# Simulation and Optimization of Electromagnetic Absorption of Polycarbonate/CNT Composites Using Machine Learning

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problematic and Objective

## 3. Materials and Data Collection

^{®}OD2015 polycarbonate. The CNTs were multi-walled NC 7000 nanotubes provided by NanoCyl SA, Belgium. The nanocomposite compounds were melt-blended at 280 °C for 5 min at 150 RPM in a micro 15 DSM micro-compounder. The composite pellets were twice hot-pressed under six different operating conditions adapted to the viscosity of the pellets in a Fontijne press to produce films with various thicknesses, as shown in Table 1. It is important to mention that PC-xxxCNT and T°/press./time represents the composite name and the pressing conditions (temperature, pressure force, and pressing time, respectively).

## 4. The Proposed System

#### 4.1. MLP Neural Network

- Flexibility of neural networks

- Yielding of important experimental results

- Relevance of the analyzed data

#### Implementation of the MLP Neural Network

- -
**Step 1:**Setting the number of hidden layers

- -
**Step 2:**Determining the number of neurons

- -
**Step 3:**Choosing the activation function

- -
**Step 4:**Choosing the learning

#### 4.2. Evaluation

## 5. Prediction of the Optimal Weight Loading of CNT Using Rozanov Formalism

- 1.
- The measurement of the reflection coefficient of PC/CNT films back coated with a PEC was performed using a vector network analyzer (VNA) and a waveguide configuration.
- 2.
- The Rozanov performance was calculated according to:

- 3.
- This equation was used to calculate the theoretical thinnest film of PC/CNT composite following the Rozanov formalism.
- 4.
- Finally, a graph of the figure of merit (FOM) defined by the ratio

## 6. Results

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Haenlein, M.; Kaplan, A. A brief history of artificial intelligence: On the past, present, and future of artificial intelligence. Calif. Manag. Rev.
**2019**, 61, 5–14. [Google Scholar] [CrossRef] - Pannu, A. Artificial intelligence and its application in different areas. Artif. Intell.
**2015**, 4, 79–84. [Google Scholar] - Schütt, K.T.; Gastegger, M.; Tkatchenko, A.; Müller, K.R.; Maurer, R.J. Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions. Nat. Commun.
**2019**, 10, 1–10. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Carrasquilla, J. Machine learning for quantum matter. arXiv
**2020**, arXiv:2003.1104. Available online: https://arxiv.org/abs/2003.11040 (accessed on 14 August 2020). [CrossRef] - Radzuan, N.A.; Sulong, A.B.; Sahari, J. A review of electrical conductivity models for conductive polymer composite. Int. J. Hydrog. Energy
**2017**, 42, 9262–9273. [Google Scholar] [CrossRef] - Fernández, J.D.; Vico, F. AI methods in algorithmic composition: A comprehensive survey. J. Artif. Intell. Res.
**2013**, 48, 513–582. [Google Scholar] [CrossRef] - Jenkins, A.; Gupta, V.; Lenoir, M. General Regression Neural Networks, Radial Basis Function Neural Networks, Support Vector Machines, and Feedforward Neural Networks. arXiv
**2019**, arXiv:1911.07115. Available online: https://arxiv.org/abs/1911.07115 (accessed on 14 August 2020). - Al-Naymat, G.; Al-Kasassbeh, M.; Abu-Samhadanh, N.; Sakr, S. Classification of VoIP and non-VoIP traffic using machine learning approaches. J. Theor. Appl. Inf. Technol.
**2016**, 92, 403–414. [Google Scholar] - Dinca, I.; Ban, C.; Stefa, A.; Pelin, G. Nanocomposites as advanced materials for aerospace industry. Incas Bull.
**2012**, 4, 73. [Google Scholar] - McNally, T.; Pötschke, P.; Halley, P.; Murphy, M.; Martin, D.; Bell, S.; Brennan, G.P.; Bein, D.; Lemoine, P.; Quinn, J.P. Polyethylene multiwalled carbon nanotube composites. Polymer
**2015**, 46, 8222–8232. [Google Scholar] [CrossRef] - Huynen, I. Parametric study of microwave absorption in lossy dielectric slabs. Int. J. Microw. Eng.
**2016**, 1, 1–12. [Google Scholar] [CrossRef] - Emplit, A.; Huynen, I. Study of Absorption in Carbon Nanotube Composites from 1HZ to 40GHz. Int. J. Microw. Eng.
**2017**, 2, 1. [Google Scholar] [CrossRef] - Danlée, Y.; Mederos-Henry, F.; Hermans, S.; Bailly, C.; Huynen, I. Ranking Broadband Microwave Absorption Performance of Multilayered Polymer Nanocomposites Containing Carbon and Metallic Nanofillers. Front. Mater.
**2020**, 7, 214. [Google Scholar] [CrossRef] - Kompoliti, K.; Verhagen, L. Encyclopedia of Movement Disorders; Academic Press: Cambridge, MA, USA, 2010; Volume 1. [Google Scholar]
- Shahzad, F.; Alhabeb, M.; Hatter, C.B.; Anasori, B.S.; Hong, S.M.; Koo, C.M.; Gogotsi, Y. Electromagnetic interference shielding with 2D transition metal carbides (MXenes). Science
**2016**, 353, 1137–1140. [Google Scholar] [CrossRef] [Green Version] - Singh, A.K.; Shishkin, A.; Koppel, T.; Gupta, N. A review of porous lightweight composite materials for electromagnetic interference shielding. Compos. Part B Eng.
**2018**, 149, 188–197. [Google Scholar] [CrossRef] - Ao, D.; Tang, Y.; Xu, X.; Xiang, X.; Yu, J.; Li, S.; Zu, X. Highly Conductive PDMS Composite Mechanically Enhanced with 3D-Graphene Network for High-Performance EMI Shielding Application. Nanomaterials
**2020**, 10, 768. [Google Scholar] [CrossRef] - Bagotia, N.; Choudhary, V.; Sharma, D. Studies on toughened polycarbonate/multiwalled carbon nanotubes nanocomposites. Compos. Part B Eng.
**2017**, 124, 101–110. [Google Scholar] [CrossRef] - Danlée, Y.; Bailly, C.; Huynen, I. Thin and flexible multilayer polymer composite structures for effective control of microwave electromagnetic absorption. Compos. Sci. Technol.
**2014**, 100, 182–188. [Google Scholar] [CrossRef] - Pozar, D.M. Microwave Engineering, 4th ed.; Wiley: Hoboken, NJ, USA, 2011. [Google Scholar]
- Rozanov, K.N. Ultimate thickness to bandwidth ratio of radar absorbers. IEEE Trans. Antennas Propag.
**2000**, 48, 1230–1234. [Google Scholar] [CrossRef] - Jaiswar, R.; Danlée, Y.; Mesfin, H.; Delcorte, A.; Hermans, S.; Bailly, C.; Raskin, J.P.; Huynen, I. Absorption modulation of FSS-polymer nanocomposites through incorporation of conductive nanofillers. Appl. Phys. A
**2017**, 123, 164. [Google Scholar] [CrossRef] - Raschka, S. Model evaluation, model selection, and algorithm selection in machine learning. arXiv
**2018**, arXiv:1811.12808. Available online: https://arxiv.org/abs/1811.12808 (accessed on 14 August 2020). - Chouai, M.; Merah, M.; Sancho Gómez, J.L.; Mimi, M. A machine learning color-based segmentation for object detection within dual X-ray baggage images. In Proceedings of the 3rd International Conference on Networking, Information Systems & Security, Marrakech, Morocco, 31 March–2 April 2020; pp. 1–11. [Google Scholar]
- Ebbels, T.M. Non-linear Methods for the Analysis of Metabolic Profiles. In The Handbook of Metabonomics and Metabolomics; Elsevier: Amsterdam, The Netherlands, 2007; pp. 201–226. [Google Scholar]
- Sharifzadeh, M.; Sikinioti-Lock, A.; Shah, N. Machine-learning methods for integrated renewable power generation: A comparative study of artificial neural networks, support vector regression, and Gaussian Process Regression. Renew. Sustain. Energy Rev.
**2019**, 108, 513–538. [Google Scholar] [CrossRef] - Yaseen, Z.M.; Al-Juboori, A.M.; Beyaztas, U.; Al-Ansari, N.; Chau, K.-W.; Qi, C.; Ali, M.; Salih, S.G.; Shahid, S. Prediction of evaporation in arid and semi-arid regions: A comparative study using different machine learning models. Eng. Appl. Comput. Fluid Mech.
**2020**, 14, 70–89. [Google Scholar] [CrossRef] [Green Version] - Qi, C.; Tang, X. Slope stability prediction using integrated metaheuristic and machine learning approaches: A comparative study. Comput. Ind. Eng.
**2018**, 118, 112–122. [Google Scholar] [CrossRef] - Gomez-Sanchis, J.; Martín-Guerrero, J.D.; Soria-Olivas, E.; Vila-Francés, J.; Carrasco, J.L.; Valle-Tascón, S. Neural networks for analysing the relevance of input variables in the prediction of tropospheric ozone concentration. Atmos. Environ.
**2006**, 40, 6173–6180. [Google Scholar] [CrossRef] - Han, J.; Moraga, C. The influence of the sigmoid function parameters on the speed of backpropagation learning. In Proceedings of the International Workshop on Artificial Neural Networks, Perth, Australia, 27 November–1 December 1995. [Google Scholar]
- Goodfellow, I.; Bengio, Y.; Courville, A. Back-Propagation and Other Differentiation Algorithms. In Deep Learning; MIT Press: Cambridge, MA, USA, 2016; pp. 200–220. [Google Scholar]
- Basha, M.; Rajput, S. Survey on Evaluating the Performance of Machine Learning Algorithms: Past Contributions and Future Roadmap. In Deep Learning and Parallel Computing Environment for Bioengineering Systems; Academic Press: Cambridge, MA, USA, 2019; pp. 153–164. [Google Scholar]
- Karlsson, A.; Kazemzadeh, A. On the physical limit of radar absorbers. In Proceedings of the International Symposium on Electromagnetic Theory (EMTS), Berlin, Germany, 16–19 August 2010; pp. 25–28. [Google Scholar]
- Jha, A.; Chandrasekaran, A.; Kim, C.; Ramprasad, R. Impact of dataset uncertainties on machine learning model predictions: The example of polymer glass transition temperatures. Model. Simul. Mater. Sci. Eng.
**2019**, 27, 024002. [Google Scholar] [CrossRef] [Green Version] - Charte, F.; Rivera, A.; Del Jesus, M.J.; Herrera, F. On the impact of dataset complexity and sampling strategy in multilabel classifiers performance. In Proceedings of the International Conference on Hybrid Artificial Intelligence System (HAIS), Seville, Spain, 18–20 April 2016; pp. 500–511. [Google Scholar]
- Danlée, Y.; Jaiswar, R.; Mederos-Henry, F.; Mesfin, H.; Bailly, C.; Delcorte, A.; Hermans, S.; Huynen, I. Nano4Waves: A metamaterial approach towards smart nanocomposites for nanosecond signal control. In Proceedings of the IEEE 15th International Conference on Nanotechnology, Roma, Italy, 27–30 July 2015; pp. 188–191. [Google Scholar]

**Figure 1.**Block diagram of a multilayer perceptron. Adapted from Al-Naymat, G., et al. Classification of VoIP and non-VoIP traffic using machine learning approaches [8].

**Figure 3.**Logarithmic scale plot showing the hyper-parameter optimization process via the hold-out validation method. Figures show the optimal values (red points) of the number of neurons of multilayer perceptron (MLP) from the lowest carbon nanotube (CNT) load (

**a**) up to the highest load (

**o**).

**Figure 4.**System evaluation on the test set, the blue and red lines, respectively, show the actual and predicted absorption of the measured sample MLP from the lowest CNT load (

**a**) up to the highest load (

**o**).

**Figure 5.**Relationship between training data, the mean absorption index from Table 1, and systems accuracy.

Formulation Designation | Freq. Range (GHz) | Av. Conduct. (S/m) | Thick. (µm) | wt.% CNT | Absorption Index (%) | No. of Data | Pressing Conditions (T°/Press./t) |
---|---|---|---|---|---|---|---|

PC-0.25CNT | 2–40 | 1 | 125 | 0.25 | 1.516–11.689 | 3507 | 290 °C/7.5T/2.5 min |

PC-0.50CNT | 2–40 | 3 | 135 | 0.50 | 8.645–25.066 | 3507 | |

PC-0.75CNT | 2–40 | 8 | 360 | 0.75 | 30.804–44.389 | 1602 | 250 °C/10T/3 min |

PC-1.00CNT | 4–115 | 5 | 175 | 1 | 17.258–74.173 | 5607 | 290 °C/7.5T/2.5 min |

PC-1.25CNT | 2–40 | 6 | 530 | 1.25 | 24.228–32.661 | 1602 | 250 °C/10T/3 min |

PC-1.50CNT | 2–40 | 10 | 130 | 1.50 | 30.007–55.943 | 3507 | 290 °C 7.5T 2.5 min |

PC-2.50CNT | 2–40 | 28 | 180 | 2.5 | 39.397–51.462 | 3507 | |

PC-3.00CNT | 2–40 | 45 | 140 | 3 | 40.361–52.931 | 3507 | |

PC-3.50CNT | 12–26 | 65 | 140 | 3.50 | 43.805–54.509 | 1002 | |

PC-4.00CNT | 2–26 | 85 | 155 | 4 | 40.005–50.244 | 2505 | |

PC-4.50CNT | 2–26 | 90 | 145 | 4.50 | 39.964–51.732 | 2505 | |

PC-5.00CNT | 26–40 | 80 | 400 | 5 | 36.104–56.713 | 501 | 280 °C/10T/2 min |

PC-10.0CNT | 26–40 | 110 | ~160 | 10 | 23.470–43.539 | 501 | |

PC-15.0CNT | 26–40 | 125 | ~160 | 15 | 24.364–43.226 | 501 | 280 °C/10T/3 min |

PC-20.0CNT | 26–40 | 130 | ~160 | 20 | 19.184–38.222 | 501 | 280 °C/10T/4 min |

Name | Precision Accuracy | Calculation Time |
---|---|---|

PC-0.25CNT | 99.8325% | 0.009921 s |

PC-0.50CNT | 99.3121% | 0.010471 s |

PC-0.75CNT | 99.9481% | 0.007242 s |

PC-1.00CNT | 99.4115% | 0.009182 s |

PC-1.25CNT | 99.9511% | 0.007256 s |

PC-1.50CNT | 99.3395% | 0.008063 s |

PC-2.50CNT | 99.8953% | 0.010935 s |

PC-3.00CNT | 99.8475% | 0.007603 s |

PC-3.50CNT | 99.9481% | 0.007591 s |

PC-4.00CNT | 99.9041% | 0.007694 s |

PC-4.50CNT | 99.9102% | 0.011504 s |

PC-5.00CNT | 99.9448% | 0.007437 s |

PC-10.0CNT | 99.9373% | 0.007264 s |

PC-15.0CNT | 99.9326% | 0.007259 s |

PC-20.0CNT | 99.8815% | 0.007183 s |

Mean | 99.7997% | 0.008440 s |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sidi Salah, L.; Chouai, M.; Danlée, Y.; Huynen, I.; Ouslimani, N.
Simulation and Optimization of Electromagnetic Absorption of Polycarbonate/CNT Composites Using Machine Learning. *Micromachines* **2020**, *11*, 778.
https://doi.org/10.3390/mi11080778

**AMA Style**

Sidi Salah L, Chouai M, Danlée Y, Huynen I, Ouslimani N.
Simulation and Optimization of Electromagnetic Absorption of Polycarbonate/CNT Composites Using Machine Learning. *Micromachines*. 2020; 11(8):778.
https://doi.org/10.3390/mi11080778

**Chicago/Turabian Style**

Sidi Salah, Lakhdar, Mohamed Chouai, Yann Danlée, Isabelle Huynen, and Nassira Ouslimani.
2020. "Simulation and Optimization of Electromagnetic Absorption of Polycarbonate/CNT Composites Using Machine Learning" *Micromachines* 11, no. 8: 778.
https://doi.org/10.3390/mi11080778