Feature Frequency Extraction Based on Principal Component Analysis and Its Application in Axis Orbit

Abstract

Vibration-based diagnosis has been employed as a powerful tool in maintaining the operating efficiency and safety for large rotating machinery. However, the extraction of malfunction features is not accurate enough by using traditional vibration signal processing techniques, owing to their intrinsic shortcomings. In this paper, the relationship between effective eigenvalues and frequency components was investigated, and a new characteristic frequency separation method based on PCA (CFSM-PCA) was proposed. Certain feature frequency could be purified by reconstructing the specified eigenvalues. Furthermore, three significant perspectives were studied via the distribution of effective eigenvalues, and theoretical derivations were subsequently illustrated. More importantly, this proposed scheme could also be used to synthesize axis orbits of larger machines. Purified curves were so explicit and the CFSM-PCA exhibited higher efficiency than harmonic wavelet and wavelet packet.

Frequency-separated principal component analysis of cortical population activity

“…with amplitude A, phase shift , and frequency F is known to have rank(H) ϭ 2 and hence has exactly two nonzero eigenvalues of its covariance matrix (Li et al 2018). Therefore, two columns of V, or in other words two dimensions, will be sufficient to capture the original signal x.…”

“…2D, blue and red circles, respectively). The presence of paired eigenvalues in the eigenspectrum of Hankel matrices is a general property that has been studied in mathematical theory (Li et al 2018). Each pair of eigenvalues can be employed to reconstruct a particular component of the original signal by an approach similar to that outlined above for a single sine wave but extended to a multilinear scenario.…”

“…For instance, with data composed of two sine waves, there are 2f ϩ 1 ϭ 5 nonzero eigenvalues, with the two highest pairs corresponding to each of the characteristic frequencies of the sine waves. The mathematical justification for the emergence of paired eigenvalues in Hankel matrices is addressed elsewhere (Li et al 2018).…”

Detection and localization of fatigue-induced transverse crack in a rotor shaft using principal component analysis

“…Since all the sub-data sets are from a single sensor have the same units, each sub-data set is re-scaled to zero mean only. Eigen-decomposition and reconstruction 44 of matrix Y is performed by employing the PCA method, as discussed in section ‘PCA model’. The eigenvalues associated with the noise have smaller values (close to 0), whereas eigenvalues associated to signal frequency components have larger values.…”

“…The eigenvalues associated with the noise have smaller values (close to 0), whereas eigenvalues associated to signal frequency components have larger values. 44 Therefore, a denoised signal is reconstructed using PCs whose eigenvalues correspond only to the larger signal frequency components. Unlike the traditional signal filters, this filtering technique does not introduce phase distortion of signal spectral components.…”