#
Real-Time Hardware Identification of Complex Dynamical Plant by Artificial Neural Network Based on Experimentally Processed Data by Smart Technologies^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Signals

## 3. Artificial Neural Networks

#### 3.1. Fully Connected Feedforward Neural Networks

#### 3.2. Recurrent Neural Networks

#### 3.3. Implementation of Neural Network Models in Real-Time Hardware

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Mitrishkin, Y.V.; Korenev, P.S.; Prokhorov, A.A.; Kartsev, N.M.; Patrov, M.I. Plasma control in tokamaks. Part 1. Controlled thermonuclear fusion problem. Tokamaks. Components of control systems. Adv. Syst. Sci. Appl.
**2018**, 18, 26–52. [Google Scholar] [CrossRef] - Mitrishkin, Y.V.; Kartsev, N.M.; Kuznetsov, E.A.; Korostelev, A.Y. Metodi i Sistemi Magnitnogo Upravleniya Plazmoi vs. Tokamakakh [Methods and Systems of Plasma Magnetic Control in Tokamaks]; KRASAND: Moscow, Russia, 2020. (In Russian) [Google Scholar]
- Korenev, P.S.; Mitrishkin, Y.V.; Patrov, M.I. Rekonstruktsiya ravnovesnogo raspredeleniya parametrov plasmi tokamaka po vneshnim magnitnim izmereniyam i postroyeniye lineynikh plazmennikh modeley [Reconstruction of equilibrium distribution of plasma parameters on the base of external magnetic measurements and construction of plasma linear models]. Mechatron. Autom. Control
**2016**, 17, 254–265. (In Russian) [Google Scholar] - Mitrishkin Yuri, V.; Korenev Pavel, S.; Konkov Artem, E.; Kruzhkov Valerii, I.; Ovsyannikov Nicolai, E. New Identification Approach and Methods for Plasma Equilibrium Reconstruction in D-Shaped Tokamaks. Mathematics
**2022**, 10, 40. [Google Scholar] [CrossRef] - Bishop, C.M.; Haynes, P.S.; Smith, M.E.U.; Todd, T.N.; Trotman, D.L. Real-Time Control of a Tokamak Plasma Using Neural Networks. Neural Comput.
**1995**, 7, 206–217. [Google Scholar] [CrossRef] - Coccorese, E.; Morabito, C.; Martone, R. Identification of noncircular plasma equilibria using a neural network approach. Nucl. Fusion
**1994**, 34, 1349–1363. [Google Scholar] [CrossRef] - Lister, J.B.; Schnurrenberger, H. Fast non-linear extraction of plasma equilibrium parameters using a neural network mapping. Nucl. Fusion
**1991**, 31, 1291–1300. [Google Scholar] [CrossRef] [Green Version] - Albanese, R.; Coccorese, E.; Gruber, O.; Martone, R.; McCarthy, P.; Morabito, F.C. Identification of Plasma Equilibria in ITER from Magnetic Measurements Via Functional Parameterization and Neural Networks. Fusion Technol.
**1996**, 30, 219–236. [Google Scholar] [CrossRef] - Joung, S.; Kim, J.; Kwak, S.; Bak, J.G.; Lee, S.; Han, H.; Ghim, Y. Deep neural network Grad-Shafranov solver constrained with measured magnetic signals. Nucl. Fusion
**2019**, 60, 016034. [Google Scholar] [CrossRef] [Green Version] - Prokhorov, A.; Mitrishkin, Y.; Korenev, P.; Patrov, M. The Plasma Shape Control System in the Tokamak with the Neural Network as a Plasma Equilibrium Reconstruction Algorithm; Elsevier Ltd.: London, UK, 2020; pp. 857–862. [Google Scholar] [CrossRef]
- Mitrishkin, Y.V. Plasma magnetic control systems in D-shaped tokamaks and imitation digital computer platform in real time for controlling plasma current and shape. Adv. Syst. Sci. Appl. Int. Inst. Gen. Syst. Stud.
**2022**, 22, 1–15. [Google Scholar] - Minaev, V.B.; Gusev, V.K.; Sakharov, N.V.; Varfolomeev, V.I.; Bakharev, N.N.; Belyakov, V.A.; Bondarchuk, E.N.; Brunkov, P.N.; Chernyshev, F.V.; Davydenko, V.I.; et al. Spherical tokamak Globus-M2: Design, integration, construction. Nucl. Fusion
**2017**, 57, 066047. [Google Scholar] [CrossRef] - Rosenblatt, F. The perceptron: A probabilistic model for information storage and organization in the brain. Psychol. Rev.
**1958**, 65, 386. [Google Scholar] [CrossRef] [Green Version] - Schmidhuber, J. Deep learning in neural networks: An overview. Neural Netw. Off. J. Int. Neural Netw. Soc.
**2015**, 61, 85–117. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Goodfellow, I.; Bengio, Y.; Courville, A. Deep learning. Genet. Program. Evolvable Mach.
**2018**, 19, 305–307. [Google Scholar] [CrossRef] [Green Version] - Kingma, D.; Ba, J. Adam: A Method for Stochastic Optimization. In Proceedings of the International Conference on Learning Representations, Banff, AB, Canada, 14–16 April 2014. [Google Scholar]

**Figure 1.**(

**a**) Globus-M2 tokamak (

**b**) Vertical cross-section with poloidal system, diagnostic probes (red dots) and points on separatrix (g1–g6).

**Figure 2.**Experimental signals from shot #37255 and Gaps reconstructed by the FCDI algorithm at a divertor phase of the plasma discharge.

**Figure 3.**Structure of the fully connected feedforward neural network containing two hidden layers at a size of s. Input size is k, output size is m.

**Figure 4.**Dependency of accuracy on hyperparameter values of the fully connected feedforward neural network. Accuracy is measured on test data.

**Figure 5.**Results of the FCDI identification by the fully connected feedforward neural network with one hidden layer of the size of 100 neurons and the LeakyReLU activation function. In total, 5 test signals from Globus-M2 shots #37336, #37338, #37702, #37712 and #37320 are shown.

**Figure 6.**Dependency of accuracy on hyperparameter values of the recurrent neural network. Accuracy is measured on test data.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kruzhkov, V.I.; Mitrishkin, Y.V.; Pavlova, E.A.
Real-Time Hardware Identification of Complex Dynamical Plant by Artificial Neural Network Based on Experimentally Processed Data by Smart Technologies. *Eng. Proc.* **2023**, *33*, 17.
https://doi.org/10.3390/engproc2023033017

**AMA Style**

Kruzhkov VI, Mitrishkin YV, Pavlova EA.
Real-Time Hardware Identification of Complex Dynamical Plant by Artificial Neural Network Based on Experimentally Processed Data by Smart Technologies. *Engineering Proceedings*. 2023; 33(1):17.
https://doi.org/10.3390/engproc2023033017

**Chicago/Turabian Style**

Kruzhkov, Valerii I., Yuri V. Mitrishkin, and Eugenia A. Pavlova.
2023. "Real-Time Hardware Identification of Complex Dynamical Plant by Artificial Neural Network Based on Experimentally Processed Data by Smart Technologies" *Engineering Proceedings* 33, no. 1: 17.
https://doi.org/10.3390/engproc2023033017