Design of frequency selective surface comprising of dipoles using artificial neural network

Received Apr 16, 2020 Revised Jun 14, 2020 Accepted Jun 18 2020 This paper depicts the design of Frequency Selective Surface (FSS) comprising of dipoles using Artificial Neural Network (ANN). It has been observed that with the change of the dimensions and periodicity of FSS, the resonating frequency of the FSS changes. This change in resonating frequency has been studied and investigated using simulation software. The simulated data were used to train the proposed ANN models. The trained ANN models are found to predict the FSS characteristics precisely with negligible error. Compared to traditional EM simulation softwares (like ANSOFT Designer), the proposed technique using ANN models is found to significantly reduce the FSS design complexity and computational time. The FSS simulations were made using ANSOFT Designer v2 software and the neural network was designed using MATLAB software.


INTRODUCTION
In microwave engineering, Frequency Selective Surfaces (FSSs) are planar periodic arrays of metal patches on a substrate or slots on a conducting sheet that function as a filter for free space radiation [1]. Many authors have made analysis on FSS through EM numerical methods, such as the Method of Moment [2]. But these numerical methods require high computational cost. So to avoid this, Artificial Neural Network (ANN) which are previously trained with results obtained by Method of Moment can be used for analysis of FSS [3][4]. Also, other algorithms like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) can be blended with ANN for faster and accurate training of the ANN [5][6][7][8][9][10][11][12][13][14][15][16].
In this paper, patch type FSS consisting of dipoles (as shown in Figure 1) is used whose dimensions (i.e. patch length 'L', patch width 'W', x-periodicity 'Tx' and y-periodicity 'Ty') are varied and the corresponding resonating frequencies are noted. Then using these simulated results, some neural network models are designed and trained, which can be used for faster analysis and design of FSS comprising of dipoles.

BACKPROPAGATION TRAINING ALGORITHM
The Backpropagation is an algorithm for supervised training of ANN in which the error is propagated backward for update of weights of different layers of the neural network. A Multi-Layer Perceptron (MLP) is shown in Figure 2, having one input layer, one hidden layer and one output layer.  Steps 3 to 10 are performed when stopping condition is false. 3. Steps 4 to 9 are performed for each training pair. 4. Each input unit receives input signal (ii) and sends it to the hidden unit. 5. Each hidden unit sums its weighted input signals to calculate the net input (net hi). net h1 = w1 i1 + w3 i2 + a1 net h2 = w2 i1 + w4 i2 + b1 Then an Activation function is applied to the net input to calculate the output of the hidden unit (hi). The output of the hidden layer is then sent to the output layer units. hi = f(net hi) Here Bipolar Sigmoid Activation Function is used: f(x) = 1 / (1 + e-x) 6. Similarly, for each output unit the net input (net oi) is calculated and the activation function is applied to compute the output signals (oi).
wi(new)=wi(old) +Δwi ai (new)=ai (old) +Δai bi (new)=bi (old) +Δbi 10. The stopping condition is checked. The stopping condition may be certain number of epochs reached or when there is previously settled minimum error between actual output and target output.

RESEARCH METHOD
Here 5 MLPs are used. Each of them have 4 inputs and 1 output as shown in Figure 3, but the inputs and outputs are different as shown in Table 1.

RESULTS AND ANALYSIS
Initially, the proposed ANN models are trained using the simulation results obtained from ANSOFT Designer v2 software. The training data set is provided in Table 2. Next, the performance of the proposed ANN models in accurately predicting the FSS characteristics is validated using a test data. Here, an FSS comprising of dipoles having dimensionsL = 15 mm, W = 1.5 mm, Tx = 22 mm, Ty = 8 mm (as shown in Figure. 1) is used as a test data for the proposed ANN model validation. The dimensions considered here for testing the ANN models is not included in the data set used for training the MLPs. The FSS is simulated using ANSOFT Designer v2 software and its resonant frequency obtained is 8.15 GHz. Next, this data is used for checking the error of all the 5 MLPs, as shown in Table 3. Finally, the 1st MLP (having L, W, Tx and Ty as inputs and resonating frequency (RF) as output) is used to perform parametric study as given in Section 4.2.

Single value check (interpolation) of the proposed ANN
The validation result of the 5 MLPs using the single test data is given in Table 3. MLP1 is found to predict the resonating frequency (RF) of the FSS for the given set of FSS design parameters with 0.076% error. MLP 2-5 predicts the FSS design parameter (y-periodicity, x-periodicity, Patch Width, and Patch Length, respectively) with 0.94%, 1.724%, 0.0298%, and 0.056% error, respectively for the given input set as shown in Table 3 An FSS is fabricated using parameters corresponding to MLP1 given in Table 3. The fabricated prototype is shown in Figure 4(a). The transmission characteristic of the fabricated FSS is measured using R&S VNA (ZNB20) and Tx/Rx horn antennas. The simulated and measured transmission (S21) characteristic of the fabricated FSS is given in Figure 4(b). It is found that the resonant frequency of the proposed FSS is nearly same in both simulation and measurement.

Parametric study
In this section, extensive study has been conducted to test the performance of MLP 1. MLP 1 can only provide the resonating frequency (RF) as the output for the change in FSS design parameters-Patch Length, Patch Width, x-periodicity and y-periodicity. The values of FSS design parameters for this parametric study are tabulated in Table 4. Here, comparison is done between the simulated result obtained from Ansoft Designer and ANN.  Figure 5 shows the results of Parametric Study 1 where Patch Width, x-periodicity, y-periodicityare kept constant and Patch Length is varied. Figure 6 shows the results of Parametric Study 2 where Patch Length, x-periodicity, y-periodicity are kept constant and Patch Width is varied. In Figure 7 the results of Parametric Study 3 is given where Patch Length, Patch Width, y-periodicity are kept constant and xperiodicity is varied. Figure 8  x-periodicity = 22.5 mm and y-periodicity = 15 mm is taken. |S21| vs. Frequency plot is done from 2 GHz to 12 GHz with low step count and for this the time elapsed is 6 minutes. From this plot the approximate resonant frequency is located somewhere between 6 GHz and 7.5 GHz. Then again plot is done from 6 GHz to 7.5 GHz with high step count which took 2 minutes time and the resonant frequency obtained is 6.83 GHz. So, the total simulation time required is 8 minutes.
Then an FSS with patch-length = 8 mm, patch-width = 0.9 mm, x-periodicity = 22.5 mm and yperiodicity = 15 mm is taken. |S21| vs. Frequency plot is done from 2 GHz to 12 GHz with low step count and for this the time elapsed is 4 minutes. From this plot the approximate resonant frequency is located somewhere between 10 GHz and 11.5 GHz. Then again plot is done from 10 GHz to 11.5 GHz with high step count which took 2 minutes time and the resonant frequency obtained is 10.76 GHz. So, total simulation time required is 6 minutes. But in case of ANN, generation of |S21| vs. Frequency plot is not required, as it directly gives resonant frequency as output. In first case the resonant frequency obtained is 6.8348 GHz, and in the second case the resonant frequency obtained is 10.7404 GHz. Here in both the cases the ANN gave resonant frequency output in less than 1 sec time (i.e. in the first case 0.36036 sec and in the second case 0.27701 sec). The percentage reduction in computational time is 99.9249 % in the first case and 99.9230 % in the second case, as shown in Table 5.

CONCLUSION
In this paper, an Artificial Neural Network model is trained using data obtained from ANSOFT Designer v2 software which uses Method of Moment for analysis of FSS. Hence, the ANN is properly trained and gives negligible error. Using this ANN, the results are obtained very quickly which saves time and also reduces the computational cost and complexity.