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For antenna modeling and optimization design, high-fidelity full-wave electromagnetic simulation software can generally be used to obtain training samples. However, this process takes a long time. To solve this problem, a two-stage Gaussian process (GP) considering electromagnetic sensitivity information is proposed. Based on the coarse grid and fine grid of electromagnetic simulation software, the first stage learns the mapping relationships of antenna performance and sensitivity of each parameter, simultaneously. In the second stage, the accurate surrogates are established based on the mapping relationships above obtained. Because the method in this study takes sensitivity information into consideration during the modeling process, it can better reflect the mapping relationship between antenna input and output, which can develop a more accurate surrogate model. The proposed two-stage GP surrogate model considering sensitivity information can significantly reduce the demand of high-fidelity training samples for modeling, and greatly save the simulation time of calling electromagnetic simulation software. Therefore, this method is more suitable for the problems of insufficient electromagnetic simulation samples. The proposed approach is evaluated by modeling and optimization of an inverted F antenna and an ultra-wideband planar monopole antenna. The results show that the method has high modeling accuracy with limited training samples given by high-fidelity electromagnetic simulation, which further verify its effectiveness and efficiency.

When modeling and optimizing electromagnetic components, it is the most time consuming for obtaining the training samples with labels from full-wave electromagnetic simulation software. The traditional machine learning (ML) model is usually effective in the training process, unfortunately, its generalization ability is limited for practical application. Inspired by the artificial neural network (ANN) and the Gaussian process (GP) kernel learning model, a deep kernel learning (DKL) model with multiple-nonlinear-mapping layers is proposed based on particle swarm optimization (PSO) algorithm. In this work, correlation characteristics of training samples are transformed by multiple layers, and then they act as inputs of the GP model. Simultaneously, we use PSO to optimize the weights, biases of each mapping layer, and GP hyperparameters, aiming to determine and optimize the DKL model structure. As a result, the proposed DKL is suitable for processing small samples, as well as has the generalization ability of a deep network, which avoids the phenomenon of gradient disappearance to some extent caused by error back propagation (BP) in the deep network and improves the modeling accuracy while effectively ensuring the modeling efficiency. In this study, the performance of the DKL model is evaluated by using the resonant frequencies of two microstrip antennas (MSAs), and the predicted results of the DKL model are compared with those via different modeling methods. The results show that prediction accuracy of the DKL is 18.906% higher than that of the GP, 38.926% higher than the ANN, and 46.660% higher than the neural network ensemble (NNE).

Gaussian process (GP) is a rapidly developing supervised machine learning (ML) method in recent years, which has been widely used in the establishment of surrogate models in the field of electromagnetics. However, it has the problems of large sample demand, high computational complexity and low accuracy when processing high dimensional data. To solve this problem, a manifold Gaussian process (MGP) ML method based on differential evolution (DE) algorithm is proposed in this study. For the proposed method, the DE algorithm is used to get dimension reduction parameters, and the method can work very well with the optimized parameters. Compared with the traditional GP model, the dimensionality reduction method based on Isomap is adopted to simplify the mapping relationship between data pairs. Therefore, the model is more suitable for the problem of insufficient samples and high data dimension. In this study, the proposed DE-based MGP (DE-MGP) is applied to the extraction of coupling coefficients of the fourth-order and sixth-order coupling filters, in which the test error of the fourth-order coupling filter surrogate model can be reduced to 0.84%, and the test error of the sixth-order coupling filter is expected to be reduced to 1.53%, which proves that the proposed method is very effective.

For the optimal design of electromagnetic components, surrogate model methods can usually be used, but obtaining labeled training samples from full-wave electromagnetic simulation software is most time-consuming. How to use relatively few labeled samples to obtain a relatively high-precision surrogate model is the current electromagnetic research hotspot. This article proposes a semi-supervised co-training algorithm based on Gaussian process (GP) and support vector machine (SVM). By using a small number of initial training samples, the initial GP model and initial SVM model can be trained by some basic parameter settings. Moreover, the accuracy of these two models can be improved by using the differences between these two models and combining with unlabeled samples for jointly training. In the co-training process, to ensure the performance of the proposed algorithm, a stop criterion set in advance to control the number of unlabeled samples introduced. Therefore, the accuracy of the model can be prevented from being reduced by introducing too much unlabeled samples, which can find the best solution in the limited time. The proposed co-training algorithm is evaluated by benchmark functions, optimal design of Yagi microstrip antenna (MSA) and GPS Beidou dual-mode MSA. The results show that the proposed algorithm fits the benchmark functions well. For the problem of resonant frequency modeling of the above two different MSAs, under the condition of using the same labeled samples, the predictive ability of the proposed algorithm is improved compared with the traditional supervised learning method. Moreover, for the groups of antenna sizes that meet the design requirements, the fitting effects of their return loss curve (S11) are well. The effectiveness of the proposed co-training algorithm has been well verified, which can be used to replace the time-consuming electromagnetic simulation software for prediction.

Scattering of electromagnetic plane waves from normal chiral materials, chiral metamaterials, chiral nihility materials are presented. Based on the volume equivalence principle, the integral equati...

In order to design the antenna that meets the requirements conveniently and reduce the tedious manual operation in the process of antenna optimization, a new antenna design method is proposed in this paper, which calls the Gaussian process surrogate model of antenna through differential evolution algorithm. According to the proposed method, when designing the antenna, we not only can optimize the physical parameters by intelligent optimization algorithm, but also avoid the huge time consumption caused by using electromagnetic simulation software. In this study, we apply the proposed method to the design experiment of WlAN dual band monopole antenna, and finally get a set of physical parameters, by these parameters, the antenna model response meets the design requirements.

We present a rectangular loop Yagi–Uda antenna based on the three-dimensional (3-D) printing technology. The antenna comprises a ground plane, a rectangular loop driven element, and rectangular loop directors. The loop driven element is about λ0/20 above the ground plane and is fed by a 50 Ω microstrip feedline. We fabricated the Yagi–Uda antenna by two materials 3-D printing technology and the following chemical plating process. The measured results show the antenna's working frequency is at 2.392 GHz while the |S 11|, gain, and efficiency are –12.63 dB, 8.99 dBi, and 79.5%, respectively. The experimental results are in a good agreement with the design. Our loop Yagi–Uda antenna features good antenna performances, small size, and easy fabrication, which can be an excellent candidate for antenna arrays and applications that need directional radiation property. Our work paves the way to the application of 3-D printing technology in the field of antennas.

In this paper, a symmetric stepped-impedance coupled line (SSICL) is proposed to realize dual-band quarter-wave coupled line (DQCL), giving the same equivalent even and odd characteristic impedances at two different frequencies. The DQCL can be directly used to design dual-band parallel-line coupler (DBPC) with arbitrary coupling coefficient and large frequency ratio, resulting in even shorter total length when compared with traditional quarter-wave parallel-line coupler working at lower frequency $f_{1}$ . In addition, broad DBPC (BDPC) is constructed by cascading multiple sections of SSICLs, as the SSICL is quite similar with quarter-wave coupled line in circuit. For demonstrating the design methods, in the first step, two edge-coupled 20-dB DBPCs and one broadside coupled 6-dB DBPC, working at 1/5.2, 1/7.5, and 1/5.2 GHz, respectively, are designed, fabricated and measured, exhibiting good features like large frequency ratio, high isolations, and compact dimensions. Then, for broadening bandwidths, three-section BDPC working at 1 GHz/5.2 GHz is designed and measured, resulting in working bandwidths larger than 1.2 GHz. These good features have proved the feasibility of the proposed circuits and the corresponding design methods.

When using Gaussian process (GP) machine learning as a surrogate model combined with the global optimization method for rapid optimization design of electromagnetic problems, a large number of covariance calculations are required, resulting in a calculation volume which is cube of the number of samples and low efficiency. In order to solve this problem, this study constructs a deep GP (DGP) model by using the structural form of convolutional neural network (CNN) and combining it with GP. In this network, GP is used to replace the fully connected layer of the CNN, the convolutional layer and the pooling layer of the CNN are used to reduce the dimension of the input parameters and GP is used to predict output, while particle swarm optimization (PSO) is used algorithm to optimize network structure parameters. The modeling method proposed in this paper can compress the dimensions of the problem to reduce the demand of training samples and effectively improve the modeling efficiency while ensuring the modeling accuracy. In our study, we used the proposed modeling method to optimize the design of a multiband microstrip antenna (MSA) for mobile terminals and obtained good optimization results. The optimized antenna can work in the frequency range of 0.69–0.96 GHz and 1.7–2.76 GHz, covering the wireless LTE 700, GSM 850, GSM 900, DCS 1800, PCS1900, UMTS 2100, LTE 2300, and LTE 2500 frequency bands. It is shown that the DGP network model proposed in this paper can replace the electromagnetic simulation software in the optimization process, so as to reduce the time required for optimization while ensuring the design accuracy.

For the optimal design of electromagnetic devices, it is the most time consuming to obtain the training samples from full wave electromagnetic simulation software, including HFSS, CST, and IE3D. Traditional machine learning methods usually use only labeled samples or unlabeled samples, but in practical problems, labeled samples and unlabeled samples coexist, and the acquisition cost of labeled samples is relatively high. This paper proposes a semisupervised learning Gaussian Process (GP), which combines unlabeled samples to improve the accuracy of the GP model and reduce the number of labeled training samples required. The proposed GP model consists two parts: initial training and self-training. In the process of initial training, a small number of labeled samples obtained by full wave electromagnetic simulation are used for training the initial GP model. Afterwards, the trained GP model is copied to another GP model in the process of self-training, and then the two GP models will update after crosstraining with different unlabeled samples. Using the same test samples for testing and updating, a model with a smaller error will replace another. Repeat the self-training process until a predefined stopping criterion is met. Four different benchmark functions and resonant frequency modeling problems of three different microstrip antennas are used to evaluate the effectiveness of the GP model. The results show that the proposed GP model has a good fitting effectiveness on benchmark functions. For microstrip antennas resonant frequency modeling problems, in the case of using the same labeled samples, its predictive ability is better than that of the traditional supervised GP model.

In order to reduce the time of designing microstrip antenna, this paper proposes a self-renewing fitness estimation of particle swarm optimization algorithm (SFEPSO) to improve the design efficiency. Firstly, a fitness predictive model of the particles is constructed according to the evolution formula of particle swarm optimization (PSO). From the third generation of the algorithm, the fitness of particles is given by the prediction model instead of the full-wave electromagnetic simulation. Aiming to keep the right direction of evolution, the prediction model will be proofed every N generation during the optimization process. If the prediction model accuracy is lower than the threshold, it will be updated and then continue iterating until the particles satisfy the demands. Compared with the traditional optimization method, this method greatly reduces the evaluation time and improves the design efficiency. The method is validated by the optimized design of E-type dual-frequency microstrip antenna and WLAN/WiMAX multiband antenna. The optimized results show that the purpose of rapid optimization can be achieved while ensuring the design accuracy.

When microwave devices are designed by knowledge-based neural network (KBNN), the empirical formula is always used as priori knowledge. However, it is difficult to derive the corresponding formulas for the most electromagnetic problems, especially for complex electromagnetic problems, the formula derivation is almost impossible. In this article, they combine neural network with simulation software and use results of Agilent ADS as priori knowledge and HFSS as teaching signal to train the neural network by particle swarm optimization (PSO), which solves the difficulty in obtaining priori knowledge and effectively reduces the complexity of the neural network structure. Based on the KBNN, the microwave filters are designed. The results of optimization satisfy the required specifications which show the effectiveness and superiority of the method.

In order to improve the radio frequency stealth ability of phased array radars, a novel resource scheduling method of the radar network for target tracking in clutter is presented. Firstly, the relationship model between radar resource and tracking accuracy is built, and the sampling interval, power, and waveform will influence predicted error covariance matrix through transition matrix and measurement noise. Then, radar resource scheduling algorithm based on Markov decision process which is converted to be a binary optimization problem is proposed, and an improved binary wind-driven optimization method is presented to solve that problem. The radar and its radiation parameters will be selected for better radio frequency stealth performance and tracking accuracy. Simulation results show that the proposed algorithm not only has excellent tracking accuracy in clutter but also has better radio frequency stealth ability comparing with other methods.