Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent

Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent

This study classified chaotic time series data, including smooth and nonsmooth problems in a dynamic system, using a convolutional neural network (CNN) and verified it through the Lyapunov exponent. For this, the classical nonlinear differential equation by the Lorenz model was used to analyze a smo...

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Main Authors: Jaehyeon Nam, Jaeyoung Kang
Format: Article
Language:English
Published: MDPI AG 2021-12-01
Series:Applied Sciences
Subjects:
convolutional neural network
Lyapunov exponent
recurrence plot
chaos
Online Access:https://www.mdpi.com/2076-3417/11/1/77
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spelling doaj-0dd8828784dc4397a1c251a7aca4c6ad2020-12-25T00:00:17ZengMDPI AGApplied Sciences2076-34172021-12-0111777710.3390/app11010077Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov ExponentJaehyeon Nam0Jaeyoung Kang1Department of Mechanical Engineering, Inha University, Incheon 22212, KoreaDepartment of Mechanical Engineering, Inha University, Incheon 22212, KoreaThis study classified chaotic time series data, including smooth and nonsmooth problems in a dynamic system, using a convolutional neural network (CNN) and verified it through the Lyapunov exponent. For this, the classical nonlinear differential equation by the Lorenz model was used to analyze a smooth dynamic system. The vibro-impact model was used for the nonsmooth dynamic system. Recurrence is a fundamental property of a dynamic system, and a recurrence plot is a representative method to visualize the recurrence characteristics of reconstructed phase space. Therefore, this study calculated the Lyapunov exponent by parametric analysis and visualized the corresponding recurrence matrix to show the dynamic characteristics as an image. In addition, the dynamic characteristics were classified using the proposed CNN model. The proposed CNN model determined chaos with an accuracy of more than 92%.https://www.mdpi.com/2076-3417/11/1/77convolutional neural networkLyapunov exponentrecurrence plotchaos
collection DOAJ
language English
format Article
sources DOAJ
author Jaehyeon Nam
Jaeyoung Kang
spellingShingle Jaehyeon Nam
Jaeyoung Kang
Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent
Applied Sciences
convolutional neural network
Lyapunov exponent
recurrence plot
chaos
author_facet Jaehyeon Nam
Jaeyoung Kang
author_sort Jaehyeon Nam
title Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent
title_short Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent
title_full Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent
title_fullStr Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent
title_full_unstemmed Classification of Chaotic Signals of the Recurrence Matrix Using a Convolutional Neural Network and Verification through the Lyapunov Exponent
title_sort classification of chaotic signals of the recurrence matrix using a convolutional neural network and verification through the lyapunov exponent
publisher MDPI AG
series Applied Sciences
issn 2076-3417
publishDate 2021-12-01
description This study classified chaotic time series data, including smooth and nonsmooth problems in a dynamic system, using a convolutional neural network (CNN) and verified it through the Lyapunov exponent. For this, the classical nonlinear differential equation by the Lorenz model was used to analyze a smooth dynamic system. The vibro-impact model was used for the nonsmooth dynamic system. Recurrence is a fundamental property of a dynamic system, and a recurrence plot is a representative method to visualize the recurrence characteristics of reconstructed phase space. Therefore, this study calculated the Lyapunov exponent by parametric analysis and visualized the corresponding recurrence matrix to show the dynamic characteristics as an image. In addition, the dynamic characteristics were classified using the proposed CNN model. The proposed CNN model determined chaos with an accuracy of more than 92%.
topic convolutional neural network
Lyapunov exponent
recurrence plot
chaos
url https://www.mdpi.com/2076-3417/11/1/77
work_keys_str_mv AT jaehyeonnam classificationofchaoticsignalsoftherecurrencematrixusingaconvolutionalneuralnetworkandverificationthroughthelyapunovexponent
AT jaeyoungkang classificationofchaoticsignalsoftherecurrencematrixusingaconvolutionalneuralnetworkandverificationthroughthelyapunovexponent
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