Parametric phase coupling in the vibration spectra of rolling element bearings

Baugh, K.W.

doi:10.1006/mssp.1994.1017

Cited by 5 publications

(10 citation statements)

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“…A k exp(j2¼® k f n n) + º n (1) in which fx n g denotes the observations process and º n is an additive noise process, assumed white and complex Gaussian, and n 2 f1, Ng. Here there are a number K of sinusoids that share a common frequency-modulation process ff n g, assumed to be slowly varying; but each complex sinusoid is multiplied by its own complex amplitude A k and has its own harmonic number ® k , which are not necessarily integral.…”

Section: A Observation Modelsmentioning

confidence: 99%

“…A k exp(j2¼¯kn) # exp(j2¼f n n) + º n (2) in which a set of low-frequency tones is mixed with a higher frequency carrier may still be termed a harmonic set, but differs from (1) in the nature of the coherence of the harmonic processes. We also propose a third model x n = » n ?…”

Section: A Observation Modelsmentioning

confidence: 99%

“…that the observations are simply white and complex Gaussian. Models other than the above are possible: for example, the fixed amplitudes fA k g in (1) and (2) could be made to vary with time.…”

Section: A Observation Modelsmentioning

confidence: 99%

“…Because each has unknown parameters, the hypothesis test under each of models (1), (2), and 3is composite and one must use either a generalized likelihood ratio (GLR) [7] or some ad hoc scheme.…”

Section: B Ramifications Of Model Choicementioning

confidence: 99%

“…Harmonic Set Models for the Signal: If one of models (1) or (2) is true, then it is very appropriate to consider an estimator/detector structure. That is, according to the GLR formulation, the amplitudes fA k g, basic frequency modulation ff n g, and either harmonic numbers f® k g or frequencies f¯kg must first be estimated from the data.…”

Section: B Ramifications Of Model Choicementioning

confidence: 99%

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Detection of long-duration narrowband processes

Wang

Willett

Streit³

2002

IEEE Trans. Aerosp. Electron. Syst.

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Detecting long, weak signals that are narrowband but of unknown frequency structure is an important signal processing challenge, with many applications in remote sensing and process monitoring. An ad hoc scheme is developed. Its stages include the discrete Fourier transform (DFT), a multiresolution decomposition in the frequency domain, and a generalized likelihood ratio test (GLRT). The computational load is light, and the performance is remarkably good. This is so not just in the original narrowband situation, but also, due to an inherent adaptivity to the data, in the detection of signals that are relatively broadband in nature. Generalizations are given to constant false alarm rate (CFAR) operation in both prewhitened and unwhitened cases, and to the detection of multiband signals. As regards the last, it is discovered that there is little loss from overestimating the number of bands.

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Section: A Observation Modelsmentioning

confidence: 99%

Section: A Observation Modelsmentioning

confidence: 99%

Section: A Observation Modelsmentioning

confidence: 99%

Section: B Ramifications Of Model Choicementioning

confidence: 99%

Section: B Ramifications Of Model Choicementioning

confidence: 99%

See 3 more Smart Citations

Detection of long-duration narrowband processes

Wang

Willett

Streit³

2002

IEEE Trans. Aerosp. Electron. Syst.

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Bispectral and trispectral features for machine condition diagnosis

McCormick

Nandi

1999

IEE Proc., Vis. Image Process.

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On parametrically phase-coupled random harmonic processes

Baugh

[1993 Proceedings] IEEE Signal Processing Workshop on Higher-Order Statistics

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In this paper, we will present the concept of a parametrically phase-coupled random harmonic process. It will be argued that such processes will be present in the vibration signature of a simple mechanical system, and as such would be of interest in the analysis of vibrations for condition-based maintenance. It is shown that conventional higher-order spectral (HOS) techniques reveal only limited features of parametrically phase-coupled processes and would prove of limited utility in the analysis of such signals. A modified second order cumulant spectrum is then introduced, which has the advantage of revealing all parametric phase relationships in the signal of interest. The results of testing using simulated vibration signals are presented. INTRODUCTION.A time series, { x(t)}, is said to be a random almostharmonic process if it can be expressed as a sum of sinusoids whose amplitudes are deterministic, but whose initial phases are random, i.e., where the {on} are distinct frequencies [ 11. In classical time series analysis, it is typically assumed that the {$n) are a set of i.i.d. random variables uniformly distributed over (0, 2n). It is straightforward to show that this assumption regarding { $n} implies that { x(t)} is widesense stationary. However, this assumption requires that no underlying phase relationship exist between the spectral components of {x(t)}. Now assume that the { a n } and the {$n) of (1-1) satisfy the relationship and where the set of {hn} are distinct, deterministic parameters, wo is some deterministic fundamental frequency, and $o is some random underlying initial phase uniformly distributed over (0, 2n). We will say that a random, almost harmonic, process satisfying (1-2) and (1-3) exhibits parametric phase coupling.As an example of a simple system which produces signals exhibiting parametric phase coupling, consider the cam and follower indicated schematically in Figure 1.1. It is assumed that the cam rotates about a fixed center, 0, at a constant rate of wo and with some random initial phase, q0. Let R denote angular displacement about 0 relative to some fixed radial line on the cam, and let p(Q) denote the surface of the cam at R. If we assume that the surface of the cam is continuous, then p(R) admits the Fourier series representation p(Q) = E rk cos(ks2) + qk sin(ks2) .(1-4) kThe radial displacement velocity of the follower, v(t), is given by dP dP a n v(t) =-=--, dt dR dt (1)(2)(3)(4)(5) or (1-6) -kr sin kw t + k 4 k ( 0 0 Note that the mechanical vibrations produced by this simple cam and follower arrangement will exhibit parametric phase coupling at harmonics of the shaft rate. In a more complicated rotating mechanical system, we may observe vibrations which exhibit parametric phase coupling at both harmonic and non-harmonic multiples of the applied shaft rate [2]. Moreover, these vibrations are often indicators of mechanical wear, and as such are of great interest in the area of condition-based maintenance

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Parametric phase coupling in the vibration spectra of rolling element bearings

Cited by 5 publications

References 0 publications

Detection of long-duration narrowband processes

Detection of long-duration narrowband processes

Bispectral and trispectral features for machine condition diagnosis

On parametrically phase-coupled random harmonic processes

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