Electromagnetic ultrasonic transducer parameter design method based on S-SAMODE algorithm

Abstract

The invention discloses an electromagnetic ultrasonic transducer parameter design method based on an S-SAMODE algorithm. The method comprises the following steps: constructing an electromagnetic ultrasonic transducer model and a joint simulation platform; acquiring sample data, initialization parameters, an initialization population, a sample database and a high-quality file; using the samples in the database to construct an RBF proxy model; performing variation and crossover operation on the parent population according to five variation strategies to obtain test vectors; and evaluating an objective function value of the test vector by using the proxy model, executing a selection operation to obtain a filial generation population, selecting a next generation population, selecting a filling solution from a new population, transmitting parameters of the filling solution to the electromagnetic ultrasonic transducer model for simulation evaluation, updating a high-quality archive and a sample database, and outputting an optimal solution set. According to the method, the multi-objective optimization problem in the electromagnetic ultrasonic transducer design is solved by using the S-SAMODE algorithm, and the objective function value of the population individual is predicted by using the proxy model to replace the simulation evaluation, so that the computing resources can be saved to a great extent.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic ultrasonic transducer manufacturing, and in particular relates to an electromagnetic ultrasonic transducer parameter design method based on an S-SAMODE algorithm. Background Art

[0002] Electromagnetic ultrasonic transducer is a device that uses electromagnetic principles to generate and receive ultrasonic waves. It is widely used in industrial non-destructive testing, medical imaging and other fields. Through reasonable parameter design, the structure of electromagnetic ultrasonic transducer is optimized, which can improve the performance and quality of electromagnetic ultrasonic transducer, optimize its energy efficiency and reliability, reduce manufacturing cost, and provide better help for practical applications. The structural optimization problem of electromagnetic ultrasonic transducer involves multiple goals, and it is necessary to maximize the single point amplitude and minimize the amplitude ratio at the same time. Moreover, there are generally conflicts between these goals, and it is impossible to achieve the optimal at the same time. Optimizing one goal may harm other goals, so it is necessary to find a balance between different goals. In addition, obtaining each target value requires time-consuming COMSOL simulation analysis. The single simulation analysis time is long, which is a typical multi-objective expensive optimization problem. Its high computational cost leads to low optimization efficiency. How to efficiently solve such problems and how to improve the optimization efficiency of electromagnetic ultrasonic transducers is an urgent topic to study.

[0003] Due to the high computational cost of expensive multi-objective optimization problems, traditional optimization algorithms consume a lot of computing resources and are inefficient when solving such problems. Therefore, special optimization strategies and algorithms are needed to accelerate the solution process and improve the optimization solution efficiency. In recent years, researchers have proposed using evolutionary algorithms assisted by surrogate models to solve expensive multi-objective optimization problems. Evolutionary algorithms have strong global search capabilities and robustness, and can effectively search for global optimal or near-optimal solutions in complex spaces. They have been widely used in many fields and achieved remarkable results. In addition, in order to reduce the consumption of computing resources in the optimization process, using the established surrogate model to predict the objective function value instead of expensive real evaluation can greatly reduce the number of real evaluations, and can find high-quality solutions within limited computing resources, thereby improving the efficiency and feasibility of solving practical application problems and effectively promoting the development of science and engineering.

[0004] In the process of implementing the present invention, the inventors found that the prior art has the following technical problems:

[0005] Although there are some methods that use surrogate model-assisted evolutionary algorithms to solve expensive multi-objective optimization problems, their potential has not yet been fully explored. On the one hand, surrogate model-assisted evolutionary algorithms usually include multiple parameters or strategies, such as the selection of surrogate models, adaptive strategies and parameters, etc. Dynamic adjustment of various parameters can adapt to different optimization problems and the needs of different optimization stages, which helps to balance the global search and model prediction capabilities so as to converge to the Pareto frontier faster. Therefore, how to choose appropriate parameters or strategies to obtain the best performance of the algorithm may be a challenge. On the other hand, the error between the model prediction value and the true value in the surrogate model-assisted evolutionary algorithm is large. The update strategy of the surrogate model will affect the accuracy of the model prediction and thus affect the performance of the algorithm. The model update strategy involves how to update the model in the iteration of the evolutionary algorithm. The key lies in how to select samples for training the surrogate model. If the samples are insufficient or unrepresentative, the accuracy of the model prediction may be reduced. Summary of the invention

[0006] The purpose of the present invention is to solve the above problems. The present invention discloses an electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm. By using a proxy model to assist a multi-objective differential evolution algorithm, the electromagnetic ultrasonic transducer parameter design problem can be efficiently solved.

[0007] The technical solution adopted by the present invention is: an electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm, comprising the following steps:

[0008] S1, use COMSOL simulation software to establish an electromagnetic ultrasonic transducer simulation model and build a MATLAB-COMSOL simulation platform;

[0009] S2, obtain sample data, initialization parameters, population, sample database and high-quality archive;

[0010] S3, construct the RBF proxy model using samples in the database;

[0011] S4, perform mutation and crossover operations on the parent population according to five mutation strategies to obtain the test vector;

[0012] S5, using the surrogate model to evaluate the objective function value of the test vector, performing a selection operation to obtain five offspring populations;

[0013] S6, select the next generation population from the five sub-populations, select the filling solution from the new population and perform simulation evaluation, and update the high-quality archive and sample database;

[0014] S7, determine whether the maximum number of true evaluations has been reached; if so, stop the evolution and output the Pareto solution set; otherwise, go to S3 to continue the search process.

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

[0016] S11, establishing a finite element model for electromagnetic ultrasonic transducer simulation in COMSOL simulation software with multiple physical field modules, selecting materials and setting parameters, selecting and setting physical fields for the constructed model, adding excitation sources to the model and performing meshing;

[0017] S12, the design goal of the multi-objective electromagnetic ultrasonic transducer model is to minimize the single-point amplitude of the A0 mode and S0 mode at the sampling point. The objective function is expressed as follows:

[0018] Min F(x)={f 1 (x),f 2 (x)}

[0019]

[0020] Where x is the sampling point, f 1 and f 2 Respectively represent the single point amplitude of A0 mode and S0 mode, and They are the sampling point x and the target value f 1 and f 2 The unknown relationship between them; each sampling point contains five decision variables, x = [R m1 ,R m2 ,H m ,g C ,I], where R m1 is the radius of the cylindrical magnet, R m2 is the inner diameter of the ring magnet, H m is the magnet height, g C is the lift-off distance, I represents the excitation current;

[0021] S13, build a MATLAB-COMSOL joint simulation platform to realize the functions of calling COMSOL models in Matlab, modifying optimization variable values, simulating and outputting optimization targets, that is, realizing the automatic operation of the electromagnetic ultrasonic transducer parameter optimization algorithm and real-time feedback of simulation results.

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

[0023] S21, initialization population size NP, maximum number of true evaluations F max , the maximum number of iterations G m , learn algebraic LP;

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

[0025] S23, transmit the data of each individual in the initial population to the simulation software through the MATLAB-COMSOL joint simulation platform, set the parameters of the electromagnetic ultrasonic transducer and run the simulation to calculate the single-point amplitude of the A0 mode and the S0 mode, output the results to Matlab, obtain 100 real samples and store them in the database;

[0026] S24, non-dominated sorting is performed on the initial samples according to the objective function value to divide them into different levels, and the crowding distance of all individuals in each level is calculated;

[0027] S25, using the elite strategy to select NP individuals from the initial sample as the initial population, and store them in the database;

[0028] S26: Store the individuals with non-dominated level 1 in the initial population into the high-quality archive EXA, that is, the non-dominated solution saved by EXA.

[0029] Further, the specific steps of S25 are:

[0030] S251, first put the individuals with non-dominant level 1 into the initial population, then put the individuals with non-dominant level 2 into the initial population, and so on;

[0031] S252, if after all the individuals of level m are placed in the initial population, the number of individuals in the population is less than NP, and after all the individuals of level m+1 are placed in the initial population, the number of individuals in the population is greater than NP, then all individuals of level m+1 are sorted in descending order according to the crowding distance, and are placed in the initial population one by one until the number of individuals in the population is equal to NP, and the remaining individuals are eliminated.

[0032] Furthermore, the specific steps of S3 include:

[0033] S31, if the number of samples in the database is greater than 2NP, then retain 2NP individuals according to the elite strategy described in S25 and delete other samples;

[0034] S32, randomly select NP individuals from the database as training samples to train the RBF proxy model.

[0035] Furthermore, the specific steps of S4 include:

[0036] S41, adaptively adjust the mutation operator F, the mutation operator F controls the amplification effect of the deviation variable, in order to balance the global search ability and local development ability of the algorithm, set the mutation operator F in each generation to change dynamically according to the following formula:

[0037]

[0038] Among them, G m represents the maximum number of iterations, gen represents the current number of iterations, and F 0 is set to 0.4 as a constant;

[0039] S42, mutation operation. The differential evolution algorithm uses mutation operation to generate mutation vectors for each individual in the current population. For each target vector x i,G , generate mutation vector v according to the following five mutation methods i,G ;

[0040] 1)DE / rand / 1:

[0041]

[0042] 2)DE / best / 1:

[0043]

[0044] 3)DE / rand-to-best / 1:

[0045]

[0046] 4)DE / best / 2:

[0047]

[0048] 5)DE / rand / 2:

[0049]

[0050] In the formula, x best,G It is randomly selected from the premium archives and x i,G Different individuals; randomly selected sequence number r 1 , r 2 , r 3 , r 4 , r 5 Different from the target vector serial number i;

[0051] S43, adaptively adjust the crossover operator CR, the crossover operator CR of the k-th mutation strategy is composed of the normal distribution N(CRm k , std) generates a set of CR values ​​and assigns them to each target vector;

[0052] Among them, CRm k and std are the mean and variance respectively, and CRm is initialized kThe value of is 0.5, and the value of std is 0.1;

[0053] At the same time, a CRMemory k The archive is used to store the CR values ​​of the trial vectors generated by the k-th strategy in the previous LP generation that can successfully enter the next generation; in the previous LP generation, the CR value of the k-th strategy is generated by N(0.5, 0.1); in each generation after the LP generation, CRm k Set to CRMemory k The average value of the data is stored in the CR value of the k-th strategy is N(CRm k , 0.1) generated;

[0054] S44, crossover operation, in order to increase the diversity of the interference parameter vector, a binomial crossover operation is introduced after the mutation operation is completed to generate the test vector u ji,G :

[0055]

[0056] Where randb(j) represents the jth estimate of a random number generator between [0,1]; D represents the dimension of the problem; rnbr(i)∈1,2,…,D represents a randomly selected sequence to ensure that u i,G At least from v i,G Get a parameter;

[0057] Furthermore, the specific steps of S5 include:

[0058] S51, predicting the objective function value of the test vector using the contemporary trained RBF surrogate model;

[0059] S52, selection operation, to determine the test vector u i,G Will it enter the next generation population? The test vector u i,G With the target vector x i,G For comparison, if u i,G Dominate x i,G , then the test vector u i,G is retained to the next generation of population; if u i,G x i,G Dominance, then the target vector x i,G be retained to the next generation population; if the two do not dominate each other, then u i,G 、x i,G Merge with the high-quality archive EXA, perform non-dominated sorting on the merged population and calculate the crowding distance. If u i,G The non-dominated level of is smaller, then the test vector u i,G is retained to the next generation of population; if x i,G The non-dominated level of is smaller, then the target vector xi,G is retained to the next generation population; if the non-dominated levels of the two are the same, the vector with the larger crowding distance is selected and retained to the next generation; if the test vector u i,G If it is retained to the next generation of population, its CR value is stored in CRMemory k middle.

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

[0061] S61, merge the five sub-populations obtained from S5 into a large population, perform non-dominated sorting on the individuals in the large population to divide them into different non-dominated levels, and calculate the crowding distance of all individuals in each level; select NP individuals from the large population as the next generation population, i.e., the new sub-population, according to the elite selection strategy;

[0062] S62, randomly select five individuals with non-dominated level 1 in the new offspring population as filling solutions, transmit their values ​​to the COMSOL simulation software through the MATLAB-COMSOL joint simulation platform, set parameters for the electromagnetic ultrasonic transducer, run the simulation to calculate the single-point amplitudes of the A0 mode and the S0 mode, output the results to Matlab and update its objective function value;

[0063] S63, determining whether the individual evaluated by simulation is in the database; if not, adding the individual and its objective function value to the database;

[0064] S64, storing the individuals with non-dominated level 1 in the new offspring population into the high-quality archive EXA, and performing non-dominated sorting on all individuals in EXA, retaining only the individuals with non-dominated level 1 and deleting the other individuals.

[0065] The beneficial effects produced by the present invention are:

[0066] 1. Adaptive selection mutation strategy can speed up convergence and find higher quality solutions;

[0067] 2. Adaptive adjustment of mutation operators and crossover operators can balance the algorithm's global search capability and local development capability;

[0068] 3. Using the proxy model to predict the individual objective function value can significantly reduce computing resources, save computing costs, and improve the solution speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of the method of the present invention;

[0070] Figure 2 It is a structural schematic diagram of the electromagnetic ultrasonic transducer model. DETAILED DESCRIPTION

[0071] The present invention will be further described below in conjunction with the accompanying drawings.

[0072] like Figure 1 As shown, the present invention is an electromagnetic ultrasonic transducer parameter design method based on a proxy model assisted multi-objective differential evolution S-SAMODE algorithm, comprising the following steps:

[0073] S1, use COMSOL software to establish an electromagnetic ultrasonic transducer simulation model and build a MATLAB-COMSOL joint simulation platform; the specific steps include:

[0074] S11, establish a finite element model for electromagnetic ultrasonic transducer simulation in COMSOL simulation software with multiple physical field modules, select materials and set parameters, select and set the physical field of the constructed model, add excitation sources to the model and perform meshing.

[0075] The model established in the present invention is as follows Figure 2 As shown in the figure, in the designed omnidirectional Lamb wave multi-target electromagnetic ultrasonic transducer model, the coaxial meander line coil generates eddy currents, and the concentric opposite polarity permanent magnet pair provides a static magnetic field. Lamb wave is one of the guided waves propagating in the plate-like structure, which has a symmetric mode (S0 mode) dominated by out-of-plane displacement and an asymmetric mode (A0 mode) dominated by in-plane displacement. In addition, since the wavelength of the A0 mode is shorter than that of the S0 mode, the A0 mode is more sensitive to defects than the S0 mode. Therefore, in this design, the A0 mode Lamb wave with this advantage is excited, while the S0 mode Lamb wave is suppressed as much as possible.

[0076] S12, the design goal of the multi-objective electromagnetic ultrasonic transducer model is to minimize the single-point amplitude (negative) of the A0 mode and S0 mode of the sampling point. The objective function is expressed as follows:

[0077] Min F(x)={f 1 (x),f 2 (x)}

[0078]

[0079] Where x is the sampling point, f 1 and f 2 Respectively represent the single point amplitude of A0 mode and S0 mode, and They are the sampling point x and the target value f 1 and f 2 The unknown relationship between them; each sampling point contains five decision variables, x = [R m1 ,R m2 ,H m ,g C ,I], where Rm1 is the radius of the cylindrical magnet, R m2 is the inner diameter of the ring magnet, G m is the magnet height, g C is the lift-off distance, and I is the excitation current.

[0080] S13, build a MATLAB-COMSOL joint simulation platform to realize the functions of calling COMSOL models in Matlab, modifying optimization variable values, simulating and outputting optimization targets, that is, realizing the automatic operation of the electromagnetic ultrasonic transducer parameter optimization algorithm and real-time feedback of simulation results.

[0081] S2, obtain sample data, initialize parameters, population, sample database and high-quality archive; the specific steps include:

[0082] S21, initialization population size NP, maximum number of true evaluations F max , the maximum number of iterations G m , learn algebraic LP.

[0083] S22, randomly generate 100 groups of data as initial population individuals within the parameter variation range of each optimization variable, that is, each individual corresponds to a set of optimization parameters.

[0084] 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 amplitude of the A0 mode and the S0 mode, and the results are output to Matlab to obtain 100 real samples and store them in the database.

[0085] S24, the initial samples are non-dominatedly sorted according to the objective function value to divide them into different levels, and the crowding distance of all individuals in each level is calculated.

[0086] S25, using the elite strategy to select NP individuals from the initial sample as the initial population, and store them in the database; the specific steps are:

[0087] S251, first put the individuals with non-dominant level 1 into the initial population, then put the individuals with non-dominant level 2 into the initial population, and so on;

[0088] S252, if after all the individuals of level m are placed in the initial population, the number of individuals in the population is less than NP, and after all the individuals of level m+1 are placed in the initial population, the number of individuals in the population is greater than NP, then all individuals of level m+1 are sorted in descending order according to the crowding distance, and are placed in the initial population one by one until the number of individuals in the population is equal to NP, and the remaining individuals are eliminated.

[0089] S26, storing the individuals with non-dominated level 1 in the initial population into the high-quality archive EXA, that is, the non-dominated solutions obtained by EXA.

[0090] S3, construct the RBF proxy model using samples in the database; the specific steps are:

[0091] S31, if the number of samples in the database is greater than 2NP, retain 2NP individuals according to the elite strategy described in S225 and delete other samples.

[0092] S32, randomly select NP individuals from the database as training samples to train the RBF proxy model.

[0093] S4, perform mutation and crossover operations on the parent population according to five mutation strategies to obtain the test vector; the specific steps are:

[0094] S41, adaptively adjust the mutation operator F, the mutation operator F controls the amplification effect of the deviation variable, in order to balance the global search ability and local development ability of the algorithm, set the mutation operator F in each generation to change dynamically according to the following formula:

[0095]

[0096] Among them, G m represents the maximum number of iterations, gen represents the current number of iterations, and F 0 The constant is set to 0.4.

[0097] S42, mutation operation. The differential evolution algorithm uses mutation operation to generate mutation vectors for each individual in the current population. For each target vector x i,G , generate mutation vector v according to the following five mutation methods i,G ;

[0098] 1)DE / rand / 1:

[0099]

[0100] 2)DE / best / 1:

[0101]

[0102] 3)DE / rand-to-best / 1:

[0103]

[0104] 4)DE / best / 2:

[0105]

[0106] 5)DE / rand / 2:

[0107]

[0108] In the formula, x best,G It is randomly selected from the premium archives and x i,G Different individuals; randomly selected sequence number r 1 , r 2 , r 3 , r 4 , r 5 Different from the target vector number i.

[0109] S43, adaptively adjust the crossover operator CR, the crossover operator CR of the k-th mutation strategy is composed of the normal distribution N(CRm k , std) generates a set of CR values ​​and assigns them to each target vector; among them, CRm k and std are the mean and variance respectively, and CRm is initialized k The value of is 0.5, and the value of std is 0.1;

[0110] At the same time, a CRMemory k The archive is used to store the CR values ​​of the trial vectors generated by the k-th strategy in the previous LP generation that can successfully enter the next generation. Specifically, in the previous LP generation, the CR value of the k-th strategy is generated by N(0.5, 0.1); in each generation after the LP generation, CRm k Set to CRMemory k The average value of the data is stored in the CR value of the k-th strategy is N(CRm k , 0.1) is generated.

[0111] S44, crossover operation, in order to increase the diversity of the interference parameter vector, a binomial crossover operation is introduced after the mutation operation is completed to generate the test vector u ji,G :

[0112]

[0113] Where randb(j) represents the jth estimate of a random number generator between [0,1]; D represents the dimension of the problem; rnbr(i)∈1,2,…,D represents a randomly selected sequence to ensure that u i,G At least from v i,G Gets a parameter.

[0114] S5, using the surrogate model to evaluate the objective function value of the test vector, performing a selection operation to obtain five offspring populations; the specific steps are:

[0115] S51: Predict the objective function value of the trial vector using the contemporary trained RBF surrogate model.

[0116] S52: Selection operation to determine the test vector u i,G Will it enter the next generation population? The test vector u i,G With the target vector x i,G For comparison, if u i,G Dominate x i,G , then the test vector u i,G is retained to the next generation of population; if u i,G x i,G Dominance, then the target vector x i,G be retained to the next generation population; if the two do not dominate each other, then u i,G 、x i,G Merge with the high-quality archive EXA, perform non-dominated sorting on the merged population and calculate the crowding distance. If u i,G The non-dominated level of is smaller, then the test vector u i,G is retained to the next generation of population; if x i,G The non-dominated level of is smaller, then the target vector x i,G is retained to the next generation population; if the non-dominated levels of the two are the same, the vector with the larger crowding distance is selected and retained to the next generation; at the same time, if the test vector u i,G If it is retained to the next generation of population, its CR value is stored in CRMemory k middle.

[0117] S6, select the next generation population from the five sub-populations, select the filling solution from the new population and perform simulation evaluation, and update the high-quality archive and sample database; the specific steps are:

[0118] S61, in order to select NP most promising individuals from the five sub-populations obtained in S5 as the next generation population, the five sub-populations are merged into a large population, the individuals in the large population are non-dominated sorted to divide them into different non-dominated levels, and the crowding distance of all individuals at each level is calculated; according to the elite selection strategy described in S225, NP individuals are selected from the large population as the next generation population, i.e., the new offspring population.

[0119] S62, randomly select five individuals with non-dominated level 1 in the new offspring population as filling solutions, pass their values ​​to the COMSOL simulation software through the MATLAB-COMSOL joint simulation platform, set the parameters of the electromagnetic ultrasonic transducer, and run the simulation to calculate the single-point amplitudes of the A0 mode and S0 mode, output the results to Matlab and update its objective function value.

[0120] S63, determining whether the individual evaluated by simulation is in the database; if not, adding the individual and its objective function value to the database.

[0121] S64, storing the individuals with non-dominated level 1 in the new offspring population into the high-quality archive EXA, and performing non-dominated sorting on all individuals in EXA, retaining only the individuals with non-dominated level 1 and deleting the other individuals.

[0122] S7, determine whether the maximum number of true evaluations has been reached; if so, stop the evolution and output the Pareto solution set; otherwise, go to S3 to continue the search process.

[0123] In order to test the ability of the agent-assisted multi-objective differential evolution algorithm S-SAMODE designed in this invention to solve the expensive multi-objective optimization problem of electromagnetic ultrasonic transducer parameter design, the proposed S-SAMODE algorithm is compared with the multi-objective differential evolution algorithm SAMODE without using the agent model. The population size of all algorithms is set to NP = 20, and the maximum number of true evaluations is set to F max = 30. In view of the limited computing resources, all algorithms were run independently once. All algorithms were run on the MATLAB-COMSOL joint simulation platform. The true evaluation of the optimal individual was performed on the COMSOL software. Matlab and COMSOL communicated with each other through the API interface.

[0124] Table 1 Experimental results of electromagnetic ultrasonic transducer parameter design

[0125]

[0126] The optimization results obtained by a single run of all algorithms are shown in Table 1. The optimization goal of the electromagnetic ultrasonic transducer designed in this experiment is to maximize the single-point signal amplitude of the A0 mode and the S0 mode. It can be observed from the table that the optimization results of the S-SAMODE algorithm designed by the present invention are 9.08e-8 and 1.45e-8, and the optimization results of the SAMODE algorithm assisted by the non-proxy model are 8.30e-8 and 1.26e-8. The S-SAMODE algorithm achieves better results than the SAMODE algorithm. In addition, in terms of time overhead, the time consumed by the S-SAMODE algorithm is significantly lower than that of the SAMODE algorithm. The comprehensive experimental results show that the S-SAMODE algorithm designed by the present invention can effectively handle the structural optimization design problem of the electromagnetic ultrasonic transducer.

[0127] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it 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 on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. The electromagnetic ultrasonic transducer parameter design method based on S-SAMODE algorithm is characterized by: The following steps are involved: S1, use COMSOL simulation software to establish an electromagnetic ultrasonic transducer simulation model and build a MATLAB-COMSOL joint simulation platform; S2, obtain sample data, initialization parameters, population, sample database and high-quality archive; S3, construct the RBF proxy model using samples in the database; S4, perform mutation and crossover operations on the parent population according to five mutation strategies to obtain the test vector; S5, using the surrogate model to evaluate the objective function value of the test vector, performing a selection operation to obtain five offspring populations; S6, select the next generation population from the five sub-populations, select the filling solution from the new population and perform simulation evaluation, and update the high-quality archive and sample database; S7, determine whether the maximum number of true evaluations has been reached; if so, stop the evolution and output the Pareto solution set; otherwise, go to S3 to continue the search process.

2. The electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm according to claim 1, characterized in that: The specific steps of S1 include: S11, establishing a finite element model for electromagnetic ultrasonic transducer simulation in a simulation software having multiple physical field modules, selecting materials and setting parameters, selecting and setting physical fields for the constructed model, adding an excitation source to the model and performing meshing; S12, the design goal of the multi-objective electromagnetic ultrasonic transducer model is to minimize the single-point amplitude of the A0 mode and S0 mode at the sampling point. The objective function is expressed as follows: Min F(x)={f1(x),f2(x)} Where x is the sampling point, f1 and f2 represent the single-point amplitude of A0 mode and S0 mode respectively. and They are the unknown relationships between the sampling point x and the target values ​​f1 and f2; each sampling point contains five decision variables, x = [R m1 ,R m2 ,H m ,g C ,I], where R m1 is the radius of the cylindrical magnet, R m2 is the inner diameter of the ring magnet, H m is the magnet height, g C is the lift-off distance, I represents the excitation current; S14: Build a MATLAB-COMSOL joint simulation platform to realize the functions of calling COMSOL models in Matlab, modifying optimization variable values, simulating and outputting optimization targets, that is, realizing the automatic operation of the electromagnetic ultrasonic transducer parameter optimization algorithm and real-time feedback of simulation results.

3. The electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm according to claim 1, characterized in that: The specific steps of S2 include: S21, initialization population size NP, maximum number of true evaluations F max , the maximum number of iterations G m , learn algebraic LP; S22, randomly generate 100 sets of data as initial population individuals within the parameter variation range of each optimization variable, that is, each individual corresponds to a set of optimization parameters; S23, transmit the data of each individual in the initial population to COMSOL software through the MATLAB-COMSOL joint simulation platform, set the parameters of the electromagnetic ultrasonic transducer and run the simulation to calculate the single-point amplitude of the A0 mode and the S0 mode, output the results to Matlab, obtain 100 real samples and store them in the database; S24, non-dominated sorting is performed on the initial samples according to the objective function value to divide them into different levels, and the crowding distance of all individuals in each level is calculated; S25, using the elite strategy to select NP individuals from the initial sample as the initial population, and store them in the database; S26: Store the individuals with non-dominated level 1 in the initial population into the high-quality archive EXA, that is, the non-dominated solution saved by EXA.

4. The electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm according to claim 3 is characterized in that: The specific steps of S25 are: S251, first put the individuals with non-dominant level 1 into the initial population, then put the individuals with non-dominant level 2 into the initial population, and so on; S252, if after all the individuals of level m are placed in the initial population, the number of individuals in the population is less than NP, and after all the individuals of level m+1 are placed in the initial population, the number of individuals in the population is greater than NP, then all individuals of level m+1 are sorted in descending order according to the crowding distance, and are placed in the initial population one by one until the number of individuals in the population is equal to NP, and the remaining individuals are eliminated.

5. The electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm according to claim 1, characterized in that: The specific steps of S3 include: S31, if the number of samples in the database is greater than 2NP, 2NP individuals are retained according to the elite strategy and other samples are deleted; S32, randomly select NP individuals from the database as training samples to train the RBF proxy model.

6. The electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm according to claim 1, characterized in that: The specific steps of S4 include: S41, adaptively adjust the mutation operator F, the mutation operator F controls the amplification effect of the deviation variable, in order to balance the global search ability and local development ability of the algorithm, set the mutation operator F in each generation to change dynamically according to the following formula: Among them, G m represents the maximum number of iterations, gen represents the current number of iterations, and F0 is a constant set to 0.4; S42, mutation operation. The differential evolution algorithm uses mutation operation to generate mutation vectors for each individual in the current population. For each target vector x i,G , generate mutation vector v according to the following five mutation methods i,G ; 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, x best,G It is randomly selected from the premium archives and x i,G Different individuals; the randomly selected serial numbers r1, r2, r3, r4, r5 are different from the target vector serial number i; S43, adaptively adjust the crossover operator CR, the crossover operator CR of the k-th mutation strategy is composed of the normal distribution N(GRm k , std) generates a set of CR values ​​and assigns them to each target vector; Among them, CRm k and std are the mean and variance respectively, and CRm is initialized k The value of is 0.5, and the value of std is 0.1; At the same time, a CRMemory k The archive is used to store the CR values ​​of the trial vectors generated by the k-th strategy in the previous LP generation that can successfully enter the next generation; in the previous LP generation, the CR value of the k-th strategy is generated by N(0.5, 0.1); in each generation after the LP generation, CRm k Set to CRMemory k The average value of the data is stored in the CR value of the k-th strategy is N(CRm k , 0.1) generated; S44, crossover operation, after the mutation operation is completed, a binomial crossover operation is introduced to generate a test vector u ji,G : (i=1,2,…,NP; j=1,2,…,D) Where randb(j) represents the jth estimate of a random number generator between [0,1]; D represents the dimension of the problem; rnbr(i)∈1,2,…,D represents a randomly selected sequence to ensure that u i,G At least from v i,G Gets a parameter.

7. The electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm according to claim 1, characterized in that: The specific steps of S5 include: S51: Predict the objective function value of the test vector using the contemporary trained RBF surrogate model; S52: Selection operation to determine the test vector u i,G Will it enter the next generation population? The test vector u i,G With the target vector x i,G For comparison, if u i,G Dominate x i,G , then the test vector u i,G is retained to the next generation of population; if u i,G x i,G Dominance, then the target vector x i,G be retained to the next generation population; if the two do not dominate each other, then u i,G 、x i,G Merge with the high-quality archive EXA, perform non-dominated sorting on the merged population and calculate the crowding distance. If u i,G The non-dominated level of is smaller, then the test vector u i,G is retained to the next generation of population; if x i,G The non-dominated level of is smaller, then the target vector x i,G is retained to the next generation population; if the non-dominated levels of the two are the same, the vector with the larger crowding distance is selected and retained to the next generation; if the test vector u i,G If it is retained to the next generation of population, its CR value is stored in CRMemory k middle.

8. The electromagnetic ultrasonic transducer parameter design method based on the S-SAMODE algorithm according to claim 1, characterized in that: The specific steps of S6 include: S61, merge the five sub-populations obtained from S5 into a large population, perform non-dominated sorting on the individuals in the large population to divide them into different non-dominated levels, and calculate the crowding distance of all individuals in each level; select NP individuals from the large population as the next generation population, i.e., the new sub-population, according to the elite selection strategy; S62, randomly select five individuals with non-dominated level 1 in the new offspring population as filling solutions, transmit their values ​​to the COMSOL simulation software through the MATLAB-COMSOL joint simulation platform, set parameters for the electromagnetic ultrasonic transducer, run the simulation to calculate the single-point amplitudes of the A0 mode and the S0 mode, output the results to Matlab and update its objective function value; S63, determining whether the individual evaluated by simulation is in the database; if not, adding the individual and its objective function value to the database; S64, storing the individuals with non-dominated level 1 in the new offspring population into the high-quality archive EXA, and performing non-dominated sorting on all individuals in EXA, retaining only the individuals with non-dominated level 1 and deleting the other individuals.

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