of node features depends on the feature aggregation of its adjacent edges and the fusion of its own state. Specifically, the node receives feature information from its neighboring nodes through edge connections, and in the update stage, it uses the MLP to fuse this information with its own representation. The specific calculation process is shown in Equation (9).

[0107]

[0108] in, It is the edge feature between nodes; Indicates the edge features of the next layer; For the set of neighboring nodes; This represents a message passing function; It is an update function; The features are concatenated into tensors; This represents the updated node characteristics.

[0109] Step 3.4, Physical Consistency Constraint. To improve the physical consistency and generalization ability of the model in magnetic energy loss prediction, this invention introduces a similar operating condition consistency constraint term into the loss function of SCReg-PGNN as a physical supplement to the data-driven prediction results. This constraint is based on the consistency of magnetic energy loss of giant magnetostrictive rods under similar operating conditions, constraining the model's output under different operating conditions to conform to the actual physical situation, thereby reducing the deviation between the prediction results and physical reality. This effectively avoids unreasonable loss jumps in the model under similar operating conditions, improving the physical interpretability and continuity of the prediction. The loss function consists of two parts: first, a prediction error term, which uses mean squared error to measure the difference between the model output and the actual loss value; second, a physical consistency constraint term, used to evaluate whether the model output violates the loss distribution law under similar operating conditions.

[0110] The overall loss function is in the form of equation (10):

[0111]

[0112]

[0113]

[0114] in, Indicates working conditions and working conditions Similarity; For working conditions Predicted magnetic energy loss values ​​under the following conditions; The hyperparameters for controlling the regularization strength; This represents the prediction loss of the model nodes; This represents the loss due to physical consistency constraints.

[0115] Step 4: Process and train the sample database.

[0116] Step 4.1: Under different working conditions, the magnetic energy loss of supermagnetostrictive rods with different diameters and cutting methods was tested to obtain the training dataset for the magnetic energy loss model of supermagnetostrictive rods. The hyperparameters of SCReg-PGNN were optimized using Bayesian methods to achieve the optimal balance between performance and efficiency. The training process was based on a 7:3 split between the training and test sets to ensure the model's generalization ability at different data stages. The hidden layer dimension was set to 128, the message passing steps were 4, and the dropout rate was 0.005 to suppress overfitting. The aggregation method was SUM, and residual connections were included to alleviate the difficulty of training deep networks and prevent oversmoothing. Throughout the training process, 600 training samples were iteratively trained over 100 epochs with a batch size of 20, 30 iterations per epoch, and a total of 3000 iterations to fully utilize fine-grained feature information in small sample scenarios. Meanwhile, the optimizer Adam is improved by proposing a hybrid rule optimization method with adaptive capabilities, as shown in Equation (13), where the decay step is 500. This strategy can dynamically adjust the learning rate according to the changes in training loss, thereby achieving fine control over the gradient update process and improving the stability, convergence speed, and generalization ability of model training.

[0117]

[0118] The trends of training loss, validation loss, and learning rate during the training of the SCReg-PGNN model are as follows: Figure 5As shown, although the training loss and validation loss fluctuate to some extent with the increase of training rounds, they generally show a downward trend. To evaluate the predictive performance of the proposed SCReg-PGNN model, this invention uses Mean Absolute Error (MAE) as the loss function. After determining the hyperparameters through Bayesian optimization and completing the training, the model's performance on different datasets is as follows: the minimum loss on the training set is 0.0354, and the minimum loss on the validation set is 0.0366. The results show that the model fits well on the training set and maintains a low error on the test set, verifying that the proposed model has good generalization ability and stability, and can accurately predict the magnetic energy loss behavior of GMM bars under different working conditions. In addition, this loss model incorporates an adaptive decay learning rate mechanism, and the learning rate strategy includes two stages: adaptive linear decrease and direct decay. When the change in training loss tends to be gradual, the learning rate enters the direct decay stage. The blue curve in the figure represents the trend of learning rate change, clearly showing the alternation of linear decrease and direct decay processes. It is worth noting that during the rapid decay phase of the learning rate, the training loss and validation loss also fluctuated briefly, further demonstrating the effectiveness of the adaptive learning rate mechanism in improving training efficiency and model stability.

[0119] Step 4.2: Evaluation of the SCReg-PGNN magnetic energy loss model for giant magnetostrictive rods, and accuracy analysis of the loss model under different operating conditions. The magnetic energy loss of giant magnetostrictive rods under different operating conditions is predicted and calculated using the SCReg-PGNN magnetic energy loss model. The calculation results are as follows: Figure 6 As shown in the figure, the horizontal axis represents the sample operating conditions, and the vertical axis represents the experimentally tested magnetic energy loss value and the SCReg-PGNN predicted value of the supermagnetostrictive rod under specific operating conditions. The figure shows that the SCReg-PGNN's predicted magnetic energy loss of the rod is consistent with the experimental results, with a maximum error of 7.56% and an average error of only 0.95%, indicating good prediction performance. Furthermore, the trained model's single-run computation time is only 0.0016 seconds, demonstrating that this method can quickly and accurately obtain the magnetic energy loss of the supermagnetostrictive rod, which is also a necessary prerequisite for subsequent optimization of its magnetic energy loss.

[0120] Step 5: Considering the electromagnetic energy loss of the excitation coil under complex operating conditions, construct the SCReg-PGNN electromagnetic energy loss model for a high-power super magnetostrictive transducer:

[0121] S5.1 Consider the electromagnetic energy loss of the excitation coil under complex operating conditions. Unlike the magnetic energy loss of the giant magnetostrictive rod, the loss of the excitation coil is mainly composed of joule loss. For example... Figure 7As shown, under high-frequency alternating magnetic field conditions, the additional resistance of the coil increases due to the skin effect, proximity effect, and edge effect of the flat copper wire, as shown in equations (14), (15), and (16). As the coil temperature rises, the resistivity of the material changes continuously. To accurately calculate the coil loss, temperature characteristics need to be considered, as shown in equation (17).

[0122]

[0123]

[0124]

[0125]

[0126] In the formula, Additional resistance to account for the skin effect; The empirical coefficient for the skin effect is taken as 0.3~0.4; The thickness of the flat copper wire in the coil; For flat copper wires, the skin depth is required. Additional resistance to account for proximity effect; The nearest neighbor effect is the empirical coefficient, ranging from 0.1 to 0.3. This refers to the number of coil turns. The width of the flat copper wire in the coil; The spacing between the flat copper coils; Additional resistance to account for edge effects; The empirical coefficient for the edge effect is 0.03 to 0.07. The frequency correlation index is taken as 1.5 to 2; for The coil resistance below; The temperature coefficient of resistance is taken as 0.00393℃. -1 .

[0127] Due to the presence of the giant magnetostrictive rod, the reverse magnetic field generated by the eddy currents causes further changes in the coil magnetic field and equivalent permeability. Therefore, the influence of the iron core on coil losses can be considered by adding an impedance. Additional resistance and additional reactance are introduced from the real and imaginary parts of the iron core permeability, as shown in equations 18 and 19.

[0128]

[0129]

[0130] In the formula, The additional resistance introduced by the iron core; Cross-sectional area of ​​the supermagnetostrictive rod; This represents the real part of the permeability of the iron core. This represents the imaginary part of the core's permeability. Let be the length of the equivalent magnetic circuit. Therefore, the electromagnetic loss of the excitation coil of the giant magnetostrictive electroacoustic transducer can be expressed as:

[0131]

[0132] In the formula, To account for the electromagnetic energy loss of the coil under high-frequency excitation; This is the effective value of the excitation current; Additional resistance is required to account for skin, proximity, and edge effects.

[0133] S5.2 Considering the electromagnetic energy loss of the excitation coil under complex operating conditions, an SCReg-PGNN electromagnetic energy loss model for a high-power supermagnetostrictive transducer is constructed. Although the magnetic energy loss of the supermagnetostrictive rod and the electromagnetic loss of the excitation coil are coupled, they can be coupled through the complex permeability of the supermagnetostrictive rod. Therefore, the electromagnetic loss model of the high-power supermagnetostrictive transducer can be expressed as:

[0134]

[0135] Step 6: Optimize the electromagnetic structure of the high-power super magnetostrictive transducer using a swarm intelligence optimization algorithm based on non-dominated sorting.

[0136] Step 6.1, Optimization Objective. Since the excitation coil is made of a multi-turn single wire, the size of the single wire and the winding method determine the outer diameter and height of the coil. The relationship between the size of the single wire and the outer diameter and height of the coil is shown in equation (22).

[0137]

[0138] in, The outer diameter of the coil. The inner diameter of the coil. The width of the single conductor cross-section. The number of turns of a single conductor in the radial direction of the coil. The height of the coil, The thickness of the cross-section of a single conductor. The number of coil turns in the height direction. Let be the total number of turns in the coil. Therefore, the optimization variable for coil size can be transformed into... , .

[0139] Besides the significant impact of coil size and excitation current on coil copper loss, the magnetic energy loss of the giant magnetostrictive rod is a crucial factor affecting transducer output efficiency. Its diameter, cutting method, and operating conditions are directly related to its magnetic energy loss. Therefore, minimizing the electromagnetic energy loss of the excitation module of a high-power giant magnetostrictive transducer can be used as an optimization target, as shown in equation (23). However, while minimizing the magnetic energy loss of the excitation module, it is necessary to ensure that the coil has the ability to provide the target magnetic field for the giant magnetostrictive rod, and on the other hand, it is necessary to ensure that the giant magnetostrictive rod can provide the desired output force. This achieves the goal of minimizing energy consumption while ensuring high-performance output of the high-power giant magnetostrictive transducer. Therefore, the amplitude of the AC excitation magnetic field provided by the excitation coil and the amplitude of the output force of the giant magnetostrictive rod can be used as physical constraint targets, as shown in equations (23 and 24).

[0140]

[0141]

[0142]

[0143] Where max() represents taking the maximum value; This indicates the total number of turns of the excitation coil. Indicates the outer diameter of the excitation coil. Indicates the coil height. This represents the radial distance from a point inside the giant magnetostrictive rod to the central axis of the coil; Young's modulus of the supermagnetostrictive rod; This represents the cross-sectional area of ​​the supermagnetostrictive rod. The saturation magnetostrictive strain of the supermagnetostrictive rod; This represents the saturation magnetic field strength. The prestress coupling coefficient; The excitation magnetic field for the supermagnetostrictive rod.

[0144] Step 6.2, Optimization Strategy. To achieve multi-objective collaborative optimization of the transducer excitation module, the Pareto principle is introduced into PSO, and the optimization model is shown in equation (26):

[0145]

[0146] in, This is the total magnetic energy loss model; min() represents taking the minimum value.

[0147] Before optimization, the dimensions of the coil and the giant magnetostrictive rod need to be constrained according to the dimensions of the magnetic circuit and the housing. That is, the coil needs to be placed entirely inside the housing, so the external dimensions of the excitation module should meet the range shown in Table 1.

[0148] Table 1 Excitation Module Parameter Range

[0149]

[0150] The excitation module of the transducer was optimized under excitation conditions of 1000Hz, 25MPa, and 0.2T. The optimization results are as follows: Figure 8 As shown. Although the output performance of the transducer is directly related to the magnetic field strength and output force in the giant magnetostrictive rod, the magnetic energy loss of the excitation module directly determines the output efficiency of the transducer. Furthermore, excessive magnetic energy loss causes a sharp increase in the internal temperature of the transducer, thus affecting its operating condition and reducing its service life. Therefore, optimizing the magnetic energy loss index of the excitation module has the highest priority. Therefore, the final selection... Figure 8 The red circles in the diagram represent the final optimized results. Target 1 is 1161.05 W, Target 2 is 21.13 kA / m, and Target 3 is 6200 N. The maximum magnetic field strength is close to the target values, meeting the requirement of maximizing the utilization of the linear region. The optimal solution corresponding to the red circles in the diagram is: , , , , , , , Due to limitations in coil winding and processing technology, the final optimized dimensions of the magnetostrictive rod were determined to be: 30mm in diameter, 55mm in height, and 7 transverse staggered slits; the optimized excitation coil parameters were: 38mm inner diameter, 62mm outer diameter, 2.65*1.4mm flat copper wire, and 944 coil turns.

[0151] The lake test results of the two high-power super magnetostrictive transducers before and after optimization are shown in Table 2. Table 2: Comparison of transducer output efficiency before and after optimization.

[0152]

[0153] Table 2 fully demonstrates that a non-dominated sorting group intelligent optimization algorithm, which balances energy loss and output performance, was constructed with the optimization objectives of minimizing magnetic energy loss, maximizing the excitation magnetic field strength of the coil, and maximizing the output force of the giant magnetostrictive rod. This algorithm can achieve efficient optimization of the transducer excitation structure parameters. The optimization results show that the transducer's electroacoustic conversion efficiency increased from 58.54% to 71.82%, an improvement of 13.28%, verifying the effectiveness and engineering applicability of the proposed efficiency improvement strategy.

[0154] Furthermore, this invention also provides a modeling and optimization system for electromagnetic energy loss of a high-power supermagnetic-strict transducer based on SCReg-PGNN, including one or more processors and a memory. The memory stores one or more programs, which, when executed by the one or more processors, cause the one or more processors to perform the steps of the method described above. The specific steps of this method are as described in the above embodiments. Since this analysis system adopts all the technical solutions of all the above embodiments, it possesses at least all the beneficial effects brought about by the technical solutions of the above embodiments, and will not be elaborated further here.

[0155] 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 the scope of protection of the present invention. 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 essence and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing electromagnetic energy loss in a giant magnetostrictive transducer based on SCReg-PGNN, characterized in that, Includes the following steps: Step 1: Construct the SCReg-PGNN electromagnetic energy loss model of the high-power super magnetostrictive transducer; the SCReg-PGNN electromagnetic energy loss model of the high-power super magnetostrictive transducer includes a total magnetic energy loss model and a constraint function; the total magnetic energy loss model includes the SCReg-PGNN magnetic energy loss model of the super magnetostrictive rod and the electromagnetic energy loss function of the excitation coil. Step 2: Construct a training dataset for supermagnetostrictive rods; Step 3: Input the training dataset into the SCReg-PGNN magnetic energy loss model of the giant magnetostrictive rod for training, and obtain the trained SCReg-PGNN magnetic energy loss model of the giant magnetostrictive rod and the corresponding trained SCReg-PGNN electromagnetic energy loss model of the high-power giant magnetostrictive transducer. Step 4: Based on the size range of the magnetic circuit and shell of the giant magnetostrictive transducer, the size of each part of the excitation coil and giant magnetostrictive rod is constrained. Then, the size of each part of the giant magnetostrictive transducer is optimized by the particle swarm optimization algorithm with non-dominated sorting and the trained SCReg-PGNN electromagnetic energy loss model of the high-power giant magnetostrictive transducer. The size data of the giant magnetostrictive rod and the size data of the excitation coil when the electromagnetic energy loss of the high-power giant magnetostrictive transducer is minimized are obtained. The constraint function mentioned in step one includes the amplitude constraint function of the AC excitation magnetic field. and the amplitude constraint function of the output force of the supermagnetostrictive rod The SCReg-PGNN electromagnetic energy loss model of the high-power super magnetostrictive transducer. as follows: ; in, This is the total magnetic energy loss model; min() represents taking the minimum value; ； Where min() represents taking the minimum value, The constraint functions include The electromagnetic energy loss function of the excitation coil; The SCReg-PGNN magnetic energy loss model for supermagnetostrictive rods; Indicates the thickness of the flat copper wire in the excitation coil. Indicates the width of the flat copper wire in the excitation coil. This indicates the inner diameter of the excitation coil. This indicates the number of turns of a single conductor in the radial direction of the excitation coil. This indicates the number of coil turns in the height direction of the excitation coil. This represents the effective value of the excitation current. Indicates ambient temperature. The imaginary part of the complex permeability of a supermagnetostrictive rod is represented by the following: Indicates the frequency of the excitation current. Indicates the diameter of the magnetostrictive rod. Indicates the number of kerfs in the magnetostrictive rod. This represents the magnetic flux density of the magnetostrictive rod. This indicates the prestress in the magnetostrictive rod. The bias magnetic field representing the supermagnetostrictive rod; The constraint function includes the amplitude constraint function of the AC excitation magnetic field. and the amplitude constraint function of the output force of the supermagnetostrictive rod ; ； Where max() represents taking the maximum value; This indicates the total number of turns of the excitation coil. Indicates the outer diameter of the excitation coil. Indicates the coil height. This represents the radial distance from a point inside the giant magnetostrictive rod to the central axis of the coil; Young's modulus of the supermagnetostrictive rod; The cross-sectional area of ​​the supermagnetostrictive rod; The saturation magnetostrictive strain of the supermagnetostrictive rod; This represents the saturation magnetic field strength. The prestress coupling coefficient; The excitation magnetic field for the supermagnetostrictive rod.

2. The method for optimizing electromagnetic energy loss of a giant magnetostrictive transducer based on SCReg-PGNN as described in claim 1, characterized in that, The SCReg-PGNN magnetic energy loss model of the super magnetostrictive rod adopts the SCReg-PGNN neural network model; the SCReg-PGNN neural network model includes, in order of data processing, a feature adaptive sparse graph structure module, a feature encoding module, an information transmission and feature fusion module, and a graph recovery module. The input to the adaptive sparse graph structure module is the original graph structure information, which includes the node feature matrix constructed from the geometric structure data of the giant magnetostrictive rod and the working condition data. The adaptive sparse graph structure module first calculates the cosine similarity of the working conditions between each node, and then determines whether to retain the connection relationship between the nodes based on the preset similarity threshold. Node pairs with similarity higher than the threshold retain the edges, while node pairs with similarity lower than the threshold have their edges pruned, thereby obtaining the sparse graph structure information and outputting the sparse graph structure information matrix. The feature encoding module performs high-dimensional embedding mapping on the node features in the output sparse graph structure information matrix through a multilayer perceptron and outputs a node embedding matrix to extract discriminative features and enhance node representation capabilities. The input to the information transmission and feature fusion module is a node embedding matrix, which includes information about the node and its nearby nodes, as well as edge information. The information transmission and feature fusion module is based on the message transmission mechanism of graph neural networks. It performs multiple rounds of iterative aggregation of the node embedding matrix and the corresponding neighboring node information, and at the same time fuses the edge feature information to improve the globality and context relevance of node features, and outputs the fused node embedding matrix. The graph restoration module maps the node embedding features of the node embedding matrix to the specific task target space through the decoder and regression prediction unit, and outputs the node-level prediction results, namely the electromagnetic energy loss values ​​of the giant magnetostrictive rod at each node.

3. The method for optimizing electromagnetic energy loss of a giant magnetostrictive transducer based on SCReg-PGNN as described in claim 2, characterized in that, The adaptive sparsification graph structure module introduces a graph construction strategy based on cosine similarity to achieve sparsification of the graph structure and relation filtering: ； In the formula, Indicates working conditions , Indicates working conditions , Indicates working conditions , Similarity between them This indicates the threshold for similarity in operating conditions. Represents the adjacency matrix. Represents the dimension of a vector. express The One portion, express The Each component.

4. The method for optimizing electromagnetic energy loss of a supermagnetic-strict transducer based on SCReg-PGNN as described in claim 2, characterized in that, The information transmission and feature fusion module introduces a residual connection mechanism to superimpose the node features of the previous layer with the current update result. That is, after completing the message transmission and feature transformation of the current layer, the input features of the previous layer are superimposed with the calculation results of the current layer to form the final output. The first step of the residual connection mechanism is to calculate intermediate features for the current layer by passing messages: ； In the formula, Indicates the current layer. Represents the neighborhood aggregation function. Represents the learnable weight matrix. This represents the input features of the previous layer. This indicates that the current layer is not inactive for output; The second step of the residual join mechanism is residual path processing, which involves linear projection if the dimensions do not match. ； In the formula, Represents the residual path feature matrix. Represents a learnable linear projection matrix; The third step of the residual connection mechanism is feature overlay, which adds the current layer result to the residual path features: ； In the formula, This represents the output of the current layer after residual connection. Indicates the activation function; The information transmission and feature fusion module is for connecting nodes and edge The update process consists of two phases: in the message construction phase, node features of the current layer are extracted from the nodes at both ends of the edge. and and the characteristics of the edge itself. Concatenating to form a message vector During the state update phase, the message vector is... The input MLP obtains the updated features of the edges through nonlinear mapping. The specific update process is shown in the following equation: ； in, Indicates the edge features of the next layer; Node features The update depends on the feature aggregation of its adjacent edges and the fusion of its own state. Nodes receive feature information from neighboring nodes through edge connections and, during the update phase, use MLP to process the message vector. The fusion with its own representation is calculated as follows: ； in, It is the edge feature between nodes; For the set of neighboring nodes; This represents a message passing function; It is an update function; The features are concatenated into tensors; This represents the updated node characteristics.

5. The method for optimizing electromagnetic energy loss of a giant magnetostrictive transducer based on SCReg-PGNN as described in claim 1, characterized in that, The loss function of the SCReg-PGNN magnetic energy loss model for the supermagnetostrictive rod. as follows: ； in, Indicates working conditions and working conditions Similarity; For working conditions Predicted magnetic energy loss values ​​under the following conditions; The hyperparameters for controlling the regularization strength; This represents the prediction loss of the model nodes; This represents the loss due to physical consistency constraints.

6. The method for optimizing electromagnetic energy loss of a giant magnetostrictive transducer based on SCReg-PGNN as described in claim 1, characterized in that, The method for constructing the magnetic energy loss dataset of the supermagnetostrictive rod in step two is as follows: 2.1) Construct a magnetic energy loss testing platform for supermagnetostrictive rods; 2.2) Determine the calculation method for magnetic energy loss of giant magnetostrictive rods: Constitutive relations of supermagnetostrictive rods characterized by complex permeability ； Indicates an excitation magnetic field. This represents the amplitude of the excitation magnetic field. Represents a complex exponential function. Indicates magnetic flux density. Indicates the amplitude of magnetic flux density. Represents a complex exponential function. Indicates an alternating excitation magnetic field and magnetic induction intensity The phase difference between them Indicates angular velocity, Indicates time, The symbol representing the imaginary part of a complex number. Represents the permeability of free space. The real part of the complex permeability of the supermagnetostrictive rod is represented by . denoted by represents the imaginary part of the complex permeability of a supermagnetostrictive rod; Furthermore, the magnetic energy loss of the magnetostrictive rod Represented as: ； In the formula, Indicates the frequency of the excitation magnetic field; This indicates the volume of the supermagnetostrictive rod. This represents the magnetic energy loss per unit volume of a giant magnetostrictive rod; ； In the formula, Represents the relative permeability of the magnetostrictive rod; 2.3) Obtain magnetic energy loss data of supermagnetostrictive rods under different prestress and temperature, different temperature and excitation frequency, different temperature and magnetic induction intensity, different prestress and excitation frequency, different prestress and magnetic induction intensity, and different excitation frequency and magnetic induction intensity respectively, and form a magnetic energy loss dataset. 2.4) The magnetic energy loss dataset is constructed to form the training dataset. One data set in the training dataset includes the diameter of the supermagnetostrictive rod. Number of kerfs in supermagnetostrictive rods Excitation frequency of giant magnetostrictive rods Magnetic flux density of supermagnetostrictive rods Temperature of supermagnetostrictive rods Prestressed supermagnetostrictive rods and the bias magnetic field of the supermagnetostrictive rod .

7. The method for optimizing electromagnetic energy loss of a giant magnetostrictive transducer based on SCReg-PGNN as described in claim 1, characterized in that, When training the SCReg-PGNN magnetic energy loss model of the supermagnetic-strictive rod, the hyperparameters of the SCReg-PGNN magnetic energy loss model of the supermagnetic-strictive rod are optimized using Bayesian methods. The hidden layer dimension of the SCReg-PGNN magnetic energy loss model of the supermagnetic-strictive rod is set to 128, the message passing step is 4 steps, and the dropout rate is 0.005 to suppress the risk of overfitting. The aggregation method is SUM, and residual connection is also provided to alleviate the difficulty of training deep networks and prevent oversmoothing. During the entire training process, the training samples are iterated within 100 rounds, the batch size is set to 20, and each round is iterated 30 times. The learning rate uses an adaptive learning rate processing method: ； In the formula, The learning rate at which decay begins. Indicates the attenuation factor. This represents the total number of decay steps. Indicates the current round number. Indicates the number of rounds from which decay begins. This represents the minimum learning rate. This represents the learning rate obtained after the update.

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