Metamaterial Antenna is a special class of antennas that uses metamaterial to enhance their performance. Antenna size affects the quality factor and the radiation loss of the antenna. Metamaterial antennas can overcome the limitation of bandwidth for small antennas. Machine learning (ML) model is recently applied to predict antenna parameters. ML can be used as an alternative approach to the trial-and-error process of finding proper parameters of the simulated antenna. The accuracy of the prediction depends mainly on the selected model. Ensemble models combine two or more base models to produce a better-enhanced model. In this paper, a weighted average ensemble model is proposed to predict the bandwidth of the Metamaterial Antenna. Two base models are used namely: Multilayer Perceptron (MLP) and Support Vector Machines (SVM). To calculate the weights for each model, an optimization algorithm is used to find the optimal weights of the ensemble. Dynamic Group-Based Cooperative Optimizer (DGCO) is employed to search for optimal weight for the base models. The proposed model is compared with three based models and the average ensemble model. The results show that the proposed model is better than other models and can predict antenna bandwidth efficiently.

Metamaterial antenna is extensively reported in the literature because of its unusual properties [

To design an antenna, the dimension of the antenna can be calculated by researchers by using a mathematical formula. Then a simulator can be employed to find the parameters such as bandwidth. In case that the parameters don’t meet the expectation, the simulated antenna’s dimension should be adjusted. This is repeated until the desired parameters are reached. Researchers are doing this process usually by trial-and-error method and this process can take long time [

Metamaterials are widely used in various applications such as Metamaterial absorber [

To estimate the effect of metamaterial, simulation software is used [

Machine Learning (ML) is a very popular research topic that has been extensively used in several applications in literature [

In Metamaterial simulation, ML can be used as an alternative approach to the trial-and-error process of finding proper parameters of the simulated antenna. ML model can be a quick prediction if it has been trained using a dataset. The accuracy of the prediction depends mainly on the selected model. Many machine learning models are reported in the literature such as Artificial Neural Networks (ANN) [

In this paper, a weighted average ensemble model is proposed to predict the bandwidth of the Metamaterial Antenna. Two base models are used namely: Multilayer Perceptron (MLP) and Support Vector Machines (SVM). To calculate the weights for each model, an optimization algorithm is used to find the optimal weights of the ensemble. In this paper, Dynamic Group-Based Cooperative Optimizer (DGCO) [

This paper is structured as follows: Literature review is presented in Section 2. Data preprocessing and the proposed ensemble model is explained in Section 3. Results are shown and discussed in Section 4. Finally, the conclusion of the presented work is discussed in Section 6.

Machine learning models have been extended in several areas such as telecommunication [

There are many machine learning algorithms such as Artificial Neural Network (ANN) [

ANN has been used in various applications in the literature. For instance, in [

Support Vector Machines (SVM) [

In literature, researchers combine two or model machine learning models to enhance the performance and overcome the disadvantages of single weak learners (base models). These model combinations are called ensemble models [

In [

Dynamic Group-Based Cooperative Optimization algorithm (DGCO) [

where

On the other hand, the exploitation group is responsible for improving existing solutions by finding more promising locations around them. To achieve that, individuals in the exploration group apply two strategies. The first strategy is to move towards the best solution using random walks. This strategy is modeled as follows:

where vector

where vectors

One of the merits of the DGCO algorithm is its ability to perform a good balance between exploration and exploitation. In each iteration, DGCO dynamically changes the number of individuals in each group based on the convergence history. It starts with a higher number of individuals in the exploration group (70% for instance) then over the course of iterations this number decreases and the number of individuals in the exploitation group increases. Based on the convergence history of the last three iterations, DGCO decides whether to increase the number of individuals in the exploration group or note. This balance helps in enhancing the performance of the optimization process as well as avoiding local optima stagnation. Finally, DGOC randomly interchanges the roles of individuals of each group in each iteration to enhance the diversity of the population. The flow chart of the DGCO algorithm is presented in

In this section, the proposed ensemble model will be presented and explained in detail. First, the dataset is presented. An expletory analysis of the dataset is presented. Then, the preprocessing techniques applied to the dataset will be discussed. Second, for the calculation of the weights for base models, the Dynamic Group-Based Cooperative Optimizer (DGCO) algorithm is used to find the optimal weights of the ensemble model as shown in

The dataset used in this work contains 11 features of the Metamaterial Antenna project. The dataset has been downloaded from Kaggle [

# | Feature | Description |
---|---|---|

Wm | Split ring resonator’s width and height | |

W0m | Gap between rings | |

Dm | Distance between rings | |

Tm | Width of rings | |

SRR_num | # Split ring resonator cells | |

Xa | Distance between antenna patch and array | |

Ya | Distance between split ring resonator cells | |

Gain | Gain of antenna | |

VSWR | Antenna’s voltage standing wave ration | |

Bandwidth | Antenna’s bandwidth | |

S11 | Return loss |

In order to prepare data for the machine learning model, some preprocessing tasks have been applied. First, the null values in the bandwidth values have been handled by taking the average of the non-missing values of previous and next values of the missing value. In machine learning, data value ranges may affect the learning process and as a result the performance of the model will be impacted. For instance, KNN used Euclidean distance to measure the distance between data points. Features with higher bound will dominate and affect the calculation process. Therefore, it is an essential process to scale and normalize data to guarantee that all features lay in the same bounds and will be treated similarly by the machine learning model. One of the simple ways to scale data is the min-max scaler in which data features are scaled and bounded between the range of 0 and 1 using the min-max scaler. The following equation is used by the min-max scaler to perform its task.

Feature | Wm | W0m | dm | tm | Xa |
---|---|---|---|---|---|

572.0000 | 572.0000 | 572.000 | 572.0000 | 572.00000 | |

2244.0482 | 400.5941 | 275.4257 | 224.4048 | 4063.2463 | |

691.5788 | 184.9052 | 150.901130 | 69.157890 | 3287.8620 | |

2142.9000 | 162.8600 | 77.1430 | 214.2900 | 0.000 | |

2142.9000 | 162.8600 | 77.14300 | 214.2900 | 1132.8000 | |

2142.9000 | 325.7100 | 214.2900 | 214.2900 | 3543.5000 | |

2142.9000 | 488.5700 | 351.4300 | 214.2900 | 5954.3000 | |

6964.3000 | 651.4300 | 488.5700 | 696.4300 | 10776.000 | |

572.000000 | 572.0000 | 572.0000 | 572.0000 | 572.0000 | |

6947.4697 | 2.6785 | 2.09492 | 117.8989 | −16.1049 | |

5136.193313 | 0.683242 | 1.914750 | 11.233272 | 7.897142 | |

2142.9000 | −5.6543 | 1.041183 | 32.7599 | −33.9031 | |

2142.9000 | 2.815006 | 1.187911 | 116.9174 | −21.3215 | |

6964.3000 | 2.876220 | 1.438023 | 122.2199 | −14.9108 | |

11786.000 | 2.921877 | 1.725260 | 123.0597 | −11.4982 | |

16607.000 | 3.238539 | 8.377999 | 124.7401 | −2.08343 |

DT | KNN | SVM | Average ensemble | Weight average ensemble |
---|---|---|---|---|

0.014926 | 0.015987 | 0.015529 | 0.014368 | 0.014080 |

The proposed weighted average ensemble model is based on optimize the weights for base models and then calculate the average ensemble on the weighted results. The Dynamic Group-Based Cooperative Optimizer (DGCO) algorithm is used to get the optimal weights for the ensemble model. As shown in

The Mean Square Error (MSE) is employed in this work as the main performance metric. The MSE metric can be calculated as follow to assess the performance.

where

The prediction of regression by the proposed weighted average ensemble model and the original values are shown in

SS | DF | MS | F (DFn, DFd) | P value | |
---|---|---|---|---|---|

Treatment (between columns) | 4.67E−05 | 4 | 1.17E−05 | F (4, 90) = 148.4 | P < 0.0001 |

Residual (within columns) | 7.08E−06 | 90 | 7.87E−08 | – | – |

Total | 5.38E−05 | 94 | – | – | – |

In this paper, a weighted average ensemble model is proposed to predict the bandwidth of the Metamaterial Antenna. To calculate the weights for base models, an optimization algorithm is used to find the optimal weights of the ensemble. Dynamic Group-Based Cooperative Optimizer (DGCO) is employed to search for optimal weight for the base models. The proposed model is compared with three based models and the average ensemble model. The results show that the proposed model is better than other models and can predict antenna bandwidth efficiently. The predicted and the actual residual values using residual, homoscedasticity, and QQ plots confirm the performance of the proposed weighted average ensemble model to predict antenna bandwidth efficiently. ANOVA test confirms the statistical differences between the proposed weighted average ensemble model and other models. In the future work, justification of the proposed model results compared to the EM simulation based on the optimized design parameters from other models as well as the proposed model will be considered. The proposed model will also be compared to other antenna optimization approaches such as antenna optimization using particle swarm optimization algorithm and genetic algorithm.