A Rapid Design Method for Electromagnetic Ultrasonic Transducers Based on the S-SADE Algorithm

Abstract

This invention discloses a rapid design method for electromagnetic ultrasonic transducers based on the S-SADE algorithm. The method includes constructing an electromagnetic ultrasonic transducer model and a co-simulation platform; acquiring initial sample data and parameters; initializing the population and sample database; constructing an RBF surrogate model using samples from the database; performing mutation and crossover operations on parent population individuals according to five mutation strategies to obtain offspring populations; using the RBF surrogate model to predict the fitness values ​​of offspring individuals; transmitting the parameters of the optimal individual to the electromagnetic ultrasonic transducer model for simulation evaluation and updating the database; selecting the most promising offspring population from the five subpopulations as the next generation population; and outputting the optimal parameter design scheme. The adaptive differential evolution algorithm in this invention can select appropriate mutation strategies and control parameters at different evolutionary stages, and uses the surrogate model to predict the objective function values ​​of population individuals instead of expensive simulation evaluation, thus significantly saving computational resources.

Description

Technical Field

[0001] This invention relates to the fields of electromagnetic ultrasonic transducer manufacturing and evolutionary computation, and particularly to a rapid design method for electromagnetic ultrasonic transducers based on the S-SADE algorithm. Background Technology

[0002] Electromagnetic ultrasonic transducers are a new type of electroacoustic converter based on electromagnetic-ultrasonic conversion technology. They are also non-contact transducers integrating ultrasonic transmitters and receivers, widely used in ultrasonic non-destructive testing. Structural optimization of electromagnetic ultrasonic transducers can improve energy conversion efficiency, enhance frequency response characteristics, and reduce manufacturing complexity, thereby improving manufacturing and assembly convenience and providing higher reliability for their applications. Structural optimization of electromagnetic ultrasonic transducers typically involves optimizing five parameters: magnet radius, magnet height, CML coil width, lifting distance, and alternating current. The optimization objective is to maximize signal amplitude, which is a single-objective optimization problem. Furthermore, the design and optimization of electromagnetic ultrasonic transducers often require extensive and time-consuming model simulations using COMSOL Multiphysics software. The high simulation time cost significantly reduces the solution efficiency of existing optimization methods, making improving the optimization efficiency of electromagnetic ultrasonic transducers a pressing task.

[0003] For such expensive optimization problems, traditional evolutionary algorithms are computationally costly and inefficient, consuming significant resources. Therefore, specialized optimization strategies and algorithms are needed to accelerate the solution process and improve efficiency. In recent years, researchers have proposed evolutionary algorithms assisted by surrogate models to solve these expensive optimization problems. This method combines the global search capability of evolutionary algorithms with the high computational efficiency of surrogate models. To reduce computational resource consumption during optimization, a surrogate model is constructed using solutions evaluated by the true objective function. The surrogate model then predicts the objective function value instead of the expensive true evaluation, significantly reducing the number of true evaluations, lowering time costs, and enabling the finding of high-quality solutions within limited computational resources. Using evolutionary algorithms assisted by surrogate models for parameter design of electromagnetic ultrasonic transducers can improve their conversion performance and increase the efficiency of non-destructive testing, which has significant practical implications for promoting industrial automation.

[0004] In the process of realizing this invention, the inventors discovered the following technical problems in the prior art:

[0005] While some adaptive differential evolution algorithms have been used to solve single-objective optimization problems, their potential remains largely untapped. On one hand, some adaptive differential evolution algorithms do not simultaneously consider multiple mutation strategies and different control parameters, thus failing to select the most suitable strategy and parameters at different evolutionary stages. On the other hand, to obtain higher-quality solutions during the optimization process, a large amount of time-consuming trial-and-error searching is usually required to find the most suitable strategy and related parameter values. This process consumes a significant amount of function evaluation, resulting in low optimization efficiency. Furthermore, in some adaptive differential evolution algorithms assisted by surrogate models, the error between the model's predictions and the actual values ​​is large. The update strategy of the surrogate model affects the accuracy of the model's predictions and consequently, the algorithm's performance. The model update strategy involves how to update the model during the iteration of the evolutionary algorithm, and the key lies in how to select the sample data used to train the surrogate model. If the sample is insufficient or unrepresentative, it may reduce the accuracy of the model's predictions. Summary of the Invention

[0006] The purpose of this invention is to solve the above-mentioned problems by developing a rapid design method for electromagnetic ultrasonic transducers based on the S-SADE algorithm. This method integrates a surrogate model and an adaptive differential evolution algorithm, which can efficiently solve the parameter design problem of electromagnetic ultrasonic transducers.

[0007] The technical solution adopted in this invention is: a rapid design method for electromagnetic ultrasonic transducers based on the S-SADE algorithm, comprising the following steps:

[0008] S1. Use COMSOL software to establish a simulation model of the electromagnetic ultrasonic transducer and build a MATLAB-COMSOL co-simulation platform.

[0009] S2, acquire sample data, initialize parameters, population and sample database;

[0010] S3, during the evolution process, uses samples from the database to build an RBF surrogate model;

[0011] S4, five offspring populations are obtained by performing mutation and crossover operations on the parent population according to five mutation strategies;

[0012] S5, use the surrogate model to evaluate the objective function value of the offspring individuals and perform the selection operation, pass the parameters of the best individual in each offspring population to the electromagnetic ultrasonic transducer model and perform simulation evaluation, update the database and the global best individual in the offspring population;

[0013] S6: Select the most promising offspring from the five offspring populations as the next generation population;

[0014] S7: Determine if the maximum number of true evaluations has been reached; if yes, stop evolution and output the optimal parameter design scheme; otherwise, proceed to S3 to continue the search process.

[0015] Furthermore, the specific steps of S1 include:

[0016] S11. In COMSOL simulation software with multiple physics modules, a finite element model for electromagnetic ultrasonic transducer simulation is built. Materials are selected and parameters are set. The physical fields of the constructed model are selected and set. Excitation sources are added to the model and mesh is generated.

[0017] S12, construct a finite element model using the AC / DC module and the magnetic field module, and the structural mechanics module for the generation and transmission of SV waves; the finite element model consists of a CML coil, a cylindrical magnet, an aluminum plate, surrounding air, and an infinite domain;

[0018] S13, the optimization objective is to maximize the single-point signal amplitude of the designed electromagnetic ultrasonic transducer model. The objective function can be defined as:

[0019] Max f(x)=A w,i(x)

[0020] Among them, A w,i(x) It is the signal amplitude at the i-th observation point. Each observation point x = [R, H, W, L, I] contains multiple optimized parameters, where R is the magnet radius, H is the magnet height, W is the CML coil width, L is the lifting distance, and I is the alternating current.

[0021] S14. Construct a MATLAB-COMSOL co-simulation platform to realize the functions of calling COMSOL models, modifying optimization variable values, performing simulation calculations and outputting optimization objectives in MATLAB, that is, to realize the automated operation of the electromagnetic ultrasonic transducer parameter optimization algorithm and the real-time feedback of simulation results.

[0022] Furthermore, the specific steps of S2 include:

[0023] S21, Initialize population size NP, maximum number of true evaluations F max Maximum number of iterations G m Learn algebraic LP;

[0024] S22, 100 sets of data are randomly generated within the parameter variation range of each optimization variable as the initial population individuals, that is, each individual corresponds to a set of optimization parameters;

[0025] S23, the data of each individual in the initial population is transmitted to the COMSOL software through the MATLAB-COMSOL joint simulation platform, the parameters of the electromagnetic ultrasonic transducer are set and the simulation is run to calculate the single-point signal amplitude, the results are output to Matlab, 100 real samples are obtained and stored in the database.

[0026] S24. For the maximization problem, sort the initial samples according to the objective function value from largest to smallest, select the top NP individuals with the largest objective function value as the initial population, and store them in the database.

[0027] Furthermore, the specific steps of S3 include:

[0028] S31, If ​​the number of samples in the database is greater than 2NP, sort them in descending order of objective function value, keep the first 2NP samples, and delete the other samples;

[0029] S32, randomly select NP samples from the database as training data to train the RBF proxy model.

[0030] Furthermore, the specific steps of S4 include:

[0031] S41, Adaptive adjustment of the mutation operator F. The mutation operator F controls the amplification effect of the deviation variable. To balance the global search capability and local exploitation capability of the algorithm, the mutation operator F in each generation is set to change dynamically according to the following formula:

[0032]

[0033] Among them, G m This represents the maximum number of iterations, gen represents the current number of iterations, and F0 is a constant set to 0.4.

[0034] S42, Mutation Operation: In the differential evolution algorithm, the mutation operation is used to generate a mutation vector for each individual in the current population. For each target vector x... i,G The mutation vector v is generated according to the following five mutation methods respectively. i,G ;

[0035] 1) DE / rand / 1,

[0036]

[0037] 2) DE / best / 1,

[0038]

[0039] 3) DE / rand-to-best / 1,

[0040]

[0041] 4) DE / best / 2,

[0042]

[0043] 5) DE / rand / 2,

[0044]

[0045] In the formula, x best,G It is the best individual in the current population; the randomly selected indices r1, r2, r3, r4, r5 are all different from the target vector indices i.

[0046] S43, Adaptive adjustment of the crossover operator CR. Before the LP generation, the crossover operator CR of the k-th mutation strategy is determined by a normal distribution N(CRm). k (std) generates a set of CR values, which are assigned to each target vector;

[0047] Among them, CRm k `std` and `mean` represent the mean and variance, respectively. Initialize `CRm`. k The value of is 0.5, and the value of std is 0.1;

[0048] At the same time, a system named CRMemory was created. k The archive is used to store the CR values ​​of the test vectors generated by the k-th policy in the previous LP generations that can successfully enter the next generation. After the LP generations, CRMemory... k The archive stores the CR values ​​of the previous LP generations; in the previous LP generations, the CR value of the k-th policy is generated by N(0.5, 0.1); in each generation after the LP generation, CRm is... k Set as CRMemory k The average value of the stored data, the CR value of the k-th strategy is determined by N(CRm) k Generate, 0.1);

[0049] S44, Crossover Operation: To increase the diversity of the disturbance parameter vector, a binomial crossover operation is introduced after the mutation operation to generate the test vector u. ji,G :

[0050]

[0051] (i=1,2,…,NP; j=1,2,…,D)

[0052] In the formula, randb(j) represents the j-th estimate of the random number generator between [0,1]; D represents the dimension of the problem; rnbr(i)∈1,2,…,D represents a randomly selected sequence.

[0053] Furthermore, the specific steps of S5 include:

[0054] S51, using a contemporary trained RBF surrogate model to predict the objective function value of offspring individuals;

[0055] S52, Selection operation, to determine the test vector u i,G Whether it will enter the next generation of the population depends on the greedy behavior of the experimental vector u. i,G With the target vector x i,G Comparison, if the test vector u i,G If the objective function value is larger, then the test vector u i,G It is preserved to the next generation of the population, and its CR value is stored in CRMemory. k middle;

[0056]

[0057] S53, select the individual with the largest objective function value in each offspring population as the filling solution, and transmit their values ​​to the COMSOL simulation software through the MATLAB-COMSOL co-simulation platform to set the parameters of the electromagnetic ultrasonic transducer, run the simulation to calculate the single-point signal amplitude, output the results to Matlab and update its objective function value;

[0058] S54, determine whether the individual exists in the database; if not, add the individual and its objective function value to the database;

[0059] S55. Compare the objective function value of this individual with that of the global best individual in the current subpopulation. If the objective function value of this individual is larger, then update this individual as the global best individual.

[0060] Furthermore, the specific steps of S6 include:

[0061] S61 is used to select the most promising subpopulation from the five subpopulations obtained from S5. The average fitness value of all individuals in each subpopulation is calculated, and the subpopulation with the highest average fitness value will be used as the initial subpopulation for the next generation. The calculation formula is as follows:

[0062]

[0063] S62, select the subpopulation as the initial population for the next generation, and update the globally optimal individual in the subpopulation to the globally optimal individual.

[0064] The beneficial effects of this invention are:

[0065] 1. Adaptive selection mutation strategy can select appropriate strategies at different stages of evolution, thereby accelerating the convergence speed;

[0066] 2. Adaptive adjustment of mutation and crossover operators can balance the global search capability and local exploitation capability of the algorithm;

[0067] 3. Using surrogate models to predict the objective function values ​​of individuals in the population can reduce the number of real simulation evaluations in the parameter design of electromagnetic ultrasonic transducers, save computing resources, and improve the solution speed. Attached Figure Description

[0068] Figure 1 This is a flowchart of the algorithm of the present invention;

[0069] Figure 2 This is a schematic diagram of the electromagnetic ultrasonic transducer model. Detailed Implementation

[0070] The invention will now be further described with reference to the accompanying drawings.

[0071] like Figure 1 As shown, this invention is a rapid design method for electromagnetic ultrasonic transducers based on the S-SADE algorithm, comprising the following steps:

[0072] S1. Use COMSOL software to establish a simulation model of the electromagnetic ultrasonic transducer and build a MATLAB-COMSOL co-simulation platform; the specific steps are as follows:

[0073] S11. In COMSOL simulation software with multiple physics modules, a finite element model for electromagnetic ultrasonic transducer simulation is built. Materials are selected and parameters are set. The physical fields of the constructed model are selected and set. Excitation sources are added to the model and mesh is generated.

[0074] S12, the constructed finite element model is as follows Figure 2 As shown, the model uses an AC / DC module and a magnetic field module, while a structural mechanics module is used for the generation and transmission of SV waves. This finite element model consists of a CML coil, a cylindrical magnet, an aluminum plate, surrounding air, and an infinite domain, acting on infinite space to ensure the stability and convergence of the solution.

[0075] S13, the optimization objective is to maximize the single-point signal amplitude of the designed electromagnetic ultrasonic transducer model. The objective function can be defined as:

[0076] Max f(x)=A w,i(x)

[0077] Where A w,i(x) It is the signal amplitude at the i-th observation point. Each observation point x = [R, H, W, L, I] contains multiple optimized parameters, where R is the magnet radius, H is the magnet height, W is the CML coil width, L is the lifting distance, and I is the alternating current.

[0078] S14. Construct a MATLAB-COMSOL co-simulation platform to realize the functions of calling COMSOL models, modifying optimization variable values, performing simulation calculations and outputting optimization objectives in MATLAB, that is, to realize the automated operation of the electromagnetic ultrasonic transducer parameter optimization algorithm and the real-time feedback of simulation results.

[0079] S2, acquire sample data, initialize parameters, population, and sample database; specific steps are as follows:

[0080] S21, Initialize population size NP, maximum number of true evaluations F max Maximum number of iterations G m Learn algebraic LP.

[0081] S22, 100 sets of data are randomly generated within the parameter variation range of each optimization variable as the initial population individuals, that is, each individual corresponds to a set of optimization parameters.

[0082] S23. The data of each individual in the initial population is transmitted to the COMSOL software through the MATLAB-COMSOL co-simulation platform. The parameters of the electromagnetic ultrasonic transducer are set and the simulation is run to calculate the single-point signal amplitude. The results are output to Matlab to obtain 100 real samples and store them in the database.

[0083] S24. For the maximization problem, sort the initial samples according to the objective function value from largest to smallest, select the top NP individuals with the largest objective function value as the initial population, and store them in the database.

[0084] S3, during the evolutionary process, utilizes samples from the database to construct an RBF surrogate model; the specific steps are as follows:

[0085] S31. If the number of samples in the database is greater than 2NP, sort them in descending order of objective function value, retain the first 2NP samples, and delete the other samples.

[0086] S32, randomly select NP samples from the database as training data to train the RBF proxy model.

[0087] S4, perform mutation and crossover operations on the parent population according to five mutation strategies to obtain five offspring populations; the specific steps are as follows:

[0088] S41, Adaptive adjustment of the mutation operator F. The mutation operator F controls the amplification effect of the deviation variable. To balance the global search capability and local exploitation capability of the algorithm, the mutation operator F in each generation is set to change dynamically according to the following formula:

[0089]

[0090] Among them, G m This represents the maximum number of iterations, gen represents the current number of iterations, and F0 is a constant set to 0.4.

[0091] S42, Mutation Operation: In the differential evolution algorithm, the mutation operation is used to generate a mutation vector for each individual in the current population. For each target vector x... i,G The mutation vector v is generated according to the following five mutation methods respectively. i,G :

[0092] 1) DE / rand / 1:

[0093]

[0094] 2) DE / best / 1:

[0095]

[0096] 3) DE / rand-to-best / 1:

[0097]

[0098] 4) DE / best / 2:

[0099]

[0100] 5) DE / rand / 2:

[0101]

[0102] In the formula, x best,G It is the best individual in the current population; the randomly selected indices r1, r2, r3, r4, r5 are all different from the target vector indices i.

[0103] S43, Adaptive adjustment of the crossover operator CR. Before the LP generation, the crossover operator CR of the k-th mutation strategy is determined by a normal distribution N(CRm). k (std) generates a set of CR values, which are assigned to each target vector. Where CRm k `std` and `mean` represent the mean and variance, respectively. Initialize `CRm`. k The value of is 0.5, and the value of std is 0.1; at the same time, a memory named CRMemory is created. k The archive is used to store the CR values ​​of the test vectors generated by the k-th policy in the previous LP generations that can successfully enter the next generation. After the LP generations, CRMemory... kThe archive stores the CR values ​​of the previous LP generations. Specifically, in the previous LP generations, the CR value of the k-th policy is generated by N(0.5, 0.1); in each generation after the LP generation, the CRm is... k Set as CRMemory k The average value of the stored data, the CR value of the k-th strategy is determined by N(CRm) k ,0.1) generated.

[0104] S44, Crossover Operation: To increase the diversity of the disturbance parameter vector, a binomial crossover operation is introduced after the mutation operation to generate the test vector u. ji,G :

[0105]

[0106] (i=1,2,…,NP; j=1,2,…,D)

[0107] In the formula, randb(j) represents the j-th estimate of the random number generator between [0,1]; D represents the dimension of the problem; rnbr(i)∈1,2,…,D represents a randomly selected sequence.

[0108] S5, using a surrogate model to evaluate the objective function value of offspring individuals and perform a selection operation, passing the parameters of the optimal individual in each offspring population to the electromagnetic ultrasonic transducer model for simulation evaluation, and updating the database and the globally optimal individual in the subpopulation; the specific steps are as follows:

[0109] S51, using a contemporary trained RBF surrogate model to predict the objective function value of offspring individuals;

[0110] S52, Selection operation, to determine the test vector u i,G Whether it will enter the next generation of the population depends on the greedy behavior of the experimental vector u. i,G With the target vector x i,G Comparison, if the test vector u i,G If the objective function value is larger, then the test vector u i,G It is preserved to the next generation of the population, and its CR value is stored in CRMemory. k middle;

[0111]

[0112] S53. Select the individual with the largest objective function value in each offspring population as the filling solution, and transmit their values ​​to the COMSOL simulation software through the MATLAB-COMSOL co-simulation platform to set the parameters of the electromagnetic ultrasonic transducer. Run the simulation to calculate the single-point signal amplitude, output the results to Matlab and update its objective function value.

[0113] S54, determine whether the individual is in the database; if not, add the individual and its objective function value to the database.

[0114] S55. Compare the objective function value of this individual with that of the global best individual in the current subpopulation. If the objective function value of this individual is larger, then update this individual as the global best individual.

[0115] S6, select the most promising offspring from the five offspring populations as the next generation population; the specific steps are as follows:

[0116] S61 is used to select the most promising subpopulation from the five subpopulations obtained from S5. The average fitness value of all individuals in each subpopulation is calculated, and the subpopulation with the highest average fitness value will be used as the initial subpopulation for the next generation. The calculation formula is as follows:

[0117]

[0118] S62, select the subpopulation as the initial population for the next generation, and update the globally optimal individual in the subpopulation to the globally optimal individual.

[0119] S7: Determine if the maximum number of true evaluations has been reached; if yes, stop evolution and output the optimal parameter design scheme; otherwise, proceed to S3 to continue the search process.

[0120] To verify the ability of the fusion surrogate model and the adaptive differential evolution algorithm S-SADE designed in this invention to solve the electromagnetic ultrasonic transducer parameter design problem, the proposed S-SADE algorithm is compared with the adaptive differential evolution algorithm SADE without using a surrogate model. The population size for all algorithms is set to NP = 20, and the maximum number of true evaluations is set to F. max =50. Due to limited computing resources, all algorithms were run independently once. All algorithms were run on the MATLAB-COMSOL co-simulation platform. The simulation evaluation of the optimal individual was performed in the COMSOL software. MATLAB and COMSOL communicate with each other through an API interface.

[0121] Table 1 shows the approximate global optimal solutions and objective values ​​obtained by all algorithms in a single run. The optimization objective of the electromagnetic ultrasonic transducer designed in this experiment is to maximize the single-point signal amplitude. As observed in the table, the optimization result of the S-SADE algorithm designed in this invention is 1.2207e-6, while the optimization result of the SADE algorithm without surrogate model assistance is 1.1592e-6. The S-SADE algorithm achieves a better optimization result than the SADE algorithm. Furthermore, in terms of time overhead, the S-SADE algorithm consumes significantly less time than the SADE algorithm. The comprehensive experimental results demonstrate that the S-SADE algorithm designed in this invention can effectively handle the structural optimization design problem of electromagnetic ultrasonic transducers.

[0122] Table 1. Experimental Results of Electromagnetic Ultrasonic Transducer Parameter Design

[0123]

[0124] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A rapid design method for electromagnetic ultrasonic transducers based on the S-SADE algorithm, characterized in that, Includes the following steps: S1. Use COMSOL software to establish a simulation model of the electromagnetic ultrasonic transducer and build a MATLAB-COMSOL co-simulation platform; specific steps include: S11. In COMSOL simulation software with multiple physics modules, a finite element model for electromagnetic ultrasonic transducer simulation is built. Materials are selected and parameters are set. The physical fields of the constructed model are selected and set. Excitation sources are added to the model and mesh is generated. S12, the constructed finite element model uses AC / DC module and magnetic field module, and structural mechanics module for the generation and transmission of SV waves; the finite element model consists of CML coil, cylindrical magnet, aluminum plate, surrounding air and infinite domain; S13, the optimization objective is to maximize the single-point signal amplitude of the designed electromagnetic ultrasonic transducer model. The objective function can be defined as: in, It is the signal amplitude at the i-th observation point, and each observation point It includes several optimized parameters, where R is the magnet radius, H is the magnet height, W is the CML coil width, L is the lifting distance, and I is the alternating current; S14. Construct a MATLAB-COMSOL co-simulation platform, call the COMSOL model in Matlab, modify the value of optimization variables, perform simulation calculations and output the optimization target, realize the automated operation of the electromagnetic ultrasonic transducer parameter optimization algorithm and the real-time feedback of simulation results; S2, acquire sample data, initialize parameters, population, and sample database; specific steps include: S21, Initialize population size NP, Maximum number of true evaluations Maximum number of iterations Learn algebraic LP; S22, 100 sets of data are randomly generated within the parameter variation range of each optimization variable as the initial population individuals, that is, each individual corresponds to a set of optimization parameters; S23, the data of each individual in the initial population is transmitted to the COMSOL software through the MATLAB-COMSOL joint simulation platform, the parameters of the electromagnetic ultrasonic transducer are set and the simulation is run to calculate the single-point signal amplitude, the results are output to Matlab, 100 real samples are obtained and stored in the database. S24. For the maximization problem, sort the initial samples according to the objective function value from largest to smallest, select the top NP individuals with the largest objective function value as the initial population, and store them in the database. S3, during the evolutionary process, utilizes samples from the database to construct an RBF surrogate model; specific steps include: S31, If ​​the number of samples in the database is greater than 2NP, sort them in descending order of objective function value, keep the first 2NP samples, and delete the other samples; S32, randomly select NP samples from the database as training data to train the RBF surrogate model; S4 involves performing mutation and crossover operations on the parent population using five different mutation strategies to obtain five offspring populations; the specific steps include: S41, Adaptive adjustment of the mutation operator F. The mutation operator F controls the amplification effect of the deviation variable. To balance the global search capability and local exploitation capability of the algorithm, the mutation operator F in each generation is set to change dynamically according to the following formula: in, The maximum number of iterations is represented by 'gen', and the current number of iterations is represented by 'gen'. Set the constant to 0.4; S42, Mutation Operation: In the Differential Evolutionary Algorithm, the mutation operation is used to generate a mutation vector for each individual in the current population. For each target vector... Generate mutation vectors according to the following five mutation methods. ; 1) DE / rand / 1: 2) DE / best / 1: 3) DE / rand-to-best / 1: 4) DE / best / 2: 5) DE / rand / 2: In the formula, It is the best individual in the current population; the randomly selected sequence number. , , , , With the target vector index They are all different; S43, adaptively adjust the crossover operator CR. Before the LP generation, the crossover operator CR of the k-th mutation strategy is determined by the normal distribution N( (std) generates a set of CR values, which are assigned to each target vector; in, `std` and `mean` represent the mean and variance, respectively. (Initial settings) The value of is 0.5, and the value of std is 0.1; At the same time, a name was established The archive is used to store the CR values ​​of the test vectors that can successfully enter the next generation generated by the k-th policy in the previous LP generations. After the LP generations, The archive stores the CR values ​​of the previous LP generations; in the previous LP generations, the CR value of the k-th policy is generated by N(0.5, 0.1); in each generation after the LP generation, the CR value will be... Set as The average value of the stored data, the CR value of the k-th strategy is determined by N ( Generate, 0.1); S44, Crossover Operation: To increase the diversity of the disturbance parameter vectors, a binomial crossover operation is introduced after the mutation operation to generate the test vectors. : In the formula, Indicates generation The j-th estimate of the random number generator; D represents the dimension of the problem; Represents a randomly selected sequence; S5, using a surrogate model to evaluate the objective function value of offspring individuals and perform a selection operation, passing the parameters of the optimal individual in each offspring population to the electromagnetic ultrasonic transducer model for simulation evaluation, and updating the database and the globally optimal individual in the offspring population; specific steps include: S51, using a contemporary trained RBF surrogate model to predict the objective function value of offspring individuals; S52, Select operation, to determine the test vector Whether it will enter the next generation of the population, according to the greedy law, the experimental vector will be... With the target vector Comparison, if the test vector If the objective function value is larger, then the experimental vector It is preserved to the next generation of the population, and its CR value is stored in middle; ； S53, select the individual with the largest objective function value in each offspring population as the filling solution, transmit their values ​​to the COMSOL simulation software through the MATLAB-COMSOL co-simulation platform, set the parameters of the electromagnetic ultrasonic transducer, run the simulation to calculate the single-point signal amplitude, output the results to Matlab and update its objective function value; S54, determine whether the individual exists in the database; if not, add the individual and its objective function value to the database; S55: Compare the objective function value of this individual with that of the global best individual in the current subpopulation. If the objective function value of this individual is larger, then update this individual as the global best individual. S6, select the most promising offspring from the five offspring populations as the next generation population; the specific steps include: S61 is used to select the most promising subpopulation from the five subpopulations obtained from S5. The average fitness value of all individuals in each subpopulation is calculated, and the subpopulation with the highest average fitness value will be used as the initial subpopulation for the next generation. The calculation formula is as follows: ； S62, select the subpopulation as the initial population for the next generation, and update the globally optimal individual in the subpopulation to the globally optimal individual; S7: Determine if the maximum number of true evaluations has been reached; if yes, stop evolution and output the optimal parameter design scheme; otherwise, proceed to S3 to continue the search process.

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