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

2020 ◽  
pp. 095440622093294
Author(s):  
J Awrejcewicz ◽  
VA Krysko ◽  
SA Mitskievich ◽  
IE Kutepov ◽  
IV Papkova ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Colored Noise ◽  
Wavelet Packet ◽  
Additive White Gaussian Noise ◽  
Mechanical Systems ◽  
Principal Component ◽  
Component Analysis ◽  
External Noise ◽  
Spherical Shells ◽  
First Time

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.

Generation of critical aftershocks using stochastic neural networks and wavelet packet transform

2019 ◽  
Vol 26 (5-6) ◽  
pp. 331-351
Author(s):  
Elham Rajabi ◽  
Gholamreza Ghodrati Amiri
Keyword(s):  
Neural Networks ◽  
Principal Component Analysis ◽  
Response Spectrum ◽  
Wavelet Packet ◽  
Principal Component ◽  
Response Spectra ◽  
Component Analysis ◽  
Wavelet Packet Transform ◽  
Stochastic Neural Networks ◽  
Transform Coefficients

This paper proposes a methodology using wavelet packet transform, principal component analysis, and neural networks in order to generate artificial critical aftershock accelerograms which are compatible with the response spectra. This procedure uses the learning abilities of neural networks, principal component analysis as a dimension reduction technique, and decomposing capabilities of wavelet packet transform on consecutive earthquakes. In fact, the proposed methodology consists of two steps and expands the knowledge of the inverse mapping from mainshock response spectrum to aftershock response spectrum and aftershock response spectrum to wavelet packet transform coefficients of the aftershocks. This procedure results in a stochastic ensemble of response spectra of aftershock (first step) and corresponding wavelet packet transform coefficients (second step) which are then used to generate the aftershocks through applying the inverse wavelet packet transform. Finally, in order to demonstrate the effectiveness of the proposed method, three examples are presented in which recorded critical successive ground motions are used to train and test the neural networks.

scholarly journals Fault Data Detection of Traffic Detector Based on Wavelet Packet in the Residual Subspace Associated with PCA

2019 ◽  
Vol 9 (17) ◽  
pp. 3491 ◽  
Author(s):  
Xiaolu Li ◽  
Xi Zhang ◽  
Peng Zhang ◽  
Guangyu Zhu
Keyword(s):  
Principal Component Analysis ◽  
Traffic Flow ◽  
Intelligent Transportation System ◽  
Wavelet Packet ◽  
Recognition Rate ◽  
Principal Component ◽  
Component Analysis ◽  
Data Detection ◽  
Analysis Model ◽  
Traffic Detector

To improve the accuracy and efficiency of fault data identification of traffic detectors is crucial in order to decrease the probability of unexpected failures of the intelligent transportation system (ITS). Since convolutional fault data recognition based on traffic flow three-parameter law has a poor capability for multiscale of fault data, PCA (principal component analysis) is adopted for traffic fault data identification. This paper proposes the fault data detection models based on the PCA model, MSPCA (multiscale principal component analysis) model and improved MSPCA model, respectively. In order to improve the recognition rate of traffic detectors’ fault data, the improved MSPCA model combines the wavelet packet energy analysis and PCA to achieve traffic detector data fault identification. On the basis of traditional MSPCA, wavelet packet multi-scale decomposition is used to get detailed information, and principal component analysis models are established on different scale matrices, and fault data are separated by wavelet packet energy difference. Through case analysis, the feasibility verification of traffic flow data identification method is carried out. The results show that the improved method proposed in this paper is effective for identifying traffic fault data.

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