Leonid Gelman

The new multidimensional time/multi-frequency transform for higher order spectral analysis

A new multidimensional time/multi-frequency higher order spectral(HOS) transform is proposed for transient signals with nonlinear polynomial variation of instantaneous frequency: the short time higher order chirp spectra (HOCS) based on the higher order chirp-Fourier transform and time-domain windowing technique. The proposed transform is compared with the classical multi-frequency HOS based on the Fourier transform. It is shown that the proposed transform is more effective for processing of transient processes in comparison with the classical transform.

Signal recognition: Fourier transform vs. Hartley transform

Abstract The new generic feature representation approach was utilized for Gaussian recognition. Approach consists of using simultaneously two new recognition features: real and imaginary Fourier components with taking into account the covariance between features. Advanced time–frequency technique, short time Fourier transform was considered. The recognition effectiveness between the new approach and Hartley based approach was compared. It was shown for Gaussian recognition that Hartley approach is not an optimal and is not even a particular case of the proposed approach. The use of the proposed approach provides an essential effectiveness gain in comparison with Hartley approach.

Usage of Wigner–Ville distribution for vibroacoustical forced oscillation diagnostics of cracks

For diagnostics of fatigue cracks using vibration and noise, the new low‐frequency vibroacoustical method of forced oscillations with nonstationary excitation is considered. The usage of an advanced time‐frequency signal‐processing technique based on Wigner–Ville distribution is proposed and developed to improve the effectiveness of diagnostics. The simulation results are presented.

Signal recognition: fourier transform vs. Cosine transform

A new feature representation approach, the simultaneous usage of the real and imaginary Fourier components with taking into account the covariance between these components, was compared with the Cosine transform approach for Gaussian recognition.

Vibration monitoring for local tooth damage in multistage gearboxes

An adaptive approach was applied for local tooth damage diagnostics in gearboxes. The expediency of adaptation was proved experimentally for the new diagnostic feature, the sum of normalized sideband amplitudes. The positive correlation between mesh amplitudes and their sideband amplitudes was found experimentally for the first time. Novel adaptive vibration condition monitoring technology for local tooth damage in gearboxes was developed and experimentally validated. The experimental results showed an increase in effectiveness of the diagnostics when the adaptive technology was used.

Fatigue crack monitoring in aero-engines: simulation and experiments

A new genetic approach to fatigue crack monitoring in aero-engine blades is presented. The approach consists of simultaneously using two diagnostic features: the real and imaginary parts of the Fourier transform of vibroacoustical signals. This approach is more fundamental than traditional approaches based on the power spectral density, phase spectrum and Hartley transform; each of these approaches is a special case of the proposed approach. Numerical examples are given based on the processing of signals generated using a nonlinear model of tested blades. The generated signals are the forced vibroacoustical oscillations of cracked and un-cracked blades. The numerical examples show that crack detection ismore effective when using the new approach than when u sing the power spectral density approach. The presented experimental results using un-cracked and cracked turbuine blades from an aero-engine are matched with numerical results. The proposed approach offers an effectiveness improvement over the traditional approach based on power spectral density.

Acoustical crack detection of the structure: Wigner–Ville distribution versus short time Fourier transform

The innovative acoustical forced oscillation method with nonstationary excitation for fatigue crack diagnostics of the structure is considered. Because of the nonstationarity of the acoustical structure response, the modern time‐frequency technique is used for diagnostics. The numerical simulation is carried out to investigate the diagnostic capabilities of the time‐frequency signal processing technique based on Wigner–Ville distribution. Results from the Wigner–Ville procedure are compared to results from the short time Fourier transform. [Financial support of the U.S. National Research Council Twinning Program with Ukraine (Senior Program Officer Kelly Robbins) is thankfully acknowledged.]

Diagnostics of vibration and noise via Fourier transforms: A new approach

A new general optimal approach and new diagnostic features are proposed, for those cases where one‐ and multidimensional Fourier transforms are used for diagnostics of vibration and noise. For the forced oscillation vibroacoustical diagnostics method with Gaussian excitation, the optimal nonlinear transformation of the proposed features is received. It was shown (1) The power spectral density is optimal transformation for considered diagnostics only for specific situations; (2) The phase spectrum is not optimal transformation for considered diagnostics; and (3) The proposed approach provides the increment of diagnostics effectiveness in contrast with usage of power spectral density. This is in contrast to most applications concerning diagnostics of vibration and noise, where power spectral density is used.