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

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.

Approximate greatest common divisor of several polynomials from Hankel matrices

This paper is devoted to present a new method for computing the approximate Greatest Common Divisor (GCD) of several polynomials (not pairwise) from the generalized Hankel matrix. Our approach based on the calculation of cofactors is tested for several sets of polynomials.

EEMD and Multiscale PCA-Based Signal Denoising Method and Its Application to Seismic P-Phase Arrival Picking

Signal denoising is one of the most important issues in signal processing, and various techniques have been proposed to address this issue. A combined method involving wavelet decomposition and multiscale principal component analysis (MSPCA) has been proposed and exhibits a strong signal denoising performance. This technique takes advantage of several signals that have similar noises to conduct denoising; however, noises are usually quite different between signals, and wavelet decomposition has limited adaptive decomposition abilities for complex signals. To address this issue, we propose a signal denoising method based on ensemble empirical mode decomposition (EEMD) and MSPCA. The proposed method can conduct MSPCA-based denoising for a single signal compared with the former MSPCA-based denoising methods. The main steps of the proposed denoising method are as follows: First, EEMD is used for adaptive decomposition of a signal, and the variance contribution rate is selected to remove components with high-frequency noises. Subsequently, the Hankel matrix is constructed on each component to obtain a higher order matrix, and the main score and load vectors of the PCA are adopted to denoise the Hankel matrix. Next, the PCA-denoised component is denoised using soft thresholding. Finally, the stacking of PCA- and soft thresholding-denoised components is treated as the final denoised signal. Synthetic tests demonstrate that the EEMD-MSPCA-based method can provide good signal denoising results and is superior to the low-pass filter, wavelet reconstruction, EEMD reconstruction, Hankel–SVD, EEMD-Hankel–SVD, and wavelet-MSPCA-based denoising methods. Moreover, the proposed method in combination with the AIC picking method shows good prospects for processing microseismic waves.

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

Enhanced low-rank matrix estimation for simultaneous denoising and reconstruction of five-dimensional seismic data

Noise and missing traces usually influence the quality of multidimensional seismic data. It is, therefore, necessary to e stimate the useful signal from its noisy observation. The damped rank-reduction (DRR) method has emerged as an effective method to reconstruct the useful signal matrix from its noisy observation. However, the higher the noise level and the ratio of missing traces, the weaker the DRR operator becomes. Consequently, the estimated low-rank signal matrix includes a unignorable amount of residual noise that influences the next processing steps. This paper focuses on the problem of estimating a low-rank signal matrix from its noisy observation. To elaborate on the novel algorithm, we formulate an improved proximity function by mixing the moving-average filter and the arctangent penalty function. We first apply the proximity function to the level-4 block Hankel matrix before the singular value decomposition (SVD), and then, to singular values, during the damped truncated SVD process. The relationship between the novel proximity function and the DRR framework leads to an optimization problem, which results in better recovery performance. The proposed algorithm aims at producing an enhanced rank-reduction operator to estimate the useful signal matrix with a higher quality. Experiments are conducted on synthetic and real 5-D seismic data to compare the effectiveness of our approach to the DRR approach. The proposed approach is shown to obtain better performance since the estimated low-rank signal matrix is cleaner and contains less amount of artifacts compared to the DRR algorithm.