Disclosure of Invention
The invention aims to: the invention provides a planar inverted F antenna resonant frequency prediction method based on semi-supervised learning, which aims to solve the problems that in the existing electromagnetic optimization design, a plurality of marked samples are needed, electromagnetic simulation software HFSS is required to be called for multiple times, the calculation cost is high, the time consumption is long and the like in the process of training a model, and the precision of resonant frequency prediction is improved by utilizing marked data and unmarked data to carry out cooperative training.
The technical scheme is as follows: a planar 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 unlabeled data set, and constructing a GP model and an SVM model of the resonant frequency of the planar inverted F-type 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;
step 3: selecting N from unlabeled dataset1 Inputting the samples X into the GP model trained in the step 2 to obtain corresponding output gp.Y, marking the corresponding output gp.Y as a pseudo-marked sample CO.GP (X, gp.Y), and inputting the N1 The samples X are input into the SVM model obtained by training in the step 2,obtaining a corresponding output svm.Y, and marking the corresponding output svm.Y as a pseudo-mark sample CO.SVM (X, svm.Y);
step 4: further training the SVM model obtained by training in the step 2 by adopting a pseudo-label sample CO.GP (X, gp.Y) to obtain the SVMtime A model; meanwhile, the GP model obtained by training in the step 2 is further trained by adopting a pseudo-marker sample CO.SVM (X, svm.Y) to obtain GPtime A model;
step 5: test set test. G is adopted to respectively pair SVMtime Model and GPtime Model test, GPtime Test error of the model is marked as e1 ，SVMtime Test error of the model is marked as e2 ；
Step 6; judging min (e)1 ，e2 ) If the error is smaller than the preset error, ending the process, and obtaining a usable semi-supervised collaborative training model; if it is greater than, further compare e1 And e2 If e1 ≥e2 The pseudo-marked sample CO.GP (X, gp.Y) generated in the step 3 and test data test.G corresponding to the iteration number in the test set are processedi Adding an initial training set, and further training the SVM model and the GP model obtained by training in the step 2; if e1 ＜e2 The pseudo-label sample CO.SVM (X, svm.Y) generated in the step 3 and test data test.G corresponding to the iteration number in the test set are processedi Adding an initial training set, and further training the SVM model and the GP model obtained by training in the step 3;
step 7: judging whether an iteration stopping condition is met, if so, ending the iteration to obtain a usable semi-supervised collaborative training model; otherwise, the test data test.G which is currently added into the initial training seti Deleting the residual test data from the test set test.G, taking the residual test data as a test set for the next iteration test, and turning to the step 3;
step 8: after the usable semi-supervised collaborative training model is obtained, 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 collaborative training model to obtain corresponding resonant frequency, and 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 by using HFSS simulation;
the test data in the test set test.G comprises 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 actually measured resonance frequency;
the sample data in the unlabeled dataset includes a width of the shorting metal sheet, a length of the radiating metal sheet, a width of the radiating metal sheet, and a height of the radiating metal sheet.
Compared with traditional supervised learning, for the antenna resonant frequency modeling problem, unlabeled samples and labeled samples (with measured resonant frequency points) are independent and distributed at the same time, and the contained data distribution information has certain use for model training. The unlabeled samples are used for collaborative training, useful information is provided for improving the prediction precision of the model, the method belongs to no waste of data resources, meanwhile, the time of electromagnetic simulation is saved, and the efficiency of optimizing the prediction capacity is improved.
Further, 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-shaped antenna.
Further, the test error is an average relative error:
wherein y ispred For the tag values predicted by GP model or SVM model, ytest To test the true tag value of the sample.
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 the test error of the previous iteration, and the test error of the previous iteration reaches an error threshold.
The beneficial effects are that: the invention establishes a mapping relation between four related parameters of 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, and performs iterative training by combining unlabeled data by using a collaborative training method of the Gaussian process and the support vector machine, and the trained semi-supervised collaborative training model can be used for predicting the resonant frequencies of other planar inverted-F antennas. The method can solve the problems of high calculation cost and long time consumption of the traditional electromagnetic optimization design that more marking samples are needed when a model is trained, and electromagnetic simulation software HFSS is required to be called for multiple times; 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) According to the invention, two different proxy models are cross-trained by using the same unlabeled sample, and the two models are updated by using the pseudo-labeled data with higher accuracy and the corresponding test data, so that satisfactory prediction accuracy is achieved, the times of calling the HFSS to obtain the precise labeled data are reduced in the training process, and the time for obtaining the labeled sample is saved;
(2) The invention sets iteration conditions, controls the number of the unmarked data introduced and the number of model updating times until reaching a preset termination condition, and prevents excessive introduction of the unmarked data and reduces the prediction accuracy of the model.
(3) For the problem of PIFA type antenna resonance frequency modeling, the algorithm provided by the invention has the advantages that under the condition of using less marking data, the prediction capability of the algorithm is enhanced compared with that of the traditional supervised learning mode, and the time and labor cost for acquiring the marking data are saved;
(4) On the basis of using the same mark true value, the prediction capability of the semi-supervised collaborative training model is improved compared with that of the traditional supervised learning model for the PIFA antenna resonant frequency prediction problem.
Detailed Description
The technical scheme of the invention is further described with reference to the accompanying drawings and the embodiments.
Aiming at the problem that the calculation time is too long due to the fact that a plurality of required marking samples are relatively large when the PIFA antenna resonant frequency is modeled in the traditional supervised learning modeling mode, the collaborative training method based on the GP model and the SVM model is designed and realized on the basis of the existing semi-supervised collaborative training, the resonant frequency of the PIFA antenna is modeled, the quantity of marking data required during modeling is reduced, and the accuracy of the model is improved.
The invention relates to a planar inverted F antenna resonance frequency prediction method based on GP and SVM cooperative training, which comprises the following steps:
the first step: modeling of GP and SVM
1) Acquisition of training samples
And establishing a mapping relation between relevant parameters of the antenna (including the size of a radiation sheet, the thickness of a dielectric substrate and the like) and the actually measured resonant frequency, and completing the establishment of a model. The trained model can predict the resonant frequencies of other antenna sizes, the method has obvious advantages in accuracy compared with the traditional method, and the time for calling the HFSS to perform electromagnetic simulation can be saved. According to the size parameter information of the planar inverted F Antenna (Planar Inverted F-shaped Antenna, PIFA), different size information, namely different input variables, are set, and the measured resonance frequency point simulated by HFSS is used as data marking information, namely teacher signals. And taking the obtained small amount of marked data as an initial training set.
2) Structure of GP model
A gaussian process is a set of infinite random variables, any subset of which obeys a gaussian distribution. The GP properties are determined jointly by the mean and covariance functions:
wherein x, x' e Rd 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) +epsilon, the observed target value y is contaminated by additive noise epsilon, epsilon is a random variable obeying normal distribution, the mean value is 0, and the variance is sigman2 Expressed as:
ε～N(0，σn2 ) (3)
then the a priori distribution of y is
y～N(0,K+σn2 I) (4)
K=k (X, X) is an n×n order symmetric positive definite covariance matrix, Kij Metric xi And xj Correlation between them. n training sample outputs y and n* Output f of test samples* 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 superparameters, and the maximum likelihood function can be used to find the optimal superparameter. And solving bias guide for the super-parameters by establishing a log likelihood function of the conditional probability of the training sample, and searching an optimal solution of the super-parameters by adopting a conjugate gradient optimization method. The negative log-likelihood function is in the form of:
after the optimal super parameters are obtained, the trained GP can be utilized to carry out relevant prediction.
Given a new inputx* Under the condition of the input value X and the observation target value y of the training set, deducing y* The most probable predictive posterior distribution:
y* |x* ,X,y～N(m,∑) (7)
m and Σ are the prediction mean and covariance:
m＝K(X* ,X)K(X,X)-1 y
∑＝K(X* ,X* )-K(X* ,X)K(X,X)-1 K(X,X* ) (8)
the prediction mean and covariance describe the gaussian distribution to which the prediction output may be subject. The magnitude of the prediction variance reflects the accuracy of the model at that point, with the smaller the variance, the higher the model accuracy.
3) Construction of SVM model
For the linear inseparable problem, the SVM uses the kernel function to replace the inner product operation in the high-dimensional feature space by defining the kernel function, namelyAnd the dimension disaster is avoided. Taking fault tolerance into consideration, a relaxation variable, i.e. y, is added to a fixed value 1i [(ω·xi )+b]≥1-ξi ,ξi Not less than 0, and meanwhile, a penalty factor C needs to be added to a certain sample of error classification, and at the moment, the optimization problem is changed into:
yi [ω·xi +b]≥1-ξi ,ξi ≥0(i＝1,2,...,l) (10)
ξi how far the corresponding outlier is, C is the degree of importance to the loss that the outlier brings.
The Lagrange optimization method is utilized to change the Lagrange optimization method into a dual problem, and the final optimized classification function is as follows:
wherein x isi Is a support vector for the support of the support vector,is the corresponding Lagrange coefficient, b* The threshold value of the classification can be obtained by taking the median value from any pair of support vectors in the two classes.
Mapping the original nonlinear space into a high-dimensional dot product space (also known as feature space) using nonlinear transformation becomes a linearly separable problem. The function K is sought such that when it accepts input values in a low dimensional space, two types of data that are linearly separable can be obtained in a high dimensional feature space, such function K is called a kernel function, the requirement of which is that the Mercer condition must be satisfied, and the final classification function obtained by nonlinear transformation of s input vectors becomes:
wherein K (x)i X) is called a kernel function. Common kernel functions are: linear kernel functions, polynomial kernel functions, radial basis kernel functions, etc.
Support vector regression (Support Vector Regression, SVR) is an important branch in SVM. The sample points of the SVR are of one type only, and the optimal hyperplane that it seeks is not the "most open" of the two or more types of sample points, but minimizes the total deviation of all sample points from the optimal hyperplane, i.e., the "distance" to the sample point furthest from the hyperplane.
4) Training and testing of GP model and SVM model
Step 1: setting the relevant size information of the antenna by using electromagnetic simulation software HFSS to obtain N0 Marking the samples;
step 2: by N0 The number of the mark training samples are used for training the GP and SVM models, so that the models are converged rapidly, and the GP models and the SVM models with relatively low precision are obtained.
Step 3: and (3) testing the original GP model and the SVM model constructed in the step (2) by using a test sample set, verifying whether the predicted output is consistent with the result of the high-frequency structure simulation HFSS, and respectively obtaining initial training errors of the models. Wherein the relative error is used for a single test value and the average relative error is used for the whole test set.
And a second step of: structure of semi-supervised learning collaborative training model
Step 1: selecting N from unlabeled sample sets1 Inputting the samples into a model GP to obtain corresponding output; similarly, the N is1 And inputting the unlabeled data into the model SVM to obtain corresponding output.
Step 2: and respectively obtaining two groups of pseudo-marker data, and cross-training the GP model and the SVM model by using the two groups of pseudo-marker samples.
Step 3: and testing the GP model and the SVM model respectively by using the test set. Test error of GP model is marked as e1 The test error of the SVM model is denoted as e2 。
Step 4: comparative e1 And e2 Is of a size of (a) and (b). If e1 >e2 In the iteration, the precision of the GP model is higher than that of the SVM, pseudo-mark data generated by the GP model and test data corresponding to the iteration times in a test set are added into an original training set, and the GP model and the SVM model are further trained; and otherwise, adding pseudo-mark data generated by the SVM and test data corresponding to the iteration times in the test data set into an original training set, and further training the GP model and the SVM model.
Step 5: setting an iteration stop 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 value, so that the iteration is stopped. Judgment e1 And e2 Whether the smaller error value of the error threshold is reached. If so, the cycle ends; if not, continuing iteration, and turning to step 1. And removing the test data added to the training set from the test data set in the last iteration, and taking the rest of test data as the test data set of the next iteration.
The invention will be further described with reference to the drawings and the specific examples.
The PIFA antenna is a typical miniaturized low-profile antenna, and has been widely used because of its remarkable characteristics of small size, light weight, low profile, low cost, high gain, and being not easily interfered. Fig. 1 is a schematic structural diagram of a PIFA antenna, the basic structure comprising four parts: a ground plane 1, a radiating element 2, a shorting metal plate 3 and a coaxial feed line 4. The radiating element 2 is a metal sheet parallel to the ground plane 1, and the shorting metal sheet 3 is for connecting the radiating element 2 and the ground plane 1, and the coaxial feed line 4 is for signal transmission. Resonant frequency point of PIFA and width SW of short-circuit metal sheet, length L of radiating metal sheet1 Width W1 And a height H. With short-circuit metal sheet width SW and length L of radiating metal sheet1 Width W1 Height H sets different dimensions for the variables and fig. 2 is a three-dimensional perspective view of the PIFA in an HFSS environment. Setting 31 groups of input variables in total, selecting 11 groups of input variables from the 31 groups of input variables, performing HFSS simulation to obtain corresponding resonant frequencies as initial training data, obtaining corresponding actual measured resonant frequencies by using the HFSS simulation for the other 10 groups, and using the rest 10 groups as unlabeled data sets as test sets.
Fig. 3 is a schematic structural diagram of a co-training algorithm based on a GP model and an SVM model. With 11 training data, in SW, W1 ，L1 H is an input variable, fHFSS For output, a GP model and an SVM model are established, respectively. In the cooperative training process, the data without actually measured resonant frequency is utilized, namely, the unlabeled data is combined for cooperative training, so that the accuracy of the model is continuously improved. Table 1 lists 31 sets of data, 11 sets of data with +.suffix as initial training data, 10 sets of data with +.suffix as test data, and 10 sets of data with # suffix as unlabeled data, wherein the corresponding resonance frequency was also simulated using HFSS as verification of the algorithm proposed in this embodiment. The top-down order in the table is the order in which the samples in the three data sets correspond.
Table 1 training samples, unlabeled samples, test samples for PIFA antenna resonant frequency prediction
Fig. 4 is a flowchart of an algorithm for modeling the resonant frequency of a PIFA antenna by co-training GP and SVM, 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 resonant frequency of the PIFA antenna 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 rapidly, and a GP model and an SVM model with relatively low precision are obtained; when initial training is carried out, the required marking data is relatively less, and only a small amount of marking data is needed to obtain a GP model and an SVM model with relatively low initial precision.
After testing the two models using the test dataset, initial errors were obtained, see table 2.
TABLE 2 initial error
| Model | GP | SVM |
| Initial error | 0.0282 | 0.0902 |
Wherein a Relative Error (RE) is used for the test Error of each test data, and an average Relative Error (Mean Relative Error, MRE) is used for the test Error of the whole test set.
Wherein y ispred For the tag values predicted by GP model or SVM model, ytest To test the true tag value of the sample.
Step 3: 1 sample X is selected from the unlabeled sample set and is input into a model GP, so that a corresponding output gp.Y is obtained, and the unlabeled sample is marked as CO.GP (X, gp.Y); similarly, the unlabeled data is input into a model SVM to obtain a corresponding output svm.Y, and the corresponding output svm.Y is recorded as a CO.SVM (X, svm.Y);
step 4: further training of SVM models using CO.GP (X, gp.Y), noted as SVMtime Similarly, the GP model was further trained using CO.SVM (X, svm.Y) and denoted as GPtime Both models are further updated.
Step 5: GP pairs respectively using test set test.Gtime Model and SVMtime The model is tested. GP (GP)time Test error of the model is marked as e1 ，SVMtime Test error of the model is marked as e2 。
Step 6: comparative e1 And e2 Is of a size of (a) and (b). If e1 >e2 Then in this iteration, the SVMtime The precision of the model is higher than GPtime While SVMtime The model adopts the pseudo-marking data generated by the GP model to further train, and the pseudo-marking 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 obtainedi Adding an original training set, and further training GP and SVM models; conversely, the pseudo-labeling data generated by the SVM, namely CO.SVM (X, svm.Y), and the sum test data are concentrated and overlappedTest data test. G corresponding to the number of generationsi And adding the original training set to further train the GP and SVM models.
The GP model and the SVM model predict the same group of unlabeled data and then compare the unlabeled data in each iteration, and the generated pseudo-labeled data are used for cross training of the two models. And predicting by adopting the same test data set, comparing the test data set with the measured resonance frequency of the input variable to obtain a model with stronger prediction capability, and further updating by using the pseudo mark data and the test data utilized by the model with stronger prediction capability.
Step 7: setting an iteration stop 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 value, so that the iteration is stopped, and the error threshold value of the experiment is 1e-02. Judgment e1 And e2 Whether the smaller error value of the error threshold is reached. If so, the cycle ends; if not, continuing iteration, and adding the test data test.G in the training seti Deleting the rest of the test data from the test data set to serve as the test set for testing of the next iteration, and turning to the step 3.
Table 3 records the test errors at each iteration when modeling the PIFA antenna resonant frequency, and fig. 5 is an iterative error graph. Table 4 shows the test results of the prior modeling method, i.e., SVM model of mixed core, SVM model of Poly core, SVM model of Cauchy core, ANN model and semi-supervised collaborative training model of this embodiment for PIFA antenna resonance frequency prediction.
Table 3 test errors per iteration
| Number of iterations | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Test error | 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 and the model of the present example
The analysis of table 3, fig. 5 and table 4 is as follows:
(1) The test error of the 8 th iteration is the smallest, which is 0.0045, and the iteration ends at the 9 th iteration according to the set iteration termination condition. According to the iteration result, the semi-supervised learning model reaches the preset precision requirement within 10 iterations, and the precision is higher, so that the efficiency of modeling of the invention is higher.
(2) Comparison with the traditional supervised learning mode: the test error of the 8 th iteration is minimum, 7 test values are introduced into the training set, the updated training set, namely 18 training data are respectively trained into a GP model and an SVM model in a supervised learning mode, and the test set in the 8 th iteration is used for testing, so that the test errors are respectively 0.0104 and 0.0228, and are respectively larger than 0.0045. As can be seen from the result of data comparison, the predictive power of the semi-supervised collaborative training model is improved compared with that of the traditional supervised learning model on the basis of using the same marked true values.
(3) For PIFA resonant frequency modeling experiments, the results of experiments performed in table 4 using three different core SVM models and an ANN model, each trained using 26 sets of marker data, were tested on 5 sets of test data in table 4, and the final 1 in table 4 is the prediction results of the semi-supervised co-training model of the present invention for these several test data.
As shown by comparison results, the total absolute error of the semi-supervised collaborative training model provided by the invention is smaller than that of the SVM model of the mixed core, the SVM model of the Poly core, the SVM model of the Cauchy core and the ANN model, and the accuracy is improved. On the basis, the optimal semi-supervised learning model is trained by adopting 17 groups of marking data, and the marking data used by the model is less than that of the models. Therefore, the semi-supervised co-training model provided by the invention has certain advantages in the prediction of the resonance frequency of the PIFA antenna on the basis of using less marked data.