Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations

Krysko, Anton V.; Awrejcewicz, Jan; Папкова, И. В.; Szymanowska, Olga; Krysko, Vadim A.

doi:10.1155/2017/3038179

Cited by 10 publications

(3 citation statements)

References 12 publications

(19 reference statements)

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“…Further, a sparse-based method [ 21 ] has been used to derive useful spectral features. Nevertheless, PCA seeks out the best orthogonal vectors for representing information from HSIs [ 22 , 23 ] with minimized spectral dimension (up to 85%). On the contrary, it improves the separability among classes, decreases, and brings a balance of the interclass and intraclass.…”

Section: Introductionmentioning

confidence: 99%

[Retracted] A 3D‐2D Convolutional Neural Network and Transfer Learning for Hyperspectral Image Classification

Nyabuga

Song

et al. 2021

Computational Intelligence and Neuroscience

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As one of the fast evolution of remote sensing and spectral imagery techniques, hyperspectral image (HSI) classification has attracted considerable attention in various fields, including land survey, resource monitoring, and among others. Nonetheless, due to a lack of distinctiveness in the hyperspectral pixels of separate classes, there is a recurrent inseparability obstacle in the primary space. Additionally, an open challenge stems from examining efficient techniques that can speedily classify and interpret the spectral-spatial data bands within a more precise computational time. Hence, in this work, we propose a 3D-2D convolutional neural network and transfer learning model where the early layers of the model exploit 3D convolutions to modeling spectral-spatial information. On top of it are 2D convolutional layers to handle semantic abstraction mainly. Toward simplicity and a highly modularized network for image classification, we leverage the ResNeXt-50 block for our model. Furthermore, improving the separability among classes and balance of the interclass and intraclass criteria, we engaged principal component analysis (PCA) for the best orthogonal vectors for representing information from HSIs before feeding to the network. The experimental result shows that our model can efficiently improve the hyperspectral imagery classification, including an instantaneous representation of the spectral-spatial information. Our model evaluation on five publicly available hyperspectral datasets, Indian Pines (IP), Pavia University Scene (PU), Salinas Scene (SA), Botswana (BS), and Kennedy Space Center (KSC), was performed with a high classification accuracy of 99.85%, 99.98%, 100%, 99.82%, and 99.71%, respectively. Quantitative results demonstrated that it outperformed several state-of-the-arts (SOTA), deep neural network-based approaches, and standard classifiers. Thus, it has provided more insight into hyperspectral image classification.

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Section: Introductionmentioning

confidence: 99%

[Retracted] A 3D‐2D Convolutional Neural Network and Transfer Learning for Hyperspectral Image Classification

Nyabuga

Song

et al. 2021

Computational Intelligence and Neuroscience

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“…And in [ 31 , 32 ], anomaly and change detection was carried out with great success in hyperspectral imaging. Yet, [ 33 ] suggests PCA as yet a powerful preprocessing step to denoise data. Similarly to numerous other noise reduction methods including patents [ 34 ], PCA works under the assumption that the signal needs to be cleaned from the same global noise.…”

Section: Related Workmentioning

confidence: 99%

A Robust Context‐Based Deep Learning Approach for Highly Imbalanced Hyperspectral Classification

Rochac

Zhang

Thompson

et al. 2021

Computational Intelligence and Neuroscience

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Hyperspectral imaging is an area of active research with many applications in remote sensing, mineral exploration, and environmental monitoring. Deep learning and, in particular, convolution-based approaches are the current state-of-the-art classification models. However, in the presence of noisy hyperspectral datasets, these deep convolutional neural networks underperform. In this paper, we proposed a feature augmentation approach to increase noise resistance in imbalanced hyperspectral classification. Our method calculates context-based features, and it uses a deep convolutional neuronet (DCN). We tested our proposed approach on the Pavia datasets and compared three models, DCN, PCA + DCN, and our context-based DCN, using the original datasets and the datasets plus noise. Our experimental results show that DCN and PCA + DCN perform well on the original datasets but not on the noisy datasets. Our robust context-based DCN was able to outperform others in the presence of noise and was able to maintain a comparable classification accuracy on clean hyperspectral images.

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“…Nagai et al 23 and Yanagisawa et al 24 presented the experimental results and analytical studies on the chaotic vibrations of a clamped and supported beam with concentrated mass using Fourier spectra, Poincare´maps, Lyapunov exponents, and PCA. In the paper by Krysko et al, 25 PCA was applied to investigate the nonlinear dynamics of beams.…”

Section: Introductionmentioning

confidence: 99%

Principal component analysis in the linear theory of vibrations: Continuous mechanical systems driven by different kinds of external noise

Awrejcewicz

Кrysko

Mitskievich

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, an analysis of mechanical vibrations influenced by external additive white Gaussian noise and colored noise is conducted using the principal component analysis. The principal component analysis is widely employed for encoding images in image processing, biology, economics, sociology, and political science. However, it is hereby applied to analyze nonlinear dynamics of continuous mechanical systems for the first time. A rich class of objects, including straight beams, beams on Winkler foundations and spherical shells, is investigated in the present paper. The basic differential equations are obtained based on the Bernoulli–Euler hypothesis, and solutions of the linear PDEs are analyzed by means of the principal component analysis. Results obtained with the principal component analysis are compared with those for the method of empirical modal decomposition and the wavelet-packet decomposition.

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Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations

Cited by 10 publications

References 12 publications

[Retracted] A 3D‐2D Convolutional Neural Network and Transfer Learning for Hyperspectral Image Classification

[Retracted] A 3D‐2D Convolutional Neural Network and Transfer Learning for Hyperspectral Image Classification

A Robust Context‐Based Deep Learning Approach for Highly Imbalanced Hyperspectral Classification

Principal component analysis in the linear theory of vibrations: Continuous mechanical systems driven by different kinds of external noise

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