CN113987962B - Microstrip antenna optimization method and optimization system based on student T process - Google Patents
Microstrip antenna optimization method and optimization system based on student T process Download PDFInfo
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Abstract
The invention discloses a microstrip antenna optimizing method and optimizing system based on student T process, which predicts resonant frequency corresponding to physical size of antenna by constructing STP proxy model based on student T process, when the predicting result does not accord with design target, searching new physical size of antenna by collecting function, and predicting resonant frequency corresponding to physical size of antenna by using STP proxy model again until it accords with design target. The method can find the optimal size parameter of the microstrip antenna by carrying out fewer iterations within the specified boundary under the condition of few training data.
Description
Technical Field
The invention belongs to the technical field of microstrip antenna design, and particularly relates to a microstrip antenna optimization method and system based on student T process.
Background
In the field of optimization design of electromagnetic devices, methods combining numerical simulation calculation or electromagnetic simulation software such as HFSS (High Frequency Structure Simulator) with an optimization algorithm are commonly used. High-precision results can be obtained through HFSS software simulation to obtain marked training data for training. When the HFSS is called through the optimizing algorithm, if the microwave device has a complex structure, a large size and multiple frequency bands, the HFSS is called for multiple times, a great amount of time is consumed for evaluating an individual each time, and the calculation cost is high and the time consumption is long.
The invention discloses a planar inverted F antenna resonance frequency prediction method based on semi-supervised learning, and the invention discloses a planar inverted F antenna resonance frequency prediction method based on semi-supervised learning, wherein a Gaussian process and a support vector machine are used for establishing a mapping relation between four relevant parameters of the width of a short-circuit metal sheet of a planar inverted F antenna, the length of a radiation metal sheet, the width of the radiation metal sheet and the height of the radiation metal sheet and actual measured resonance frequency, and the resonance frequency of other planar inverted F antennas can be predicted by using a Gaussian process and support vector machine collaborative training method and combining unmarked data for iterative training, and a training semi-supervised collaborative training model can be used for predicting the resonance frequency of the other planar inverted F antennas. The method requires complex model collaborative training, two models are required to be trained simultaneously, and the time cost is high; and cannot automatically find the optimal dimensional parameters of the antenna in a constant design space.
Disclosure of Invention
The invention aims to: the invention provides a microstrip antenna optimization method and an optimization system based on a student T process, which can find the optimal microstrip antenna size parameter by carrying out fewer iterations within a specified boundary under the condition of few training data.
The technical scheme is as follows: the invention discloses a microstrip antenna optimization method based on a student T process, which comprises the following steps:
S1, constructing a sample set: adopting simulation software to obtain resonance frequencies under different antenna physical dimensions to form a sample set S= { (x i,yi) }, wherein (x i,yi) represents an ith sample, x i is an antenna physical dimension vector of the ith sample, and y i is a resonance frequency corresponding to x i obtained by the simulation software; i=1, 2, …, n, n is the total number of samples;
s2, constructing an STP proxy model based on a student T process: y=stp (v+n, μ (X), σ (X));
The input X of the STP proxy model is an antenna physical size vector, and the output Y is the resonant frequency corresponding to X; where v is the initial value of the degree of freedom parameter of the STP proxy model, μ (X) is the predicted mean of the input X, σ (X) is the predicted variance of the input X:
μ(X)＝k(X,xi)k(xi,xi)-1yi，
σ(X)＝k(X,X)-k(X,xi)k(xi,X)-1k(xi,X)
k (,) is a kernel function;
S3, training the STP proxy model by using the sample set S to obtain a trained STP proxy model;
S4, initializing: setting the maximum iteration times T max, and the upper and lower boundaries of the values of each element in the physical size vector of the antenna; initializing the iteration times t to 1, taking the physical size parameter of the antenna to be optimized as an initial value X 0 of the physical size vector of the antenna, acquiring a resonant frequency Y 0 corresponding to X 0 by using a trained STP proxy model, and calculating an initial error f 0＝(fa-Y0)2,fa as a target resonant frequency of the antenna to be optimized; initializing a minimum error f best＝f0, and setting an optimal antenna physical size vector X best to X 0;
S5, acquiring new antenna size parameters in the range of the upper and lower boundaries of the values of each element in the antenna physical size vector through an acquisition function, wherein the acquisition function is as follows:
where mu t-1(xi) and σ t-1(xi) are the predicted mean and predicted variance respectively resulting from the last iteration, M 0＝maxτ∈[1,t-1]Yτ,Yτ is the output of STP proxy model in the τ iteration, and Φ () is the cumulative distribution function obeying the student T distribution;
S6, acquiring a resonant frequency Y t corresponding to a new antenna size parameter X t by using a trained STP proxy model, and calculating a current error: f t＝(fa-Yt)2, if f t is smaller than the minimum error f best, let f best take on the value of f t,Xbest take on the value of X 0;
Judging whether the current iteration number T reaches the maximum iteration number T max or not, if so, ending the iteration, and obtaining X best as the optimized antenna physical size vector; if not, let t add one, jump to step S5 for the next iteration.
Preferably, the kernel function k (,) is a square-index kernel function: wherein the superscript T denotes a vector transpose,/> Is a hyper-parameter of the kernel function, representing the scale of the input.
The simulation software in the invention is full-wave three-dimensional electromagnetic simulation software HFSS.
On the other hand, the invention also discloses an optimizing system for realizing the optimizing method, which comprises the following steps:
The sample set construction module is used for acquiring resonance frequencies under different antenna physical dimensions by adopting simulation software to form a sample set S= { (x i,yi) }, wherein (x i,yi) represents an ith sample, x i is an antenna physical dimension vector of the ith sample, and y i is a resonance frequency corresponding to x i acquired by the simulation software; i=1, 2, …, n, n is the total number of samples;
the STP proxy model building module is used for building an STP proxy model based on the student T process: ;
The input X of the STP proxy model is an antenna physical size vector, and the output Y is the resonant frequency corresponding to X; where v is the initial value of the degree of freedom parameter of the STP proxy model, μ (X) is the predicted mean of the input X, σ (X) is the predicted variance of the input X:
μ(X)＝k(X,xi)k(xi,xi)-1yi，
σ(X)＝k(X,X)-k(X,xi)k(xi,X)-1k(xi,X)
k (,) is a kernel function;
the training module is used for training the STP proxy model by adopting the sample set S;
The initialization module is used for initializing iteration parameters, and comprises: setting the maximum iteration times T max, and the upper and lower boundaries of the values of each element in the physical size vector of the antenna; initializing the iteration times t to 1, taking the physical size parameter of the antenna to be optimized as an initial value X 0 of the physical size vector of the antenna, acquiring a resonant frequency Y 0 corresponding to X 0 by using a trained STP proxy model, and calculating an initial error f 0＝(fa-Y0)2,fa as a target resonant frequency of the antenna to be optimized; initializing a minimum error f best＝f0, and setting an optimal antenna physical size vector X best to X 0;
The new antenna size parameter obtaining module is used for obtaining new antenna size parameters within the range of the upper and lower boundaries of the values of each element in the antenna physical size vector through an acquisition function, wherein the acquisition function is as follows:
where mu t-1(xi) and σ t-1(xi) are the predicted mean and predicted variance respectively resulting from the last iteration, M 0＝maxτ∈[1,t-1]Yτ,Yτ is the output of STP proxy model in the τ iteration, and Φ () is the cumulative distribution function obeying the student T distribution;
The error calculation module is used for obtaining the resonant frequency Y t corresponding to the new antenna size parameter X t by using the trained STP proxy model, and calculating the current error: f t＝(fa-Yt)2; if f t is less than the minimum error f best, then let f best take on the value f t,Xbest and take on the value X 0; judging whether the current iteration number T reaches the maximum iteration number T max or not, if so, ending the iteration, and obtaining X best as the optimized antenna physical size vector; if the antenna size parameter does not reach the preset value, adding one to t, and acquiring a new antenna size parameter again by using a new antenna size parameter acquisition module to perform the next iteration.
The beneficial effects are that: the microstrip antenna optimization method and the microstrip antenna optimization system based on the student T process have the following advantages:
1. The student T process is used as a proxy model, so that the defect of insufficient robustness when the Gaussian process is used as the proxy model in the traditional Bayesian optimization algorithm is overcome;
2. The acquisition function of the Bayesian optimization algorithm is used, a complex manual updating test set is avoided, the acquisition function can automatically acquire a new antenna size value within the design range of the size parameter, meanwhile, the student T process in the Bayesian algorithm can predict the antenna resonant frequency at the new size parameter, so that the simulation time required by electromagnetic simulation software is greatly reduced, and meanwhile, the improved Bayesian algorithm can find the optimal size parameter of the antenna only by a few iterations, and the optimization speed is accelerated.
Drawings
Fig. 1 is a flowchart of a microstrip antenna optimization method based on student T process disclosed in the present invention;
FIG. 2 is a schematic diagram of printed dipole antenna dimensions according to an embodiment;
FIG. 3 is a graph of the HFSS simulation result S11 used in the example;
fig. 4 is a schematic diagram of the composition of a microstrip antenna optimization system based on student T process.
Detailed Description
The invention discloses a microstrip antenna optimization method based on a student T process, and the flow of the microstrip antenna optimization method is shown in figure 1. The following describes in detail the printed dipole antenna with the dimensions optimized as shown in fig. 2.
S1, constructing a sample set: adopting simulation software to obtain resonance frequencies under different antenna physical dimensions to form a sample set S= { (x i,yi) }, wherein (x i,yi) represents an ith sample, x i is an antenna physical dimension vector of the ith sample, and y i is a resonance frequency corresponding to x i obtained by the simulation software; i=1, 2, …, n, n is the total number of samples;
the dimensions to be optimized and the range of values of the printed dipole antenna in fig. 2 are shown in table 1:
TABLE 1
| Variable name | Minimum value | Maximum value |
| L1(mm) | 21 | 23 |
| L2(mm) | 20 | 22.5 |
| L3(mm) | 9 | 10.6 |
| L4(mm) | 11.5 | 13 |
| W3(mm) | 3 | 5 |
The length L1 of the transmission line of the dipole antenna is printed, one arm length L2 of the dipole, the right-angle side length L3 of the side of the balun triangle, the other right-angle side length L4 and the width W3 of the rectangular part of the microwave balun. The influence of the other dimensions on the antenna performance is small, and a fixed value is adopted in the embodiment and is not used as an optimization parameter. The design target of the antenna is that the resonant frequency is 2.45GHz, and S11< -15dB corresponding to the resonant frequency point. Whereby the antenna physical size vector is a 5-dimensional vector, f a =2.45 GHz. In the embodiment, frequency scanning simulated by combining full-wave three-dimensional electromagnetic simulation family HFSS with MATLAB is set to be 2GHz-3GHz, the step length is 0.01, and 50 groups of training data are obtained through orthogonal experiments to form a sample set.
S2, constructing an STP proxy model based on a student T process: y=stp (v+n, μ (X), σ (X));
The input X of the STP proxy model is an antenna physical size vector, and the output Y is the resonant frequency corresponding to X; where v is the initial value of the degree of freedom parameter of the STP proxy model, μ (X) is the predicted mean of the input X, σ (X) is the predicted variance of the input X:
μ(X)＝k(X,xi)k(xi,xi)-1yi，
σ(X)＝k(X,X)-k(X,xi)k(xi,X)-1k(xi,X)
k (,) is a kernel function; the kernel function k (,) in this embodiment is a square-exponent kernel function: wherein the superscript T denotes a vector transpose,/> Is a hyper-parameter of the kernel function, representing the scale of the input.
S3, training the STP proxy model by using the sample set S to obtain a trained STP proxy model;
The training process predicts the most likely output value corresponding to x i on the basis of the sample set according to the bayesian principle. The objective of using bayesian theory is to continuously update the probability prediction distribution with the observed real data, i.e. given the new input x *, sample set x i and y i, infer the maximum possible prediction posterior distribution of y * corresponding to x *, thus yielding the value of y *.
S4, initializing: setting the maximum iteration number T max =50, and the upper and lower boundaries of the values of each element in the physical size vector of the antenna (as shown in table 1); the iteration times t is initialized to 1, the physical size parameter of the antenna to be optimized is taken as an initial value X 0 of the physical size vector of the antenna, in the embodiment, X 0 is randomly initialized within the range limited by the table 1, the resonant frequency Y 0 corresponding to X 0 is obtained by using a trained STP proxy model, and an initial error f 0＝(fa-Y0)2,fa is calculated as a target resonant frequency of the antenna to be optimized; initializing a minimum error f best＝f0, and setting an optimal antenna physical size vector X best to X 0;
S5, acquiring new antenna size parameters in the range of the upper and lower boundaries of the values of each element in the antenna physical size vector through an acquisition function, wherein the acquisition function is as follows:
where mu t-1(xi) and σ t-1(xi) are the predicted mean and predicted variance respectively resulting from the last iteration, M 0＝maxτ∈[1,t-1]Yτ,Yτ is the output of STP proxy model in the τ iteration, and Φ () is the cumulative distribution function obeying the student T distribution;
S6, acquiring a resonant frequency Y t corresponding to a new antenna size parameter X t by using a trained STP proxy model, and calculating a current error: f t＝(fa-Yt)2, if f t is smaller than the minimum error f best, let f best take on the value of f t,Xbest take on the value of X 0;
Judging whether the current iteration number T reaches the maximum iteration number T max or not, if so, ending the iteration, and obtaining X best as the optimized antenna physical size vector; if not, let t add one, jump to step S5 for the next iteration.
The optimized results of this embodiment are shown in table 2, and the S11 curve of HFSS simulation results is shown in fig. 3 according to the physical dimensions of the antenna obtained in table 2.
TABLE 2
As can be seen from FIG. 3, the resonant frequency of the antenna is 2.45GHz, and the return loss S11< -15dB corresponding to the resonant point meets the design requirement.
An optimization system for implementing the above optimization method is shown in fig. 4, and includes:
The sample set constructing module 1 is configured to acquire resonance frequencies under different antenna physical dimensions by using simulation software, and form a sample set s= { (x i,yi) }, where (x i,yi) represents an ith sample, x i is an antenna physical dimension vector of the ith sample, and y i is a resonance frequency corresponding to x i acquired by the simulation software; i=1, 2, …, n, n is the total number of samples;
the STP proxy model building module 2 is used for building an STP proxy model based on a student T process: y=stp (v, μ (X), σ (X));
The input X of the STP proxy model is an antenna physical size vector, and the output Y is the resonant frequency corresponding to X; where v is the degree of freedom parameter of the STP proxy model, μ (X) is the predicted mean of the input X, σ (X) is the predicted variance of the input X:
μ(X)＝k(X,xi)k(xi,xi)-1yi，
σ(X)＝k(X,X)-k(X,xi)k(xi,X)-1k(xi,X)
k (,) is a kernel function;
The training module 3 is used for training the STP proxy model by adopting the sample set S;
An initialization module 4, configured to initialize iteration parameters, including: setting the maximum iteration times T max, and the upper and lower boundaries of the values of each element in the physical size vector of the antenna; initializing the iteration times t to1, taking the physical size parameter of the antenna to be optimized as an initial value X 0 of the physical size vector of the antenna, acquiring a resonant frequency Y 0 corresponding to X 0 by using a trained STP proxy model, and calculating an initial error f 0＝(fa-Y0)2,fa as a target resonant frequency of the antenna to be optimized; initializing a minimum error f best＝f0, and setting an optimal antenna physical size vector X best to X 0;
the new antenna size parameter obtaining module 5 is configured to obtain new antenna size parameters within the range of the upper and lower bounds of the values of each element in the antenna physical size vector through an acquisition function, where the acquisition function is:
where mu t-1(xi) and σ t-1(xi) are the predicted mean and predicted variance respectively resulting from the last iteration, M 0＝maxτ∈[1,t-1]Yτ,Yτ is the output of STP proxy model in the τ iteration, and Φ () is the cumulative distribution function obeying the student T distribution;
The error calculation module 6 is configured to obtain a resonant frequency Y t corresponding to the new antenna size parameter X t by using the trained STP proxy model, and calculate a current error: f t＝(fa-Yt)2; if f t is less than the minimum error f best, then let f best take on the value f t,Xbest and take on the value X 0; judging whether the current iteration number T reaches the maximum iteration number T max or not, if so, ending the iteration, and obtaining X best as the optimized antenna physical size vector; if the antenna size parameter does not reach the preset value, adding one to t, and acquiring a new antenna size parameter again by using a new antenna size parameter acquisition module to perform the next iteration.
Claims (6)
1. The microstrip antenna optimization method based on student T process is characterized by comprising the following steps:
S1, constructing a sample set: adopting simulation software to obtain resonance frequencies under different antenna physical dimensions to form a sample set S= { (x i,yi) }, wherein (x i,yi) represents an ith sample, x i is an antenna physical dimension vector of the ith sample, and y i is a resonance frequency corresponding to x i obtained by the simulation software; i=1, 2, …, n, n is the total number of samples;
s2, constructing an STP proxy model based on a student T process: y=stp (v+n, μ (X), σ (X));
The input X of the STP proxy model is an antenna physical size vector, and the output Y is the resonant frequency corresponding to X; where v is the initial value of the degree of freedom parameter of the STP proxy model, μ (X) is the predicted mean of the input X, σ (X) is the predicted variance of the input X:
μ(X)＝k(X,xi)k(xi,xi)-1yi，
σ(X)＝k(X,X)-k(X,xi)k(xi,X)-1k(xi,X)
k (,) is a kernel function;
S3, training the STP proxy model by using the sample set S to obtain a trained STP proxy model;
S4, initializing: setting the maximum iteration times T max, and the upper and lower boundaries of the values of each element in the physical size vector of the antenna; initializing the iteration times t to 1, taking the physical size parameter of the antenna to be optimized as an initial value X 0 of the physical size vector of the antenna, acquiring a resonant frequency Y 0 corresponding to X 0 by using a trained STP proxy model, and calculating an initial error f 0＝(fa-Y0)2,fa as a target resonant frequency of the antenna to be optimized; initializing a minimum error f best＝f0, and setting an optimal antenna physical size vector X best to X 0;
S5, acquiring new antenna size parameters in the range of the upper and lower boundaries of the values of each element in the antenna physical size vector through an acquisition function, wherein the acquisition function is as follows:
where mu t-1(xi) and σ t-1(xi) are the predicted mean and predicted variance respectively resulting from the last iteration, M 0＝maxτ∈[1,t-1]Yτ,Yτ is the output of STP proxy model in the τ iteration, and Φ () is the cumulative distribution function obeying the student T distribution;
S6, acquiring a resonant frequency Y t corresponding to a new antenna size parameter X t by using a trained STP proxy model, and calculating a current error: f t＝(fa-Yt)2, if f t is smaller than the minimum error f best, let f best take on the value of f t,Xbest take on the value of X 0;
Judging whether the current iteration number T reaches the maximum iteration number T max or not, if so, ending the iteration, and obtaining X best as the optimized antenna physical size vector; if not, let t add one, jump to step S5 for the next iteration.
2. The microstrip antenna optimization method according to claim 1, wherein said kernel function k (,) is a square-index kernel function: where the superscript T denotes the vector transpose and l is the hyper-parameter of the kernel, indicating the scale of the input.
3. The microstrip antenna optimization method according to claim 1, wherein said simulation software is a full wave three-dimensional electromagnetic simulation software HFSS.
4. A microstrip antenna optimization system based on student T-process, comprising:
The sample set construction module is used for acquiring resonance frequencies under different antenna physical dimensions by adopting simulation software to form a sample set S= { (x i,yi) }, wherein (x i,yi) represents an ith sample, x i is an antenna physical dimension vector of the ith sample, and y i is a resonance frequency corresponding to x i acquired by the simulation software; i=1, 2, …, n, n is the total number of samples;
The STP proxy model building module is used for building an STP proxy model based on the student T process: y=stp (v+n, μ (X), σ (X));
The input X of the STP proxy model is an antenna physical size vector, and the output Y is the resonant frequency corresponding to X; where v is the initial value of the degree of freedom parameter of the STP proxy model, μ (X) is the predicted mean of the input X, σ (X) is the predicted variance of the input X:
μ(X)＝k(X,xi)k(xi,xi)-1yi，
σ(X)＝k(X,X)-k(X,xi)k(xi,X)-1k(xi,X)
k (,) is a kernel function;
the training module is used for training the STP proxy model by adopting the sample set S;
The initialization module is used for initializing iteration parameters, and comprises: setting the maximum iteration times T max, and the upper and lower boundaries of the values of each element in the physical size vector of the antenna; initializing the iteration times t to 1, taking the physical size parameter of the antenna to be optimized as an initial value X 0 of the physical size vector of the antenna, acquiring a resonant frequency Y 0 corresponding to X 0 by using a trained STP proxy model, and calculating an initial error f 0＝(fa-Y0)2,fa as a target resonant frequency of the antenna to be optimized; initializing a minimum error f best＝f0, and setting an optimal antenna physical size vector X best to X 0;
The new antenna size parameter obtaining module is used for obtaining new antenna size parameters within the range of the upper and lower boundaries of the values of each element in the antenna physical size vector through an acquisition function, wherein the acquisition function is as follows:
where mu t-1(xi) and σ t-1(xi) are the predicted mean and predicted variance respectively resulting from the last iteration, M 0＝maxτ∈[1,t-1]Yτ,Yτ is the output of STP proxy model in the τ iteration, and Φ () is the cumulative distribution function obeying the student T distribution;
The error calculation module is used for obtaining the resonant frequency Y t corresponding to the new antenna size parameter X t by using the trained STP proxy model, and calculating the current error: f t＝(fa-Yt)2; if f t is less than the minimum error f best, then let f best take on the value f t,Xbest and take on the value X 0; judging whether the current iteration number T reaches the maximum iteration number T max or not, if so, ending the iteration, and obtaining X best as the optimized antenna physical size vector; if the antenna size parameter does not reach the preset value, adding one to t, and acquiring a new antenna size parameter again by using a new antenna size parameter acquisition module to perform the next iteration.
5. The student T process based microstrip antenna optimization system according to claim 4, wherein said kernel function k (,) is a square-index kernel function: where the superscript T denotes the vector transpose and l is the hyper-parameter of the kernel, indicating the scale of the input.
6. The student T process based microstrip antenna optimization system according to claim 4, wherein said simulation software is a full wave three-dimensional electromagnetic simulation software HFSS.
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