CN113076699A - Antenna optimization method based on multi-output Gaussian process Bayesian optimization - Google Patents
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Abstract
The invention discloses an antenna optimization method based on multi-output Gaussian process Bayes optimization, which utilizes a small amount of high-precision electromagnetic simulation and a large amount of low-precision electromagnetic simulation to construct a proxy model, and uses Bayes optimization on the basis of the proxy model, thereby greatly improving the optimization speed of an antenna. The antenna optimization process typically requires multiple iterations of electromagnetic simulations, consuming a significant amount of computational resources and time. High-precision electromagnetic simulation can obtain more accurate antenna response, but the simulation consumes long time; the antenna response obtained by low-precision electromagnetic simulation is rough, but the simulation time is short. A proxy model is established based on a small amount of high-precision simulation data and a large amount of low-precision simulation data by utilizing a multi-output Gaussian process, and then iteration is performed by using a Bayesian optimization method on the basis. The invention is based on a mature mathematical model, has clear logic, and obviously improves the optimization speed on the premise of ensuring the optimization result compared with the traditional Bayesian optimization.
Description
Technical Field
The invention belongs to the technical field of antenna optimization methods, and particularly relates to an antenna optimization method based on multi-output Gaussian process Bayesian optimization.
Background
In the design and optimization of the antenna, electromagnetic simulation consumes a large amount of computing resources and time, and as the design of the antenna tends to be complex, the number of physical sizes of the antenna to be optimized is continuously increased, and the efficiency of the antenna design is restricted by an antenna optimization algorithm. The optimization problem of the antenna can be classified as a problem of optimizing the black box function. In order to find a solution meeting the requirements by using the iteration times as few as possible, a proxy model is established according to the sampled samples for fitting the black box function, so that the iteration times are reduced. In bayesian optimization, a gaussian process is typically used as a proxy model.
Based on the posterior mean and variance of the Gaussian process, the Bayesian optimization uses the obtained function balance to explore and utilize.
In 2015, the scholars of Sergio Ledesms et al published on "IEEE Antennas and Propagation Magazine" entitled "A Hybrid Method to Design Wire Antennas: an article of Design and optimization of using the intellectual interference. The article combines a plurality of targets of the antenna and the limiting condition into a comprehensive objective function by establishing the comprehensive objective function.
In 2014, Slawomir Koziel et al published an article entitled "Efficient Multi-Objective Simulation-drive Antenna Design Using Co-Kriging" on "IEEE Transactions on antennas and Propagation" and fused high and low precision electromagnetic Simulation by Using Co-Kriging method to improve the efficiency of establishing a proxy model, and then iterated by Using an evolutionary algorithm.
In 2018, Wenlong Lyu et al, in "IEEE Transactions on Circuits and Systems I: regular Papers "published An article entitled" An effective Bayesian Optimization application for Automated Optimization of Analog Circuits, "and Bayesian Optimization was used to optimize the circuit, verifying that the efficiency of Bayesian Optimization far exceeds that of evolutionary algorithms.
In 2018, Haitao Li et al published an article entitled "Optimization design of skin Antenna based on Bayesian Optimization" on 20177 th IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies, and used Bayesian Optimization for skin Antenna Optimization using Bayesian Optimization, and the proxy model used therein was a traditional Gaussian process.
In 2020, the scholars of Qi Wu et al published an article entitled "Multistage chromatography matrix learning and its application to anti-encoding modeling and optimization" on IEEE Transactions on Antennas and Propagation, and established a proxy model using ICM in the multi-output Gaussian process, but iterated using an evolutionary algorithm.
In the existing antenna optimization method, a proxy model is established based on high-precision and low-precision electromagnetic simulation, and then an evolutionary algorithm is used; or based on general bayesian optimization using only high precision simulations. Therefore, a novel efficient optimization algorithm is needed to be provided for antenna design, and a better choice is adopted in both the proxy model establishment and the iteration process, namely, a multi-output gaussian process is used for fusing high-precision simulation data and low-precision simulation data to establish the proxy model, and an obtained function in bayesian optimization is used for iteration.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides an antenna optimization method based on multi-output Gaussian process Bayesian optimization, which uses a proxy model established in the multi-output Gaussian process to fuse high-precision electromagnetic simulation and low-precision electromagnetic simulation, and then uses an obtained function to iterate, thereby realizing acceleration of antenna optimization.
In order to achieve the purpose, the invention adopts the technical scheme that:
the invention provides an antenna optimization method based on multi-output Gaussian process Bayesian optimization, which comprises the following steps:
And 2, randomly sampling a plurality of sample points in the value range of the parameter to be optimized to perform high-precision or low-precision electromagnetic simulation to obtain a comprehensive objective function value of the sample points, and taking the comprehensive objective function value as an initialization sample set.
And 3, training an agent model by using a multi-output Gaussian process based on the sample set for fitting a comprehensive objective function.
And 4, calculating posterior mean and variance according to the proxy model, solving the solution of the maximum obtained function, taking the solution as an input value of the next electromagnetic simulation, performing corresponding electromagnetic simulation according to a coefficient q for controlling the high-precision simulation quantity proportion and the low-precision simulation quantity proportion to obtain a comprehensive objective function value, and adding new data into the sample set.
And 5, judging whether the iteration end condition is met, if the iteration end condition is not met, returning to the step 3, and if the iteration end condition is met, turning to the step 6.
And 6, selecting k optimal low-precision simulation solutions, performing high-precision simulation on the k optimal low-precision simulation solutions, wherein k is a smaller number relative to the total sample number, and obtaining a comprehensive objective function value.
And 7, outputting the optimal high-precision simulation solution.
Further, the antenna parameters to be optimized refer to various physical dimensions of the antenna which need to be determined optimally.
Further, the antenna optimization comprehensive objective function can be regarded as a black box function, and the antenna optimization problem is a problem of solving an optimal solution for the black box function.
Furthermore, the high-precision electromagnetic simulation is that a convergence condition meeting requirements is set in simulation software, and solution is carried out at a frequency point with sufficient detail according to a real antenna model; the low-precision electromagnetic simulation is characterized in that convergence conditions are set relatively loosely in simulation software, antenna models can be set to be simplified in some places, solved frequency points can be set to be relatively sparse, and the like, so that the effect of shortening simulation time is achieved. And setting a q value for representing the ratio between the total simulation quantity and the high-precision simulation quantity.
Further, the multi-output gaussian process may use an ICM model, whose prior distribution is shown in equations (2) - (5), a proxy model prediction is shown in equations (6) - (8), and a model training is shown in equation (9).
Further, the gain function finds the next simulated input point by maximizing the gain function based on the posterior mean and variance of the proxy model.
Further, after iteration is finished, k sample points with the most potential in low-precision samples are selected for high-precision simulation, comprehensive objective function values of the k sample points are obtained, and then the optimal solution of the high-precision simulation sample is selected as the optimal solution of the whole optimization process.
Compared with the prior art, the invention has the beneficial effects that:
1. the agent model is established by using a multi-output Gaussian process, high-precision electromagnetic simulation data and low-precision electromagnetic simulation data are fused, and the efficiency of establishing the agent model is greatly improved.
2. Iteration is carried out by using an acquired function in Bayesian optimization, and the posterior mean and variance provided by the proxy model are fully utilized.
3. By utilizing a low-precision simulation data reuse mechanism, namely selecting a plurality of low-precision solutions with the most potential to carry out high-precision simulation after iteration is finished, the obvious effect improvement can be obtained possibly under the condition of smaller additional time overhead.
Drawings
Fig. 1 is a flowchart of an antenna optimization method based on a multi-output gaussian process bayesian optimization according to the present invention.
Fig. 2 is a schematic diagram of an antenna used to verify the algorithm of the present invention.
Fig. 3 is a schematic diagram of an optimization process of the algorithm in the verification antenna.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects of the present invention more apparent, the following embodiments further describe the present invention in detail. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1-2, the present invention provides an antenna optimization method based on bayesian optimization of a multi-output gaussian process, which is implemented by joint simulation of Python and HFSS, and includes the following steps:
1) the antenna optimization aims at
Meaning that the maximum S11 value is made as small as possible while the average gain of the antenna is made as large as possible within the target frequency band. Convert it to a synthetic objective function:
f(x)＝fs(-10-max(S11))+7(mean(Gain)-4) (2)
where x represents the antenna size to be optimized. f. ofs(t) is used to guide the optimization of S11, giving smaller coefficients when S11 is between-13 dB to-15 dB; the portion of S11 below-15 dB was assigned a very small coefficient, indicating that little benefit was gained from further optimizing S11 at this time.
2) The antenna size parameter to be optimized and its range are (in mm)
The initial sample set size was set to 100, with 80 for the number of low accuracy simulations and 20 for the number of high accuracy simulations. In the high-precision simulation, Δ S is set to 0.01, and the response of the antenna is solved on 11 evenly distributed frequency points within 10 GHz-11 GHz. In the low-precision simulation, Δ S is set to 0.1, and the response of the antenna is solved at 6 evenly distributed frequency points within 10GHz to 11 GHz. The number of steps of the iteration is set to 200 and q is set to 5.
3) And (3) aiming at the updated sample set, training the updated sample set by using a multi-output Gaussian process to obtain an updated proxy model, wherein the formulas are shown in formulas (2) - (5) and (9).
4) As shown in equations (6) to (8), the posterior mean and variance are estimated from the proxy model, and then the solution of the maximum gain function is solved. Commonly used get functions include Upper Confidence Bound (UCB) or Expected Improvement (EI), etc.; the get function used here is the Upper Confidence Bound (UCB):
κ is a coefficient used to balance exploration and utilization. And (4) bringing the solution of the maximum obtained function into HFSS software for simulation, solving a comprehensive objective function value according to a simulation result, and adding the comprehensive objective function value into the sample set.
5) Judging whether the iteration end condition is met, if the iteration end condition is not met, returning to the step 3), and if the iteration end condition is met, turning to the step 6).
6) And 5 optimal low-precision simulation solutions are selected, and high-precision simulation is carried out on the solutions.
7) And outputting an optimal high-precision simulation solution.
The method is randomly repeated three times, and the Bayesian optimization based on high-precision electromagnetic simulation is also performed three times as comparison, and the results are shown in the following table and the optimization process (taking the average of three experiments) is shown in FIG. 3. The method provided by the invention further improves the objective function value through a low-precision data reuse mechanism in two experiments. As can be seen from the comparison of the optimization result and the optimization process, the optimization efficiency is further improved on the basis of ensuring the optimization result.
The invention discloses an antenna optimization method based on multi-output Gaussian process Bayes optimization, which utilizes a small amount of high-precision electromagnetic simulation and a large amount of low-precision electromagnetic simulation to construct a proxy model, and uses Bayes optimization on the basis of the proxy model, thereby greatly improving the optimization speed of an antenna. The antenna optimization process typically requires multiple iterations of electromagnetic simulations, consuming a significant amount of computational resources and time. High-precision electromagnetic simulation can obtain more accurate antenna response, but the simulation consumes long time; the antenna response obtained by low-precision electromagnetic simulation is rough, but the simulation time is short. The high-precision simulation data and the low-precision simulation data have strong correlation, a proxy model is established based on a small amount of high-precision simulation data and a large amount of low-precision simulation data by utilizing a multi-output Gaussian process, and then iteration is performed by using a Bayesian optimization method on the basis. The invention is based on a mature mathematical model, has clear logic, and obviously improves the optimization speed on the premise of ensuring the optimization result compared with the traditional Bayesian optimization.
The above-described embodiment is only one of the embodiments that can implement the technical solution of the present invention, and the scope of the present invention is not limited by the embodiment, but includes any variations, substitutions and other embodiments that can be easily conceived by those skilled in the art within the technical scope of the present invention disclosed.
Claims (8)
1. An antenna optimization method based on multi-output Gaussian process Bayesian optimization is characterized by comprising the following steps:
step 1, designing an antenna optimization comprehensive objective function, wherein the antenna comprehensive objective function comprises a sub-objective to be optimized and a limiting condition; the optimized comprehensive objective function of the antenna is mathematically described by the formula (1):
F＝ggn(Fgn)+gs11(FS11)+gAR(FAR)+… (1)
in the formula, FgnAn objective function representing the gain of the antenna, FS11Representing the objective function, F, of the antenna S11ARAn objective function, g, representing the axial ratio of the antennaxxThe method comprises the following steps of (1) representing that a composite function is taken for each branch objective function, so that the branch objective functions have different sensitivities to different variation ranges;
step 2, randomly sampling a plurality of sample points in the value range of the parameter to be optimized to perform high-precision or low-precision electromagnetic simulation to obtain a comprehensive objective function value of the sample points, and taking the comprehensive objective function value as an initialization sample set;
step 3, training an agent model by using a multi-output Gaussian process based on the sample set, and fitting a comprehensive objective function;
step 4, solving the solution of the maximum obtained function according to the posterior mean value and the variance of the proxy model, taking the solution as the input value of the next electromagnetic simulation, performing corresponding electromagnetic simulation according to the coefficient q for controlling the high-precision simulation quantity proportion and the low-precision simulation quantity proportion to obtain a target function value, and adding new data into a sample set;
step 5, judging whether an iteration end condition is met, if the iteration end condition is not met, returning to the step 3, and if the iteration end condition is met, turning to the step 6;
step 6, k optimal low-precision simulation solutions are selected, k is a smaller number relative to the total sample number, and high-precision simulation is carried out on the k optimal low-precision simulation solutions to obtain comprehensive objective function values of the k optimal low-precision simulation solutions;
and 7, outputting the optimal high-precision simulation solution to obtain an antenna optimization result.
2. The antenna optimization method based on the multi-output Gaussian process Bayesian optimization as recited in claim 1, wherein the antenna parameters to be optimized refer to physical dimensions of the antenna that need to be determined optimally.
3. The method as claimed in claim 1, wherein the antenna optimization objective is expressed as a synthetic objective function, and thus the antenna optimization problem is a problem of solving an optimal solution to a black-box function.
4. The antenna optimization method based on the multi-output Gaussian process Bayesian optimization according to claim 1 is characterized in that during high-precision electromagnetic simulation, convergence conditions meeting requirements are set in simulation software, and solution is performed at frequency points in sufficient detail according to a real antenna model; in low-precision electromagnetic simulation, convergence conditions are set relatively loosely in simulation software, antenna models can be set to be simplified in some places, solved frequency points can be set to be relatively sparse, and the like, so that the purpose of shortening simulation time is achieved.
5. The antenna optimization method based on the Bayesian optimization of the multi-output Gaussian process according to claim 1, wherein a proxy model of a comprehensive objective function is constructed by fusing high-precision simulation data and low-precision simulation data by using the multi-output Gaussian process; an ICM model in a multi-output gaussian process is used, the mathematical analysis of which is as follows:
1) assuming a Gaussian process
Sampling twice to obtain u1(x) And u2(x) The two functions of correlation can be expressed as equation (2):
2) then the covariance for f (x) can be expressed as:
wherein, B ═ a1(a1)T+a2(a2)T，
3) For data sets
Exist of
Wherein,
the element of K is K (x)i，xj)，bijAn element that is B;
4) according to ICM, will
Written D ═ X, y, then for input X*The posterior distribution of (A) is:
wherein, Kf，fElement(s) of cov [ fd(xn)，fd′(xn′)]Σ denotes the observed noise of each output,
sum Σ*Similar to Kf，fAnd Σ; theta represents the hyper-parameter of the model;
5) from the training set sample data, the edge likelihood can be expressed as
By maximum likelihood estimation, the hyper-parameters of the model can be estimated.
6. The antenna optimization method based on the Bayesian optimization of the multi-output Gaussian process according to claim 5, wherein the iteration is performed by using an obtained function in the Bayesian optimization;
the posterior distribution based on ICM, as shown in equations (6) - (8), is balanced for exploration and utilization by maximizing the gain function, which includes the confidence upper bound or the expectation improvement, to find the next simulated input point, fusing the posterior mean variance with the gain function.
7. The antenna optimization method based on the Bayesian optimization of the multi-output Gaussian process according to claim 1, wherein a q value is set to represent a ratio between the total simulation quantity and the high-precision simulation quantity.
8. The antenna optimization method based on the multi-output Gaussian process Bayesian optimization according to claim 1, characterized in that after the iteration is finished, k sample points with the highest potential in the low-precision simulation samples are selected for high-precision simulation to obtain the comprehensive objective function value thereof, and finally, the optimal solution in the high-precision simulation samples is selected as the optimization result.
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