CN111709192A

CN111709192A - Plane inverted F-shaped antenna resonant frequency prediction method based on semi-supervised learning

Info

Publication number: CN111709192A
Application number: CN202010646567.1A
Authority: CN
Inventors: 高婧; 田雨波
Original assignee: Jiangsu University of Science and Technology
Current assignee: Jiangsu University of Science and Technology
Priority date: 2020-07-07
Filing date: 2020-07-07
Publication date: 2020-09-25
Anticipated expiration: 2040-07-07
Also published as: CN111709192B

Abstract

The invention discloses a plane inverted-F antenna resonant frequency prediction method based on semi-supervised learning, wherein a mapping relation is established between four related parameters, namely the width of a short-circuit metal sheet, the length of a radiation metal sheet, the width of the radiation metal sheet and the height of the radiation metal sheet of a plane inverted-F antenna and an actually measured resonant frequency by using a Gaussian process and a support vector machine, iterative training is carried out by using a cooperative training method of the Gaussian process and the support vector machine in combination with unlabeled data, and a trained semi-supervised cooperative training model can be used for predicting the resonant frequency of other plane inverted-F antennas. The method can solve the problems that in the existing electromagnetic optimization design, a large number of marked samples are needed when a model is trained, the electromagnetic simulation software HFSS needs to be called for many times, and the calculation cost is high and the time consumption is long; compared with a modeling mode based on traditional supervised learning, the resonant frequency prediction capability of the invention has certain advantages.

Description

Plane inverted F-shaped antenna resonant frequency prediction method based on semi-supervised learning

Technical Field

The invention relates to a plane inverted F-shaped antenna resonant frequency prediction method based on semi-supervised learning, and belongs to the field of electromagnetic optimization design.

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 optimization algorithms are commonly used. High-precision results can be obtained through HFSS software simulation so as to obtain labeled training data for training. When the HFSS is called by the optimization algorithm, if the microwave device has a complex structure and a large size and is multiband, the microwave device needs to be called for many times, and each time the HFSS is called to evaluate an individual, a lot of time is consumed, and the calculation cost is high and the time is long. Therefore, the modeling method is used for replacing HFSS calling to evaluate the fitness of the electromagnetic device, so that the optimization time can be saved, and the method is a hot topic of the current electromagnetic optimization design.

The resonant frequency is an important technical index in the process of antenna optimization design, and the resonant frequency is rapidly obtained through the known structural parameters of the antenna, so that the method is a hot spot of modern antenna design method research. The Gaussian Process (GP) is a machine learning method which is gradually developed in recent years, has a strict statistical theoretical basis, and is suitable for processing complex problems of small samples, high dimension, nonlinearity and the like. A Support Vector Machine (SVM) is also a common Machine learning method, and has specific advantages for solving small samples, non-linearity and high-dimensional modes. Both modeling methods are widely applied to antenna resonant frequency modeling. The trained model can establish a mapping relation between the antenna related parameters and the actually measured resonant frequency, so that the resonant frequency of other antenna parameters can be predicted, and the frequency of calling HFSS accurate simulation is reduced.

The existing modeling for electromagnetic behaviors is based on a supervised learning mode, and label training samples used for modeling are based on simulation software HFSS. Therefore, a Semi-supervised learning (SSL) method has been proposed on the basis of the existing research. The traditional machine learning technology relies on a large number of marked samples for training, and in practical application, the marked samples are difficult to obtain, and the unmarked samples are cheap and easier to obtain. The cooperative training is a common semi-supervised learning mode, belongs to a bifurcation-based semi-supervised learning method, is full in theoretical basis and wide in application range. The classification problem is concerned with in the traditional collaborative training, and the regression problem is lack of research.

Disclosure of Invention

The purpose of the invention is as follows: the invention provides a plane inverted F antenna resonant frequency prediction method based on semi-supervised learning, aiming at solving the problems that in the existing electromagnetic optimization design, more marked samples are needed during model training, the electromagnetic simulation software HFSS needs to be called for multiple times, the calculation cost is high, the consumed time is long, and the like.

The technical scheme is as follows: a plane inverted F antenna resonant frequency prediction method based on semi-supervised learning comprises the following steps:

step 1: constructing an initial training set, a test set test.G and an unmarked data set, and constructing a GP model and an SVM model of the resonant frequency of the planar inverted F antenna;

step 2: training the GP model and the SVM model in the step 1 by adopting an initial training set, and testing the GP model and the SVM model obtained by training by adopting a test set to obtain an initial error;

and step 3: selection of N from unlabeled datasets₁Inputting the sample X into the GP model obtained by training in the step 2 to obtain a corresponding output gp.Y, marking as a pseudo-mark sample CO.GP (X, gp.Y), and inputting the N₁Inputting the sample X into the SVM model obtained by training in the step 2 to obtain corresponding output svm.Y, and marking as a pseudo-labeled sample CO.SVM (X, svm.Y);

and 4, step 4: further training the SVM model obtained by training in the step 2 by adopting a pseudo-mark sample CO.GP (X, gp.Y) to obtain the SVM_timeA model; simultaneously, a pseudo-mark sample CO.SVM (X, svm.Y) is adopted to further train the GP model obtained by the training in the step 2 to obtain GP_timeA model;

and 5: respectively aligning the SVM by adopting a test set test.G_timeModel and GP_timeModel testing, GP_timeThe test error of the model is recorded as e₁，SVM_timeThe test error of the model is recorded as e₂；

Step 6; judgment of min (e)₁，e₂) Whether the error is smaller than a preset error or not is judged, if so, the operation is finished, and a usable semi-supervised cooperative training model is obtained; if so, further comparing e₁And e₂If e is large or small₁≥e₂The pseudo-labeled sample co.gp (X, gp.y) generated in step 3 and the test data test.g corresponding to the number of iterations in the test set are then compared_iAdd initial trainingTraining, namely further training the SVM model and the GP model obtained by training in the step 2; if e₁＜e₂Then, the pseudo-labeled sample co.svm (X, svm.y) generated in step 3 and the test data test.g corresponding to the number of iterations in the test set are collected_iAdding the initial training set, and further training the SVM model and the GP model obtained by the training in the step 3;

and 7: judging whether an iteration stopping condition is met, if so, ending the iteration to obtain a usable semi-supervised cooperative training model; otherwise, adding the test data test.G currently added into the initial training set_iDeleting the test data from the test set test.G, using the residual test data as a test set for the next iteration test, and turning to the step 3;

and 8: after the usable semi-supervised cooperative training model is obtained, the input parameters of the planar inverted F antenna to be predicted, namely the width of the short circuit metal sheet, the length of the radiation metal sheet, the width of the radiation metal sheet and the height of the radiation metal sheet, can be input into the usable semi-supervised cooperative training model to obtain the corresponding resonant frequency, so that the prediction of the resonant frequency is completed.

Further, the training data in the initial training set includes the width of the short-circuit metal sheet, the length of the radiation metal sheet, the width of the radiation metal sheet, the height of the radiation metal sheet, and the corresponding resonant frequency obtained after HFSS simulation;

the test data in the test set test.G comprise the width of the short circuit metal sheet, the length of the radiation metal sheet, the width of the radiation metal sheet, the height of the radiation metal sheet and the corresponding measured resonance frequency;

the sample data in the unmarked dataset comprises the width of the short circuit metal sheet, the length of the radiation metal sheet, the width of the radiation metal sheet and the height of the radiation metal sheet.

Compared with the traditional supervised learning, for the antenna resonant frequency modeling problem, the unlabeled samples and the labeled samples (with measured resonant frequency points) are independent and distributed in the same way, and the contained data distribution information has certain use for the training of the model. The unlabeled samples are used for collaborative training, useful information is provided for improving the prediction accuracy of the model, data resources are not wasted, electromagnetic simulation time is saved, and the efficiency of optimizing the prediction capability is improved.

Further, a gaussian kernel function is adopted in the step 1 to construct a GP model and an SVM model of the resonant frequency of the planar inverted F antenna.

Further, the test error is an average relative error:

in the formula, y_predFor tag values predicted by GP models or SVM models, y_testIs the true tag value of the test specimen.

Further, the iteration stop condition is: for the semi-supervised collaborative training model output by each iteration, the test error of the next iteration is higher than that of the previous iteration, and the test error of the previous iteration reaches an error threshold.

Has the advantages that: the method establishes a mapping relation between four relevant parameters, namely the width of a short-circuit metal sheet, the length of a radiation metal sheet, the width of the radiation metal sheet and the height of the radiation metal sheet, of the planar inverted-F antenna and the actually-measured resonant frequency by using a Gaussian process and a support vector machine, performs iterative training by using a cooperative training method of the Gaussian process and the support vector machine in combination with unlabeled data, and a trained semi-supervised cooperative training model can be used for predicting the resonant frequency of other planar inverted-F antennas. The method can solve the problems that in the existing electromagnetic optimization design, a large number of marked samples are needed when a model is trained, the electromagnetic simulation software HFSS needs to be called for many times, and the calculation cost is high and the time consumption is long; compared with a modeling mode based on traditional supervised learning, the resonant frequency prediction capability of the invention has certain advantages. Compared with the prior art, the method has the following advantages:

(1) the invention uses the same unlabeled sample to cross train two different agent models, uses the pseudo-labeled data with higher accuracy and the corresponding test data to update the two models, achieves the satisfactory prediction accuracy, reduces the times of calling HFSS to obtain the accurate labeled data in the training process, and saves the time of obtaining the labeled sample;

(2) the invention sets iteration conditions, controls the number of introduced unmarked data and the number of times of model updating until reaching the preset termination condition, and prevents the introduced unmarked data from being excessive and reducing the prediction precision of the model on the contrary.

(3) For the modeling problem of the resonance frequency of the PIFA antenna, the algorithm provided by the invention has the advantages that the prediction capability is enhanced compared with that of the traditional supervised learning mode under the condition of using less marking data, and the time and labor cost for obtaining the marking data are saved;

(4) on the basis of utilizing the same mark truth value, for the PIFA antenna resonant frequency prediction problem, the prediction capability of the semi-supervised cooperative training model is improved compared with that of the traditional supervised learning model.

Drawings

Fig. 1 is a structural model diagram of a PIFA antenna;

fig. 2 is a three-dimensional perspective view of a PIFA antenna in an HFSS environment;

FIG. 3 is a schematic algorithm structure diagram of the collaborative training of the present invention;

FIG. 4 is a flow chart of the algorithm of the present invention;

fig. 5 is a diagram of an iterative effect of the prediction experiment on the resonant frequency of the PIFA antenna according to the present invention.

Detailed Description

The technical solution of the present invention will be further explained with reference to the accompanying drawings and examples.

Aiming at the problem that the computation time is too long due to the fact that relatively more marking samples are needed when a traditional supervised learning modeling mode is used for modeling the resonance frequency of the PIFA antenna, the invention designs and realizes a collaborative training method based on a GP model and an SVM model on the basis of the existing semi-supervised collaborative training, models the resonance frequency of the PIFA antenna, reduces the quantity of marking data needed during modeling and improves the accuracy of the model.

The invention relates to a method for predicting the resonant frequency of a planar inverted-F antenna based on GP and SVM collaborative training, which comprises the following steps:

the first step is as follows: modeling of GP and SVM

1) Acquisition of training samples

And establishing a mapping relation between antenna related parameters (including the size of a radiating patch, the thickness of a dielectric substrate and the like) and the actually measured resonant frequency to complete the establishment of the model. The trained model can predict the resonant frequency of other antenna sizes, the method has obvious advantages in precision compared with the traditional method, and the time for calling HFSS to perform electromagnetic simulation can be saved. According to the size parameter information of a Planar Inverted F-shaped Antenna (PIFA), different size information, namely different input variables, is set, and the actually measured resonance frequency point of HFSS simulation is used as the mark information of data, namely teacher signals. And taking the obtained small amount of labeled data as an initial training set.

2) Construction of GP model

A gaussian process is a collection of an infinite number of random variables, any subset of which obeys a gaussian distribution. The nature of the GP is determined by both the mean function and the covariance function:

wherein, x, x' ∈ R^dAnd m (x) and k (x, x') are mean and covariance functions, which can be further expressed as:

f(x)～GP(m(x),k(x,x’)) (2)

for the regression model: y ═ f (x) +, the observed target value y contaminated with additive noise, as a random variable following a normal distribution, with a mean of 0 and a variance of σ_n ²Expressed as:

～N(0，σ_n ²) (3)

then the prior distribution of y is

y～N(0,K+σ_n ²I) (4)

K (X, X) is an n × n-th order symmetric positive definite covariance matrix, K_ijMeasure x_iAnd x_jThe correlation between them. n training samples output y and n^*A test specimenOutput f^*The composition joint gaussian prior distribution is:

the properties of the mean function and covariance function of the GP are determined by a set of hyper-parameters, and the maximum likelihood function can be used to find the optimal hyper-parameter. And solving the partial derivative of the hyper-parameter by establishing a log-likelihood function of the conditional probability of the training sample, and then searching the optimal solution of the hyper-parameter by adopting a conjugate gradient optimization method. The negative log-likelihood function is of the form:

after the optimal hyper-parameter is obtained, the trained GP can be used for carrying out relevant prediction.

Given a new input x^*Inferring y from the input value X of the training set and the observed target value y^*Maximum possible predicted posterior distribution:

y^*|x^*,X,y～N(m,∑) (7)

m and Σ are the predicted mean and covariance:

m＝K(X^*,X)K(X,X)^-1y

∑＝K(X^*,X^*)-K(X^*,X)K(X,X)^-1K(X,X^*) (8)

the prediction mean and covariance describe a gaussian distribution to which the prediction output may be obeyed. The magnitude of the predicted variance reflects the accuracy of the model at that point, with smaller variances giving higher model accuracy.

3) Construction of SVM models

For linear indifference problems, SVM replaces inner product operations in high dimensional feature space by defining a kernel function, i.e. a kernel function

The dimensionality disaster is avoided. Considering fault tolerance, a relaxation variable y is added to the fixed value 1_i[(ω·x_i)+b]≥1-ξ_i,ξ_iNot less than 0, and a penalty factor C needs to be added to a certain sample of the misclassification, and the optimization problem is changed into:

y_i[ω·x_i+b]≥1-ξ_i,ξ_i≥0(i＝1,2,...,l) (10)

ξ_ii.e., how far away the corresponding outlier is, C is the degree of importance placed on the loss caused by the outlier.

The Lagrange optimization method is used for changing the problem into a dual problem, and the final optimized classification function is as follows:

wherein x_iIs a support vector that is a vector of the support,

is the corresponding Lagrange coefficient, b^*The classification threshold value can be obtained by taking the median value from any pair of support vectors of the two types.

The mapping of the original non-linear space into a high-dimensional dot product space (also known as a feature space) using a non-linear transformation becomes a linear separable problem. Seeking a function K so that when the function K accepts input values of a low-dimensional space, two types of linearly separable data can be obtained in a high-dimensional feature space, wherein the function K is called a kernel function, the kernel function has the requirement that a Mercer condition must be met, and a final classification function obtained by carrying out nonlinear transformation on s input vectors becomes:

wherein K (x)_iAnd x) is called a kernel function. Commonly used kernel functions are: linear kernel functions, polynomial kernel functions, radial basis kernel functions, and the like.

Support Vector Regression (SVR) is an important branch in SVM. The sample points of the SVR are of only one type, and the optimal hyperplane it seeks does not "maximize" the separation of two or more types of sample points, but minimizes the total deviation of all sample points from the optimal hyperplane, i.e., minimizes the "distance" to the sample point furthest from the hyperplane.

4) Training and testing of GP model and SVM model

Step 1: setting relevant size information of the antenna by using HFSS (high frequency satellite System) to obtain N₀A labeled sample;

step 2: by using N₀And (3) training GP and SVM models by the mark training samples, so that the models are converged quickly, and the GP models and the SVM models with relatively low precision are obtained.

And step 3: and (3) testing the original GP model and the SVM model constructed in the step (2) by utilizing a test sample set, verifying whether the result of the prediction output is consistent with the result of the high-frequency structure simulation HFSS, and respectively obtaining the initial training error of the models. Where relative error is used for a single test value and the average relative error is used for the entire test set.

The second step is that: structure of semi-supervised learning cooperative training model

Step 1: selection of N from unlabeled sample set₁Inputting the samples into a model GP to obtain corresponding outputs; in the same way, the N₁The unlabeled data is input into the model SVM to obtain a corresponding output.

Step 2: and respectively obtaining two groups of pseudo label data, and performing cross training on the GP model and the SVM model by using the two groups of pseudo label samples.

And step 3: and respectively testing the GP model and the SVM model by using the test set. The test error of the GP model is recorded as e₁And the test error of the SVM model is recorded as e₂。

And 4, step 4: comparison e₁And e₂The size of (2). If e₁>e₂In the iteration, the precision of the GP model is higher than that of the SVM, the pseudo mark data generated by the GP model and the test data corresponding to the iteration times in the test set are added into the original training set, and the training is further carried outPracticing GP and SVM models; and otherwise, adding the pseudo mark data generated by the SVM and the test data corresponding to the iteration times in the test data set into the original training set, and further training the GP model and the SVM model.

And 5: and (4) setting an iteration stopping condition, wherein the test error of the next iteration is higher than that of the previous iteration, and the iteration is stopped when the test error of the previous iteration reaches an error threshold value. Judgment e₁And e₂If the smaller error value of the error signal reaches the error threshold. If so, the loop ends; if not, continuing the iteration and turning to the step 1. And adding the last iteration into the training set, removing the test data from the test data set, and taking the rest test data as the test data set of the next iteration.

The invention is further described with reference to the following figures and specific examples.

The PIFA is a typical small-sized low-profile antenna, and has been widely used because of its significant features of small size, light weight, low profile, low cost, high gain, and being not susceptible to interference. Fig. 1 is a schematic structural diagram of a PIFA antenna, and the basic structure includes four parts: ground 1, radiating element 2, short-circuit metal sheet 3 and coaxial feeder 4. The radiating element 2 is a metal sheet parallel to the ground plane 1, the short-circuit metal sheet 3 is used for connecting the radiating element 2 and the ground plane 1, and the coaxial feeder 4 is used for signal transmission. PIFA resonant frequency point and width SW of the shorting metal sheet, length L of the radiating metal sheet₁Width W₁And height H. The width SW of the short circuit metal sheet and the length L of the radiation metal sheet₁Width W₁The height H is set to be different sizes for variables, and the figure 2 is a three-dimensional perspective view of the PIFA in the HFSS environment. 31 groups of input variables are set in total, 11 groups of input variables are selected from the 31 groups of input variables, after HFSS simulation is carried out, corresponding resonance frequencies are obtained to serve as initial training data, another 10 groups of input variables are obtained through HFSS simulation to serve as corresponding measured resonance frequencies to serve as test sets, and the remaining 10 groups of input variables serve as unmarked data sets.

FIG. 3 is a schematic structural diagram of a collaborative training algorithm based on a GP model and an SVM model. Using 11 training data, with SW, W₁，L₁H is an input variable, f_HFSSAnd respectively establishing a GP model and an SVM model for output. In the process of the collaborative training, the data without the measured resonance frequency is utilized, namely, the data without the measured resonance frequency is combined with the unlabeled data to carry out the collaborative training, and the precision of the model is continuously improved. In table 1, 31 sets of data are listed, 11 sets of data suffixed by ● as initial training data, 10 sets of data suffixed by # as test data, and 10 sets of data suffixed by # as unlabeled data, wherein the corresponding resonant frequency is also simulated by HFSS as a verification of the algorithm proposed in the present embodiment. The sequence from top to bottom in the table is the sequence corresponding to the samples in the three data sets.

TABLE 1 PIFA antenna resonant frequency prediction training sample, unmarked sample, test sample

Fig. 4 is a flowchart of an algorithm for modeling the resonant frequency of the PIFA antenna by GP and SVM cooperative training, and the specific implementation steps are as follows:

step 1: determining parameters during modeling, such as penalty coefficients during SVM modeling, wherein the penalty coefficient of the embodiment is 0.01, and constructing a GP model and an SVM model of the PIFA antenna resonant frequency by adopting a Gaussian kernel function;

step 2: training GP and SVM models by using an original training data set, namely 11 marked training samples, so that the models are converged quickly to obtain the GP models and the SVM models with relatively low precision; during initial training, the required marking data are relatively less, and only a small amount of marking data are needed to obtain GP models and SVM models with relatively low initial precision.

After testing the two models with the test data set, the initial error was obtained, see table 2.

TABLE 2 initial error

Model (model)	GP	SVM
			Initial error	0.0282	0.0902

Wherein, a Relative Error (RE) is adopted for the test Error of each test data, and an average Relative Error (MRE) is adopted for the test Error of the whole test set.

And step 3: selecting 1 sample X from the unmarked sample set and inputting the sample X into the model GP to obtain a corresponding output gp.Y, wherein the pseudo marked sample is marked as CO.GP (X, gp.Y); similarly, inputting the unmarked data into a model SVM to obtain a corresponding output svm.Y, and marking as CO.SVM (X, svm.Y);

and 4, step 4: further training the SVM model by using CO.GP (X, gp.Y), and marking as SVM_timeSimilarly, the GP model is further trained by utilizing the CO.SVM (X, svm.Y) and is marked as GP_timeBoth models are further updated.

And 5: g test set is utilized to respectively correspond to GP_timeModel, SVM_timeModel feedingAnd (6) testing. GP_timeThe test error of the model is recorded as e₁，SVM_timeThe test error of the model is recorded as e₂。

Step 6: comparison e₁And e₂The size of (2). If e₁>e₂Then, in this iteration, the SVM_timeThe precision of the model is higher than GP_timeAnd SVM_timeThe model is further trained by adopting the pseudo mark data generated by the GP model, and the pseudo mark data CO.GP (X, gp.Y) generated by the GP model and the test data test.G corresponding to the iteration times in the test set are obtained_iAdding an original training set, and further training GP and SVM models; conversely, the pseudo label data CO.SVM (X, svm.Y) generated by the SVM and the test data test.G corresponding to the iteration number in the test data set are compared_iAnd adding the original training set to further train GP and SVM models.

And predicting the same group of unlabeled data in each iteration of the GP model and the SVM model, and then comparing the unlabeled data, and performing cross training on the generated pseudo-labeled data. And predicting by using the same test data set, comparing with the actually measured resonant frequency of the input variable to obtain a model with stronger prediction capability, and further updating by using the pseudo label data and the test data utilized by the model with stronger prediction capability.

And 7: and (4) setting an iteration stopping condition, wherein the test error of the next iteration is higher than that of the previous iteration, and the test error of the previous iteration reaches an error threshold, stopping the iteration, and the error threshold of the experiment is 1 e-02. Judgment e₁And e₂If the smaller error value of the error signal reaches the error threshold. If so, the loop ends; if not, the iteration is continued, and the test data test.G in the training set is added_iAnd (4) deleting the test data set, using the rest test data as the test set for the next iteration test, and turning to the step 3.

Table 3 records the test error at each iteration when the PIFA antenna resonant frequency is modeled, and fig. 5 is an iterative error graph. Table 4 lists the test results of the prior modeling method, i.e., the hybrid kernel SVM model, the Poly kernel SVM model, the Cauchy kernel SVM model, the ANN model, and the semi-supervised collaborative training model of this embodiment, for the PIFA antenna resonant frequency prediction.

TABLE 3 test error per iteration

Number of iterations	1	2	3	4	5	6	7	8	9
										Error of test	0.0867	0.0677	0.0326	0.0212	0.0231	0.0140	0.0072	0.0045	0.0139

TABLE 4 comparison of test results of the existing model with the model of this example

The analyses of table 3, fig. 5 and table 4 are as follows:

(1) the test error of the 8 th iteration is the minimum and is 0.0045, and the iteration is ended at the 9 th iteration according to the set iteration termination condition. From the iteration result, within 10 iterations, the semi-supervised learning model meets the preset precision requirement, and the precision is higher, so that the modeling efficiency of the method is higher.

(2) And compared with the traditional supervised learning mode: the test error of 8 th iteration is minimum, 7 test values are introduced into a training set, the updated training set, namely 18 training data are used for respectively training a GP model and an SVM model of a supervised learning mode, the test set in 8 th iteration is used for testing, the obtained test errors are respectively 0.0104 and 0.0228, and both the obtained test errors are greater than 0.0045. According to the result of data comparison, on the basis of using the same mark truth value, the prediction capability of the semi-supervised cooperative training model is improved compared with that of the traditional supervised learning model.

(3) For the PIFA resonant frequency modeling experiment, the SVM model and ANN model of three different kernels in other documents listed in table 4 were used for the experiment, each model was trained using 26 sets of labeled data, 5 sets of test data in table 4 were tested, and the last 1 in table 4 is the prediction result of the semi-supervised cooperative training model of the present invention on these test data.

According to the comparison result, the total absolute error of the semi-supervised collaborative training model provided by the invention is smaller than that of a mixed kernel SVM model, a Poly kernel SVM model, a Cauchy kernel SVM model and an ANN model, and the precision is improved. On the basis, the optimal semi-supervised learning model only adopts 17 groups of labeled data for training, and compared with the several models proposed above, the optimal semi-supervised learning model utilizes less labeled data. Therefore, the semi-supervised collaborative training model provided by the invention has certain advantages on the resonance frequency prediction of the PIFA antenna on the basis of using less marking data.

Claims

1. A plane inverted F antenna resonant frequency prediction method based on semi-supervised learning is characterized by comprising the following steps: the method comprises the following steps:

Step 6; judgment of min (e)₁，e₂) Whether the error is smaller than a preset error or not is judged, if so, the operation is finished, and a usable semi-supervised cooperative training model is obtained; if so, further comparing e₁And e₂If e is large or small₁≥e₂The pseudo-labeled sample co.gp (X, gp.y) generated in step 3 and the test data test.g corresponding to the number of iterations in the test set are then compared_iAdding intoIn the initial training set, further training the SVM model and the GP model obtained by the training in the step 2; if e₁＜e₂Then, the pseudo-labeled sample co.svm (X, svm.y) generated in step 3 and the test data test.g corresponding to the number of iterations in the test set are collected_iAdding the initial training set, and further training the SVM model and the GP model obtained by the training in the step 2;

2. The method for predicting the resonant frequency of the planar inverted-F antenna based on semi-supervised learning according to claim 1, wherein the method comprises the following steps:

the training data in the initial training set comprise the width of the short circuit metal sheet, the length of the radiation metal sheet, the width of the radiation metal sheet, the height of the radiation metal sheet and corresponding resonant frequency obtained after HFSS simulation;

3. The method for predicting the resonant frequency of the planar inverted-F antenna based on semi-supervised learning according to claim 1, wherein the method comprises the following steps: and in the step 1, a Gaussian kernel function is adopted to construct a GP model and an SVM model of the resonant frequency of the planar inverted F antenna.

4. The method for predicting the resonant frequency of the planar inverted-F antenna based on semi-supervised learning according to claim 1, wherein the method comprises the following steps: the test error is the average relative error:

5. The method for predicting the resonant frequency of the planar inverted-F antenna based on semi-supervised learning according to claim 1, wherein the method comprises the following steps: the iteration stop condition is as follows: for the semi-supervised collaborative training model output by each iteration, the test error of the next iteration is higher than that of the previous iteration, and the test error of the previous iteration reaches an error threshold.