Hilbert Vibration Decomposition Method Research Articles

Estimating quadratic and cubic stiffness nonlinearity of a nonlinear vibration absorber with geometric imperfections

This paper presents a backbone curve estimation method for the stiffness nonlinearity of a nonlinear vibration absorber consisting of a circular brass plate with geometric imperfections. The backbone curves of an asymmetric system are estimated from the free vibration signal using the Hilbert vibration decomposition method, where only a single resonant frequency is excited. The Helmholtz-Duffing oscillator is applied to illustrate the proposed approach. Experimental data obtained from the free vibration of the nonlinear vibration absorber are measured, and the stiffness parameters are estimated using the current methods. The results compare reasonably well with those obtained using the restoring force surface method. The estimated backbone curves are qualitatively similar to those obtained using the Hilbert vibration decomposition. The proposed methods can be successfully applied to estimate the stiffness parameters of asymmetric engineering structures.

Upper envelope detection of ECG signals for baseline wander correction: a pilot study

Baseline wander (BW) is a common low frequency artifact in electrocardiogram (ECG) signals. The prime cause from which BW arises is the patient's breathing and movement. To facilitate reliable visual interpretation of the ECG and to discern particular patterns in the ECG signal, BW needs to be removed. In this paper, a novel BW removal method is presented. The hypothesis is based on the observation that ECG signal variation covaries with its BW. As such, the P, Q, R, S, and T peaks will follow the baseline drift. On this basis, the following proposition is true: a reliable approximation of the baseline drift can be obtained from the shape derived from the interpolation of one form of the ECG signal peak (peak envelope). The simulation was performed by adding artificial BW to ECG signal recordings. The signal-to-noise ratio, mean squared error, and improvement factor criteria were used to numerically evaluate the performance of the proposed approach. The technique was compared to that of the Hilbert vibration decomposition method, an empirical-mode decomposition technique and mathematical morphology. The results of the simulation indicate that the proposed technique is most effective in situations where there is a considerable distortion in the baseline wandering.

Chatter identification in milling of Inconel 625 based on recurrence plot technique and Hilbert vibration decomposition

In the paper a cutting stability in the milling process of nickel based alloy Inconel 625 is analysed. This problem is often considered theoretically, but the theoretical finding do not always agree with experimental results. For this reason, the paper presents different methods for instability identification during real machining process. A stability lobe diagram is created based on data obtained in impact test of an end mill. Next, the cutting tests were conducted in which the axial cutting depth of cut was gradually increased in order to find a stability limit. Finally, based on the cutting force measurements the stability estimation problem is investigated using the recurrence plot technique and Hilbert vibration decomposition method.

An improved Hilbert vibration decomposition method for analysis of rotor fault signals

The existence of false components with the Hilbert vibration decomposition (HVD) method has seriously restricted its application in practical rotor fault diagnosis. To solve this problem, an improved HVD method was proposed by adopting Kullback–Leibler (K–L) divergence values as a distinguishing index of true and false components, which is named the KL-HVD method. First, it calculated the K–L divergence values between the HVD components and the original signal, and then, these values are compared with the set threshold. Finally, it eliminated the false components whose K–L divergence values were larger than the threshold. The experimental results of rotor fault signal analysis demonstrated that the KL-HVD method could more accurately extract the time–frequency characteristics of the faults and the K–L divergence value was more suitable as the distinguishing index of true and false components than the mutual information and correlation coefficient values.

A New Method of Voltage Flicker Detection for Hilbert Vibration Decomposition

<p>Hilbert Vibration Decomposition (HVD) is introduced to the voltage flicker analysis. When voltage flicker accompanies with high order harmonics, the instantaneous frequency of its analytic signal in principle consists of two different parts, power frequency and a rapidly varying asymmetrical oscillating part. The important property of the instantaneous frequency offers a direct way to estimate the power frequency using a low-pass filter and remove the high order harmonics without pre-treatment procedures. Corresponding voltage flicker envelope is estimated using synchronous detection. The HVD method does not involves basic functions that the wavelet transform method needs. It can also adaptively estimate the frequency and amplitude of every modulation frequency component. Simulation results prove that the proposed method could accurately detect voltage flicker with high order harmonics. It has higher calculation efficiency and detection precision than wavelet transform method. Experimental results show that the new algorithm is feasible and efficient.</p>

Detection of the Third Heart Sound Based on Nonlinear Signal Decomposition and Time-Frequency Localization.

This study presents a precise way to detect the third ( S3 ) heart sound, which is recognized as an important indication of heart failure, based on nonlinear single decomposition and time-frequency localization. The detection of the S3 is obscured due to its significantly low energy and frequency. Even more, the detected S3 may be misunderstood as an abnormal second heart sound with a fixed split, which was not addressed in the literature. To detect such S3, the Hilbert vibration decomposition method is applied to decompose the heart sound into a certain number of subcomponents while intactly preserving the phase information. Thus, the time information of all of the decomposed components are unchanged, which further expedites the identification and localization of any module/section of a signal properly. Next, the proposed localization step is applied to the decomposed subcomponents by using smoothed pseudo Wigner-Ville distribution followed by the reassignment method. Finally, based on the positional information, the S3 is distinguished and confirmed by measuring time delays between the S2 and S3. In total, 82 sets of cardiac cycles collected from different databases including Texas Heart Institute database are examined for evaluation of the proposed method. The result analysis shows that the proposed method can detect the S3 correctly, even when the normalized temporal energy of S3 is larger than 0.16, and the frequency of those is larger than 34Hz. In a performance analysis, the proposed method demonstrates that the accuracy rate of S3 detection is as high as 93.9%, which is significantly higher compared with the other methods. Such findings prove the robustness of the proposed idea for detecting substantially low-energized S3 .

Theoretical analysis and comparison of the Hilbert transform decomposition methods

This article considers the empirical mode decomposition pioneered by Huang together with the Hilbert vibration decomposition method. Both methods are intended for extracting simple components using the varying instantaneous frequency and amplitude from multicomponent non-stationary signals. The common properties of and the differences between the two methods are taken into account.

Considering high harmonics for identification of non-linear systems by Hilbert transform

The objective of this paper is to propose a new method for analysis and identification of non-linear vibration structures by considering the primary and high harmonics of the solution. The method is based on two other Hilbert transform methods: • the methods for extracting the instantaneous and average dynamic structure characteristics, • the Hilbert Vibration Decomposition method that splits non-stationary wideband oscillating signal into separate components. The study focuses on combined non-linearities and on identification of precise dynamic parameters (natural frequencies, damping, static force characteristics) for free and forced vibration.