scholarly journals The singular-value decomposition of an infinite Hankel matrix

1983 ◽  
Vol 50 ◽  
pp. 639-656 ◽  
Author(s):  
N.J. Young
Keyword(s):  
Singular Value Decomposition ◽  
Hankel Matrix ◽  
Singular Value ◽  
Value Decomposition

A New Algorithm to Compensate Ionosphere Phase Contamination

2014 ◽  
Vol 644-650 ◽  
pp. 4551-4554
Author(s):  
Hui Ai ◽  
Jin Feng Hu ◽  
Wan Ge Li ◽  
Zhi Rong Lin ◽  
Ya Xuan Zhang
Keyword(s):  
Fourier Transform ◽  
Singular Value Decomposition ◽  
Prior Information ◽  
Hankel Matrix ◽  
Singular Value ◽  
Echo Signal ◽  
Rank Reduction ◽  
Coherent Integration ◽  
Priori Information ◽  
Value Decomposition

The echo signals of sky-wave over-the-horizon radar involve ionospheric phase contamination with spectrum expansion. The bragg peaks expand and cover the frequency spectrum of low speed target. So ionospheric phase decontamination is necessary before coherent integration. The traditional Hankel Rank Reduction (HRR) phase decontamination method constructs the Hankel matrix by folding the echo signal, estimating instantaneous frequency through singular value decomposition. But HRR method requires the prior information of signal components. The estimation is invalid without priori information. The algorithm presented in this paper does not require the priori information. The algorithm based on matched fourier transform can accurately estimate the phase contamination function for the clutter noise ratio is high. Simulation shows that the proposed algorithm has better performance in phase decontamination.

scholarly journals Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition

2021 ◽  
Vol 9 (7) ◽  
pp. 768
Author(s):  
Romain Lecuyer-Le Bris ◽  
Marc Le Boulluec ◽  
Jean-Frédéric Charpentier ◽  
Mohamed Benbouzid
Keyword(s):  
Singular Value Decomposition ◽  
State Space ◽  
Kernel Function ◽  
State Space Model ◽  
Hankel Matrix ◽  
Singular Value ◽  
Radiation Forces ◽  
Function Definition ◽  
Definition Of ◽  
Value Decomposition

This paper focuses on the formulation of state–space representations of radiation forces for marine structures using Hankel Singular Value Decomposition (HSVD), a method used to obtain a state–space realization from a Hankel matrix, with the classical definition of the kernel function and its new definition given in this paper. The first part shows the influence of a term commonly neglected and the resulting improvement by taking this term into account. The second part will focus on the feedthrough matrix to understand why some models have none and why some others, such as HSVD, have one. An exact definition of the kernel function will be given underlying its discontinuity and its causality. This study also shows the interest of extrapolating hydrodynamic coefficients before approaching radiation forces by a state–space model.

Partial Discharge Random Noise Removal Using Hankel Matrix-Based Fast Singular Value Decomposition

2020 ◽  
Vol 69 (7) ◽  
pp. 4093-4102 ◽  
Author(s):  
Suganya Govindarajan ◽  
Jayalalitha Subbaiah ◽  
Andrea Cavallini ◽  
Kannan Krithivasan ◽  
Jaikanth Jayakumar
Keyword(s):  
Singular Value Decomposition ◽  
Random Noise ◽  
Partial Discharge ◽  
Hankel Matrix ◽  
Noise Removal ◽  
Singular Value ◽  
Value Decomposition

scholarly journals An Effective Gear Fault Diagnosis Method Based on Singular Value Decomposition and Frequency Slice Wavelet Transform

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Fu-Cheng Zhou ◽  
Gui-Ji Tang ◽  
Yu-Ling He
Keyword(s):  
Wavelet Transform ◽  
Singular Value Decomposition ◽  
Hankel Matrix ◽  
Engineering Application ◽  
Singular Value ◽  
Feature Extraction Method ◽  
Time Frequency ◽  
Reconstructed Signal ◽  
Gear Fault ◽  
Value Decomposition

The ability of the frequency slice wavelet transform (FSWT) to distinguish the fault feature is weak under the condition of strong background noise; in order to solve this problem, a fault feature extraction method combining the singular value decomposition (SVD) and FSWT was proposed. Firstly, the Hankel matrix was constructed using SVD, based on which the SVD order was determined according to the principle of the single side maximum value. Then, the denoised signal was further processed by the FSWT to obtain the time-frequency spectrum of the passband. Finally, the detailed analysis was carried out in the time-frequency area with concentrated energy, and the signal was reconstructed by the inverse-FSWT. The processing effect for the pitting corrosion and the tooth broken faults of the gears shows that the faulty feature can be extracted effectively from the envelope spectrum of the reconstructed signal, which means the proposed method is able to help obtain a qualified result and has the potential to be carried out for the practical engineering application.

scholarly journals Early Bearing Fault Diagnosis based on the Improved Singular Value Decomposition Method

2021 ◽  
Author(s):  
Lingli Cui ◽  
Mengxin Sun ◽  
Jinfeng Huang
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Method ◽  
Selection Index ◽  
Hankel Matrix ◽  
Singular Value ◽  
Bearing Fault ◽  
Singular Value Decomposition Method ◽  
Weak Fault ◽  
Value Decomposition ◽  
Fault Information

Abstract The traditional singular value decomposition (SVD) method is unable to diagnose the weak fault feature of bearings effectively, which means, it is difficult to retain the effective singular components (SCs). Therefore, a new singular value decomposition method, SVD based on the FIC (fault information content), is proposed, which takes the amplitude characteristics of fault feature frequency as the selection index FIC of singular components. Firstly, the Hankel matrix of the original signal is constructed and SVD is applied in the matrix. Secondly, the proposed index FIC is used to evaluate the information of the decomposed SCs. Finally, the SCs with fault information are selected and added to obtain the denoised signal. The results of bearing fault simulation signals and experimental signals show that compared with the traditional differential singular value decomposition (DS-SVD), the proposed method can select the singular components with larger amount of fault information, and is able to diagnose the fault under the heavy noise interference. The new method can be used for signal denoising and weak fault feature extraction.

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