Papers by Keyword: Hilbert Transform

Abstract: The damping property is a material's energy dissipation capacity, indicating its ability to resist vibrations. The parameters of damping characteristics can be evaluated using the traditional Fast Fourier Transformation (FFT) technique, which suffers from the loss of time. Therefore, Hilbert Transform (HT) and Wavelet Transform (WT) have been developed to overcome such problems and help comprehend damping properties precisely with time and frequency. This study evaluates and compares damping ratio assessment using HT, WT, and Log Decrement in linear and non-linear viscoelastic material models. To test the adapted HT and WT methods, we developed a homemade MATLAB code to evaluate the damping ratio of two data sets. Analytical data obtained from solving a linear viscoelastic material model and numerical data attained from the FE-model of a non-linear viscoelastic material were both subjected to vibration. The error percentages of the damping ratio estimated by HT and WT were 6.1 and 11.75, respectively, compared to 43 for Log Decrement. These results confirm that HT and WT can accurately predict the damping ratio of non-linear viscoelastic material models.

Abstract: To perform the Hilbert transform H_il of a non-integrable function φ, such as φ(x) = 1, x, in a numerical calculation-friendly way, we propose a method of rewriting H_il in terms of the resolvent for a differential operator R whose eigenfunctions satisfy the orthogonality and the completeness, so that the resolvent kernel 〈x|R^-1y〉can be given by the eigenfunction expansion. We deal with two cases for the choice of R: one is the harmonic oscillator Hamiltonian, which is commutative with the Fourier transform F; and the other is such that is commutative with H_il itself. We show how the calculation of H_ilφ is made in a numerical calculation-friendly way, to find that Π_k=0,1 H_ilf_k (f_k (x) = x^k) satisfies quite a simple relation.

Abstract: Dust-removing blower is a key equipment in sintering plants, which can provide enough wind and negative pressure. It can also improve the efficiency of dust-removing. The vibration level of a dust-removing blower in a sintering plant is very high, which is beyond its normal value. Due to the complex working condition and strong background noise, it is difficult to extract fault features from the vibration signal of the dust-removing blower. Therefore, fault analysis of the blower is very difficult. Since the modulation phenomenon existed in the vibration signal of the blower is found, the envelope analysis based on the Hilbert transform is proposed to demodulate the vibration signal. The frequency spectrum of the demodulated signal shows that the first order frequency characteristic is obvious, which can effectively reveal the dynamic unbalance of the rotor system is the main reason of the abnormal vibration of the blower. According to this diagnosis, some possible reasons for the unbalance are proposed, as well as advices regarding to the repair of the blower system. Moreover, the test and analysis are conducted on the repaired blower system. The results show that the unbalance problem is eliminated and the blower can work normally, which can validate the accuracy and reliability of the proposed diagnosis method for fault analysis of the dust-removing blower.Keywords: dynamic unbalance; modulation; dust-removing blower; Hilbert Transform

Abstract: In this paper, MEMD-based scalogram and coscalogram, and instantaneous frequency spectral are proposed to characterize the data derived from the multivariate non-stationary process. The scalogram and instantaneous frequency spectral capture spectral evolution of each component while the coscalogram reveals embedded intermittent correlation between two components. Compared with scale-based scalogram and coscalogram, frequency-based instantaneous frequency spectral provides more detailed portrayal for multivariate data. The effectiveness of the proposed MEMD-based time-frequency analysis framework is validated by numerical examples of uniformly and generally modulated ground motions.

Abstract: In the traditional processing of seismic signal, the frequency domain analysis method is always available to research some features which always vary with frequency. However, the condition of parameters which vary with time going can’t be considered in this method. So all the information in time domain have been neglected. In this article, time-frequency analysis method called HHT(Hilbert-Huang transform) is applied to analyze the Qingping wave of Wenchuan earthquake meticulously, which is the most advantaged to dissect the change features of the seismic record at different scales. Then we can get the dual properties in time domain and the frequency domain, such as the IMF function of each modal and the instantaneous frequency. For reflecting the time-frequency characteristics exactly and clearly, the Hilbert spectrum has been used to show these messages in the time-frequency plane.

Abstract: This paper puts forward a kind of gearbox fault diagnosis methods which based on empirical mode decomposition (EMD), Hilbert transform, Fast Fourier Transform (FFT) and spectrum refined techniques. This method is applicable to the analysis of the nonlinear unsteady signal. First of all used wavelet denoising to the acquisition of gearbox vibrate signal, again carries on the empirical mode decomposition (EMD), than get a certain number of intrinsic mode function (imf); Choose the specific imf, based on kurtosis value, after the Hilbert transform and Fast Fourier Transform is done, the corresponding power spectrum can be obtained; To refine the power spectrum and extract the gearbox fault characteristic frequency; Then in pattern recognition and diagnosis of the gearbox fault, and compared with the normal signal characteristics. The analysis results show that the proposed method can effectively detect the gearbox fault characteristics.

Abstract: In order to collect the fault signal of slewing bearing, design and built up the slewing bearing test rig and the signal test system. Because slewing bearing fault signal is weak, the signal containing fault characteristics was resolved and reconstructed with the wavelet theory. With the application of the Hilbert transform in demodulation and detailed spectrum analysis, the fault characteristic frequency was extracted, and the slewing bearing fault was judged. All above work shows that Wavelet analysis combined with the Hilbert analysis is effective to the diagnosis of rotary bearing local fault.

Abstract: This paper is based on the wavelet transform theory and the Hilbert transform, it aims at researching on the pressure fluctuation characteristics in the bed, through analyzing and comparing the calculated envelope spectrum of pressure signal after transforms. On the basis of self-built cold fluidized bed, we choose to change the air flow and diameter of particle in fluidized bed as the two influencing factors. For researching the pressure fluctuation characteristics of fluidized bed, we collect pressure signal of the large particle fluidized bed which under normal operation conditions. The experimental results reveal that: as the increasing of the air flow, the energy of pressure increases; and with the increase of particle size in fluidized bed, the pressure fluctuation decreases in the bed.

Abstract: Nonlinear acoustics deals with various nonlinear effects that occur in ultrasonic wave propagation. The method is suitable for material characterisation, as it uses different nonlinear phenomena associated with material imperfections. The method has been used for detecting nonlinearities in cracked solids by: measuring distortions of acoustic signals, estimating resonance frequency shifts or assessing nonlinear vibro-acosutic modulations. The latter is the most widely used non-classical approach to probe material nonlinearities. The method involves vibro-acoustic interactions of ultrasonic wave and modal vibration in damaged specimens. Modulation intensity that strongly relates to damage severity - is usually assessed in the frequency domain and often leads to confusing results when large modulations are involved. The paper investigates the time domain analysis of vibro-acoustic modulated signals. Several methods for instantaneous frequency calculation used to assess the intensity of modulation - are compared. Simulated and experimental data are used in these investigations.

Abstract: The RAPTOR telescope systems are astronomical observatories that operate in remote locations in New Mexico searching for astrophysical transients called gamma-ray bursts. Their operating condition should remain at good levels in order to have accurate observations. Currently, the first component of the RAPTOR telescopes to fail is a capstan driving mechanism that operates in a run-to failure mode. The capstans wear relatively frequently because of their manufacturing material and can cause damage to other more expensive components, such as the drive wheels and the telescope optics. Monitoring the condition of these systems seems a reasonable solution since the unpredictable rate at which the capstans experience wear, in combination with the remote locations and high duty cycles of these telescope systems, make it unprofitable to choose a strategy of replacing the capstans at chosen intervals. Experimental tests of the telescope systems reported here recorded vibration signals during clockwise and counterclockwise rotations, similar to a motion known as "homing-sequence". The Empirical Mode Decomposition (EMD) method in combination with the Hilbert Transform (HT) and a new alternative method for the estimation of the instantaneous features of a signal that applies an energy tracking operator, called Teager-Kaiser Energy operator, and an energy separation algorithm to the data being analysed, are the time-frequency analysis methods used for analysis here.