Method for antenna design optimization assisted by proxy model based on variable space data constraint

Abstract

The application discloses a kind of based on variable space data constraint's proxy model auxiliary antenna optimization method, mainly solve the time-consuming of existing optimization algorithm in whole-wave simulation is too long, population individual randomness is insufficient, easily fall into local optimal solution, population overall performance is not good, interfere with optimization process, waste computing resource problem.The application generates new population individual by adaptive random variation strategy, predicts the whole-wave simulation result of population individual using Gaussian model, and data constraint is carried out to predicted value and prediction uncertainty value.The application has stronger exploration ability, reduces the probability of falling into local optimal solution, solves the problem of waste of computing resources caused by simulation on population individual with poor comprehensive performance, and further improves the optimization speed.

Description

Technical Field

[0001] This invention belongs to the field of radar communication technology, and further relates to a surrogate model-assisted antenna design optimization method based on variable space data constraints in the field of antenna technology. This invention can be used to optimize the structural parameters of various antennas. Background Technology

[0002] The purpose of machine learning-assisted antenna design optimization is to determine suitable antenna dimensions, port locations, etc., based on design requirements and optimization objectives. Traditional antenna design optimization algorithms are mostly based on differential evolutionary algorithms, particle swarm optimization, or other derived evolutionary algorithms. However, due to the high time cost of full-wave simulation and the hundreds or thousands of iterations required for evolutionary algorithm optimization, traditional antenna design optimization algorithms consume a significant amount of time and rarely achieve satisfactory results. In recent years, with the development and application of machine learning, surrogate model-assisted antenna design optimization algorithms have gradually gained attention. Because the surrogate model constructed by machine learning can replace the time-consuming simulation process, it can significantly reduce the time cost in the antenna design optimization process, making the optimization of complex antennas possible. Therefore, in recent years, surrogate model-assisted evolutionary algorithms have become the mainstream optimization algorithm in antenna design optimization.

[0003] Shanghai Jiao Tong University disclosed an antenna design optimization method based on the bat algorithm in its patent application, "An Antenna Design Optimization Method Based on Bat Algorithm" (Patent Application No. CN201910379893.8, Publication No. CN110232212B). This method utilizes the bat algorithm to optimize the antenna's physical dimensions and calculates the fitness function through full-wave simulation. It introduces frequency adjustment during the optimization process, enabling a rapid transition from the initial global search to the later local search, thus accelerating the optimization efficiency. However, this method still has shortcomings. Full-wave simulation is the primary means of calculating the fitness function value during the optimization process, consuming significant computational resources and incurring high time costs. Therefore, this method is time-consuming and computationally expensive.

[0004] Guilin University of Electronic Technology disclosed a multi-objective optimization method for antennas based on a neural network and evolutionary algorithm game model in its patent application, "Multi-objective Optimization Method for Antennas Based on Neural Network and Evolutionary Algorithm Game Model" (Patent Application No. CN202211308783.0, Publication No. CN115563881A). This method uses PSO-GAO (Particle Swarm Optimization-GAO) to sample and construct a training set, and then utilizes the INN (Inverse Neural Network) game algorithm to predict design parameters that meet the current design objectives, achieving efficient multi-objective optimization of lens antennas. Compared to existing lens antenna design methods, the INN game algorithm can better address the problem of the difficulty in determining the size of the training set. Simultaneously, INN can assist PSO-GAO gradient descent to converge quickly. However, this method still has shortcomings. While the PSO-GAO has a better convergence speed, it is prone to getting trapped in local optima, leading to poor optimization results.

[0005] In his paper "An Efficient Surrogate Assisted Particle Swarm Optimization for Antenna Synthesis" (IEEE Transactions on Antennas and Propagation, 2022), Kai Fu disclosed a method for optimizing particle swarm antenna synthesis based on an efficient surrogate model. This method constructs two surrogate models during the optimization process: radial basis function (RBF) and simple kriging. The RBF model serves as the primary model, providing predictions, while the simple kriging model serves as the auxiliary model, providing prediction uncertainties. A hybrid pre-screening method is used to select individuals with the minimum fitness function value and the maximum prediction uncertainty for simulation. This hybrid model approach shortens the model training time, enabling faster optimization even with large amounts of data input. However, this method still has shortcomings. The hybrid pre-screening method selects candidate solutions from the population for simulation. When the overall population performance is poor, the selected candidate solutions lack excellent performance and are not helpful in exploring unknown regions, thus interfering with the optimization process and wasting computational resources. Summary of the Invention

[0006] The purpose of this invention is to address the problems existing in the prior art by proposing a surrogate model-assisted antenna design optimization method based on variable space data constraints. This method solves the problems of excessively long full-wave simulation time, insufficient randomness of individual populations, easy getting trapped in local optima, poor overall population performance, interference with the optimization process, and waste of computational resources in antenna design optimization.

[0007] The underlying principle of this invention is as follows: This invention generates a new population of individuals through an adaptive random mutation strategy. Mutation is performed on all individuals in the current iteration population, resulting in a new generation of individuals with stronger randomness. This addresses the problem of insufficient exploration capability and susceptibility to local optima in existing technologies. Furthermore, it adaptively generates a difference vector based on the difference between the current iteration population and the optimization interval, avoiding the problem of population accumulation at boundaries caused by excessively large difference vectors in existing technologies. This results in a wider distribution of population individuals and stronger algorithm exploration capability. Finally, this invention uses a Gaussian surrogate model to predict antenna simulation results and selects the best candidate solution for full-wave simulation, avoiding full-wave simulation of all individuals in the population. This solves the problem of excessively long optimization time caused by relying solely on full-wave simulation to obtain the overall antenna performance during optimization. This invention imposes data constraints on predicted values ​​and predicted uncertainties, discards individuals with poor population quality, and performs full-wave simulation on individuals with predicted values ​​greater than or equal to the simulation lower limit, thereby improving the quality of the analysis and solving the problem of wasted computational resources caused by simulating individuals with poor overall performance in the prior art. Performing full-wave simulation on individuals with predicted uncertainties greater than or equal to the simulation lower limit ensures effective exploration of individuals in unknown regions and improves the optimization results.

[0008] The specific steps to achieve the objective of this invention include the following:

[0009] Step 1: Set the parameter optimization range of the antenna to be optimized. Use Latin hypercube sampling to continuously and randomly select values ​​in each optimization range to generate an initial population of individuals. Use the initial population composed of all the individuals in the initial population as the population for the first iteration.

[0010] Step 2: Load the current iteration population into the antenna to be optimized, perform full-wave simulation on the antenna, and calculate the overall performance of the antenna;

[0011] Step 3: By adaptively adjusting the stochastic optimization strategy of the difference vector, the population of the current iteration is mutated and crossovered sequentially to generate the crossover population;

[0012] Step 4: Input the relevant data of the population parameters and antenna integrated performance of the current iteration into the Gaussian surrogate model, train and update the Gaussian surrogate model through online learning method, and obtain the trained Gaussian surrogate model.

[0013] Step 5: Input the crossover population into the trained Gaussian surrogate model, output the predicted value and prediction uncertainty value of the antenna integrated performance corresponding to the crossover population, perform confidence lower limit pre-screening on the crossover population, and obtain the individual with the best antenna integrated performance in the current population.

[0014] Step 6: Determine whether the predicted value of the individual with the best antenna overall performance in the current population is greater than or equal to the simulation lower limit. If so, perform full-wave simulation on the current individual and then proceed to step 8; otherwise, proceed to step 7.

[0015] Step 7: Is the prediction uncertainty of the individual with the best antenna performance in the current population greater than or equal to the simulation lower limit? If yes, perform full-wave simulation on the current individual and then proceed to step 8; otherwise, proceed to step 3.

[0016] Step 8: Determine whether the overall performance of the antenna meets the design targets for bandwidth and gain. If yes, proceed to step 9; otherwise, proceed to step 3.

[0017] Step 9: Use the current global optimal solution as the final parameter for antenna design.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] First, this invention uses a stochastic optimization strategy that adaptively adjusts the difference vector. It performs mutation operations on all individuals in the current iterative population, overcoming the problem of insufficient individual diversity caused by mutation operations only on the optimal solution in the prior art. The generated population has stronger randomness. Adaptively adjusting the difference vector avoids the population from accumulating at the boundary due to an excessively large difference vector. This makes the population of this invention have a wider distribution range, stronger exploration ability, and can achieve better antenna optimization results.

[0020] Secondly, this invention utilizes the simulation lower limit of the predicted value to perform full-wave simulation on individuals in the population whose predicted value is greater than or equal to the simulation lower limit. This avoids the problem of wasting computational resources caused by performing full-wave simulation on individuals in the population with poor quality in the prior art. As a result, this invention reduces the number of simulations of invalid solutions and speeds up the antenna optimization process.

[0021] Third, this invention utilizes the simulation lower bound of the predicted uncertainty value to perform full-wave simulation on individuals in the population whose predicted uncertainty value is greater than or equal to the simulation lower bound. This overcomes the deficiency in existing technologies that lack simulation capabilities for unknown individuals with high predicted uncertainty values. It ensures exploration of unknown regions within the variable space, avoiding the problem of local convergence and getting trapped in local optima in existing technologies. This allows for more antenna design possibilities during antenna optimization, improving the overall performance of the antenna. Attached Figure Description

[0022] Figure 1 This is a flowchart of the present invention;

[0023] Figure 2 This is a schematic diagram illustrating the simulation lower bound of the predicted value of an individual in the population in this invention;

[0024] Figure 3 These are dimensional diagrams used to verify the three different E-type microstrip patch antennas in this invention;

[0025] Figure 4 This is a comparison chart of the overall performance of this invention with other optimization methods;

[0026] Figure 5 This is a comparison chart of the optimized antenna performance of this invention with other optimization methods;

[0027] Figure 6 This is a dimensional diagram of the four-element linear array antenna used in the simulation experiment of this invention;

[0028] Figure 7 This is a comparison chart of the simulation results of this invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0030] Reference Figure 1 The steps for implementing the embodiments of the present invention will be further described below.

[0031] Step 1: Set optimization intervals for the antenna size parameters that need optimization. The optimization intervals should avoid negative antenna sizes, avoid contact or even overlap between antenna structures that should not be in contact, and avoid separation of port structures. Generate an initial population of individuals by continuously and randomly sampling values ​​within each optimization interval using Latin hypercube sampling. The initial population composed of all these individuals is used as the population for the first iteration.

[0032] Step 2: Load the current iteration population into the antenna to be optimized, perform full-wave simulation on the antenna, and calculate the overall antenna performance based on performance indicators such as antenna gain and bandwidth, as well as the performance weighting coefficients, using the following formula:

[0033] minimize Fitness=w1·max(S11)-w2min(Gain)

[0034] Wherein, Fitness is the overall antenna performance value, w1 and w2 represent weighting coefficients, and in this embodiment of the invention, w1 = 300 and w2 = 100. max(S11) represents the maximum self-reflection coefficient within the frequency range, and min(Gain) represents the minimum gain within the frequency range.

[0035] Step 3: Generate a new population through mutation and crossover and make predictions.

[0036] The differential evolution algorithm generates population individuals by encoding them using floating-point vectors, performs mutation and crossover operations on the current iteration population, and generates a new population after crossover.

[0037] Step 3.1, mutation operation.

[0038] Select two individuals from the current iteration population, combine them pairwise, and calculate the difference between their vectors to generate a difference vector. Combine the current iteration population individuals with the difference vector to generate the mutated individuals.

[0039] The mutation operation can be described as follows:

[0040]

[0041] Among them, X p2 (i,j) represents an individual in the current iteration of the population, V i (i,j) represents the mutated individual, F is the scaling factor, and in this embodiment of the invention, F is 1; ub is the upper limit of the optimization interval, and lb is the lower limit of the optimization interval.

[0042] Step 3.2, cross operation.

[0043] Each individual in the population consists of multiple optimization parameters. The crossover operation randomly combines the optimization parameters in the mutated individuals with the optimization parameters in the current iteration population to generate new individuals in the population.

[0044] The crossover operation can be described as follows:

[0045]

[0046] Among them, H i,j (g) represents the new population formed after crossover, V i,j (g) is a variant individual, X i,j (g) represents the individual in the current iteration population, and the crossover probability CR in this embodiment of the invention is 0.8.

[0047] Step 4: Input the population parameters and antenna performance data of the current iteration into the Gaussian surrogate model. The hyperparameters in the Gaussian surrogate model are automatically adjusted according to the previous prediction results. The Gaussian surrogate model is trained and updated through online learning methods to obtain a trained Gaussian surrogate model.

[0048] Step 5: Input the crossover population into the trained Gaussian surrogate model, output the predicted value and prediction uncertainty value of the antenna integrated performance corresponding to the crossover population, perform confidence lower bound pre-screening on the crossover population, and obtain the individual with the best antenna integrated performance in the current population.

[0049] The confidence lower limit pre-screening formula is as follows:

[0050]

[0051] Among them, y lcb (x) is the lower confidence limit. represents the predicted value of the Gaussian surrogate model for the antenna synthesis performance, w represents the weight coefficient, which is set to 2 in this embodiment of the invention, and s represents the prediction uncertainty of the Gaussian surrogate model for this prediction.

[0052] Step 6, Figure 2 This diagram illustrates the simulation lower bound for predicted values ​​of individuals in the population. The optimization direction is minimization. An optimal solution interval is constructed around the optimal solution. The predicted value of the current optimal solution is evaluated, and simulations are performed on individuals in the population whose predicted values ​​are greater than or equal to the simulation lower bound. The simulation lower bound is calculated as follows:

[0053] Step 6.1: Select the first quarter of data in the full-wave simulation where the antenna's overall performance is closest to the global optimal solution, calculate the mean y1 of this data set, and then calculate the deviation y between the data mean and the global optimal solution. b1 ;

[0054] The deviation y between the data mean and the global optimal solution b1 The calculation method is as follows:

[0055] y b1 =|y1-y0| / |y1|

[0056] Where y0 is the current global optimal solution.

[0057] We select the first quarter of data from the full-wave simulation where the antenna's overall performance is closest to the global optimum, and calculate the mean y2 of this data set. We then calculate the deviation y between the data mean and the global optimum. b2 .

[0058] The deviation y between the data mean and the global optimal solution b2 The method is as follows:

[0059] y b2 =|y2-y0| / |y2|

[0060] Step 6.2: Calculate the deviation coefficient m between full-wave simulations, which reflects the changes in the overall performance of individuals in the population during the optimization process;

[0061] The deviation coefficient m is calculated as follows:

[0062] m = |y b2 | / |y b1 +y b2 |

[0063] Step 6.3: Calculate the simulation lower limit requirement y that the prediction result should meet.low If the antenna performance of the best individual in the current population is greater than or equal to the lower limit of the predicted value simulation, then perform a full-wave simulation and add the simulation results to the dataset; otherwise, proceed to step 7.

[0064] The simulation lower limit requirement for the predicted value is y. low The calculation method is as follows:

[0065] y low =y0±m·(y2-y0)

[0066] Step 7: Calculate the simulation lower bound for the prediction uncertainty. Select the prediction uncertainty values ​​mse of the five most recent individuals from the full-wave simulation. 11 ,mse 12 ......mse 15 The prediction uncertainty mse of the five individuals with the smallest Euclidean distance d(x,y) to the current individual in the full-wave simulation is selected. 21 ,mse 22 ......mse 25 .

[0067] Calculate the simulation lower limit. If the prediction uncertainty of the current iteration population is greater than or equal to the simulation lower limit, perform a full-wave simulation and add the simulation results to the dataset; otherwise, proceed to step 3.

[0068] The Euclidean distance d(x,y) is calculated as follows:

[0069]

[0070] Where x1 is the individual component of the current iteration population, and y1 is the individual component in the full-wave simulation.

[0071] The simulation lower limit for the predicted uncertainty is calculated as follows:

[0072] mse=((mse 11 +mse 12 ....+mse 15 )-(mse 21 +mse 22 ....+mse 25 )) / 5

[0073] Step 8: Determine whether the overall performance of the antenna meets the design targets for bandwidth and gain. If yes, proceed to step 9; otherwise, proceed to step 3.

[0074] Step 9: Use the current global optimal solution as the final parameter for antenna design.

[0075] The effects of this invention will be further illustrated below with simulation experiments:

[0076] 1. Simulation experimental conditions:

[0077] The hardware platform for the simulation experiment of this invention is: a 32-core Intel(R) Xeon(R) Gold 5215 CPU with a main frequency of 2.50GHz and 1024GB of memory.

[0078] The software platform for the simulation experiments of this invention is Matlab2021b and CST2020.

[0079] 2. Simulation content and result analysis

[0080] The simulation experiment of this invention uses both the present invention and a prior art (surrogate model-assisted differential evolution algorithm) to optimize the antenna to be optimized, and obtains the overall antenna performance results, such as... Figure 4 As shown.

[0081] In simulation experiments, one existing technology used is:

[0082] The existing surrogate model-assisted differential evolution algorithm refers to the algorithm proposed by Liu Bo et al. in their paper "An efficient method for antenna design optimization based on evolutionary computation and machine learning techniques" (IEEE Trans. Antennas Propag., vol. 62, no. 1, pp. 7–18, Jan. 2014), which optimizes antennas using a Gaussian surrogate model and differential evolution algorithm.

[0083] This invention includes two simulation experiments. Simulation experiment 1 optimizes three different E-pattern antennas, and simulation experiment 2 optimizes a four-element linear array antenna.

[0084] Simulation Experiment 1:

[0085] This invention employs a surrogate model-assisted antenna design optimization method based on variable space data constraints. Figure 3 The three different E-pattern antennas were optimized. Figure 3 (a) is antenna 1. Figure 3 (b) is antenna 2. Figure 3(c) Antenna 3. All three antennas use FR4 substrate material with a relative permittivity of 4.7, a loss tangent of 0.014, a thickness of 0.8 mm, a frequency sweep range of 2-3.0 GHz, coaxial feeding, and a feed aperture diameter of 0.5 mm. Antenna 1 has an air layer thickness of 10.8 mm and a ground plane size of 192 mm * 224 mm. Antenna 2 has an air layer thickness of 5.5 mm and a ground plane size of 148 mm * 186 mm. Antenna 3 has an air layer thickness of 5.5 mm and a ground plane size of 184 mm * 236 mm.

[0086] The structural parameters of the E-shaped microstrip patch antenna are shown in Table 1:

[0087] Table 1. Summary of Structural Parameters for Type E Patch Antenna (Unit: mm)

[0088]

[0089] For antennas 1 and 2, the optimization objective is to increase the maximum gain between 2.4 GHz and 2.6 GHz, while keeping S11 less than -10 dB between 2.4 GHz and 2.6 GHz. For antenna 3, the optimization objective is to increase the maximum gain in the vicinity of 2.45 GHz.

[0090] The following is combined with Figure 4 The simulation results further illustrate the effects of the present invention.

[0091] Figure 4 In the diagram, the x-axis represents the number of iteration steps, and the y-axis represents the overall antenna performance value. Figure 4 (a) It can be seen that for the optimization problem of antenna 1, the existing technology has not yet converged after 200 iterations, while the present invention converges after 120 iterations, with an optimization efficiency 1.6 times that of the existing technology. Figure 4 (b) It can be seen that for the optimization problem of antenna 2, the existing technology converges after 150 iterations, while the present invention converges after 97 iterations, with an optimization efficiency 1.5 times that of the existing technology. Figure 4 (c) It can be seen that for the optimization problem of antenna 3, the existing technology has not yet converged after 200 iterations, while the present invention converges after 170 iterations, with an optimization efficiency 1.2 times that of the existing technology. In achieving better optimization results, the present invention has a faster search speed and higher optimization efficiency.

[0092] Optimized antenna bandwidth and gain performance are as follows Figure 5 As shown below, in conjunction with Figure 5 The simulation results further illustrate the effects of the present invention.

[0093] Figure 5 (a) Figure 5(c) Figure 5 In (e), the x-axis represents Frequency, and the y-axis represents S11 (antenna self-reflection coefficient). Figure 5 (b) Figure 5 (d) Figure 5 In (f), the x-axis represents Frequency, and the y-axis represents Gain. From Figure 5 (a) and Figure 5 (b) It can be seen that after optimization, the bandwidth of antenna 1 is 1.7-2.6 GHz, which does not meet the bandwidth optimization requirements, and the maximum gain within the bandwidth is 6 dB. After optimization by this invention, antenna 1 achieves a complete bandwidth within 2-3 GHz, meeting the bandwidth requirements, and the maximum gain within the bandwidth is 12.5 dB. Figure 5 (c) and Figure 5 (d) It can be seen that after optimization by the prior art, the bandwidth of antenna 2 is 2.3-3 GHz, which meets the bandwidth optimization requirements and the maximum gain within the bandwidth is 7 dB. After optimization by the present invention, the bandwidth of antenna 2 is 2.1-2.8 GHz, which meets the bandwidth optimization requirements and the maximum gain within the bandwidth is 12 dB. Figure 5 (e) and Figure 5 (f) It can be seen that, after optimization, the bandwidth of antenna 3 in the prior art is 2.36-2.42 GHz, and the maximum gain within the bandwidth is 7 dB. After optimization in this invention, the bandwidth of antenna 3 is 2.35-2.48 GHz, which is twice the bandwidth of the prior art, and the maximum gain within the bandwidth is 11 dB. Compared with the prior art, the optimized bandwidth of this invention is wider, and the maximum gain within the bandwidth is 1.8 times that of the prior art, resulting in better antenna performance.

[0094] Simulation Experiment 2 of this invention uses a surrogate model-assisted antenna design optimization method based on variable space data constraints. Figure 6 The four-element linear array antenna was optimized. The substrate material is FR4 with a relative permittivity of 4.7, a loss tangent of 0.014, a thickness of 0.8 mm, a frequency sweep range of 3-4.0 GHz, coaxial feeding, and a feed aperture diameter of 0.5 mm. The optimization objective was to improve the maximum gain between 3.2 and 3.8 GHz. The structural parameters of the four-element linear array antenna are shown in Table 2.

[0095] Table 2. Summary of structural parameters for a four-element linear array antenna (unit: mm)

[0096]

[0097] After optimization, the antenna bandwidth and gain performance are as follows: Figure 7 As shown below, in conjunction with Figure 7 The simulation results further illustrate the effects of the present invention.

[0098] Figure 7 In (a), the x-axis represents the number of iteration steps, and the y-axis represents the overall antenna performance value. Figure 7 (a) It can be seen that the optimization process of the present invention is smoother, and the performance meets expectations when the iteration reaches 70 times. Figure 7 In (b), the x-axis represents Frequency, and the y-axis represents S11 (antenna self-reflection coefficient). Figure 7 In (c), the x-axis represents frequency, and the y-axis represents gain. From Figure 7 (b) and Figure 7 (c) It can be seen that, after optimization, the bandwidth of the existing quaternary linear array is 3.22-3.82 GHz, which meets the bandwidth optimization requirements, and the maximum gain within the bandwidth is 10.5 dB. After optimization, the bandwidth of the quaternary linear array of this invention is 3.15-3.82 GHz, which also meets the bandwidth optimization requirements, and the maximum gain within the bandwidth is 12 dB. This invention is superior to the existing technology in both bandwidth and gain.

[0099] The simulation experiments above demonstrate that this invention, by constraining the predicted comprehensive performance of individuals in the population with data, avoids simulating individuals with poor quality, reduces the number of invalid simulations, and achieves convergence in only 50%-70% of the time required by existing technologies, thus exhibiting higher optimization efficiency. Furthermore, by employing an adaptive random mutation strategy and constraining the uncertainties in the predicted comprehensive performance of individuals in the population with data, it demonstrates stronger exploration capabilities in unknown regions and achieves better optimization results.

Claims

1. A surrogate model-assisted antenna design optimization method based on variable space data constraints, characterized in that, An adaptive adjustment strategy for the differential vector is used to predict antenna simulation results through a Gaussian surrogate model, with data constraints on the predicted values ​​and uncertainties of candidate solutions. The steps of this antenna design optimization method are as follows: Step 1: Set the parameter optimization range of the antenna to be optimized. Use Latin hypercube sampling to continuously and randomly select values ​​in each optimization range to generate an initial population of individuals. Use the initial population composed of all the individuals in the initial population as the population for the first iteration. Step 2: Load the current iteration population into the antenna to be optimized, perform full-wave simulation on the antenna, and calculate the overall performance of the antenna; Step 3: By adaptively adjusting the stochastic optimization strategy of the difference vector, the population of the current iteration is mutated and crossovered sequentially to generate the crossover population; Step 4: Input the relevant data of the population parameters and antenna integrated performance of the current iteration into the Gaussian surrogate model, train and update the Gaussian surrogate model through online learning method, and obtain the trained Gaussian surrogate model. Step 5: Input the crossover population into the trained Gaussian surrogate model, output the predicted value and prediction uncertainty value of the antenna integrated performance corresponding to the crossover population, perform confidence lower limit pre-screening on the crossover population, and obtain the individual with the best antenna integrated performance in the current population. Step 6: Determine whether the predicted value of the individual with the best antenna overall performance in the current population is greater than or equal to the lower limit of the predicted value simulation. If so, perform full-wave simulation on the current individual and then proceed to step 8; otherwise, proceed to step 7. Step 7: Is the prediction uncertainty of the individual with the best antenna performance in the current population greater than or equal to the simulation lower limit of the prediction uncertainty? If yes, perform full-wave simulation on the current individual and then proceed to step 8; otherwise, proceed to step 3. Step 8: Determine whether the overall performance of the antenna meets the bandwidth and gain design targets. If yes, proceed to step 9; otherwise, proceed to step 3. Step 9: Use the current global optimal solution as the final parameter for antenna design.

2. The surrogate model-assisted antenna design optimization method based on variable space data constraints according to claim 1, characterized in that, The mutation and crossover steps described in step 3 are as follows: The first step is to select two individuals from the current population, combine them pairwise and calculate the difference in their vectors to adaptively generate a difference vector. The mutated individuals are then generated by combining the original individuals with the difference vector. The second step is to randomly combine the components from the mutated individuals with the components from the original individuals to generate the crossover population.

3. The surrogate model-assisted antenna design optimization method based on variable space data constraints as described in claim 2, characterized in that, The adaptive generation of the difference vector mentioned in the first step is obtained by the following formula: Among them, X p2 X p3 X p1 V represents the population individual in the current iteration, i represents the index of the population individual in the current iteration, j represents the index of the optimization interval among the population individuals in the current iteration, and V i denoted by , F represents the scaling factor, ub represents the upper limit of the optimization interval, and lb represents the lower limit of the optimization interval.

4. The surrogate model-assisted antenna design optimization method based on variable space data constraints according to claim 1, characterized in that, The prediction uncertainty mentioned in step 5 is the mean square error calculated by the Gaussian surrogate model based on the actual and predicted values ​​of the antenna synthesis performance.

5. The surrogate model-assisted antenna design optimization method based on variable space data constraints according to claim 1, characterized in that, The lower limit of the predicted value simulation mentioned in step 6 is obtained by the following formula: Where y represents the simulation lower limit, y1 represents the global optimal solution, y2 represents the average value of the top quarter of data in the full-wave simulation where the antenna's overall performance is closest to the global optimal solution, and y3 represents the average value of the top ten of data in the full-wave simulation where the antenna's overall performance is closest to the global optimal solution.

6. The surrogate model-assisted antenna design optimization method based on variable space data constraints according to claim 1, characterized in that, The simulation lower limit of the prediction uncertainty mentioned in step 7 is obtained by the following formula: mse=((mse 11 +mse 12 ....+mse 15 )-(mse 21 +mse 22 ....+mse 25 )) / 5 Where mse represents the simulation lower bound of the prediction uncertainty, mse 11 ,mse 12 ......mse 15 Let mse represent the prediction uncertainty values ​​in the most recent 5 full-wave simulations. 21 ,mse 22 ......mse 25 These represent the prediction uncertainties of the five individuals with the smallest Euclidean distance from the current individual in the full-wave simulation.

Images