Bounds for the relative change of singular values of a real matrix

Abdel-Aziz, Mohammedi R.

doi:10.12988/imf.2007.07235

imf

2007

DOI: 10.12988/imf.2007.07235

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Bounds for the relative change of singular values of a real matrix

Mohammedi R. Abdel-Aziz¹

Abstract: This paper amis to derive bounds for the relative change in the singular values of a real matrix. Both the full column rank and the full row rank cases are considered. Two numerical experiments show that the introduced bounds are confirmed and their values are dependent on the element-wise perturbation of the matrix.

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2018

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A deep feature extraction method for bearing fault diagnosis based on empirical mode decomposition and kernel function

Wang

Deng

Liu

et al. 2018

Advances in Mechanical Engineering

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To avoid catastrophic failures in rotating machines, it is of great significance to continuously monitor and diagnose the running state of rolling bearings. In this article, a deep feature extraction method for rolling bearing fault diagnosis based on empirical mode decomposition and kernel function is proposed. First, the vibration signals under different states of rolling bearing are decomposed by empirical mode decomposition. Second, to extract more representative high-level features, the obtained intrinsic mode functions are preprocessed with singular value decomposition to acquire singular value parameters, which are regarded as the inputs of the proposed stacked kernel sparse autoencoder network. The proposed method does not depend on prior knowledge of fault diagnosis and even does not need the signal denoising processing, simplifying the traditional process of feature extraction of rolling bearing fault diagnosis. To validate the superiority of the proposed diagnosis network, experiments and comparisons have been made as well. The achieved results demonstrated that the proposed empirical mode decomposition and stacked kernel sparse autoencoder-based diagnosis method has a superior performance in rolling bearing fault diagnosis.

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A deep feature extraction method for bearing fault diagnosis based on empirical mode decomposition and kernel function

Wang

Deng

Liu

et al. 2018

Advances in Mechanical Engineering

View full text Add to dashboard Cite

show abstract

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Bounds for the relative change of singular values of a real matrix

Cited by 1 publication

References 12 publications

A deep feature extraction method for bearing fault diagnosis based on empirical mode decomposition and kernel function

A deep feature extraction method for bearing fault diagnosis based on empirical mode decomposition and kernel function

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