Abstract
A common approach in the literature when obtaining surrogate models of reflectarray unit cells is to include, among other variables, the angles of incidence as input variables to the model. In this work, we use support vector regression (SVR) to compare this approach with a new strategy which consists in grouping the refletarray elements under a small set of angles of incidence and train surrogate models per angle of incidence pair. In this case, the dimensionality of the SVR decreases in two with regard to the former approach. In both cases, two geometrical variables are considered for reflectarray design, obtaining 4-D and 2-D SVRs, respectively. In contrast to the common approach in the literature, the comparison between the 4-D and 2-D SVRs shows that a proper discretization of the angles of incidence is more competitive than introducing the angles as input variables in the SVR. The 2-D SVR offers a shorter training time, faster reflectarray analysis, and a similar accuracy than the 4-D SVR, making it more suitable for design and optimization procedures.
Highlights
S URROGATE models for reflectarray analysis have been proposed to speed-up the analysis, design and optimization of this kind of antenna using different machine learning techniques (MLTs) such as artificial neural network [1]–[6], support vector machines for regression (SVR) [7] and ordinary kriging (OK) [8]
Pencil beam CP XP 0.21 2.14 0.40 1.01 results were obtained in both linear polarizations. As it can be seen, the 2D support vector regression (SVR) model offers lower error in the copolar pattern, the 4D SVR is slightly better at predicting the crosspolar pattern. In light of these results, it is clear that the 4D SVR, which includes the angles of incidence (θ, φ) as input variables, offers slightly more accuracy in the prediction of the crosspolar pattern than the 2D SVR
We have carried out a study on the use of the angles of incidence in surrogate models based on support vector regression (SVR) for reflectarray design
Summary
S URROGATE models for reflectarray analysis have been proposed to speed-up the analysis, design and optimization of this kind of antenna using different machine learning techniques (MLTs) such as artificial neural network [1]–[6], support vector machines for regression (SVR) [7] and ordinary kriging (OK) [8]. The first efforts were aimed at predicting the phase-shift of the reflectarray element [1]–[4], which corresponds to the phase of the complex direct coefficients This is useful since this phase mainly controls the shape of the copolar far field pattern [9]. Two geometrical features of a reflectarray unit cell are used as input variables of the SVR in both cases, obtaining a 4D SVR model when the angles of incidence are considered as input variables, and a 2D SVR model per angle of incidence. In both cases, the training process is based on cross-validation to find the optimum model. The errors are computed with regard to the reference simulations provided by a fullwave analysis tool based on local periodicity (FW-LP) employed to generate the electromagnetic samples and analyse the reflectarray
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