Hilbert Huang Transform And Its Applications Pdf
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- Enhanced Empirical Mode Decomposition
- Hilbert-Huang Transform and Its Application in Gear Faults Diagnosis
- A Revised Hilbert–Huang Transform and Its Application to Fault Diagnosis in a Rotor System
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As a classical method to deal with nonlinear and nonstationary signals, the Hilbert—Huang transform HHT is widely used in various fields. In order to overcome the drawbacks of the Hilbert—Huang transform such as end effects and mode mixing during the process of empirical mode decomposition EMD , a revised Hilbert—Huang transform is proposed in this article.
A method called local linear extrapolation is introduced to suppress end effects, and the combination of adding a high-frequency sinusoidal signal to, and embedding a decorrelation operator in, the process of EMD is introduced to eliminate mode mixing. In addition, the correlation coefficients between the analyzed signal and the intrinsic mode functions IMFs are introduced to eliminate the undesired IMFs.
Simulation results show that the improved HHT can effectively suppress end effects and mode mixing. To verify the effectiveness of the new HHT method with respect to fault diagnosis, the revised HHT is applied to analyze the vibration displacement signals in a rotor system collected under normal, rubbing, and misalignment conditions.
The simulation and experimental results indicate that the revised HHT method is more reliable than the original with respect to fault diagnosis in a rotor system. Online monitoring is an effective method to master the running state of machine tools in industrial production.
A nonlinear and nonstationary signal is ubiquitous with respect to online monitoring, and there is no doubt that the analysis of this kind of signal is important and difficult [ 1 ]. There are several methods for analyzing nonlinear and nonstationary signals, such as the windowed Fourier transform [ 2 ], the wavelet transform [ 3 ], and the Wigner—Ville distribution [ 4 ]. However, almost all of the methods above have their own limitations.
For example, wavelet analysis has the advantage of detecting the fast and frequent fluctuations of harmonics, but it is sensitive to noise [ 5 ]. Generally, for the wavelet transform, it is important to choose the appropriate wavelet basis function, which also brings about difficulties for signal analysis. The windowed Fourier transform is based on traditional Fourier analysis, so there still remain challenges for processing nonlinear and nonstationary signals.
Huang et al. The Hilbert—Huang transform has a number of advantages over the traditional linear method in analyzing nonlinear and nonstationary signals, since it is highly adaptive in processing a signal. This method has been applied in many scientific fields, such as ocean engineering [ 7 , 8 , 9 ], business [ 10 ], mechanical engineering [ 11 , 12 , 13 , 14 , 15 , 16 , 17 ], and other scientific studies [ 18 , 19 ] due to its outstanding performance in signal analysis.
Although HHT is a promising approach to signal processing, it still has some drawbacks, such as end effects and mode mixing. The upper and lower envelopes are obtained by cubic spline interpolation during the process of EMD.
Since the local maximum and the local minimum cannot be determined at the starting point and endpoint of the data, serious problems of spline fitting will occur near the ends, where the cubic spline fitting can have large swings, which are called end effects or end swings. The end swings can eventually propagate inward and corrupt the entire data span, especially in the low-frequency components [ 6 ].
Rilling [ 20 ] did some research on improving EMD. The main methods for suppressing end effects can be divided into four categories: adding window function methods, wave continuation methods, data prediction continuation methods, and extreme continuation methods.
The core process of the adding window function methods is adding a symmetric window function, such as a hamming window, a hanning window, or a cosine window, to the data before introducing the HHT operation. The main methods of the wave continuation methods include even prolongation, mirror extending, and periodic extension.
Data series forecasting based on a neural network, a support vector regression machine, or an autoregressive moving average model [ 21 ] is the typical method of the data prediction continuation methods. Envelope extremum continuation is the main method of the extreme continuation methods. Researchers have proposed numerous methods based on the above methods to eliminate end effects. Qi et al. Zhang et al. Zhao [ 24 ] proposed an improved mirror extending method to optimize the envelopes.
Liu et al. However, there will be a morbid matrix when using this method. Afterwards, Zhu [ 26 ] put forward an orthogonal polynomial fitting algorithm to deal with the problem of end swings.
Cheng et al. Yang et al. These methods, to a certain extent, solve the problem of end effects, but they are not perfect and they have their own limitations. Although adding a window function can restrain end effects, the original data series also is changed.
As a consequence, the intrinsic mode functions IMFs that are obtained from EMD cannot express the real component of the original signal, so it is difficult for the Hilbert spectrum to reflect the characteristics of the signal accurately.
The wave continuation method requires a signal that has good symmetry, and it is not effective when processing a small amount of data. Neural networks and the autoregressive moving average model are not suitable for forecasting nonlinear and nonstationary signals. A support vector regression machine takes too much time due to the required amount of training data and the calculated quantity of data. In addition, the forecast error will gradually enlarge as the number of prediction steps increases.
The extreme continuation method has poor adaptivity, and its effect is not always ideal. Mode mixing, which is defined as either a single IMF consisting of signals of widely disparate scales or a signal of a similar scale residing in different IMF components, could not only cause serious aliasing in the time-frequency distribution, but could also make the individual IMF lose its physical meaning.
Another side effect of mode mixing is the lack of physical uniqueness [ 29 ]. The reasons for mode mixing are mainly twofold: 1 the frequencies of the composite components in a mixed signal are similar to each other; and 2 the variation in extremum series.
In order to solve the problem of mode mixing, various methods have been proposed by specialists and scholars. However, we need to understand the basic characteristics of the signal in advance before using this method. Soon afterwards, Huang et al. EEMD can eliminate mode mixing by decomposing the mixed signal that contains discontinuous signals. However, it is time-consuming due to the repeated use of EMD. Deering et al. This method effectively separates components that are similar in frequency.
Yeh and Shi [ 33 ] expanded the masking signal method into general usage. Tang et al. The ICA method can improve the orthogonality of each IMF; however, it has the limitations of amplitude and sequence uncertainty. At the same time, Tang [ 35 ] proposed a new method to eliminate mode mixing based on a revised version of blind source separation.
In order to improve the orthogonality of IMFs, Xiao et al. Embedding a decorrelation operator into the EMD process can restrain mode mixing in low-frequency ratio signals; however, it cannot be used to decompose a signal that is mixed with a discontinuous high frequency signal.
Hu et al. In order to overcome the limitations of end effects and mode mixing simultaneously, a revised Hilbert—Huang transform is proposed in this article. A new method called local linear extrapolation is introduced to suppress end effects. The advantage of this method is that it can determine the extremum of an endpoint according to the development trend of both ends without extending or predicting the data.
The structure of the original data will not be changed with this method, so more original information can be retained. The combination of adding a high-frequency sinusoidal signal to, and embedding a decorrelation operator in, the process of EMD is introduced to eliminate mode mixing. This new method has good performance in eliminating mode mixing even if the multicomponent signal is mixed with high-frequency discontinuous signals and low-frequency ratio signals.
In addition, this new method consumes little calculation time. This paper is organized as follows. The HHT method is reviewed in Section 2. Section 3 presents the revised HHT method.
In addition, the question of how to determine the frequency and amplitude of the auxiliary signal is discussed in detail. An experiment on fault diagnosis in a rotor system by the revised HHT is stated in Section 4. Finally, the conclusion is provided in Section 5. The Hilbert—Huang transform was proposed by Norden E. Huang, and it consists of two parts: EMD and the Hilbert spectral analysis.
Firstly, a data series is decomposed into a series of intrinsic mode functions by the EMD method. Secondly, with the Hilbert transform, the intrinsic mode functions yield instantaneous frequencies as functions of time that give sharp identifications of embedded structures.
Finally, an energy-frequency-time distribution can be obtained. In addition, we can also obtain the marginal spectrum of the data series. EMD is the core method of the Hilbert—Huang transform. An IMF should satisfy two conditions [ 6 ]: in the whole data set, the number of extrema and the number of zero crossings must either equal, or differ at most by, one; at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima must be zero.
The phase is readily obtained, and the instantaneous frequency of each IMF can be defined by the derivative of the phase, as shown in Equation 4. We can express the data X t in the following form, which does not contain the residue r n. With the Hilbert amplitude spectrum defined, we can also define the marginal spectrum as. Although the Hilbert—Huang transform HHT has prospects for widespread application in processing nonlinear and nonstationary signals, the problems of end effects and mode mixing unavoidably influence the accuracy of the final analysis results.
In order to obtain a more accurate analysis result, a revised HHT method is proposed. A new method, called local linear extrapolation, is introduced to suppress end effects, and the combination of adding a high frequency sinusoidal signal to, and embedding a decorrelation operator in, the process of EMD is introduced to eliminate mode mixing.
This new method has good performance in restraining end effects, and it can eliminate mode mixing even if the decomposed multicomponent signal is mixed with high-frequency discontinuous signals and low-frequency ratio signals. In addition, this new method consumes less calculation time than other methods, such as EEMD.
Based on the fundamental cause of end effects and inspired by the research achievements [ 28 , 29 , 38 ] of experts and scholars, a new method, which is called local linear extrapolation, is proposed to eliminate the problem of end effects.
The structure of the original data will not be changed with this method, so original information can be retained. Taking the determination of the right extreme points as an example, the local linear extrapolation method can be expressed as follows:. A straight line AB is determined by point A and B. Point C is the intersection point of line AB and the time axis that corresponds to the right endpoint D, as shown in Figure 1 a.
The legend for the local linear extrapolation method. Otherwise, the maximum value point is identified as the intersection point C. The method for determining the left extreme points is similar to the method for determining the right extreme points. The envelope curve will be improved by the method of local linear extrapolation.
Enhanced Empirical Mode Decomposition
Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Hilbert-Huang Transform and its Application in Seismic Signal Processing Abstract: The detection of targets in military and security applications involves the usage of sensor systems which consist of a variety of sensors such as seismic, acoustic, magnetic and image ones as well. In order to extract signal features, which characterize particular targets, using of appropriate signal processing algorithms is required. Seismic signals can be considered as nonstationary and nonlinear signals especially in near-field seismic zone.
EMD filtering is less than ideal and can lead to misleading results. This difficulty is ameliorated by first subjecting the time-series to bandpass filtration, where the pass-band frequency range is sufficiently narrow that the entire pass-band is captured in a single IMF. A series of such filtrations are required to treat a multicomponent signal. Bandpass enhanced EMD is applied to a bat chirp signal. That the fundamental, the first, second, and part of the third harmonic are expressed, demonstrates the improved sensitivity of this method over the standard HHT approach. The fundamental and harmonics of this chirp have an exponential form with a decay rate proportional to the square root of the time. Unable to display preview.
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Stork Published Hilbert Huang transform HHT is a relatively new method. It seems to be very promising for the different applications in signal processing because it could calculate instantaneous frequency and amplitude which is also important for the biomedical signals. HHT consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in biomedical research. Save to Library.
The Application of Hilbert–Huang Transforms to Meteorological Datasets (D G Duffy) · Empirical Mode Decomposition and Climate Variability (K Coughlin & K K.
Hilbert-Huang Transform and Its Application in Gear Faults Diagnosis
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The Hilbert—Huang transform HHT is a way to decompose a signal into so-called intrinsic mode functions IMF along with a trend, and obtain instantaneous frequency data. It is designed to work well for data that is nonstationary and nonlinear. In contrast to other common transforms like the Fourier transform , the HHT is more like an algorithm an empirical approach that can be applied to a data set, rather than a theoretical tool. Huang et al. Since the signal is decomposed in time domain and the length of the IMFs is the same as the original signal, HHT preserves the characteristics of the varying frequency.
Curator: Norden E. Eugene M. Norden E.
A Revised Hilbert–Huang Transform and Its Application to Fault Diagnosis in a Rotor System
Time-frequency and transient analysis have been widely used in signal processing and faults diagnosis. These methods represent important characteristics of a signal in both time and frequency domain. In this way, essential features of the signal can be viewed and analyzed in order to understand or model the faults characteristics.
Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. Hilbert-Huang Transform Based Application in Power System Fault Detection Abstract: The temporarily fault signals existing in high voltage lines and electric equipments are usually non-linear and non-stationary. Low frequency oscillation characteristic extraction from fault signals plays an important role in online fault monitoring and detection system designing. In this paper we propose a procedure to analyze power system fault signal by employing HTT method. The fault signal is firstly decomposed into intrinsic mode function IMF by the empirical mode decomposition EMD method.
Statistical and Probabilistic Approach in Monitoring-based Structure Rating and Risk Assessment
As a classical method to deal with nonlinear and nonstationary signals, the Hilbert—Huang transform HHT is widely used in various fields. In order to overcome the drawbacks of the Hilbert—Huang transform such as end effects and mode mixing during the process of empirical mode decomposition EMD , a revised Hilbert—Huang transform is proposed in this article. A method called local linear extrapolation is introduced to suppress end effects, and the combination of adding a high-frequency sinusoidal signal to, and embedding a decorrelation operator in, the process of EMD is introduced to eliminate mode mixing. In addition, the correlation coefficients between the analyzed signal and the intrinsic mode functions IMFs are introduced to eliminate the undesired IMFs. Simulation results show that the improved HHT can effectively suppress end effects and mode mixing.
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