Fault detection via sparsity-based blind filtering on experimental vibration signals

Detection of bearing faults is a challenging task since the impulsive pattern of bearing faults often fades into the noise. Moreover, tracking the health conditions of rotating machinery generally requires the characteristic frequencies of the components of interest, which can be a cumbersome constraint for large industrial applications because of the extensive number of machine components. One recent method proposed in literature addresses these difficulties by aiming to increase the sparsity of the envelope spectrum of the vibration signal via blind filtering (Peeters. et al., 2020). As the name indicates, this method requires no prior knowledge about the machine. Sparsity measures like Hoyer index, l1/l2 norm, and spectral negentropy are optimized in the blind filtering approach using Generalized Rayleigh quotient iteration. Even though the proposed method has demonstrated a promising performance, it has only been applied to vibration signals of an academic experimental test rig. This paper focuses on the real-world performance of the sparsity-based blind filtering approach on a complex industrial machine. One of the challenges is to ensure the numerical stability and the convergence of the Generalized Rayleigh quotient optimization. Enhancements are thus made by identifying a quasi-optimal filter parameter range within which blind filtering tackles these issues. Finally, filtering is applied to certain frequency ranges in order to prevent the blind filtering optimization from getting skewed by dominant deterministic healthy signal content. The outcome proves that sparsity-based blind filters are effective in tracking bearing faults on real-world rotating machinery without any prior knowledge of characteristic frequencies.

A Satellite Incipient Fault Detection Method Based on Decomposed Kullback–Leibler Divergence

Detection of faults at the incipient stage is critical to improving the availability and continuity of satellite services. The application of a local optimum projection vector and the Kullback–Leibler (KL) divergence can improve the detection rate of incipient faults. However, this suffers from the problem of high time complexity. We propose decomposing the KL divergence in the original optimization model and applying the property of the generalized Rayleigh quotient to reduce time complexity. Additionally, we establish two distribution models for subfunctions F1(w) and F3(w) to detect the slight anomalous behavior of the mean and covariance. The effectiveness of the proposed method was verified through a numerical simulation case and a real satellite fault case. The results demonstrate the advantages of low computational complexity and high sensitivity to incipient faults.

Weight Sensitivity of Temporal SNR Metrics in multi-echo fMRI

PurposeIn multi-echo fMRI (ME-fMRI), various weighting schemes have been proposed for the combination of the data across echoes. Here we introduce a framework that facilitates a deeper understanding of the weight dependence of temporal SNR measures in ME-fMRI.Theory and MethodsWe examine two metrics that have been used to characterize ME-fMRI performance: temporal SNR (tSNR) and multi-echo temporal (metSNR). Both metrics can be described using the generalized Rayleigh quotient (GRQ) and are predicted to be relatively insensitive to the weights when there is a high degree of similarity between a metric-specific matrix in the GRQ numerator and a metricindependent covariance matrix in the GRQ denominator. The application of the GRQ framework to experimental data is demonstrated using a resting-state fMRI dataset acquired with a multi-echo multi-band EPI sequence.ResultsIn the example dataset, similarities between the covariance matrix and the metSNR and tSNR numerator matrices are highest in grey matter (GM) and cerebrospinal fluid (CSF) voxels, respectively. For representative GM and CSF voxels that exhibit high matrix similarity values, the metSNR and tSNR values, respectively, are both within 4% of their optimal values across a range of weighting schemes. However, there is a fundamental tradeoff, with a high degree of weight sensitivity in the tSNR and metSNR metrics for the representative GM and CSF voxels, respectively. Geometric insight into the observed weight dependencies is provided through a graphical interpretation of the GRQ.ConclusionA GRQ framework can provide insight into the factors that determine the weight sensitivity of tSNR and metSNR measures in ME-fMRI.

Generalized Rayleigh-quotient Formulas for the Real Parts, Imaginary Parts, and Moduli of the Eigenvalues of Diagonalizable Matrices

In the present paper, generalized Rayleigh-quotient formulas for the real parts, imaginary parts, and moduli of the eigenvalues of diagonalizable matrices are derived. These formulas are new and correspond to similar formulas for the eigenvalues of self-adjoint matrices obtained recently. Numerical examples underpin the theoretical findings.

Localizing hidden regularities with known temporal structure in the EEG evoked response data

In this paper we describe a novel data driven spatial filtering technique that can be applied to the ERP analysis in order to find statistically significant hidden differential activations in the EEG data. The technique is based on the known morphological characteristics of the response. Underlying optimization problem is formulated as a generalized Rayleigh quotient maximization problem. We supply our tech-nique with a relevant randomization-based statistical test to assess the significance of the discovered phenomenon. Furthermore, we describe an application of the proposed method to the EEG data acquired in the study devoted to the analysis of the auditory neuroplasticity. We show how the mismatch negativity component, a tiny and short-lasting negative response that hallmarks the novel stimuli activating primary error-detection mechanisms, can be detected after filtration.